Boost proficiency gains for all learning levels, backgrounds, and abilities with individualized lessons that align with every US state’s math and reading standards, Common Core, and several Canadian standards.
Select your state and grade level to see your state’s math standards.
| State | Standards | Description | Grade Level |
|---|---|---|---|
| Alabama | K.FC.1 | Count forward orally from 0 to 100 by ones and by tens. Count backward orally from 10 to 0 by ones. | Kindergarten |
| Alabama | K.FC.2 | Count to 100 by ones beginning with any given number between 0 and 99. | Kindergarten |
| Alabama | K.FC.3 | Write numerals from 0 to 20. | Kindergarten |
| Alabama | K.FC.4 | Connect counting to cardinality using a variety of concrete objects. | Kindergarten |
| Alabama | K.FC.5 | Count to answer how many questions. | Kindergarten |
| Alabama | K.FC.6 | Orally identify whether the number of objects in one group is greater/more than, less/fewer than, or equal/the same as the number of objects in another group, in groups containing up to 10 objects, by using matching, counting, or other strategies. | Kindergarten |
| Alabama | K.FC.7 | Compare two numbers between 0 and 10 presented as written numerals (without using inequality symbols). | Kindergarten |
| Alabama | K.OA.8 | Represent addition and subtraction up to 10 with concrete objects, fingers, pennies, mental images, drawings, claps, or other sounds, acting out situations, verbal explanations, expressions, or equations. | Kindergarten |
| Alabama | K.OA.9 | Solve addition and subtraction word problems, ad add and subtract within 10, by using concrete objects or drawings to represent the problem. | Kindergarten |
| Alabama | K.OA.10 | Decompose numbers less than or equal to 10 into pairs of smaller numbers in more than one way, by using concrete objects or drawing, and record each decomposition by a drawing or equation. | Kindergarten |
| Alabama | K.OA.11 | For any number from 0 to 10, find the number that makes 10 when added to the given number, by using concrete objects or drawings, and record the answer with a drawing or equation. | Kindergarten |
| Alabama | K.OA.12 | Fluently add and subtract within 5. | Kindergarten |
| Alabama | K.OA.13 | Duplicate and extend simple patterns using concrete objects. | Kindergarten |
| Alabama | K.NBT.14 | Compose and decompose numbers from 11 to 19 by using concrete objects or drawings to demonstrate understanding that these numbers are composed of ten ones and one, two, three, four, five, six, seven, eight, or nine ones. | Kindergarten |
| Alabama | K.DA.15 | Classify objects into given categories of 10 or fewer; count the number of objects in each category and sort the categories by count. | Kindergarten |
| Alabama | K.M.16 | Identify and describe measurable attributes (length, weight, height) of a single object using vocabulary such as long/short, heavy/light, or tall/short. | Kindergarten |
| Alabama | K.M.17 | Directly compare two objects with a measurable attribute in common to see which object has more of or less of the attribute and describe the difference. | Kindergarten |
| Alabama | K.G.18 | Describe objects in the environment using names of shapes, and describe the relative positions of these objects using terms such as above, below, beside, in front of, behind, and next to. | Kindergarten |
| Alabama | K.G.19 | Correctly name shapes regardless of their orientations or overall sizes. | Kindergarten |
| Alabama | K.G.20 | Identify shapes as two-dimensional (lying in a plane, flat) or three-dimensional (solid). | Kindergarten |
| Alabama | K.G.21 | Analyze and compare two- and three-dimensional shapes, in different sizes and orientations, using informal language to describe their similarities, differences, parts (number of sides and vertices or corners), and other attributes. | Kindergarten |
| Alabama | K.G.23 | Use simple shapes to compose larger shapes. | Kindergarten |
| Alabama | 1.OA.1 | Use addition and subtraction to solve word problems within 20 by using concrete objects, drawings, and equations with a symbol for the unknown number to represent the problem. | Grade 1 |
| Alabama | 1.OA.3 | Apply properties of operations as strategies to add and subtract. | Grade 1 |
| Alabama | 1.OA.4 | Explain subtraction as an unknown-addend problem. | Grade 1 |
| Alabama | 1.OA.5 | Relate counting to addition and subtraction. | Grade 1 |
| Alabama | 1.OA.6 | Add and subtract within 20. | Grade 1 |
| Alabama | 1.OA.7 | Explain that the equal sign means the same as. Determine whether equations involving additions and subtraction are true or false. | Grade 1 |
| Alabama | 1.OA.8 | Solve for the unknown whole number in various positions in an addition or subtraction equation, relating three whole numbers that would make it true. | Grade 1 |
| Alabama | 1.OA.9 | Reproduce, extend, and create patterns and sequences of numbers using a variety of materials. | Grade 1 |
| Alabama | 1.NBT.10 | Extend the number sequence from 0 to 120. | Grade 1 |
| Alabama | 1.NBT.11 | Explain that the two digits of a two-digit number represent amounts of tens and ones. | Grade 1 |
| Alabama | 1.NBT.12 | Compare pairs of two-digit numbers based on the values of the tens and ones digits, recording the results of comparisons with the symbols >, =, and < and orally with the words is greater than, is equal to, and is less than. | Grade 1 |
| Alabama | 1.NBT.13 | Add within 100, using concrete models or drawings and strategies based on place value. | Grade 1 |
| Alabama | 1.NBT.14 | Given a two-digit number, mentally find 10 more or 10 less than the numbers without having to count, and explain the reasoning used. | Grade 1 |
| Alabama | 1.NBT.15 | Subtract multiples of 10 from multiples of 10 in the range 10-90 (positive or zero differences), using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction. Relate the strategy to a written method and explain the reasoning used. | Grade 1 |
| Alabama | 1.DA.16 | Organize, represent, and interpret data with up to three categories. | Grade 1 |
| Alabama | 1.M.17 | Order three objects by length; compare the lengths of two objects indirectly by using a third object. | Grade 1 |
| Alabama | 1.M.18 | Determine the length of an object using non-standard units with no gaps or overlaps, expressing the length of the object with a whole number. | Grade 1 |
| Alabama | 1.M.19 | Tell and write time to the hours and half hours using analog and digital clocks. | Grade 1 |
| Alabama | 1.M.20 | Identify pennies and dimes by name and value. | Grade 1 |
| Alabama | 1.G.21 | Build and draw shapes which have defining attributes. | Grade 1 |
| Alabama | 1.G.22 | Compose two-dimensional shapes (rectangles, squares, trapezoids, triangles, half-circles, and quarter-circles) or three-dimensional shapes (cubes, right rectangular prisms, right circular cones, and right circular cylinders) to create a composite shape, and compose new shapes from the composite shape. | Grade 1 |
| Alabama | 1.G.23 | Partition circles and rectangles into two and four equal shares and describe the shares using the words halves, fourths, and quarters, and use the phrases half of, fourth of, and quarter of. | Grade 1 |
| Alabama | 2.OA.1 | Use addition and subtraction within 100 to solve one- and two-step word problems by using drawings and equations with a symbol for the unknown number to represent the problem. | Grade 2 |
| Alabama | 2.OA.2 | Fluently add and subtract within 20 using mental strategies such as counting on, making ten, decomposing a number leading to ten, using the relationship between addition and subtraction, and creating equivalent but easier or known sums. | Grade 2 |
| Alabama | 2.OA.3 | Use concrete objects to determine whether a group of up to 20 objects is even or odd. | Grade 2 |
| Alabama | 2.OA.4 | Using concrete and pictorial representations and repeated addition, determine the total number of objects in a rectangular array with up to 5 rows and up to 5 columns. | Grade 2 |
| Alabama | 2.OA.5 | Reproduce, extend, and create, and describe patterns and sequences using a variety of materials. | Grade 2 |
| Alabama | 2.NBT.6 | Explain that the three digits of a three-digit number represent amounts of hundreds, tens, and ones. | Grade 2 |
| Alabama | 2.NBT.7 | Count within 1000 by ones, fives, tens, and hundreds. | Grade 2 |
| Alabama | 2.NBT.8 | Read and write numbers to 1000 using base-ten numerals, number names, and expanded form. | Grade 2 |
| Alabama | 2.NBT.9 | Compare two three-digit numbers based on the value of the hundreds, tens, and ones digits, recording the results of comparisons with the symbols >, =, and < and orally with the words is greater than, is equal to, and is less than. | Grade 2 |
| Alabama | 2.NBT.10 | Fluently add and subtract within 100, using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction. | Grade 2 |
| Alabama | 2.NBT.11 | Use a variety of strategies to add up to four two-digit numbers. | Grade 2 |
| Alabama | 2.NBT.12 | Add and subtract within 1000 using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method. | Grade 2 |
| Alabama | 2.NBT.13 | Mentally add and subtract 10 or 100 to a given number between 100 and 900. | Grade 2 |
| Alabama | 2.DA.15 | Measure lengths of several objects to the nearest whole unit. | Grade 2 |
| Alabama | 2.DA.16 | Create a picture graph and bar graph to represent data with up to four categories. | Grade 2 |
| Alabama | 2.M.17 | Measure the length of an object by selecting and using standard units of measurements shown on rulers, yardsticks, meter sticks, or measuring tapes. | Grade 2 |
| Alabama | 2.M.18 | Measure objects with two different units, and describe how the two measurements related to each other and the size of the unit chosen. | Grade 2 |
| Alabama | 2.M.20 | Measure to determine how much longer one objects is than another, expressing the length difference of the two objects using standard units of length. | Grade 2 |
| Alabama | 2.M.21 | Use addition and subtraction within 100 to solve word problems involving same units of length, representing the problem with drawings (such as drawings of rulers) and/or equations with a symbol for the unknown number. | Grade 2 |
| Alabama | 2.M.23 | Tell and write time from analog to digital clocks to the nearest five minutes, using a.m. and p.m. | Grade 2 |
| Alabama | 2.M.24 | Solve problems with money. | Grade 2 |
| Alabama | 2.G.25 | Identify triangles, quadrilaterals, pentagons, hexagons, and cubes. | Grade 2 |
| Alabama | 2.G.26 | Partition a rectangle into rows and columns or same-size squares, and count to find the total number of squares. | Grade 2 |
| Alabama | 2.G.27 | Partition circles and rectangles into two, three, or four equal shares. Describe the shares using terms such as halves, thirds, half of, or a third of, and describe the whole as two halves, three thirds, or four fourths. | Grade 2 |
| Alabama | 3.OA.1 | Illustrate the product of two whole numbers as equal groups by identifying the number of groups and the number in each group and represent as a written expression. | Grade 3 |
| Alabama | 3.OA.2 | Illustrate and interpret the quotient of two whole numbers as the number of objects in each group or the number of groups when the whole is partitioned into equal shares. | Grade 3 |
| Alabama | 3.OA.3 | Solve word situations using multiplication and division within 100 involving equal groups, arrays, and measurement quantities; represent the situation using models, drawings, and equations with a symbol for the unknown number. | Grade 3 |
| Alabama | 3.OA.4 | Determine the unknown whole number in a multiplication or division equation relating three whole numbers. | Grade 3 |
| Alabama | 3.OA.5 | Develop and apply properties of operations as strategies to multiple and divide. | Grade 3 |
| Alabama | 3.OA.6 | Use the relationship between multiplication and division to represent division as an equation with an unknown factor. | Grade 3 |
| Alabama | 3.OA.7 | Use strategies based on properties and patterns of multiplication to demonstrate fluency with multiplication and division within 100. | Grade 3 |
| Alabama | 3.OA.8 | Determine and justify solutions for two-step word problems using the four operations and write an equation with a letter standing for the unknown quantity. Determine reasonableness of answers using number sense, context, mental computation, and estimation strategies including rounding. | Grade 3 |
| Alabama | 3.OA.9 | Recognize and explain arithmetic patterns using properties of operations. | Grade 3 |
| Alabama | 3.NBT.10 | Identify the nearest 10 or 100 when rounding whole numbers, using place value understanding. | Grade 3 |
| Alabama | 3.NBT.11 | Use various strategies to add and subtract fluently within 1000. | Grade 3 |
| Alabama | 3.NBT.12 | Use concrete materials and pictorial models based on place value and properties of operations to find the product of a one-digit whole number by a multiple of ten (from 10 to 90). | Grade 3 |
| Alabama | 3.NBT.13 | Demonstrate that a unit fraction represents one part of an area model or length model of a whole that has been equally partitioned; explain that a numerator greater than one indicates the number of unit pieces represented by the fraction. | Grade 3 |
| Alabama | 3.NBT.14 | Interpret a fraction as a number on the number line; locate or represent fractions on a number line diagram. | Grade 3 |
| Alabama | 3.NBT.15 | Explain equivalence and compare fractions by reasoning about their size using visual fraction models and number lines. | Grade 3 |
| Alabama | 3.DA.16 | For a given or collected set of data, create a scaled (one-to-many) picture graph and scaled bar graph to represent a data set with several categories. | Grade 3 |
| Alabama | 3.DA.17 | Measure lengths using rulers marked with halves and fourths of an inch to generate data and create a line plot marked off in appropriate units to display the data. | Grade 3 |
| Alabama | 3.M.18 | Tell and write time to the nearest minute; measure time intervals in minutes (within 90 minutes). | Grade 3 |
| Alabama | 3.M.19 | Estimate and measure liquid volumes and masses of objects using liters (l), grams (g), and kilograms (kg). | Grade 3 |
| Alabama | 3.M.20 | Find the area of a rectangle with whole number side lengths by tiling without gaps or overlays and counting unit squares. | Grade 3 |
| Alabama | 3.M.21 | Count unit squares (square cm, square m, square in, square ft, and improvised or non-standard units) to determine area. | Grade 3 |
| Alabama | 3.M.22 | Relate area to the operations of multiplication using real-world problems, concrete materials, mathematical reasoning, and the distributive property. | Grade 3 |
| Alabama | 3.M.23 | Decompose rectilinear figures into smaller rectangles to find the area, using concrete materials. | Grade 3 |
| Alabama | 3.M.24 | Construct rectangles with the same perimeter and different areas or the same area and different perimeters. | Grade 3 |
| Alabama | 3.M.25 | Solve real-world problems involving perimeters of polygons, including finding the perimeter given the side lengths and finding an unknown side length of rectangles. | Grade 3 |
| Alabama | 3.G.26 | Recognize and describe polygons (up to 8 sides), triangles, and quadrilaterals (rhombuses, rectangles, and squares) used on the number of sides and the presence or absence of square corners. | Grade 3 |
| Alabama | 4.OA.1 | Interpret and write equations for multiplicative comparisons. | Grade 4 |
| Alabama | 4.OA.2 | Solve word problems involving multiplicative comparison using drawings and write equations to represent the problem, using a symbol for the unknown number. | Grade 4 |
| Alabama | 4.OA.3 | Determine and justify solutions for multi-step word problems, including problems where remainders must be interpreted. | Grade 4 |
| Alabama | 4.OA.4 | For whole numbers in the range 1 to 100, find all factor pairs, identifying a number as a multiple of each of its factors. | Grade 4 |
| Alabama | 4.OA.5 | Generate and analyze a number or shape pattern that follows a given rule. | Grade 4 |
| Alabama | 4.NBT.6 | Using models and quantitative reasoning, explain that in a multi-digit whole number, a digit in any place represents ten times what it represents in the place to its right. | Grade 4 |
| Alabama | 4.NBT.7 | Read and write multi-digit whole numbers using standard form, word form, and expanded form. | Grade 4 |
| Alabama | 4.NBT.8 | Use place value understanding to compare two multi-digit numbers using >, =, and < symbols. | Grade 4 |
| Alabama | 4.NBT.9 | Round multi-digit whole numbers to any place using place value understanding. | Grade 4 |
| Alabama | 4.NBT.10 | Use place value strategies to fluently add and subtract multi-digit whole numbers and connect strategies to the standard algorithm. | Grade 4 |
| Alabama | 4.NBT.11 | Find the product of two factors (up to four digits by a one-digit number and two two-digit numbers), using strategies based on place value and the properties of operations. | Grade 4 |
| Alabama | 4.NBT.12 | Use strategies based on place value, properties of operations, and/or the relationship between multiplication and division to find whole-number quotients and remainders with one-digit divisors and up to four-digit dividends. | Grade 4 |
| Alabama | 4.NF.13 | Using area and length fraction models, explain why one fraction is equivalent to another, taking into account that the number and size of the parts differ even though the two fractions themselves are the same size. | Grade 4 |
| Alabama | 4.NF.14 | Compare two fractions with different numerators and different denominators using concrete models, benchmarks (0, ½, 1), common denominators, and/or common numerators, recording the comparisons with symbols >, =, or <, and justifying the conclusions. | Grade 4 |
| Alabama | 4.NF.15 | Model and justify decompositions of fractions and explain addition and subtraction of fractions as joining or separating parts referring to the same whole. | Grade 4 |
| Alabama | 4.NF.16 | Apply and extend previous understanding or multiplication to multiple a whole number times a fraction. | Grade 4 |
| Alabama | 4.NF.17 | Express, model, and explain the equivalence between fractions with denominators of 10 and 100. | Grade 4 |
| Alabama | 4.NF.18 | Use models and decimal notation to represent fractions with denominators of 10 and 100. | Grade 4 |
| Alabama | 4.NF.19 | Use visual models and reasoning to compare two decimals to hundredths (referring to the same whole), recording comparisons using symbols >, =, or <, and justifying the conclusions. | Grade 4 |
| Alabama | 4.DA.20 | Interpret data in graphs (picture, bar, and line plots) to solve problems using numbers and operations. | Grade 4 |
| Alabama | 4.M.21 | Select and use an appropriate unit of measurement for a given attribute (length, mass, liquid volume, time) within one system of units: metric - km, m, cm; kg, g, l, ml; customary - lb, oz; time - hr, min, sec. | Grade 4 |
| Alabama | 4.M.22 | Use the four operations to solve measurement word problems with distance, intervals of time, liquid volume, mass of objects, and money. | Grade 4 |
| Alabama | 4.M.23 | Apply area and perimeter formulas for rectangles in real-world and mathematical situations. | Grade 4 |
| Alabama | 4.M.24 | Identify an angle as a geometric shape formed wherever two rays share a common endpoint. | Grade 4 |
| Alabama | 4.M.25 | Use a protractor to measure angles in whole-number degrees and sketch angles of specific measure. | Grade 4 |
| Alabama | 4.M.26 | Decompose an angle into non-overlapping parts to demonstrate that the angle measure of the whole is the sum of the angle measures of the parts. | Grade 4 |
| Alabama | 4.G.27 | Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines, and identify these in two-dimensional figures. | Grade 4 |
| Alabama | 4.G.28 | Identify two-dimensional figures based on the presence or absence of parallel or perpendicular lines or the presence or absence of angles of a specified size. | Grade 4 |
| Alabama | 4.G.29 | Define a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. | Grade 4 |
| Alabama | 5.OA.1 | Write, explain, and evaluate simple numerical expressions involving the four operations to solve up to two-step problems. Include expressions involving parentheses, brackets, or braces, using commutative, associative, and distributive properties. | Grade 5 |
| Alabama | 5.OA.2 | Generate two numerical patterns using two given rules and complete an input/output table for the data. | Grade 5 |
| Alabama | 5.NBT.3 | Using models and quantitative reasoning, explain that in a multi-digit number, including decimals, a digit in any place represents ten times what it represents in the place to its right and ⅒ of what it represents in the place to its left. | Grade 5 |
| Alabama | 5.NBT.4 | Read, write, and compare decimals to the thousandths. | Grade 5 |
| Alabama | 5.NBT.5 | Use place value understanding to round decimals to thousandths. | Grade 5 |
| Alabama | 5.NBT.6 | Fluently multiply multi-digit whole numbers using the standard algorithm. | Grade 5 |
| Alabama | 5.NBT.7 | Use strategies based on place value, properties of operations, and/or the relationship between multiplication and division to find whole-number quotients and remainders with up to four-digit dividends and two-digit divisors. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. | Grade 5 |
| Alabama | 5.NBT.8 | Add, subtract, multiply, and divide decimals to hundredths using strategies based on place value, properties of operations, and/or the relationships between addition/subtraction and multiplication/division; relate the strategy to a written method, and explain the reasoning used. | Grade 5 |
| Alabama | 5.NF.9 | Model and solve real-world problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally, and assess the reasonableness of answers. | Grade 5 |
| Alabama | 5.NF.10 | Add and subtract fractions and mixed numbers with unlike denominators, using fraction equivalence to calculate a sum or difference of fractions or mixed numbers with like denominators. | Grade 5 |
| Alabama | 5.NF.11 | Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers. | Grade 5 |
| Alabama | 5.NF.12 | Apply and extend previous understandings of multiplication to find the product of a fraction times a whole number or a fraction times a fraction. | Grade 5 |
| Alabama | 5.NF.13 | Interpret multiplication as scaling (resizing). | Grade 5 |
| Alabama | 5.NF.14 | Model and solve real-world problems involving multiplication of fractions and mixed numbers using visual fraction models, drawings, or equations to represent the problem. | Grade 5 |
| Alabama | 5.NF.15 | Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. | Grade 5 |
| Alabama | 5.DA.16 | Make a line plot to display a data set of measurements in fractions of a unit (½, ¼, ⅛). | Grade 5 |
| Alabama | 5.M.17 | Convert among different-sized standard measurement units within a given measurement system and use these conversions in a solving multi-step, real-world problems. | Grade 5 |
| Alabama | 5.M.18 | Identify volume as an attribute of solid figures, and measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised (non-standard) units. | Grade 5 |
| Alabama | 5.M.19 | Relate volume to the operations of multiplication and addition, and solve real-world and mathematical problems involving volume. | Grade 5 |
| Alabama | 5.G.20 | Graph points in the first quadrant of the coordinate plane, and interpret coordinate values of points to represent real-world and mathematical problems. | Grade 5 |
| Alabama | 5.G.21 | Classify triangles according to side length (isosceles, equilateral, scalene) and angle measure (acute, obtuse, right, equiangular). | Grade 5 |
| Alabama | 5.G.22 | Classify quadrilaterals in a hierarchy based on properties. | Grade 5 |
| Alabama | 5.G.23 | Explain that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. | Grade 5 |
| Alabama | 6.PR.1 | Use appropriate notations (a/b, a to b, a:b) to represent a proportional relationship between quantities and use ratio language to describe the relationship between quantities. | Grade 6 |
| Alabama | 6.PR.2 | Use unit rates to represent and describe ratio relationships. | Grade 6 |
| Alabama | 6.PR.3 | Use ratio and rate reasoning to solve mathematical and real-world problems (including but not limited to percent, measurement conversion, and equivalent ratios) using a variety of models, including tables of equivalent ratios, tape diagrams, double number lines, and equations. | Grade 6 |
| Alabama | 6.NSO.4 | Interpret and compute quotients of fractions using visual models and equations to represent problems. | Grade 6 |
| Alabama | 6.NSO.5 | Fluently divide multi-digit whole numbers using a standard algorithm to solve real-world and mathematical problems. | Grade 6 |
| Alabama | 6.NSO.6 | Add, subtract, multiply, and divide decimals using a standard algorithm. | Grade 6 |
| Alabama | 6.NSO.9 | Use signed numbers to describe quantities that have opposite directions or values and to represent quantities in real-world contexts. | Grade 6 |
| Alabama | 6.NSO.10 | Locate integers and other rational numbers on a horizontal or vertical line diagram. | Grade 6 |
| Alabama | 6.NSO.11 | Find the position of pairs of integers and other rational numbers on the coordinate plane. | Grade 6 |
| Alabama | 6.NSO.12 | Explain the meaning of absolute value and determine the absolute value of rational numbers in real-world contexts. | Grade 6 |
| Alabama | 6.NSO.13 | Compare and order rational numbers and absolute value of rational numbers with and without a number line in order to solve real-world and mathematical problems. | Grade 6 |
| Alabama | 6.AF.14 | Write, evaluate, and compare expressions involving whole number exponents. | Grade 6 |
| Alabama | 6.AF.15 | Write, read, and evaluate expressions in which letters represent numbers in real-world contexts. | Grade 6 |
| Alabama | 6.AF.16 | Generate equivalent algebraic expressions using the properties of operations, including inverse, identity, commutative, associative, and distributive. | Grade 6 |
| Alabama | 6.AF.17 | Determine whether two expressions are equivalent and justify the reasoning. | Grade 6 |
| Alabama | 6.AF.18 | Determine whether a value is a solution to an equation or inequality by using substitution to conclude whether a given value makes the equation or inequality true. | Grade 6 |
| Alabama | 6.AF.19 | Write and solve an equation in the form of x+p=q or px=q for cases in which p, q, and x are all non-negative rational numbers to solve real-world and mathematic problems. | Grade 6 |
| Alabama | 6.AF.20 | Write and solve inequalities in the form of x > c, x < c, x ≥ c, or x ≤ c to represent a constraint or condition in a real-world or mathematical problem. | Grade 6 |
| Alabama | 6.AF.21 | Identify, represent, and analyze two quantities that change in relationship to one another in real-world or mathematical situations. | Grade 6 |
| Alabama | 6.DSP.24 | Represent numerical data graphically, using dot plots, line plots, histograms, and stem and leaf plots, and box plots. | Grade 6 |
| Alabama | 6.GM.25 | Graph polygons in the coordinate plane given coordinates of the vertices to solve real-world and mathematical problems. | Grade 6 |
| Alabama | 6.GM.26 | Calculate the area of triangles, special quadrilaterals, and other polygons by composing and decomposing them into known shapes. | Grade 6 |
| Alabama | 6.GM.27 | Determine the surface area of three-dimensional figures by representing them with nets composed of rectangles and triangles to solve real-world and mathematical problems. | Grade 6 |
| Alabama | 6.GM.28 | Apply previous understanding of volume of right rectangular prisms to those with fractional edge lengths to solve real-world and mathematical problems. | Grade 6 |
| Alabama | 7.PR.1 | Calculate unit rates of length, area, and other quantities measured in like or different units that include ratios or fractions. | Grade 7 |
| Alabama | 7.PR.2 | Represent a relationship between two quantities and determine whether the two quantities are related proportionally. | Grade 7 |
| Alabama | 7.PR.3 | Solve multi-step percent problems in context using proportional reasoning, including simple interest, tax, gratuities, commissions, fees, markups and markdowns, percent increase, and percent decrease. | Grade 7 |
| Alabama | 7.NSO.4 | Apply and extend knowledge of operations of whole numbers, fractions, and decimals to add, subtract, multiply, and divide rational numbers including integers, signed fractions, and decimals. | Grade 7 |
| Alabama | 7.NSO.5 | Solve real-world and mathematical problems involving the four operations of rational numbers, including complex fractions. Apply properties of operations as strategies where applicable. | Grade 7 |
| Alabama | 7.AF.6 | Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients. | Grade 7 |
| Alabama | 7.AF.7 | Generate expressions in equivalent forms based on context and explain how the quantities are related. | Grade 7 |
| Alabama | 7.AF.8 | Solve multi-step real-world and mathematical problems involving rational numbers (integers, signed fractions and decimals), converting between forms as needed. Assess the reasonableness of answers using mental computation and estimation strategies. | Grade 7 |
| Alabama | 7.AF.9 | Use variables to represent quantities in real-world or mathematical problems and construct algebraic expressions, equations, and inequalities to solve problems by reasoning about the quantities. | Grade 7 |
| Alabama | 7.GM.17 | Solve problems involving scale drawings of geometric figures, including computation of actual lengths and areas from a scale drawing and reproduction of a scale drawing at a different scale. | Grade 7 |
| Alabama | 7.GM.18 | Construct geometric shapes (freehand, using a ruler and a protractor, and using technology), given a written description or measurement constraints with an emphasis on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle. | Grade 7 |
| Alabama | 7.GM.19 | Describe the two-dimensional figures created by slicing three-dimensional figures into plane sections. | Grade 7 |
| Alabama | 7.GM.20 | Explain the relationship among circumference, diameter, area, and radius of a circle to demonstrate understanding of formulas for the area and circumference of a circle. | Grade 7 |
| Alabama | 7.GM.21 | Use facts about supplementary, complementary, cortical, and adjacent angles in multi-step problems to write and solve simple equations for an unknown angle in a figure. | Grade 7 |
| Alabama | 7.GM.22 | Solve real-world and mathematical problems involving area, volume, and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right rectangular prisms. | Grade 7 |
| Alabama | 8.NSO.2 | Locate rational approximations of irrational numbers on a number line, compare their sizes, and estimate the values of the irrational numbers. | Grade 8 |
| Alabama | 8.AF.3 | Develop and apply properties of integer exponents to generate equivalent numerical and algebraic expressions. | Grade 8 |
| Alabama | 8.AF.4 | Use square root and cube root symbols to represent solutions to equations. | Grade 8 |
| Alabama | 8.AF.5 | Estimate and compare very large or very small numbers in scientific notation. | Grade 8 |
| Alabama | 8.AF.6 | Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. | Grade 8 |
| Alabama | 8.AF.8 | Graph proportional relationships. | Grade 8 |
| Alabama | 8.AF.9 | Interpret y=mx+b as defining a linear equation whose graph is a line with m as the slope and b as the y-intercept. | Grade 8 |
| Alabama | 8.AF.11 | Solve multi-step linear equations in one variable, including rational number coefficients, and equations that require using the distributive property and combining like terms. | Grade 8 |
| Alabama | 8.AF.12 | Solve systems of two linear equations in two variables by graphing and substitution. | Grade 8 |
| Alabama | 8.AF.13 | Determine whether a relation is a function, defining a function as a rule that assigns to each input (independent value) exactly one output (dependent value), and given a graph, table, mapping, or set of order pairs. | Grade 8 |
| Alabama | 8.AF.15 | Compare properties of functions represented algebraically, graphically, numerically in tables, or by verbal descriptions. | Grade 8 |
| Alabama | 8.AF.16 | Construct a function to model a linear relationship between two variables. | Grade 8 |
| Alabama | 8.AF.17 | Analyze the relationship (increasing or decreasing, linear or non-linear) between two quantities represented in a graph. | Grade 8 |
| Alabama | 8.DSP.18 | Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities, describing patterns in terms of positive, negative, or no association, linear and non-linear association, clustering, and outliers. | Grade 8 |
| Alabama | 8.DSP.19 | Given a scatter plot that suggests a linear association, informally draw a line to fit the data, and assess the model fit by judging the closeness of the data points to the line. | Grade 8 |
| Alabama | 8.GM.22 | Verify experimentally the properties of rigid motions (rotations, reflections, and translations): lines are taken to lines, and line segments are taken to line segments of the same length; angles are taken to angles of the same measure; and parallel lines are taken to parallel lines. | Grade 8 |
| Alabama | 8.GM.23 | Use coordinates to describe the effect of transformations (dilations, translations, rotations, and reflections) on two- dimensional figures. | Grade 8 |
| Alabama | 8.GM.24 | Given a pair of two-dimensional figures, determine if a series of dilations and rigid motions maps one figure onto the other, recognizing that if such a sequence exists the figures are similar; describe the transformation sequence that exhibits the similarity between them. | Grade 8 |
| Alabama | 8.GM.25 | Analyze and apply properties of parallel lines cut by a transversal to determine missing angle measures. | Grade 8 |
| Alabama | 8.GM.27 | Apply the Pythagorean Theorem to find the distance between two points in a coordinate plane. | Grade 8 |
| Alabama | 8.GM.28 | Apply the Pythagorean Theorem to determine unknown side lengths of right triangles, including real-world applications. | Grade 8 |
| Alabama | 8.GM.29 | Informally derive the formulas for the volume of cones and spheres by experimentally comparing the volumes of cones and spheres with the same radius and height to a cylinder with the same dimensions. | Grade 8 |
| Alabama | 8.GM.30 | Use formulas to calculate the volumes of three-dimensional figures (cylinders, cones, and spheres) to solve real-world problems. | Grade 8 |
| Alabama | G.12 | Represent data of two quantitative variables on a scatter plot, and describe how the variables are related. | Geometry with Data Analysis |
| Alabama | AP.5 | Use the structure of an expression to identify ways to rewrite it. | Algebra I with Probability |
| Alabama | AP.6 | Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression. | Algebra I with Probability |
| Alabama | AP.11 | Create equations and inequalities in one variable and use them to solve problems in context, either exactly or approximately. Extend from contexts arising from linear functions to those involving quadratic, exponential, and absolute value functions. | Algebra I with Probability |
| Alabama | AP.12 | Create equations in two or more variables to represent relationships between quantities in context; graph equations on coordinate axes with labels and scales and use them to make predictions. Limit to contexts arising from linear, quadratic, exponential, absolute value, and linear piecewise functions. | Algebra I with Probability |
| Alabama | AP.13 | Represent constraints by equations and/or inequalities, and solve systems of equations and/or inequalities, interpreting solutions as viable or nonviable options in a modeling context. Limit to contexts arising from linear, quadratic, exponential, absolute value, and linear piecewise functions. | Algebra I with Probability |
| Alabama | AP.15 | Define a function as a mapping from one set (called the domain) to another set (called the range) that assigns to each element of the domain exactly one element of the range. | Algebra I with Probability |
| Alabama | AP.17 | Combine different types of standard functions to write, evaluate, and interpret functions in context. Limit to linear, quadratic, exponential, and absolute value functions. | Algebra I with Probability |
| Alabama | AP.22 | Define sequences as functions, including recursive definitions, whose domain is a subset of the integers. | Algebra I with Probability |
| Alabama | AP.28 | For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Extend from relationships that can be represented by linear functions to quadratic, exponential, absolute value, and linear piecewise functions. | Algebra I with Probability |
| Alabama | AP.30 | Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. | Algebra I with Probability |
| Alabama | AS.6 | Factor polynomials using common factoring techniques, and use the factored form of a polynomial to reveal the zeros of the function it defines. | Algebra II with Statistics |
| Alabama | AS.13 | Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales and use them to make predictions. Extend to polynomial, trigonometric (sine and cosine), logarithmic, reciprocal, radical, and general piecewise functions. | Algebra II with Statistics |
| Alabama | AS.17 | For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Extend to polynomial, trigonometric (sine and cosine), logarithmic, reciprocal, radical, and general piecewise functions. | Algebra II with Statistics |
| Alabama | AS.20 | Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. Extend to polynomial, trigonometric (sine and cosine), logarithmic, reciprocal, radical, and general piecewise functions. | Algebra II with Statistics |
| Alabama | P.26 | Graph functions expressed symbolically and show key features of the graph, by hand and using technology. Use the equation of functions to identify key features in order to generate a graph. | Precalculus |
| Alaska | K.CC.1 | Count to 100 by ones and by tens. | Kindergarten |
| Alaska | K.CC.2 | Count forward beginning from a given number within the known sequence. | Kindergarten |
| Alaska | K.CC.3 | Write numbers from 0 to 20. Represent a number of objects with a written numeral 0 - 20 (with 0 representing a count of no objects). | Kindergarten |
| Alaska | K.CC.4 | Understand the relationship between numbers and quantities; connect counting to cardinality. | Kindergarten |
| Alaska | K.CC.5 | Count to answer “how many?” questions about as many as 20 things arranged in a line, a rectangular array or a circle, or as many as 10 things in a scattered configuration; given a number from 1-20, count out that many objects. | Kindergarten |
| Alaska | K.CC.6 | Identify whether the number of objects in one group is greater than, less than, or equal to the number of objects in another group (e.g., by using matching, counting, or estimating strategies). | Kindergarten |
| Alaska | K.CC.7 | Compare and order two numbers between 1 and 10 presented as written numerals. | Kindergarten |
| Alaska | K.G.1 | Describe objects in the environment using names of shapes and describe their relative positions (e.g., above, below, beside, in front of, behind, next to). | Kindergarten |
| Alaska | K.G.2 | Name shapes regardless of their orientation or overall size. | Kindergarten |
| Alaska | K.G.3 | Identify shapes as two-dimensional (flat) or three-dimensional (solid). | Kindergarten |
| Alaska | K.G.4 | Analyze and compare two- and three-dimensional shapes, in different sizes and orientations, using informal language to describe their similarities, differences, parts (e.g., number of sides and vertices), and other attributes (e.g., having sides of equal lengths). | Kindergarten |
| Alaska | K.G.6 | Put together two-dimensional shapes to form larger shapes (e.g., join two triangles with full sides touching to make a rectangle). | Kindergarten |
| Alaska | K.MD.1 | Describe measurable attributes of objects (e.g., length or weight). Match measuring tools to attribute (e.g., ruler to length). Describe several measurable attributes of a single object. | Kindergarten |
| Alaska | K.MD.2 | Make comparisons between two objects with a measurable attribute in common, to see which object has “more of”/“less of” the attribute, and describe the difference. | Kindergarten |
| Alaska | K.MD.3 | Classify objects into given categories (attributes). Count the number of objects in each category (limit category counts to be less than or equal to 10). | Kindergarten |
| Alaska | K.MD.6 | Identify coins by name. | Kindergarten |
| Alaska | K.NBT.1 | Compose and decompose numbers from 11 to 19 into ten ones and some further ones (e.g., by using objects or drawings) and record each composition and decomposition by a drawing or equation (e.g., 18 = 10 + 8); understand that these numbers are composed of ten ones and one, two, three, four, five, six, seven, eight or nine ones. | Kindergarten |
| Alaska | K.OA.1 | Represent addition and subtraction with objects, fingers, mental images, drawings, sounds (e.g., claps) acting out situations, verbal explanations, expressions, or equations. | Kindergarten |
| Alaska | K.OA.2 | Add or subtract whole numbers to 10 (e.g., by using objects or drawings to solve word problems). | Kindergarten |
| Alaska | K.OA.3 | Decompose numbers less than or equal to 10 into pairs in more than one way (e.g., by using objects or drawings, and record each decomposition by a drawing or equation). | Kindergarten |
| Alaska | K.OA.4 | For any number from 1- 4, find the number that makes 5 when added to the given number and, for any number from 1- 9, find the number that makes 10 when added to the given number (e.g., by using objects, drawings or 10 frames) and record the answer with a drawing or equation. | Kindergarten |
| Alaska | K.OA.5 | Fluently add and subtract numbers up to 5. | Kindergarten |
| Alaska | 1.G.1 | Distinguish between defining attributes (e.g., triangles are closed and three-sided) versus non-defining attributes. Identify shapes that have non-defining attributes (e.g., color, orientation, overall size). Build and draw shapes given specified attributes. | Grade 1 |
| Alaska | 1.G.2 | Compose (put together) two-dimensional or three-dimensional shapes to create a larger, composite shape, and compose new shapes from the composite shape. | Grade 1 |
| Alaska | 1.G.3 | Partition circles and rectangles into two and four equal shares. Describe the shares using the words, halves, fourths, and quarters and phrases half of, fourth of and quarter of. Describe the whole as two of or four of the shares. Understand for these examples that decomposing (break apart) into more equal shares creates smaller shares. | Grade 1 |
| Alaska | 1.MD.1 | Measure and compare three objects using standard or non-standard units. | Grade 1 |
| Alaska | 1.MD.2 | Express the length of an object as a whole number of length units, by laying multiple copies of a shorter object (the length unit) end to end; understand that the length measurement of an object is the number of same-size length units that span it with no gaps or overlaps. | Grade 1 |
| Alaska | 1.MD.3 | Tell and write time in half hours using both analog and digital clocks. | Grade 1 |
| Alaska | 1.MD.6 | Identify values of coins (e.g., nickel = 5 cents, quarter = 25 cents). Identify equivalent values of coins up to $1 (e.g., 5 pennies = 1 nickel, 5 nickels = 1 quarter). | Grade 1 |
| Alaska | 1.MD.7 | Organize, represent and interpret data with up to three categories. Ask and answer comparison and quantity questions about the data. | Grade 1 |
| Alaska | 1.NBT.1 | Count to 120. In this range, read, write and order numerals and represent a number of objects with a written numeral. | Grade 1 |
| Alaska | 1.NBT.2 | Model and identify place value positions of two digit numbers. | Grade 1 |
| Alaska | 1.NBT.3 | Compare two two-digit numbers based on meanings of the tens and ones digits, recording the results of comparisons with the symbols >, =, <. | Grade 1 |
| Alaska | 1.NBT.4 | Add using numbers up to 100 including adding a two-digit number and a one-digit number and adding a two-digit number and a multiple of 10. | Grade 1 |
| Alaska | 1.NBT.5 | Given a two-digit number, mentally find 10 more or 10 less than the number, without having to count; explain the reasoning used. | Grade 1 |
| Alaska | 1.NBT.6 | Subtract multiples of 10 up to 100. | Grade 1 |
| Alaska | 1.OA.1 | Use addition and subtraction strategies to solve word problems (using numbers up to 20), involving situations of adding to, taking from, putting together, taking apart and comparing, with unknowns in all positions, using a number line (e.g., by using objects, drawings and equations). Record and explain using equation symbols and a symbol for the unknown number to represent the problem. | Grade 1 |
| Alaska | 1.OA.3 | Apply properties of operations as strategies to add and subtract. (Students need not know the name of the property.) | Grade 1 |
| Alaska | 1.OA.4 | Understand subtraction as an unknown-addend problem. | Grade 1 |
| Alaska | 1.OA.5 | Relate counting to addition and subtraction (e.g., by counting on 2 to add 2). | Grade 1 |
| Alaska | 1.OA.6 | Add and subtract using numbers up to 20, demonstrating fluency for addition and subtraction up to 10. | Grade 1 |
| Alaska | 1.OA.7 | Understand the meaning of the equal sign (e.g., read equal sign as “same as”) and determine if equations involving addition and subtraction are true or false. | Grade 1 |
| Alaska | 1.OA.8 | Determine the unknown whole number in an addition or subtraction equation. | Grade 1 |
| Alaska | 2.G.1 | Identify and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces compared visually, not by measuring. Identify triangles, quadrilaterals, pentagons, hexagons and cubes. | Grade 2 |
| Alaska | 2.G.2 | Partition a rectangle into rows and columns of same-size squares and count to find the total number of them. | Grade 2 |
| Alaska | 2.G.3 | Partition circles and rectangles into shares, describe the shares using the words halves, thirds, half of, a third of, etc., and describe the whole as two halves, three thirds, four fourths. Recognize that equal shares of identical wholes need not have the same shape. | Grade 2 |
| Alaska | 2.MD.1 | Measure the length of an object by selecting and using standard tools such as rulers, yardsticks, meter sticks, and measuring tapes. | Grade 2 |
| Alaska | 2.MD.2 | Measure the length of an object twice using different length units for the two measurements. Describe how the two measurements relate to the size of the unit chosen. | Grade 2 |
| Alaska | 2.MD.4 | Measure to compare lengths of two objects, expressing the difference in terms of a standard length unit. | Grade 2 |
| Alaska | 2.MD.5 | Solve addition and subtraction word problems using numbers up to 100 involving length that are given in the same units (e.g., by using drawings of rulers). Write an equation with a symbol for the unknown to represent the problem. | Grade 2 |
| Alaska | 2.MD.7 | Tell and write time to the nearest five minutes using a.m. and p.m. from analog and digital clocks. | Grade 2 |
| Alaska | 2.MD.8 | Solve word problems involving dollar bills and coins using the $ and ¢ symbols appropriately. | Grade 2 |
| Alaska | 2.MD.9 | Collect, record, interpret, represent, and describe data in a table, graph or line plot. | Grade 2 |
| Alaska | 2.MD.10 | Draw a picture graph and a bar graph (with single-unit scale) to represent a data set with up to four categories. Solve simple put-together, take-apart and compare problems using information presented in a bar graph. | Grade 2 |
| Alaska | 2.NBT.1 | Model and identify place value positions of three digit numbers. | Grade 2 |
| Alaska | 2.NBT.2 | Count up to 1000, skip-count by 5s, 10s and 100s. | Grade 2 |
| Alaska | 2.NBT.3 | Read, write, order up to 1000 using base-ten numerals, number names and expanded form. | Grade 2 |
| Alaska | 2.NBT.4 | Compare two three-digit numbers based on the meanings of the hundreds, tens and ones digits, using >, =, < symbols to record the results. | Grade 2 |
| Alaska | 2.NBT.5 | Fluently add and subtract using numbers up to 100. | Grade 2 |
| Alaska | 2.NBT.6 | Add up to four two-digit numbers using strategies based on place value and properties of operations. | Grade 2 |
| Alaska | 2.NBT.7 | Add and subtract using numbers up to 1000. | Grade 2 |
| Alaska | 2.NBT.8 | Mentally add 10 or 100 to a given number 100-900 and mentally subtract 10 or 100 from a given number. | Grade 2 |
| Alaska | 2.OA.1 | Use addition and subtraction strategies to estimate, then solve one- and two-step word problems (using numbers up to 100) involving situations of adding to, taking from, putting together, taking apart and comparing, with unknowns in all positions (e.g., by using objects, drawings and equations). Record and explain using equation symbols and a symbol for the unknown number to represent the problem. | Grade 2 |
| Alaska | 2.OA.2 | Fluently add and subtract using numbers up to 20 using mental strategies. Know from memory all sums of two one-digit numbers. | Grade 2 |
| Alaska | 2.OA.3 | Determine whether a group of objects (up to 20) is odd or even (e.g., by pairing objects and comparing, counting by 2s). Model an even number as two equal groups of objects and then write an equation as a sum of two equal addends. | Grade 2 |
| Alaska | 2.OA.4 | Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns. Write an equation to express the total as repeated addition (e.g., array of 4 by 5 would be 5 + 5 + 5 + 5 = 20). | Grade 2 |
| Alaska | 3.G.1 | Categorize shapes by different attribute classifications and recognize that shared attributes can define a larger category. Generalize to create examples or non-examples. | Grade 3 |
| Alaska | 3.G.2 | Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole. | Grade 3 |
| Alaska | 3.MD.1 | Tell and write time to the nearest minute and measure time intervals in minutes. Solve word problems involving addition and subtraction of time intervals in minutes or hours (e.g., by representing the problem on a number line diagram or clock). | Grade 3 |
| Alaska | 3.MD.2 | Estimate and measure liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l). (Excludes compound units such as cm³ and finding the geometric volume of a container.) Add, subtract, multiply, or divide to solve and create one-step word problems involving masses or volumes that are given in the same units (e.g., by using drawings, such as a beaker with a measurement scale, to represent the problem). (Excludes multiplicative comparison problems [problems involving notions of “times as much.”]) | Grade 3 |
| Alaska | 3.MD.4 | Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and two-step “how many more” and “how many less” problems using information presented in scaled bar graphs. | Grade 3 |
| Alaska | 3.MD.5 | Measure and record lengths using rulers marked with halves and fourths of an inch. Make a line plot with the data, where the horizontal scale is marked off in appropriate units—whole numbers, halves, or quarters. | Grade 3 |
| Alaska | 3.MD.7 | Recognize area as an attribute of plane figures and understand concepts of area measurement. | Grade 3 |
| Alaska | 3.MD.8 | Measure areas by tiling with unit squares (square centimeters, square meters, square inches, square feet, and improvised units). | Grade 3 |
| Alaska | 3.MD.9 | Relate area to the operations of multiplication and addition. | Grade 3 |
| Alaska | 3.MD.10 | Solve real-world and mathematical problems involving perimeters of polygons, including: | Grade 3 |
| Alaska | 3.NBT.1 | Use place value understanding to round whole numbers to the nearest 10 or 100. | Grade 3 |
| Alaska | 3.NBT.2 | Use strategies and/or algorithms to fluently add and subtract with numbers up to 1000, demonstrating understanding of place value, properties of operations, and/or the relationship between addition and subtraction. | Grade 3 |
| Alaska | 3.NBT.3 | Multiply one-digit whole numbers by multiples of 10 in the range 10-90 (e.g., 9 x 80, 10 x 60) using strategies based on place value and properties of operations. | Grade 3 |
| Alaska | 3.NF.1 | Understand a fraction 1/𝑏 (e.g., 1/4) as the quantity formed by 1 part when a whole is partitioned into 𝑏 (e.g., 4) equal parts; understand a fraction 𝑎/𝑏 (e.g., 2/4) as the quantity formed by 𝑎 (e.g., 2) parts of size 1/𝑏. (e.g., 1/4) | Grade 3 |
| Alaska | 3.NF.2 | Understand a fraction as a number on the number line; represent fractions on a number line diagram. | Grade 3 |
| Alaska | 3.NF.3 | Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size. | Grade 3 |
| Alaska | 3.OA.1 | Interpret products of whole numbers (e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each). | Grade 3 |
| Alaska | 3.OA.2 | Interpret whole-number quotients of whole numbers (e.g., interpret 56 ÷ 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each). | Grade 3 |
| Alaska | 3.OA.3 | Use multiplication and division numbers up to 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities (e.g., by using drawings and equations with a symbol for the unknown number to represent the problem). | Grade 3 |
| Alaska | 3.OA.4 | Determine the unknown whole number in a multiplication or division equation relating three whole numbers. | Grade 3 |
| Alaska | 3.OA.5 | Make, test, support, draw conclusions and justify conjectures about properties of operations as strategies to multiply and divide. (Students need not use formal terms for these properties.) | Grade 3 |
| Alaska | 3.OA.6 | Understand division as an unknown-factor problem. | Grade 3 |
| Alaska | 3.OA.7 | Fluently multiply and divide numbers up to 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 ×5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers. | Grade 3 |
| Alaska | 3.OA.8 | Solve and create two-step word problems using any of the four operations. Represent these problems using equations with a symbol (box, circle, question mark) standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. | Grade 3 |
| Alaska | 3.OA.9 | Identify arithmetic patterns (including patterns in the addition table or multiplication table) and explain them using properties of operations. | Grade 3 |
| Alaska | 4.G.1 | Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular, parallel, and intersecting line segments. Identify these in two-dimensional (plane) figures. | Grade 4 |
| Alaska | 4.G.2 | Classify two-dimensional (plane) figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles. | Grade 4 |
| Alaska | 4.G.3 | Recognize a line of symmetry for a two-dimensional (plane) figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify line-symmetric figures and draw lines of symmetry. | Grade 4 |
| Alaska | 4.MD.1 | Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table. | Grade 4 |
| Alaska | 4.MD.2 | Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. | Grade 4 |
| Alaska | 4.MD.3 | Apply the area and perimeter formulas for rectangles in real-world and mathematical problems. | Grade 4 |
| Alaska | 4.MD.5 | Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots. | Grade 4 |
| Alaska | 4.MD.7 | Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint. | Grade 4 |
| Alaska | 4.MD.8 | Measure and draw angles in whole-number degrees using a protractor. Estimate and sketch angles of specified measure. | Grade 4 |
| Alaska | 4.MD.9 | Recognize angle measure as additive. When an angle is divided into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real-world and mathematical problems (e.g., by using an equation with a symbol for the unknown angle measure). | Grade 4 |
| Alaska | 4.NBT.1 | Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. | Grade 4 |
| Alaska | 4.NBT.2 | Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on the value of the digits in each place, using >, =, and < symbols to record the results of comparisons. | Grade 4 |
| Alaska | 4.NBT.3 | Use place value understanding to round multi-digit whole numbers to any place using a variety of estimation methods; be able to describe, compare, and contrast solutions. | Grade 4 |
| Alaska | 4.NBT.4 | Fluently add and subtract multi-digit whole numbers using any algorithm. Verify the reasonableness of the results. | Grade 4 |
| Alaska | 4.NBT.5 | Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. | Grade 4 |
| Alaska | 4.NBT.6 | Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. | Grade 4 |
| Alaska | 4.NF.1 | Explain why a fraction 𝑎/𝑏 is equivalent to a fraction (𝑛 × 𝑎)/(𝑛 × 𝑏) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. | Grade 4 |
| Alaska | 4.NF.2 | Compare two fractions with different numerators and different denominators (e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2). Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions (e.g., by using a visual fraction model). | Grade 4 |
| Alaska | 4.NF.3 | Understand a fraction 𝑎/𝑏 with 𝑎 > 1 as a sum of fractions 1/𝑏. | Grade 4 |
| Alaska | 4.NF.4 | Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. | Grade 4 |
| Alaska | 4.NF.5 | Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100. | Grade 4 |
| Alaska | 4.NF.6 | Use decimal notation for fractions with denominators 10 or 100. | Grade 4 |
| Alaska | 4.NF.7 | Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions (e.g., by using a visual model). | Grade 4 |
| Alaska | 4.OA.1 | Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 × 7 as a statement that 35 is 5 groups of 7 and 7 groups of 5 (Commutative property). Represent verbal statements of multiplicative comparisons as multiplication equations. | Grade 4 |
| Alaska | 4.OA.2 | Multiply or divide to solve word problems involving multiplicative comparison (e.g., by using drawings and equations with a symbol for the unknown number to represent the problem or missing numbers in an array). Distinguish multiplicative comparison from additive comparison. | Grade 4 |
| Alaska | 4.OA.3 | Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. | Grade 4 |
| Alaska | 4.OA.4 | Find all factor pairs for a whole number in the range 1–100. | Grade 4 |
| Alaska | 4.OA.5 | Generate a number, shape pattern, table, t-chart, or input/output function that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. Be able to express the pattern in algebraic terms. | Grade 4 |
| Alaska | 5.G.1 | Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., 𝑥-axis and 𝑥-coordinate, 𝑦-axis and 𝑦-coordinate). | Grade 5 |
| Alaska | 5.G.2 | Represent real-world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. | Grade 5 |
| Alaska | 5.G.3 | Understand that attributes belonging to a category of two-dimensional (plane) figures also belong to all subcategories of that category. | Grade 5 |
| Alaska | 5.G.4 | Classify two-dimensional (plane) figures in a hierarchy based on attributes and properties. | Grade 5 |
| Alaska | 5.MD.1 | Identify, estimate measure, and convert equivalent measures within systems English length (inches, feet, yards, miles) weight (ounces, pounds, tons) volume (fluid ounces, cups, pints, quarts, gallons) temperature (Fahrenheit) Metric length (millimeters, centimeters, meters, kilometers) volume (milliliters, liters), temperature (Celsius), (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real-world problems using appropriate tools. | Grade 5 |
| Alaska | 5.MD.3 | Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving information presented in line plots. | Grade 5 |
| Alaska | 5.MD.5 | Recognize volume as an attribute of solid figures and understand concepts of volume measurement. | Grade 5 |
| Alaska | 5.MD.6 | Estimate and measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and non-standard units. | Grade 5 |
| Alaska | 5.MD.7 | Relate volume to the operations of multiplication and addition and solve real-world and mathematical problems involving volume. | Grade 5 |
| Alaska | 5.NBT.1 | Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. | Grade 5 |
| Alaska | 5.NBT.2 | Explain and extend the patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain and extend the patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. | Grade 5 |
| Alaska | 5.NBT.3 | Read, write, and compare decimals to thousandths. | Grade 5 |
| Alaska | 5.NBT.4 | Use place values understanding to round decimals to any place. | Grade 5 |
| Alaska | 5.NBT.5 | Fluently multiply multi-digit whole numbers using a standard algorithm. | Grade 5 |
| Alaska | 5.NBT.6 | Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, number lines, real life situations, and/or area models. | Grade 5 |
| Alaska | 5.NBT.7 | Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between the operations. Relate the strategy to a written method and explain their reasoning in getting their answers. | Grade 5 |
| Alaska | 5.NF.1 | Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. | Grade 5 |
| Alaska | 5.NF.2 | Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators (e.g., by using visual fraction models or equations to represent the problem). Use benchmark fractions and number sense of fractions to estimate mentally and check the reasonableness of answers. | Grade 5 |
| Alaska | 5.NF.3 | Interpret a fraction as division of the numerator by the denominator (𝑎/𝑏 = 𝑎 ÷ 𝑏). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers (e.g., by using visual fraction models or equations to represent the problem). | Grade 5 |
| Alaska | 5.NF.4 | Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. | Grade 5 |
| Alaska | 5.NF.5 | Interpret multiplication as scaling (resizing). | Grade 5 |
| Alaska | 5.NF.6 | Solve real-world problems involving multiplication of fractions and mixed numbers (e.g., by using visual fraction models or equations to represent the problem). | Grade 5 |
| Alaska | 5.NF.7 | Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. | Grade 5 |
| Alaska | 5.OA.1 | Use parentheses to construct numerical expressions, and evaluate numerical expressions with these symbols. | Grade 5 |
| Alaska | 5.OA.2 | Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. | Grade 5 |
| Alaska | 5.OA.3 | Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. | Grade 5 |
| Alaska | 6.EE.1 | Write and evaluate numerical expressions involving whole-number exponents. | Grade 6 |
| Alaska | 6.EE.2 | Write, read, and evaluate expressions in which letters stand for numbers. | Grade 6 |
| Alaska | 6.EE.3 | Apply the properties of operations to generate equivalent expressions. Model (e.g., manipulatives, graph paper) and apply the distributive, commutative, identity, and inverse properties with integers and variables by writing equivalent expressions. | Grade 6 |
| Alaska | 6.EE.4 | Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). | Grade 6 |
| Alaska | 6.EE.5 | Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true. | Grade 6 |
| Alaska | 6.EE.6 | Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set. | Grade 6 |
| Alaska | 6.EE.7 | Solve real-world and mathematical problems by writing and solving equations of the form 𝑥 + 𝑝 = 𝑞 and 𝑝𝑥 = 𝑞 for cases in which 𝑝, 𝑞 and 𝑥 are all nonnegative rational numbers. | Grade 6 |
| Alaska | 6.EE.8 | Write an inequality of the form 𝑥 > 𝑐 or 𝑥 𝑐 or 𝑥 < 𝑐 have infinitely many solutions; represent solutions of such inequalities on number line diagrams. | Grade 6 |
| Alaska | 6.EE.9 | Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. | Grade 6 |
| Alaska | 6.G.1 | Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing or decomposing into other polygons (e.g., rectangles and triangles). Apply these techniques in the context of solving real-world and mathematical problems. | Grade 6 |
| Alaska | 6.G.2 | Apply the standard formulas to find volumes of prisms. Use the attributes and properties (including shapes of bases) of prisms to identify, compare or describe three-dimensional figures including prisms and cylinders. | Grade 6 |
| Alaska | 6.G.3 | Draw polygons in the coordinate plane given coordinates for the vertices; determine the length of a side joining the coordinates of vertices with the same first or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems. | Grade 6 |
| Alaska | 6.G.4 | Represent three-dimensional figures (e.g., prisms) using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems. | Grade 6 |
| Alaska | 6.RP.1 | Write and describe the relationship in real life context between two quantities using ratio language. | Grade 6 |
| Alaska | 6.RP.2 | Understand the concept of a unit rate (𝑎/𝑏 associated with a ratio 𝑎:𝑏 with 𝑏 ≠ 0, and use rate language in the context of a ratio relationship) and apply it to solve real-world problems (e.g., unit pricing, constant speed). | Grade 6 |
| Alaska | 6.RP.3 | Use ratio and rate reasoning to solve real-world and mathematical problems (e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations). | Grade 6 |
| Alaska | 6.SP.5 | Summarize numerical data sets in relation to their context, such as by: | Grade 6 |
| Alaska | 6.NS.1 | Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions (e.g., by using visual fraction models and equations to represent the problem). | Grade 6 |
| Alaska | 6.NS.2 | Fluently multiply and divide multi-digit whole numbers using the standard algorithm. Express the remainder as a whole number, decimal, or simplified fraction; explain or justify your choice based on the context of the problem. | Grade 6 |
| Alaska | 6.NS.3 | Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation. Express the remainder as a terminating decimal, or a repeating decimal, or rounded to a designated place value. | Grade 6 |
| Alaska | 6.NS.5 | Understand that positive and negative numbers describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explain the meaning of 0 in each situation. | Grade 6 |
| Alaska | 6.NS.6 | Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates. | Grade 6 |
| Alaska | 6.NS.7 | Understand ordering and absolute value of rational numbers. | Grade 6 |
| Alaska | 6.NS.8 | Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. | Grade 6 |
| Alaska | 7.EE.1 | Apply properties of operations as strategies to add, subtract, factor, expand and simplify linear expressions with rational coefficients. | Grade 7 |
| Alaska | 7.EE.2 | Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. | Grade 7 |
| Alaska | 7.EE.3 | Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form and assess the reasonableness of answers using mental computation and estimation strategies. | Grade 7 |
| Alaska | 7.EE.4 | Use variables to represent quantities in a real-world or mathematical problem, and construct multi-step equations and inequalities to solve problems by reasoning about the quantities. | Grade 7 |
| Alaska | 7.G.1 | Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale. | Grade 7 |
| Alaska | 7.G.2 | Draw (freehand, with ruler and protractor, and with technology) geometric shapes including polygons and circles with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle. | Grade 7 |
| Alaska | 7.G.3 | Describe the two-dimensional figures, i.e., cross-section, that result from slicing three-dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids. | Grade 7 |
| Alaska | 7.G.4 | Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle. | Grade 7 |
| Alaska | 7.G.5 | Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure. | Grade 7 |
| Alaska | 7.G.6 | Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. | Grade 7 |
| Alaska | 7.RP.1 | Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. | Grade 7 |
| Alaska | 7.RP.2 | Recognize and represent proportional relationships between quantities. Make basic inferences or logical predictions from proportional relationships. | Grade 7 |
| Alaska | 7.RP.3 | Use proportional relationships to solve multi-step ratio and percent problems. | Grade 7 |
| Alaska | 7.NS.1 | Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram. | Grade 7 |
| Alaska | 7.NS.2 | Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers and use equivalent representations. | Grade 7 |
| Alaska | 7.NS.3 | Solve real-world and mathematical problems involving the four operations with rational numbers. (Computations with rational numbers extend the rules for manipulating fractions to complex fractions.) | Grade 7 |
| Alaska | 8.EE.1 | Apply the properties (product, quotient, power, zero, negative exponents, and rational exponents) of integer exponents to generate equivalent numerical expressions. | Grade 8 |
| Alaska | 8.EE.2 | Use square root and cube root symbols to represent solutions to equations of the form 𝑥² = 𝑝 and 𝑥³ = 𝑝, where 𝑝 is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that √2 is irrational. | Grade 8 |
| Alaska | 8.EE.3 | Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other. | Grade 8 |
| Alaska | 8.EE.4 | Perform operations with numbers expressed in scientific notation, including problems where both standard notation and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities. Interpret scientific notation that has been generated by technology. | Grade 8 |
| Alaska | 8.EE.5 | Graph linear equations such as 𝑦 = 𝑚𝑥 + 𝑏, interpreting 𝑚 as the slope or rate of change of the graph and 𝑏 as the 𝑦-intercept or starting value. Compare two different proportional relationships represented in different ways. | Grade 8 |
| Alaska | 8.EE.6 | Use similar triangles to explain why the slope 𝑚 is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation 𝑦 = 𝑚𝑥 for a line through the origin and the equation 𝑦 = 𝑚𝑥 + 𝑏 for a line intercepting the vertical axis at 𝑏. | Grade 8 |
| Alaska | 8.EE.7 | Solve linear equations in one variable. | Grade 8 |
| Alaska | 8.EE.8 | Analyze and solve systems of linear equations. | Grade 8 |
| Alaska | 8.F.1 | Understand that a function is a rule that assigns to each input (the domain) exactly one output (the range). The graph of a function is the set of ordered pairs consisting of an input and the corresponding output. For example, use the vertical line test to determine functions and non-functions. | Grade 8 |
| Alaska | 8.F.2 | Compare properties of two functions, each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). | Grade 8 |
| Alaska | 8.F.3 | Interpret the equation 𝑦 = 𝑚𝑥 + 𝑏 as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. | Grade 8 |
| Alaska | 8.F.4 | Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (𝑥, 𝑦) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values. | Grade 8 |
| Alaska | 8.F.5 | Given a verbal description between two quantities, sketch a graph. Conversely, given a graph, describe a possible real-world example. | Grade 8 |
| Alaska | 8.G.1 | Through experimentation, verify the properties of rotations, reflections, and translations (transformations) to figures on a coordinate plane). | Grade 8 |
| Alaska | 8.G.2 | Demonstrate understanding of congruence by applying a sequence of translations, reflections, and rotations on two-dimensional figures. Given two congruent figures, describe a sequence that exhibits the congruence between them. | Grade 8 |
| Alaska | 8.G.3 | Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates. | Grade 8 |
| Alaska | 8.G.4 | Demonstrate understanding of similarity, by applying a sequence of translations, reflections, rotations, and dilations on two-dimensional figures. Describe a sequence that exhibits the similarity between them. | Grade 8 |
| Alaska | 8.G.5 | Justify using informal arguments to establish facts about | Grade 8 |
| Alaska | 8.G.7 | Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions. | Grade 8 |
| Alaska | 8.G.8 | Apply the Pythagorean Theorem to find the distance between two points in a coordinate system. | Grade 8 |
| Alaska | 8.G.9 | Identify and apply the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems. | Grade 8 |
| Alaska | 8.SP.1 | Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association. | Grade 8 |
| Alaska | 8.SP.2 | Explain why straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line. | Grade 8 |
| Alaska | 8.NS.2 | Order real numbers, using approximations of irrational numbers, locating them on a number line. | Grade 8 |
| Alaska | A-APR.3 | Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial. | High School |
| Alaska | A-CED.2 | Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. | High School |
| Alaska | A-CED.3 | Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. | High School |
| Alaska | A-REI.3 | Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. | High School |
| Alaska | A-SSE.2 | Use the structure of an expression to identify ways to rewrite it. | High School |
| Alaska | A-SSE.3 | Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression. | High School |
| Alaska | F-BF.1 | Write a function that describes a relationship between two quantities. | High School |
| Alaska | F-IF.2 | Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. | High School |
| Alaska | F-IF.4 | For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. | High School |
| Alaska | F-IF.7 | Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. | High School |
| Alaska | S-ID.6 | Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. | High School |
| Arizona | K.CC.A.1 | Count to 100 by ones and by tens | Kindergarten |
| Arizona | K.CC.A.2 | Count forward beginning from a given number within the known sequence (instead of having to begin at 1). | Kindergarten |
| Arizona | K.CC.A.3 | Write numbers from 0 to 20. Represent a number of objects with a written numeral 0-20 (with 0 representing a count of no objects). | Kindergarten |
| Arizona | K.CC.B.4 | Understand the relationship between numbers and quantities; connect counting to cardinality. When counting objects, say the number names in the standard order, pairing each object with one and only one number name and each number name with one and only one object. Understand that the last number name said tells the number of objects counted. The number of objects is the same regardless of their arrangement or the order in which they were counted. Understand that each successive number name refers to a quantity that is one larger. | Kindergarten |
| Arizona | K.CC.B.5 | Count to answer 'how many' questions about as many as 20 things arranged in a line, a rectangular array, or a circle, or as many as 10 things in a scattered configuration; given a number from 1-20, count out that many objects. | Kindergarten |
| Arizona | K.CC.C.6 | Identify whether the number of objects in one group is greater than, less than, or equal to the number of objects in another group, e.g., by using matching and counting strategies. | Kindergarten |
| Arizona | K.CC.C.7 | Compare two numbers between 1 and 10 presented as written numerals. | Kindergarten |
| Arizona | K.G.A.1 | Describe objects in the environment using names of shapes, and describe the relative positions of these objects using terms such as above, below, beside, in front of, behind, and next to. | Kindergarten |
| Arizona | K.G.A.2 | Correctly name shapes regardless of their orientations or overall size. | Kindergarten |
| Arizona | K.G.A.3 | Identify shapes as two-dimensional (lying in a plane, “flat”) or three-dimensional (“solid”). | Kindergarten |
| Arizona | K.G.B.4 | Analyze and compare two- and three-dimensional shapes, in different sizes and orientations, using informal language to describe their similarities, differences, parts (e.g., number of sides and vertices/“corners”) and other attributes (e.g., having sides of equal length). | Kindergarten |
| Arizona | K.G.B.6 | Compose simple shapes to form larger shapes. | Kindergarten |
| Arizona | K.MD.A.1 | Describe measurable attributes of objects, such as length or weight. Describe several measurable attributes of a single object. | Kindergarten |
| Arizona | K.MD.A.2 | Directly compare two objects with a measurable attribute in common, to see which object has “more of”/“less of” the attribute, and describe the difference. | Kindergarten |
| Arizona | K.MD.B.3 | Classify objects into given categories; count the numbers of objects in each category and sort the categories by count. | Kindergarten |
| Arizona | K.NBT.A.1 | Compose and decompose numbers from 11 to 19 into ten ones and some further ones, e.g., by using objects or drawings, and record each composition or decomposition by a drawing or equation (such as 18 = 10 + 8); understand that these numbers are composed of ten ones and one, two, three, four, five, six, seven, eight, or nine ones. | Kindergarten |
| Arizona | K.OA.A.1 | Represent addition and subtraction with objects, fingers, mental images, drawings, sounds (e.g., claps), acting out situations, verbal explanations, expressions, or equations. | Kindergarten |
| Arizona | K.OA.A.2 | Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem. | Kindergarten |
| Arizona | K.OA.A.3 | Decompose numbers less than or equal to 10 into pairs in more than one way, e.g., by using objects or drawings, and record each decomposition by a drawing or equation (e.g., 5 = 2 + 3 and 5 = 4 + 1). | Kindergarten |
| Arizona | K.OA.A.4 | For any number from 1 to 9, find the number that makes 10 when added to the given number, e.g., by using objects or drawings, and record the answer with a drawing or equation. | Kindergarten |
| Arizona | K.OA.A.5 | Fluently add and subtract within 5. | Kindergarten |
| Arizona | 1.G.A.1 | Distinguish between defining attributes (e.g., triangles are closed and three-sided) versus non-defining attributes (e.g., color, orientation, overall size); build and draw shapes to possess defining attributes. | Grade 1 |
| Arizona | 1.G.A.2 | Compose two-dimensional shapes (rectangles, squares, trapezoids, triangles, half-circles, and quarter-circles) or three-dimensional shapes (cubes, right rectangular prisms, right circular cones, and right circular cylinders) to create a composite shape, and compose new shapes from the composite shape. | Grade 1 |
| Arizona | 1.G.A.3 | Partition circles and rectangles into two and four equal shares, describe the shares using the words halves, fourths, and quarters, and use the phrases half of, fourth of, and quarter of. Describe the whole as two of, or four of the shares. Understand for these examples that decomposing into more equal shares creates smaller shares. | Grade 1 |
| Arizona | 1.MD.A.1 | Order three objects by length; compare the lengths of two objects indirectly by using a third object. | Grade 1 |
| Arizona | 1.MD.A.2 | Express the length of an object as a whole number of length units, by laying multiple copies of a shorter object (the length unit) end to end; understand that the length measurement of an object is the number of same-size length units that span it with no gaps or overlaps. | Grade 1 |
| Arizona | 1.MD.B.3 | Tell and write time in hours and half-hours using analog and digital clocks. | Grade 1 |
| Arizona | 1.MD.C.4 | Organize, represent, and interpret data with up to three categories; ask and answer questions about the total number of data points, how many in each category, and how many more or less are in one category than in another. | Grade 1 |
| Arizona | 1.NBT.A.1 | Count to 120, starting at any number less than 120. In this range, read and write numerals and represent a number of objects with a written numeral. | Grade 1 |
| Arizona | 1.NBT.B.2 | Understand that the two digits of a two-digit number represent amounts of tens and ones. Understand the following as special cases: 10 can be thought of as a bundle of ten ones - called a 'ten.'. The numbers from 11 to 19 are composed of a ten and one, two, three, four, five, six, seven, eight, or nine ones. The numbers 10, 20, 30, 40, 50, 60, 70, 80, 90 refer to one, two, three, four, five, six, seven, eight, or nine tens (and 0 ones). | Grade 1 |
| Arizona | 1.NBT.B.3 | Compare two two-digit numbers based on meanings of the tens and ones digits, recording the results of comparisons with symbols. | Grade 1 |
| Arizona | 1.NBT.C.4 | Add within 100, including adding a two-digit number and a one-digit number, and adding a two-digit number and a multiple of 10, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Understand that in adding two-digit numbers, one adds tens and tens, ones and ones; and sometimes it is necessary to compose a ten. | Grade 1 |
| Arizona | 1.NBT.C.5 | Given a two-digit number, mentally find 10 more or 10 less than the number, without having to count; explain the reasoning used. | Grade 1 |
| Arizona | 1.NBT.C.6 | Subtract multiples of 10 in the range 10-90 from multiples of 10 in the range 10-90 (positive or zero differences), using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. | Grade 1 |
| Arizona | 1.OA.A.1 | Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem. | Grade 1 |
| Arizona | 1.OA.B.3 | Apply properties of operations as strategies to add and subtract. Examples: If 8 + 3 = 11 is known, then 3 + 8 = 11 is also known. (Commutative property of addition.) To add 2 + 6 + 4, the second two numbers can be added to make a ten, so 2 + 6 + 4 = 2 + 10 = 12. (Associative property of addition.) | Grade 1 |
| Arizona | 1.OA.B.4 | Understand subtraction as an unknown-addend problem. For example, subtract 10 - 8 by finding the number that makes 10 when added to 8. Add and subtract within 20. | Grade 1 |
| Arizona | 1.OA.C.5 | Relate counting to addition and subtraction (e.g., by counting on 2 to add 2). | Grade 1 |
| Arizona | 1.OA.C.6 | Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to a ten (e.g., 13 - 4 = 13 - 3 - 1 = 10 - 1 = 9); using the relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 - 8 = 4); and creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13). | Grade 1 |
| Arizona | 1.OA.D.7 | Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false. For example, which of the following equations are true and which are false? 6 = 6, 7 = 8 - 1, 5 + 2 = 2 + 5, 4 + 1 = 5 + 2. | Grade 1 |
| Arizona | 1.OA.D.8 | Determine the unknown whole number in an addition or subtraction equation relating three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations 8 + ? = 11, 5 = _ - 3, 6 + 6 = _. | Grade 1 |
| Arizona | 2.G.A.1 | Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces. Identify triangles, quadrilaterals, pentagons, hexagons, and cubes. | Grade 2 |
| Arizona | 2.G.A.2 | Partition a rectangle into rows and columns of same-size squares and count to find the total number of them. | Grade 2 |
| Arizona | 2.G.A.3 | Partition circles and rectangles into two, three, or four equal shares, describe the shares using the words halves, thirds, half of, a third of, etc., and describe the whole as two halves, three thirds, four fourths. Recognize that equal shares of identical wholes need not have the same shape. | Grade 2 |
| Arizona | 2.MD.A.1 | Measure the length of an object by selecting and using appropriate tools such as rulers, yardsticks, meter sticks, and measuring tapes. | Grade 2 |
| Arizona | 2.MD.A.2 | Measure the length of an object twice, using length units of different lengths for the two measurements; describe how the two measurements relate to the size of the unit chosen. | Grade 2 |
| Arizona | 2.MD.A.4 | Measure to determine how much longer one object is than another, expressing the length difference in terms of a standard length unit. | Grade 2 |
| Arizona | 2.MD.B.5 | Use addition and subtraction within 100 to solve word problems involving lengths that are given in the same units, e.g., by using drawings (such as drawings of rulers) and equations with a symbol for the unknown number to represent the problem. | Grade 2 |
| Arizona | 2.MD.C.7 | Tell and write time from analog and digital clocks to the nearest five minutes, using a.m. and p.m. | Grade 2 |
| Arizona | 2.MD.C.8 | Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies, using $ and ¢ symbols appropriately. | Grade 2 |
| Arizona | 2.MD.D.9 | Generate measurement data by measuring lengths of several objects to the nearest whole unit, or by making repeated measurements of the same object. Show the measurements by making a line plot, where the horizontal scale is marked off in whole-number units. | Grade 2 |
| Arizona | 2.MD.D.10 | Draw a picture graph and a bar graph (with single-unit scale) to represent a data set with up to four categories. Solve simple put-together, take-apart, and compare problems using information presented in a bar graph. | Grade 2 |
| Arizona | 2.NBT.A.1 | Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones. Understand the following as special cases: 100 can be thought of as a bundle of ten tens - called a 'hundred.'. The numbers 100, 200, 300, 400, 500, 600, 700, 800, 900 refer to one, two, three, four, five, six, seven, eight, or nine hundreds (and 0 tens and 0 ones). | Grade 2 |
| Arizona | 2.NBT.A.2 | Count within 1000; skip-count by 5s, 10s, and 100s. | Grade 2 |
| Arizona | 2.NBT.A.3 | Read and write numbers to 1000 using base-ten numerals, number names, and expanded form. | Grade 2 |
| Arizona | 2.NBT.A.4 | Compare two three-digit numbers based on meanings of the hundreds, tens, and ones digits, using symbols to record the results of comparisons. | Grade 2 |
| Arizona | 2.NBT.B.5 | Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction. | Grade 2 |
| Arizona | 2.NBT.B.6 | Add up to four two-digit numbers using strategies based on place value and properties of operations. | Grade 2 |
| Arizona | 2.NBT.B.7 | Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method. Understand that in adding or subtracting three-digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds. | Grade 2 |
| Arizona | 2.NBT.B.8 | Mentally add 10 or 100 to a given number 100-900, and mentally subtract 10 or 100 from a given number 100-900. | Grade 2 |
| Arizona | 2.OA.A.1 | Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem. | Grade 2 |
| Arizona | 2.OA.B.2 | Fluently add and subtract within 20 using mental strategies.2 By end of Grade 2, know from memory all sums of two one-digit numbers. | Grade 2 |
| Arizona | 2.OA.C.3 | Determine whether a group of objects (up to 20) has an odd or even number of members, e.g., by pairing objects or counting them by 2s; write an equation to express an even number as a sum of two equal addends. | Grade 2 |
| Arizona | 2.OA.C.4 | Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends. | Grade 2 |
| Arizona | 3.G.A.1 | Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories. | Grade 3 |
| Arizona | 3.G.A.2 | Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole. | Grade 3 |
| Arizona | 3.MD.A.1 | Tell and write time to the nearest minute and measure time intervals in minutes. Solve word problems involving addition and subtraction of time intervals in minutes, e.g., by representing the problem on a number line diagram. | Grade 3 |
| Arizona | 3.MD.A.2 | Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l). Add, subtract, multiply, or divide to solve one-step word problems involving masses or volumes that are given in the same units, e.g., by using drawings (such as a beaker with a measurement scale) to represent the problem. | Grade 3 |
| Arizona | 3.MD.B.3 | Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and two-step “how many more” and “how many less” problems using information presented in scaled bar graphs. | Grade 3 |
| Arizona | 3.MD.B.4 | Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Show the data by making a line plot, where the horizontal scale is marked off in appropriate units-whole numbers, halves, or quarters. | Grade 3 |
| Arizona | 3.MD.C.5 | Recognize area as an attribute of plane figures and understand concepts of area measurement. | Grade 3 |
| Arizona | 3.MD.C.6 | Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units). | Grade 3 |
| Arizona | 3.MD.C.7 | Relate area to the operations of multiplication and addition. | Grade 3 |
| Arizona | 3.MD.D.8 | Solve real world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters. | Grade 3 |
| Arizona | 3.NBT.A.1 | Use place value understanding to round whole numbers to the nearest 10 or 100. | Grade 3 |
| Arizona | 3.NBT.A.2 | Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction. | Grade 3 |
| Arizona | 3.NBT.A.3 | Multiply one-digit whole numbers by multiples of 10 in the range 10-90 (e.g., 9 × 80, 5 × 60) using strategies based on place value and properties of operations. | Grade 3 |
| Arizona | 3.NF.A.1 | Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b. | Grade 3 |
| Arizona | 3.NF.A.2 | Understand a fraction as a number on the number line; represent fractions on a number line diagram. Represent a fraction 1/b on a number line diagram by defining the interval from 0 to 1 as the whole and partitioning it into b equal parts. Recognize that each part has size 1/b and that the endpoint of the part based at 0 locates the number 1/b on the number line. Represent a fraction a/b on a number line diagram by marking off a lengths 1/b from 0. Recognize that the resulting interval has size a/b and that its endpoint locates the number a/b on the number line. | Grade 3 |
| Arizona | 3.NF.A.3 | Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size. Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line. Recognize and generate simple equivalent fractions, e.g., 1/2 = 2/4, 4/6 = 2/3). Explain why the fractions are equivalent, e.g., by using a visual fraction model. Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers. Examples: Express 3 in the form 3 = 3/1; recognize that 6/1 = 6; locate 4/4 and 1 at the same point of a number line diagram. Compare two fractions with the same numerator or the same denominator by reasoning about their size. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model. | Grade 3 |
| Arizona | 3.OA.A.1 | Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each. For example, describe a context in which a total number of objects can be expressed as 5 × 7. | Grade 3 |
| Arizona | 3.OA.A.2 | Interpret whole-number quotients of whole numbers, e.g., interpret 56 ÷ 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each. For example, describe a context in which a number of shares or a number of groups can be expressed as 56 ÷ 8. | Grade 3 |
| Arizona | 3.OA.A.3 | Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem. | Grade 3 |
| Arizona | 3.OA.A.4 | Determine the unknown whole number in a multiplication or division equation relating three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations 8 × ? = 48, 5 = _ ÷ 3, 6 × 6 = ? | Grade 3 |
| Arizona | 3.OA.B.5 | Apply properties of operations as strategies to multiply and divide. Examples: If 6 × 4 = 24 is known, then 4 × 6 = 24 is also known. (Commutative property of multiplication.) 3 × 5 × 2 can be found by 3 × 5 = 15, then 15 × 2 = 30, or by 5 × 2 = 10, then 3 × 10 = 30. (Associative property of multiplication.) Knowing that 8 × 5 = 40 and 8 × 2 = 16, one can find 8 × 7 as 8 × (5 + 2) = (8 × 5) + (8 × 2) = 40 + 16 = 56. (Distributive property.) | Grade 3 |
| Arizona | 3.OA.B.6 | Understand division as an unknown-factor problem. For example, find 32 ÷ 8 by finding the number that makes 32 when multiplied by 8. | Grade 3 |
| Arizona | 3.OA.C.7 | Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 × 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers. | Grade 3 |
| Arizona | 3.OA.D.8 | Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. | Grade 3 |
| Arizona | 3.OA.D.9 | Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations. | Grade 3 |
| Arizona | 4.G.A.1 | Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures. | Grade 4 |
| Arizona | 4.G.A.2 | Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles. | Grade 4 |
| Arizona | 4.G.A.3 | Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify line-symmetric figures and draw lines of symmetry. | Grade 4 |
| Arizona | 4.MD.A.1 | Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table. | Grade 4 |
| Arizona | 4.MD.A.2 | Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. | Grade 4 |
| Arizona | 4.MD.A.3 | Apply the area and perimeter formulas for rectangles in real world and mathematical problems. | Grade 4 |
| Arizona | 4.MD.B.4 | Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots. | Grade 4 |
| Arizona | 4.MD.C.5 | Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement: | Grade 4 |
| Arizona | 4.MD.C.6 | Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure. | Grade 4 |
| Arizona | 4.MD.C.7 | Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems, e.g., by using an equation with a symbol for the unknown angle measure. | Grade 4 |
| Arizona | 4.NBT.A.1 | Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. For example, recognize that 700 / 70 = 10 by applying concepts of place value and division. | Grade 4 |
| Arizona | 4.NBT.A.2 | Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. | Grade 4 |
| Arizona | 4.NBT.A.3 | Use place value understanding to round multi-digit whole numbers to any place. | Grade 4 |
| Arizona | 4.NBT.B.4 | Fluently add and subtract multi-digit whole numbers using the standard algorithm. | Grade 4 |
| Arizona | 4.NBT.B.5 | Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. | Grade 4 |
| Arizona | 4.NBT.B.6 | Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. | Grade 4 |
| Arizona | 4.NF.A.1 | Explain why a fraction a/b is equivalent to a fraction (n x a) / (n x b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. | Grade 4 |
| Arizona | 4.NF.A.2 | Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model. | Grade 4 |
| Arizona | 4.NF.B.3 | Understand a fraction a/b with a > 1 as a sum of fractions 1/b. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation. Justify decompositions, e.g., by using a visual fraction model. Examples: 3/8 = 1/8 + 1/8 + 1/8 ; 3/8 = 1/8 + 2/8 ; 2 1/8 = 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8. Add and subtract mixed numbers with like denominators, e.g., by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators, e.g., by using visual fraction models and equations to represent the problem. | Grade 4 |
| Arizona | 4.NF.B.4 | Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Understand a fraction a/b as a multiple of 1/b. For example, use a visual fraction model to represent 5/4 as the product 5 x (1/4), recording the conclusion by the equation 5/4 = 5 x (1/4). Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number. For example, use a visual fraction model to express 3 x(2/5) as 6 x (1/5), recognizing this product as 6/5. (In general, n x (a/b) = (n x a) / b.) Solve word problems involving multiplication of a fraction by a whole number, e.g., by using visual fraction models and equations to represent the problem. For example, if each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie? | Grade 4 |
| Arizona | 4.NF.C.5 | Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100.2 For example, express 3/10 as 30/100, and add 3/10 + 4/100 = 34/100. | Grade 4 |
| Arizona | 4.NF.C.6 | Use decimal notation for fractions with denominators 10 or 100. For example, rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram. | Grade 4 |
| Arizona | 4.NF.C.7 | Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual model. | Grade 4 |
| Arizona | 4.OA.A.1 | Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 x 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations. | Grade 4 |
| Arizona | 4.OA.A.2 | Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison. | Grade 4 |
| Arizona | 4.OA.A.3 | Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. | Grade 4 |
| Arizona | 4.OA.A.3.1 | Solve a variety of problems based on the multiplication principle of counting. | Grade 4 |
| Arizona | 4.OA.B.4 | Find all factor pairs for a whole number in the range 1 - 100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1 — 100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1 - 100 is prime or composite. | Grade 4 |
| Arizona | 4.OA.C.5 | Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. For example, given the rule 'Add 3' and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way. | Grade 4 |
| Arizona | 5.G.A.1 | Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and the given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate). | Grade 5 |
| Arizona | 5.G.A.2 | Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. | Grade 5 |
| Arizona | 5.G.B.3 | Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. | Grade 5 |
| Arizona | 5.G.B.4 | Classify two-dimensional figures in a hierarchy based on properties. | Grade 5 |
| Arizona | 5.MD.A.1 | Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. | Grade 5 |
| Arizona | 5.MD.B.2 | Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. | Grade 5 |
| Arizona | 5.MD.C.3 | Recognize volume as an attribute of solid figures and understand concepts of volume measurement. | Grade 5 |
| Arizona | 5.MD.C.4 | Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. | Grade 5 |
| Arizona | 5.MD.C.5 | Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume. | Grade 5 |
| Arizona | 5.NBT.A.1 | Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. | Grade 5 |
| Arizona | 5.NBT.A.2 | Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. | Grade 5 |
| Arizona | 5.NBT.A.3 | Read, write, and compare decimals to thousandths. | Grade 5 |
| Arizona | 5.NBT.A.4 | Use place value understanding to round decimals to any place. | Grade 5 |
| Arizona | 5.NBT.B.5 | Fluently multiply multi-digit whole numbers using the standard algorithm. | Grade 5 |
| Arizona | 5.NBT.B.6 | Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. | Grade 5 |
| Arizona | 5.NBT.B.7 | Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. | Grade 5 |
| Arizona | 5.NF.A.1 | Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. | Grade 5 |
| Arizona | 5.NF.A.2 | Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators by using visual models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. | Grade 5 |
| Arizona | 5.NF.B.3 | Interpret a fraction as division of the numerator by the denominator (a/b = a / b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie? | Grade 5 |
| Arizona | 5.NF.B.4 | Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. | Grade 5 |
| Arizona | 5.NF.B.5 | Interpret multiplication as scaling (resizing), by comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication. | Grade 5 |
| Arizona | 5.NF.B.6 | Solve real world problems involving multiplication of fractions and mixed numbers by using visual fraction models or equations to represent the problem. | Grade 5 |
| Arizona | 5.NF.B.7 | Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. | Grade 5 |
| Arizona | 5.OA.A.1 | Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. | Grade 5 |
| Arizona | 5.OA.A.2 | Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them (e.g., express the calculation add 8 and 7, then multiply by 2 as 2 x (8 + 7). Recognize that 3 x (18,932 + 921) is three times as large as 18,932 + 921, without having to calculate the indicated sum or product). | Grade 5 |
| Arizona | 5.OA.B.3 | Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. For example, given the rule “Add 3” and the starting number 0, and given the rule “Add 6” and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so. | Grade 5 |
| Arizona | 5.OA.B.4 | Understand primes have only two factors and decompose numbers into prime factors. | Grade 5 |
| Arizona | 6.EE.A.1 | Write and evaluate numerical expressions involving whole-number exponents. | Grade 6 |
| Arizona | 6.EE.A.2 | Write, read, and evaluate expressions in which letters stand for numbers. | Grade 6 |
| Arizona | 6.EE.A.3 | Apply the properties of operations to generate equivalent expressions. | Grade 6 |
| Arizona | 6.EE.A.4 | Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). | Grade 6 |
| Arizona | 6.EE.B.5 | Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true. | Grade 6 |
| Arizona | 6.EE.B.6 | Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set. | Grade 6 |
| Arizona | 6.EE.B.7 | Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers. | Grade 6 |
| Arizona | 6.EE.B.8 | Write an inequality of the form x > c or x c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams. | Grade 6 |
| Arizona | 6.EE.C.9 | Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. | Grade 6 |
| Arizona | 6.G.A.1 | Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems. | Grade 6 |
| Arizona | 6.G.A.2 | Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas 𝘝 = 𝘭 𝘸 𝘩 and 𝘝 = 𝘣 𝘩 to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems. | Grade 6 |
| Arizona | 6.G.A.3 | Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. | Grade 6 |
| Arizona | 6.G.A.4 | Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems. | Grade 6 |
| Arizona | 6.NS.A.1 | Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions. | Grade 6 |
| Arizona | 6.NS.B.2 | Fluently divide multi-digit numbers using the standard algorithm. | Grade 6 |
| Arizona | 6.NS.B.3 | Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation. | Grade 6 |
| Arizona | 6.NS.C.5 | Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation. | Grade 6 |
| Arizona | 6.NS.C.6 | Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates. | Grade 6 |
| Arizona | 6.NS.C.7 | Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram. | Grade 6 |
| Arizona | 6.NS.C.8 | Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. | Grade 6 |
| Arizona | 6.NS.C.9 | Convert between expressions for positive rational numbers, including fractions, decimals, and percents. | Grade 6 |
| Arizona | 6.RP.A.1 | Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. | Grade 6 |
| Arizona | 6.RP.A.2 | Understand the concept of a unit rate a/b associated with a ratio a:b with b ≠ 0, and use rate language in the context of a ratio relationship. For example, This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar. We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger. | Grade 6 |
| Arizona | 6.RP.A.3 | Use ratio and rate reasoning to solve real-world and mathematical problems, by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams or equations. | Grade 6 |
| Arizona | 6.SP.B.5 | Summarize numerical data sets in relation to their context, such as by: | Grade 6 |
| Arizona | 7.EE.A.1 | Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients. | Grade 7 |
| Arizona | 7.EE.A.2 | Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. | Grade 7 |
| Arizona | 7.EE.B.3 | Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. | Grade 7 |
| Arizona | 7.EE.B.4 | Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. | Grade 7 |
| Arizona | 7.G.A.1 | Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale. | Grade 7 |
| Arizona | 7.G.A.2 | Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle. | Grade 7 |
| Arizona | 7.G.A.3 | Describe the two-dimensional figures that result from slicing three-dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids. | Grade 7 |
| Arizona | 7.G.B.4 | Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle. | Grade 7 |
| Arizona | 7.G.B.5 | Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure. | Grade 7 |
| Arizona | 7.G.B.6 | Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. | Grade 7 |
| Arizona | 7.NS.A.1 | Describe situations in which opposite quantities combine to make 0. For example, a hydrogen atom has 0 charge because its two constituents are oppositely charged. | Grade 7 |
| Arizona | 7.NS.A.2 | Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as (-1)(-1) = 1 and the rules for multiplying signed numbers. Interpret products of rational numbers by describing real-world contexts. | Grade 7 |
| Arizona | 7.NS.A.3 | Solve real-world and mathematical problems involving the four operations with rational numbers. | Grade 7 |
| Arizona | 7.RP.A.1 | Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. For example, if a person walks 1/2 mile in each 1/3 hour, compute the unit rate as the complex fraction 1/2 divided by 1/4 per hour, equivalently 2 miles per hour. | Grade 7 |
| Arizona | 7.RP.A.2 | Recognize and represent proportional relationships between quantities. | Grade 7 |
| Arizona | 7.RP.A.3 | Use proportional relationships to solve multistep ratio and percent problems. | Grade 7 |
| Arizona | 8.EE.A.1 | Know and apply the properties of integer exponents to generate equivalent numerical expressions. | Grade 8 |
| Arizona | 8.EE.A.2 | Use square root and cube root symbols to represent solutions to equations of the form 𝘹² = 𝘱 and 𝘹³ = 𝘱, where 𝘱 is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that √2 is irrational. | Grade 8 |
| Arizona | 8.EE.A.3 | Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much ones is than the other. | Grade 8 |
| Arizona | 8.EE.A.4 | Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities. Interpret scientific notation that has been generated by technology. | Grade 8 |
| Arizona | 8.EE.B.5 | Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed. | Grade 8 |
| Arizona | 8.EE.B.6 | Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b. | Grade 8 |
| Arizona | 8.EE.C.7 | Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x = a, a = a, or a = b results (where a and b are different numbers). | Grade 8 |
| Arizona | 8.EE.C.8 | Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously. | Grade 8 |
| Arizona | 8.F.A.1 | Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output. | Grade 8 |
| Arizona | 8.F.A.2 | Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a linear function represented by a table of values and a linear function represented by an algebraic expression, determine which function has the greater rate of change. | Grade 8 |
| Arizona | 8.F.A.3 | Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. For example, the function A = s2 giving the area of a square as a function of its side length is not linear because its graph contains the points (1,1), (2,4) and (3,9), which are not on a straight line. | Grade 8 |
| Arizona | 8.F.B.4 | Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values. | Grade 8 |
| Arizona | 8.F.B.5 | Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally. | Grade 8 |
| Arizona | 8.G.A.1 | Verify experimentally the properties of rotations, reflections, and translations: | Grade 8 |
| Arizona | 8.G.A.2 | Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them. | Grade 8 |
| Arizona | 8.G.A.3 | Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates. | Grade 8 |
| Arizona | 8.G.A.4 | Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two-dimensional figures, describe a sequence that exhibits the similarity between them. | Grade 8 |
| Arizona | 8.G.A.5 | Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. | Grade 8 |
| Arizona | 8.G.B.7 | Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions. | Grade 8 |
| Arizona | 8.G.B.8 | Apply the Pythagorean Theorem to find the distance between two points in a coordinate system. | Grade 8 |
| Arizona | 8.G.C.9 | Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems. | Grade 8 |
| Arizona | 8.NS.A.2 | Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g., π²). | Grade 8 |
| Arizona | 8.SP.A.1 | Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association. | Grade 8 |
| Arizona | 8.SP.A.2 | Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line. | Grade 8 |
| Arizona | A-APR.B.3 | Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial. | Algebra |
| Arizona | A-CED.A.2 | Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. | Algebra |
| Arizona | A-CED.A.3 | Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context. | Algebra |
| Arizona | A-REI.B.3 | Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. | Algebra |
| Arizona | A-SSE.A.2 | Use the structure of an expression to identify ways to rewrite it. | Algebra |
| Arizona | A-SSE.B.3 | Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression. | Algebra |
| Arizona | F-BF.A.1 | Write a function that describes a relationship between two quantities. | Algebra |
| Arizona | F-IF.A.2 | Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. | Algebra |
| Arizona | F-IF.B.4 | For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. | Algebra |
| Arizona | F-IF.C.7 | Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. | Algebra |
| Arizona | S-ID.B.6 | Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. | Algebra |
| Arkansas | K.NPV.A.1 | Students know the number names and count sequence while exploring the relationships between numbers. Count to 100 by ones and tens; count forward by ones from any given number up to 100. | Kindergarten |
| Arkansas | K.NPV.A.2 | Students know the number names and count sequence while exploring the relationships between numbers. Count a set of objects up to 20 using one-to-one correspondence, demonstrating that the last number stated indicates the number of objects in the set regardless of the arrangement. | Kindergarten |
| Arkansas | K.NPV.B.5 | Students understand the base ten place value system. Read, write, and represent whole numbers from 0 to 20. | Kindergarten |
| Arkansas | K.NPV.B.6 | Students understand the base ten place value system. Show equivalent forms of whole numbers up to 20 as groups of tens and ones, using manipulatives and drawings. | Kindergarten |
| Arkansas | K.NPV.C.7 | Students use place value understanding to compare numbers. Use matching and counting strategies to compare the number of objects in one group to the number of objects in another group (0 to 10) using the terms greater than, less than, or equal. | Kindergarten |
| Arkansas | K.NPV.C.8 | Students use place value understanding to compare numbers. Compare two whole numbers, using the terms greater than, less than, or equal. | Kindergarten |
| Arkansas | K.CAR.A.1 | Students perform operations using place value understanding and properties of operations Use objects, fingers, mental images, drawings, sounds, acting out situations, or verbal explanations to represent addition and subtraction from 0 to 10. | Kindergarten |
| Arkansas | K.CAR.A.2 | Students perform operations using place value understanding and properties of operations Use objects or drawings to decompose numbers less than or equal to 10 into pairs in more than one way, recording each decomposition. | Kindergarten |
| Arkansas | K.CAR.A.3 | Students perform operations using place value understanding and properties of operations Use a drawing or equation to find the number that makes 10 when added to a given number. | Kindergarten |
| Arkansas | K.CAR.A.4 | Students perform operations using place value understanding and properties of operations Use manipulatives and various strategies to fluently add and subtract within 10. | Kindergarten |
| Arkansas | K.CAR.B.5 | Students solve real-world problems. Solve real-world problems involving addition and subtraction within 10, using objects, drawings, or equations to represent the problem. | Kindergarten |
| Arkansas | K.GM.A.1 | Students analyze attributes of shapes to develop generalizations about their properties. Describe the positions of objects and geometric shapes in the environment. Terms include: inside, outside, between, above, below, near, far, under, over, up, down, behind, in front of, next to, to the left of, and to the right of | Kindergarten |
| Arkansas | K.GM.A.2 | Students analyze attributes of shapes to develop generalizations about their properties. Name shapes correctly regardless of their orientation or overall size. Shapes include: squares, circles, triangles, rectangles, hexagons, cubes, cones, cylinders, and spheres | Kindergarten |
| Arkansas | K.GM.A.3 | Students analyze attributes of shapes to develop generalizations about their properties. Identify two-dimensional attributes of three-dimensional objects. | Kindergarten |
| Arkansas | K.GM.A.4 | Students analyze attributes of shapes to develop generalizations about their properties. Analyze and sort a variety of two and three-dimensional shapes using informal language to describe their similarities, differences, and other attributes. | Kindergarten |
| Arkansas | K.GM.A.5 | Students analyze attributes of shapes to develop generalizations about their properties. Compose and draw shapes found in the world using objects (e.g., straws, toothpicks, clay balls). | Kindergarten |
| Arkansas | K.GM.B.6 | Students develop understanding of measurement terms and concepts. Make direct comparisons of the length, capacity, weight, and temperature of objects, recognizing which object is shorter/longer, lighter/heavier, warmer/cooler, or holds more. | Kindergarten |
| Arkansas | K.GM.C.8 | Students explore time and money values and concepts. Identify pennies and dimes by name and value. | Kindergarten |
| Arkansas | K.DA.A.1 | Students organize and analyze data. Collect, sort, and organize data into two or three categories, using real-object graphs and picture graphs. | Kindergarten |
| Arkansas | 1.NPV.A.2 | Students extend the counting sequence. Skip count forward by multiples of fives within 120. | Grade 1 |
| Arkansas | 1.NPV.B.3 | Students understand the base ten place value system. Explain the place value of ones and tens in two-digit numbers, using concrete models, diagrams, numbers, or words. | Grade 1 |
| Arkansas | 1.NPV.B.4 | Students understand the base ten place value system. Read, write, and represent whole numbers up to 120, using concrete models or drawings, word form, base ten numerals, and expanded form. | Grade 1 |
| Arkansas | 1.NPV.B.5 | Students understand the base ten place value system. Use concrete models or drawings to subtract multiples of 10 from multiples of 10 (within the range of 10-90), relate the strategy to a written expression or equation, and explain the reasoning used to solve. | Grade 1 |
| Arkansas | 1.NPV.B.6 | Students understand the base ten place value system. Use mental strategies to find 10 more or 10 less than a given two-digit number. | Grade 1 |
| Arkansas | 1.NPV.C.7 | Students use place value understanding to compare numbers. Compare two two-digit numbers using symbols () based on the value of tens and ones in the given numbers. | Grade 1 |
| Arkansas | 1.NPV.D.8 | Students build a conceptual understanding of fractions. Partition circles and rectangles into two and four equal shares, describing the shares using the words halves, fourths, and quarters; understand that decomposing into more equal pieces creates smaller pieces. | Grade 1 |
| Arkansas | 1.CAR.A.1 | Students perform operations using place value understanding and properties of operations. Add and subtract fluently within 10 with mastery by the end of first grade. | Grade 1 |
| Arkansas | 1.CAR.A.2 | Students perform operations using place value understanding and properties of operations. Use computational fluency to add and subtract within 20 using manipulatives and/or a variety of strategies. | Grade 1 |
| Arkansas | 1.CAR.A.3 | Students perform operations using place value understanding and properties of operations. Apply properties of operations to add and subtract within 20. | Grade 1 |
| Arkansas | 1.CAR.A.4 | Students perform operations using place value understanding and properties of operations. Use concrete models or drawings to add within 100, including a two-digit number and a one-digit number as well as a two-digit number and a multiple of ten; relate strategy used to a written expression or equation and explain reasoning. | Grade 1 |
| Arkansas | 1.CAR.A.5 | Students perform operations using place value understanding and properties of operations. Demonstrate the relationship between addition and subtraction by solving problems, using an inverse operation. | Grade 1 |
| Arkansas | 1.CAR.B.6 | Students solve real-world problems. Solve real-world problems involving addition and subtraction within 20. Problem types include: adding to, taking from, putting together, taking apart, and comparing with unknowns present throughout the addition and subtraction problem. | Grade 1 |
| Arkansas | 1.CAR.C.8 | Students develop and apply understanding of foundational algebraic concepts. Apply understanding of the equal sign to determine if equations involving addition and subtraction are true or false. | Grade 1 |
| Arkansas | 1.CAR.C.9 | Students develop and apply understanding of foundational algebraic concepts. Determine the unknown whole number in an addition or subtraction equation relating three whole numbers. | Grade 1 |
| Arkansas | 1.GM.A.1 | Students analyze attributes of shapes to develop generalizations about their properties. Understand the difference between defining attributes (e.g., triangles are closed and three-sided shapes) and non-defining attributes (e.g., color, orientation, overall size), using that understanding to build and draw shapes that exhibit defining attributes. | Grade 1 |
| Arkansas | 1.GM.A.2 | Students analyze attributes of shapes to develop generalizations about their properties. Create a composite shape using two-dimensional or three-dimensional shapes. Two-dimensional include: rectangle, square, trapezoid, triangle, hexagon, half circle, and quarter circle. Three-dimensional include: cube, rectangular prism, cone, and cylinder. | Grade 1 |
| Arkansas | 1.GM.B.3 | Students investigate measurement with non-standard units. Express the length of an object as a whole number of units by laying multiple copies of a shorter object end-to-end, understanding that the length of one object is equal to the number of same-size units that span the object with no gaps or overlaps. | Grade 1 |
| Arkansas | 1.GM.B.4 | Students investigate measurement with non-standard units. Order three objects by their length, indirectly comparing the lengths of two objects by using a third object. | Grade 1 |
| Arkansas | 1.GM.C.5 | Students explore time and money values and concepts. Tell and write time to the nearest hour and half hour using analog clocks; understand how to read hours and minutes using digital clocks. | Grade 1 |
| Arkansas | 1.GM.C.6 | Students explore time and money values and concepts. Identify coins by name and value, including penny, nickel, dime, and quarter. | Grade 1 |
| Arkansas | 1.GM.C.7 | Students explore time and money values and concepts. Count collections of like coins including pennies, nickels, and dimes to determine their total value up to 100 cents. | Grade 1 |
| Arkansas | 1.DA.A.2 | Students organize and analyze data. Ask and answer questions about the total number represented such as how many in each category and how many more or less in one category compared to another. | Grade 1 |
| Arkansas | 2.NPV.A.1 | Students extend the counting sequence. Count within 1,000 forwards and backwards by ones, tens, and hundreds from any given number. | Grade 2 |
| Arkansas | 2.NPV.B.2 | Students understand the base ten place value system. Identify the value of hundreds, tens, and ones place in a three-digit number. | Grade 2 |
| Arkansas | 2.NPV.B.3 | Students understand the base ten place value system. Read, write, and represent whole numbers up to 1,000 using concrete models or drawings, number names, and a variety of expanded forms. | Grade 2 |
| Arkansas | 2.NPV.B.4 | Students understand the base ten place value system. Mentally add 10 or 100 to a given number in the range of 100-900 and mentally subtract 10 or 100 from a given number in the range of 100-900. | Grade 2 |
| Arkansas | 2.NPV.C.5 | Students use place value understanding to compare numbers. Compare two three-digit numbers using symbols () based on the value of hundreds, tens, and ones in the given numbers. | Grade 2 |
| Arkansas | 2.NPV.D.6 | Students build a conceptual understanding of fractions. Partition circles and rectangles into two, three, or four equal shares, describing the shares using the words halves, thirds, and fourths (or quarters). | Grade 2 |
| Arkansas | 2.NPV.D.7 | Students build a conceptual understanding of fractions. Recognize that equal shares of identical wholes need not have the same shape. | Grade 2 |
| Arkansas | 2.CAR.A.2 | Students perform operations using place value understanding and properties of operations. Use computational fluency to add and subtract within 100 using strategies based on place value, properties of operations, or the relationship between addition and subtraction. | Grade 2 |
| Arkansas | 2.CAR.A.3 | Students perform operations using place value understanding and properties of operations. Add up to four two-digit numbers with sums not exceeding 100 using strategies based on place value and properties of operations. | Grade 2 |
| Arkansas | 2.CAR.A.5 | Students perform operations using place value understanding and properties of operations. Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends. | Grade 2 |
| Arkansas | 2.CAR.B.7 | Students solve real-world problems. Solve one and two-step real-world problems involving addition and subtraction within 100 in situations of adding to, taking from, putting together, taking apart, and comparing unknowns in all positions. | Grade 2 |
| Arkansas | 2.CAR.C.8 | Students develop and apply understanding of foundational algebraic concepts. Determine whether a group of objects up to 20 has an odd or even number of members; write an equation to express an even number as a sum of two equal addends. | Grade 2 |
| Arkansas | 2.GM.A.1 | Students analyze attributes of shapes to develop generalizations about their properties. Identify, describe, and draw two-dimensional shapes. Shapes include: triangles, regular pentagons, regular hexagons, and quadrilaterals (square, rectangle, trapezoid, parallelogram, rhombus) | Grade 2 |
| Arkansas | 2.GM.B.3 | Students investigate measurement using rulers. Select appropriate measurement tools to estimate and measure the length of an object to the nearest whole inch or whole centimeters. | Grade 2 |
| Arkansas | 2.GM.B.4 | Students investigate measurement using rulers. Demonstrate how the length of an object does not change, regardless of the units used to measure it, by measuring the length of an object twice; use two different length units, describing how the two measurements relate to the size of the chosen unit. | Grade 2 |
| Arkansas | 2.GM.B.5 | Students investigate measurement using rulers. Measure to determine how much longer or shorter one object is than another, expressing the length difference in terms of a standard length whole unit. | Grade 2 |
| Arkansas | 2.GM.B.6 | Students investigate measurement using rulers. Solve real-world problems involving lengths of the same units, using addition and subtraction within 100. | Grade 2 |
| Arkansas | 2.GM.C.7 | Students explore the perimeter and area of shapes. Solve real-world and mathematical problems to find the perimeter of polygons. | Grade 2 |
| Arkansas | 2.GM.C.8 | Students explore the perimeter and area of shapes. Partition a rectangle into rows and columns of same-size squares, counting the total number of squares to find the area. | Grade 2 |
| Arkansas | 2.GM.D.9 | Students explore time and money values and concepts. Using an analog clock, tell and write time to the nearest five minutes using colon notation and indicate a.m. or p.m. | Grade 2 |
| Arkansas | 2.GM.D.12 | Students explore time and money values and concepts. Count collections of mixed coins and solve real-world problems involving quarters, dimes, nickels, and pennies within 99¢ and whole dollar amounts. | Grade 2 |
| Arkansas | 2.DA.A.2 | Students organize and analyze data. Ask and answer simple put together, take apart, and compare problems, using information presented in the bar graphs, picture graphs, and line plots. | Grade 2 |
| Arkansas | 3.NPV.A.1 | Students understand the base ten place value system. Round four-digit whole numbers to the nearest 10 or 100, using place value understanding. | Grade 3 |
| Arkansas | 3.NPV.B.5 | Students use place value understanding to compare numbers. Compare two fractions with the same numerator or denominator by reasoning about their size based on the same whole; use symbols () and justify the conclusion using visual fraction models, concrete objects, or words. | Grade 3 |
| Arkansas | 3.NPV.C.7 | Students build a conceptual understanding of fractions. Partition squares, regular hexagons, and equilateral triangles into parts with equal shares, explaining the shares of each part as a unit fraction of the whole. Fractions include: denominators 2, 3, 4, 6, and 8. | Grade 3 |
| Arkansas | 3.NPV.C.8 | Students build a conceptual understanding of fractions. Identify and represent a unit fraction as a number on the number line. Fractions include: denominators 2, 3, 4, 6, and 8. | Grade 3 |
| Arkansas | 3.NPV.C.9 | Students build a conceptual understanding of fractions. Identify and represent a non-unit fraction as a number on the number line, including fractions greater than one. Fractions include: denominators 2, 3, 4, 6, and 8. | Grade 3 |
| Arkansas | 3.NPV.C.10 | Students build a conceptual understanding of fractions. Decompose and compose a non-unit fraction 𝑎/𝑏 as the quantity formed by the sum of unit fractions. Fractions include: denominators 2, 3, 4, 6, and 8. | Grade 3 |
| Arkansas | 3.CAR.A.1 | Students perform operations using place value understanding and properties of operations. Use computational fluency to add and subtract three-digit whole numbers, using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction. | Grade 3 |
| Arkansas | 3.CAR.A.2 | Students perform operations using place value understanding and properties of operations. Use basic fact fluency to multiply and divide whole numbers with mastery by the end of third grade. | Grade 3 |
| Arkansas | 3.CAR.A.3 | Students perform operations using place value understanding and properties of operations. Apply properties of operations as strategies to multiply and divide. Properties include: Distributive, Commutative, and Associative Properties of Multiplication | Grade 3 |
| Arkansas | 3.CAR.A.4 | Students perform operations using place value understanding and properties of operations. Use strategies to multiply one-digit numbers by multiples of 10 ranging from 10-90; strategies are based on place value and properties of operations (e.g., 9∙80,5∙60). | Grade 3 |
| Arkansas | 3.CAR.A.5 | Students perform operations using place value understanding and properties of operations. Identify arithmetic patterns including, but not limited to, patterns in an addition or multiplication table, explaining use of properties of operations appropriate to the pattern. | Grade 3 |
| Arkansas | 3.CAR.B.6 | Students solve real-world problems. Solve real-world problems using multiplication and division within 100 involving equal groups, arrays, partitive and measurement division. | Grade 3 |
| Arkansas | 3.CAR.B.7 | Students solve real-world problems. Solve two-step real-world situations using addition, subtraction, multiplication, and division, representing these problems using equations with a symbol standing for an unknown quantity. | Grade 3 |
| Arkansas | 3.CAR.C.8 | Students develop and apply an understanding of foundational algebraic concepts. Determine the unknown whole number in a multiplication or division equation relating three whole numbers. | Grade 3 |
| Arkansas | 3.CAR.C.9 | Students develop and apply an understanding of foundational algebraic concepts. Understand division as an unknown-factor problem. | Grade 3 |
| Arkansas | 3.GM.A.1 | Students analyze attributes of shapes to develop generalizations about their properties. Understand that quadrilaterals in different categories may share attributes; those attributes (e.g., four equivalent sides) can define a larger category (e.g., quadrilaterals) or subcategory (e.g., rhombus and square). | Grade 3 |
| Arkansas | 3.GM.A.3 | Students analyze attributes of shapes to develop generalizations about their properties. Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, identifying and/or drawing examples of quadrilaterals that do not belong to any of these subcategories. | Grade 3 |
| Arkansas | 3.GM.B.4 | Students investigate measurement using rulers. Measure lengths of objects to the nearest half and quarter inch, using a ruler. | Grade 3 |
| Arkansas | 3.GM.C.5 | Students calculate the area of rectangles and liquid volume. Describe area as the number of unit squares that cover a plane figure without gaps and overlaps. | Grade 3 |
| Arkansas | 3.GM.C.6 | Students calculate the area of rectangles and liquid volume. Find the area of a rectangle with whole number side lengths by modeling with unit squares and multiplying the side lengths to show the results are the same. | Grade 3 |
| Arkansas | 3.GM.C.7 | Students calculate the area of rectangles and liquid volume. Multiply side lengths to find areas of rectangles with whole number side lengths in the context of solving real-world and mathematical problems. | Grade 3 |
| Arkansas | 3.GM.C.8 | Students calculate the area of rectangles and liquid volume. Measure and estimate liquid volumes and masses of objects using standard units. | Grade 3 |
| Arkansas | 3.GM.C.9 | Students calculate the area of rectangles and liquid volume. Solve one-step real-world problems involving liquid volumes and masses of objects in the same units, using all four operations. | Grade 3 |
| Arkansas | 3.GM.D.10 | Students tell time and solve problems about elapsed time. Tell and write time to the nearest minute, using analog clocks. | Grade 3 |
| Arkansas | 3.GM.D.11 | Students tell time and solve problems about elapsed time. Solve word problems involving addition and subtraction of time intervals in minutes. | Grade 3 |
| Arkansas | 3.DA.A.1 | Students organize and analyze data. Represent a data set with multiple categories, using a scaled picture graph, scaled bar graph, and a line plot. | Grade 3 |
| Arkansas | 3.DA.A.2 | Students organize and analyze data. Solve one and two-step problems, using categorical data represented with a scaled picture graph, scaled bar graph, and a line plot. | Grade 3 |
| Arkansas | 4.NPV.A.3 | Students understand the base ten place value system. Use place value understanding to round five-digit and six-digit whole numbers to any place. | Grade 4 |
| Arkansas | 4.NPV.B.4 | Students use place value understanding to compare numbers. Compare two five-digit whole numbers and six-digit whole numbers, using symbols () to record the results of comparisons. | Grade 4 |
| Arkansas | 4.NPV.B.5 | Students use place value understanding to compare numbers. Compare two fractions with different numerators and different denominators using symbols () to record the results of comparisons (e.g., by creating common denominators or numerators or by comparing to a benchmark of 0, ½, 1). | Grade 4 |
| Arkansas | 4.NPV.B.6 | Students use place value understanding to compare numbers. Compare two decimals to the hundredths place, using symbols () to record the results of comparisons. | Grade 4 |
| Arkansas | 4.NPV.D.8 | Students develop and apply equivalent fraction understanding. Explain why a fraction 𝑎/𝑏 is equivalent to a fraction (𝑛∙𝑎)/(𝑛 ∙ 𝑏), using visual fraction models, generating equivalent fractions using the principle 𝑎/𝑏 = (𝑛∙𝑎)/(𝑛 ∙ 𝑏). Fractions include denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100. | Grade 4 |
| Arkansas | 4.NPV.D.9 | Students develop and apply equivalent fraction understanding. Add two fractions with denominators of 10 and 100 by expressing the denominator of 10 as an equivalent fraction with a denominator of 100. | Grade 4 |
| Arkansas | 4.NPV.D.10 | Students develop and apply equivalent fraction understanding. Apply decimal notation for fractions with denominators 10 or 100. | Grade 4 |
| Arkansas | 4.CAR.A.1 | Students perform operations, using place value understanding and properties of operations. Find the factor pairs for a given number in the range of 1-100, identifying whether a number is prime or composite; determine whether a given whole number in the range of 1-100 is a multiple of a given one-digit number. | Grade 4 |
| Arkansas | 4.CAR.A.2 | Students perform operations, using place value understanding and properties of operations. Use computational fluency to add and subtract whole numbers up to 1,000,000 by using strategies and algorithms, including the standard algorithm, with mastery by the end of fourth grade. | Grade 4 |
| Arkansas | 4.CAR.A.3 | Students perform operations, using place value understanding and properties of operations. Use strategies based on place value and the properties of operations to multiply four-digit by one-digit whole numbers and two two-digit whole numbers. | Grade 4 |
| Arkansas | 4.CAR.A.4 | Students perform operations, using place value understanding and properties of operations. Use strategies based on place value, the properties of operations, and the relationship between multiplication and division to divide whole numbers with four-digits by one-digit divisors; quotients should be with and without whole number remainders. | Grade 4 |
| Arkansas | 4.CAR.A.6 | Students perform operations, using place value understanding and properties of operations. Multiply a fraction by a whole number using visual fraction models and equations. Fractions include: denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100. | Grade 4 |
| Arkansas | 4.CAR.B.7 | Students solve real-world problems. Solve real-world problems involving multiplicative comparison, using drawings and/or equations with a symbol for the unknown number, and distinguish between multiplicative comparison and additive comparison. | Grade 4 |
| Arkansas | 4.CAR.B.8 | Students solve real-world problems. Solve multi-step, real-world problems posed with whole numbers and having whole-number answers, using addition, subtraction, multiplication, and division; include problems in which remainders must be interpreted and represent these problems using equations with symbols standing for the unknown quantity. | Grade 4 |
| Arkansas | 4.CAR.B.9 | Students solve real-world problems. Solve real-world problems involving the addition and subtraction of fractions; include mixed numbers with like denominators, using visual fraction models or equations. Fractions include: denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100 | Grade 4 |
| Arkansas | 4.CAR.B.10 | Students solve real-world problems. Solve real-word problems involving the multiplication of a fraction by a whole number using visual fraction models or equations. Fractions include: denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100 | Grade 4 |
| Arkansas | 4.CAR.C.11 | Students develop and apply an understanding of foundational algebraic concepts. Generate a number or shape pattern that follows a given rule, identifying apparent features of the pattern that are not explicit in the rule itself. | Grade 4 |
| Arkansas | 4.GM.A.1 | Students expand knowledge of shapes by analyzing sides and angles. Identify angles as geometric shapes that are formed where two rays share a common endpoint, understanding that angles are measured with reference to a circle so that an angle that turns through a 1/360 of a circle is called a “one-degree angle” and an angle that turns through 𝑛 one-degree angles is said to have an angle measure of n degree. | Grade 4 |
| Arkansas | 4.GM.A.2 | Students expand knowledge of shapes by analyzing sides and angles. Measure angles in whole-number degrees, using a protractor, drawing angles of specified measure. | Grade 4 |
| Arkansas | 4.GM.A.3 | Students expand knowledge of shapes by analyzing sides and angles. Solve real-word problems finding unknown angle measures, using addition and subtraction when an angle is decomposed into non-overlapping parts. | Grade 4 |
| Arkansas | 4.GM.A.4 | Students expand knowledge of shapes by analyzing sides and angles. Identify and draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines, identifying these in quadrilaterals and triangles. | Grade 4 |
| Arkansas | 4.GM.A.5 | Students expand knowledge of shapes by analyzing sides and angles. Classify two-dimensional figures based on the presence or absence of parallel lines, perpendicular lines, or angles of a specified size, involving quadrilaterals and triangles. Shapes include: quadrilaterals (trapezoid, parallelogram, rectangle, square, rhombus) and triangles (right, acute, obtuse). | Grade 4 |
| Arkansas | 4.GM.A.6 | Students expand knowledge of shapes by analyzing sides and angles. Identify and/or draw lines of symmetry for a two-dimensional figure. | Grade 4 |
| Arkansas | 4.GM.B.7 | Students calculate the perimeter of polygons, area of rectangles, and liquid volume. Apply the area and perimeter formulas for rectangles and figures composed of two or more rectangles in real-world situations. | Grade 4 |
| Arkansas | 4.GM.C.8 | Students apply measurement knowledge to solve real-world problems. Convert measurements of length, weight/mass, and liquid volume within the same system of measurement, metric and customary, expressing measurements from a larger unit in terms of a smaller unit. | Grade 4 |
| Arkansas | 4.GM.C.11 | Students apply measurement knowledge to solve real-world problems. Solve real-world problems involving distances, liquid volume, and masses of objects, including problems that require expressing measurements given in a larger unit in terms of a smaller unit. | Grade 4 |
| Arkansas | 4.DA.A.2 | Students organize and analyze data. Use a line plot to display a data set of measurements in fractions of a unit, solving problems involving addition and subtraction of fractions with like denominators using data presented in line plots. | Grade 4 |
| Arkansas | 5.NPV.A.1 | Students understand the base ten place value system. Recognize that, in a multi-digit number, a digit in a given place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. | Grade 5 |
| Arkansas | 5.NPV.A.2 | Students understand the base ten place value system. Explain patterns in the number of zeros and/or the decimal point when multiplying or dividing a number by a power of 10, using whole-number exponents to denote powers of 10. | Grade 5 |
| Arkansas | 5.NPV.A.3 | Students understand the base ten place value system. Read and write decimals to thousandths, using base-ten numerals, word form, and a variety of expanded forms. | Grade 5 |
| Arkansas | 5.NPV.A.4 | Students understand the base ten place value system. Apply place value understanding to round decimals to any place up to the thousandths. | Grade 5 |
| Arkansas | 5.CAR.A.1 | Students perform operations using place value understanding and properties of operations. Use computational fluency to multiply multi-digit whole numbers by using strategies and algorithms, including the standard algorithm, with mastery by the end of fifth grade. | Grade 5 |
| Arkansas | 5.CAR.A.2 | Students perform operations using place value understanding and properties of operations. Calculate whole number quotients of whole numbers with up to four-digit dividends and two-digit divisors using strategies based on place value, properties of operations, divisibility rules, and the relationship between multiplication and division. | Grade 5 |
| Arkansas | 5.CAR.A.3 | Students perform operations using place value understanding and properties of operations. Add and subtract decimals to the hundredths using concrete models or drawings and strategies based on place value, properties of operations, or the relationship between addition and subtraction. | Grade 5 |
| Arkansas | 5.CAR.A.4 | Students perform operations using place value understanding and properties of operations. Multiply and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, or the relationship between multiplication and division. | Grade 5 |
| Arkansas | 5.CAR.A.5 | Students perform operations using place value understanding and properties of operations. Add and subtract fractions with like and unlike denominators by using equivalent fractions {𝑎/𝑏 = (𝑛 ∙ 𝑎)/(𝑛 ∙ 𝑏)} to create common denominators; include real-world problems. Fractions include: mixed numbers. | Grade 5 |
| Arkansas | 5.CAR.A.8 | Students perform operations using place value understanding and properties of operations. Apply previous understanding of division to divide unit fractions by whole numbers and whole numbers by unit fractions. | Grade 5 |
| Arkansas | 5.CAR.B.9 | Students solve real-world problems. Solve and create real-world problems involving multiplication of fractions and mixed numbers. | Grade 5 |
| Arkansas | 5.CAR.B.10 | Students solve real-world problems. Solve real-world problems involving the division of natural numbers leading to answers in the form of fractions or mixed numbers using visual models and equations. | Grade 5 |
| Arkansas | 5.CAR.B.11 | Students solve real-world problems. Solve real-world problems involving the division of unit fractions by whole numbers and whole numbers by unit fractions, using visual fraction models and equations. | Grade 5 |
| Arkansas | 5.CAR.C.12 | Students develop and apply an understanding of foundational algebraic concepts. Evaluate numerical expressions with parentheses or brackets and exponents with the base of ten, using the Order of Operations. | Grade 5 |
| Arkansas | 5.CAR.C.13 | Students develop and apply an understanding of foundational algebraic concepts. Write simple expressions that record calculations with numbers, interpreting numerical expressions without evaluating them. | Grade 5 |
| Arkansas | 5.CAR.C.14 | Students develop and apply an understanding of foundational algebraic concepts. Generate two numerical patterns given two rules, identifying the relationship between the corresponding terms by graphing the terms in the first quadrant of the coordinate grid. | Grade 5 |
| Arkansas | 5.GM.A.1 | Students expand knowledge of shapes by analyzing sides and angles. Classify two-dimensional figures in a hierarchy based on properties with the focus on quadrilaterals and triangles when teaching hierarchies. | Grade 5 |
| Arkansas | 5.GM.B.3 | Students solve the area of rectangles and volume of rectangular prisms. Measure volumes by counting unit cubes using cubic cm (𝑐𝑚³), cubic in (𝑖𝑛³), cubic ft (ft³), and improvised units (𝑢³). | Grade 5 |
| Arkansas | 5.GM.B.4 | Students solve the area of rectangles and volume of rectangular prisms. Solve real-world and mathematical problems involving the volume of rectangular prisms with whole number side lengths by applying the formulas (𝑉=𝑙∙𝑤∙ℎ or 𝑉=𝐵∙ℎ) and the properties of operations. | Grade 5 |
| Arkansas | 5.GM.B.5 | Students solve the area of rectangles and volume of rectangular prisms. Solve real-world problems by calculating volumes of solid figures composed of two non-overlapping right rectangular prisms by adding the volumes of the non-overlapping parts. | Grade 5 |
| Arkansas | 5.GM.C.6 | Students apply measurement knowledge to solve real-world problems. Convert among different-sized standard measurement units within the same system, including both the metric and customary systems, and solve multi-step, real-world problems using conversions. | Grade 5 |
| Arkansas | 5.GM.D.7 | Students develop an understanding of the coordinate system. Graph points with whole number coordinates on a coordinate plane in the first quadrant, explaining how the coordinates relate to the horizontal and vertical axes to describe the location of points in the plane. | Grade 5 |
| Arkansas | 5.GM.D.8 | Students develop an understanding of the coordinate system. Represent real-world and mathematical problems by graphing points in the first quadrant on a coordinate plane, interpreting coordinate values of points in the context of the situation. | Grade 5 |
| Arkansas | 5.DA.A.2 | Students organize and analyze data. Use a line plot to display a data set of measurements in fractions of a unit solving problems involving all four operations with fractions (excluding division of a fraction by fraction) using data presented in line plots. | Grade 5 |
| Arkansas | 6.NCC.A.1 | Students use fractions, decimals, integers, and absolute values to represent real-world situations. Explain positive and negative integers as being opposite values or directions and the meaning of 0 in a real-world context. | Grade 6 |
| Arkansas | 6.NCC.A.2 | Students use fractions, decimals, integers, and absolute values to represent real-world situations. Find and plot rational numbers on horizontal and vertical number lines in real-world and mathematical problems. | Grade 6 |
| Arkansas | 6.NCC.A.3 | Students use fractions, decimals, integers, and absolute values to represent real-world situations. Compare rational numbers, using inequalities (,≤,≥,≠) and order on a number line. | Grade 6 |
| Arkansas | 6.NCC.B.7 | Students extend previous knowledge of operations to decimals and fractions, involving positive rational numbers. Solve problems involving the division of fractions in real-world and mathematical problems. Fractions include all forms of fractions. | Grade 6 |
| Arkansas | 6.NCC.B.8 | Students extend previous knowledge of operations to decimals and fractions, involving positive rational numbers. Divide multi-digit numbers fluently in real-world and mathematical problems. | Grade 6 |
| Arkansas | 6.NCC.B.9 | Students extend previous knowledge of operations to decimals and fractions, involving positive rational numbers. Use any standard algorithm to fluently add and subtract multi-digit decimals and fractions in real-world and mathematical problems. | Grade 6 |
| Arkansas | 6.NCC.B.10 | Students extend previous knowledge of operations to decimals and fractions, involving positive rational numbers. Use any standard algorithm to fluently multiply and divide multi-digit decimals and fractions in real-world and mathematical problems. | Grade 6 |
| Arkansas | 6.PR.A.1 | Students understand ratio concepts and use proportional reasoning to solve problems. Use precise ratio language and notation to describe a ratio as a relationship between two quantities. | Grade 6 |
| Arkansas | 6.PR.A.2 | Students understand ratio concepts and use proportional reasoning to solve problems. Calculate unit rates to include unit pricing and constant speed. | Grade 6 |
| Arkansas | 6.PR.A.4 | Students understand ratio concepts and use proportional reasoning to solve problems. Create various representations to compare ratios and find missing values to solve real-world and mathematical problems. | Grade 6 |
| Arkansas | 6.ALG.A.1 | Students extend their understanding of arithmetic to algebraic expressions. Read and write expressions in real-world or mathematical problems in which letters stand for numbers. | Grade 6 |
| Arkansas | 6.ALG.A.3 | Students extend their understanding of arithmetic to algebraic expressions. Write and evaluate expressions for given values of variables, using order of operations, including expressions with whole number exponents. | Grade 6 |
| Arkansas | 6.ALG.A.4 | Students extend their understanding of arithmetic to algebraic expressions. Generate equivalent expressions by applying the associative, commutative, distributive, and identity properties. | Grade 6 |
| Arkansas | 6.ALG.A.5 | Students extend their understanding of arithmetic to algebraic expressions. Identify when two expressions are equivalent by using properties of operations including like terms. | Grade 6 |
| Arkansas | 6.ALG.B.6 | Students focus on reasoning about and solving equations and inequalities. Use substitution to determine if a given value in a specified set makes an equation or inequality true. Include the following inequality symbols: ,≤,≥,≠. | Grade 6 |
| Arkansas | 6.ALG.B.7 | Students focus on reasoning about and solving equations and inequalities. Write and solve one-step equations in real-world and mathematical problems, involving positive rational numbers and zero. | Grade 6 |
| Arkansas | 6.ALG.B.8 | Students focus on reasoning about and solving equations and inequalities. Write, solve, and graph one-step inequalities in real-world and mathematical problems. | Grade 6 |
| Arkansas | 6.GM.A.1 | Students solve problems involving area, volume, and surface area. Find the area of triangles, quadrilaterals, and polygons by composing or decomposing to solve real-world and mathematical problems. | Grade 6 |
| Arkansas | 6.GM.A.2 | Students solve problems involving area, volume, and surface area. Apply the formulas 𝑉=𝑙𝑤ℎ and 𝑉=𝐵ℎ to find the volume of right rectangular prisms with fractional edge lengths to solve real-world and mathematical problems, including solving for an unknown dimension. | Grade 6 |
| Arkansas | 6.GM.A.3 | Students solve problems involving area, volume, and surface area. Construct nets of a rectangular prism, rectangular pyramid, triangular prism, and triangular pyramid, using the nets to find the surface area of these prisms. | Grade 6 |
| Arkansas | 6.GM.B.4 | Students graph points in all four quadrants. Find and graph pairs of rational numbers in all four quadrants of the coordinate plane in real-world and mathematical problems. | Grade 6 |
| Arkansas | 6.GM.B.5 | Students graph points in all four quadrants. Draw polygons in the coordinate plane when given coordinates for the vertices. | Grade 6 |
| Arkansas | 6.GM.B.6 | Students graph points in all four quadrants. Use coordinates to calculate vertical and horizontal distances between points with the same x-coordinate or the same y-coordinate to solve real-world and mathematical problems. | Grade 6 |
| Arkansas | 6.SP.C.7 | Students summarize and describe distributions. Represent numerical data on a number line, histogram, and box plot. | Grade 6 |
| Arkansas | 7.NCC.A.1 | Students model and compute with rational numbers. Represent addition and subtraction of rational numbers in real-world contexts using a variety of forms. | Grade 7 |
| Arkansas | 7.NCC.B.7 | Students apply all properties and operations to all rational numbers. Use addition and subtraction with rational numbers in any form to solve multi-step problems in real-world and mathematical contexts. | Grade 7 |
| Arkansas | 7.NCC.B.8 | Students apply all properties and operations to all rational numbers. Use multiplication and division with rational numbers in any form to solve multi-step problems in real-world and mathematical contexts. | Grade 7 |
| Arkansas | 7.PR.A.2 | Students analyze and use unit rates to solve problems. Calculate unit rates in real-world contexts that include complex fractions. | Grade 7 |
| Arkansas | 7.PR.A.3 | Students analyze and use unit rates to solve problems. Solve multi-step ratio and percent problems in a real-world context, including percent error and percent increase and decrease. | Grade 7 |
| Arkansas | 7.PR.B.4 | Students analyze proportional relationships and solve multi-step ratio and percent problems. Determine whether two quantities represent proportional relationships by using equivalent ratios in a table and by graphing on a coordinate plane. | Grade 7 |
| Arkansas | 7.PR.B.5 | Students analyze proportional relationships and solve multi-step ratio and percent problems. Compare two different proportional relationships represented in different forms. | Grade 7 |
| Arkansas | 7.ALG.A.1 | Students apply properties of operations to create equivalent expressions. Generate and justify equivalent expressions, using properties of operations to add, subtract, factor, and expand linear expressions with rational coefficients within mathematical and real-world problems. | Grade 7 |
| Arkansas | 7.ALG.C.4 | Students use understanding of algebraic expressions and equations to represent relationships between two quantities. Write an equation to express two quantities in terms of the dependent and independent variables. | Grade 7 |
| Arkansas | 7.GM.A.2 | Students solve problems involving area, volume, and surface area. Use area and circumference formulas of a circle to solve real-world and mathematical problems. | Grade 7 |
| Arkansas | 7.GM.A.3 | Students solve problems involving area, volume, and surface area. Apply the formulas for the volume and surface area of right rectangular prisms, rectangular pyramids, triangular prisms, and triangular pyramids to solve real-world and mathematical problems. | Grade 7 |
| Arkansas | 7.GM.B.4 | Students describe cross sections of three-dimensional figures. Describe the two-dimensional figure that results from slicing a three-dimensional figure parallel and perpendicular to the base. Three-dimensional figures include: right rectangular prisms, triangular prisms, and cylinders. | Grade 7 |
| Arkansas | 7.GM.C.5 | Students solve problems using various angle properties of lines. Solve multi-step problems involving supplementary, complementary, vertical, and adjacent angles to include solving for an unknown angle in a figure. | Grade 7 |
| Arkansas | 7.GM.D.6 | Students understand and use scale factor. Calculate the scale factor, compute the actual lengths from the scale in a drawing, and reproduce a scale drawing using another scale. | Grade 7 |
| Arkansas | 8.NCC.A.2 | Students understand relationships among numbers and the real number system. Compare the size of irrational numbers and locate them on a number line by finding the rational approximations. | Grade 8 |
| Arkansas | 8.NCC.A.3 | Students understand relationships among numbers and the real number system. Know and apply the properties of integer exponents to generate equivalent numerical expressions. | Grade 8 |
| Arkansas | 8.NCC.A.4 | Students understand relationships among numbers and the real number system. Write very large and very small numbers in scientific notation using positive and negative exponents. | Grade 8 |
| Arkansas | 8.NCC.A.6 | Students understand relationships among numbers and the real number system. Solve real-world and mathematical problems by performing operations with numbers written in standard and scientific notation. | Grade 8 |
| Arkansas | 8.NCC.B.7 | Students work with square and cube roots. Solve equations in the form of 𝑥² = 𝑝 or 𝑥³ = 𝑝 where 𝑝 is a positive rational number. | Grade 8 |
| Arkansas | 8.NCC.B.8 | Students work with square and cube roots. Evaluate square roots of perfect squares and cube roots of perfect cubes. | Grade 8 |
| Arkansas | 8.FN.A.1 | Students understand slope using previous learning of proportional relationships. Graph proportional relationships, interpreting the unit rate as the slope of the graph. | Grade 8 |
| Arkansas | 8.FN.A.2 | Students understand slope using previous learning of proportional relationships. Explain, using similar right triangles, how the slope of a line is the same between two points on a non-vertical line or non-horizontal line. Slope includes: positive, negative, horizontal (zero), and vertical (undefined). | Grade 8 |
| Arkansas | 8.FN.B.3 | Students understand that a function is a rule that assigns each input exactly one output. Determine whether a relation is a function or not when given a function map, table, graph, equation, or set of ordered pairs. | Grade 8 |
| Arkansas | 8.FN.B.4 | Students understand that a function is a rule that assigns each input exactly one output. Compare the rate of change (slope) and y-intercept (initial value) of two linear functions each represented in different forms. Functions are represented algebraically, graphically, numerically in tables, or by verbal descriptions. | Grade 8 |
| Arkansas | 8.FN.B.6 | Students understand that a function is a rule that assigns each input exactly one output. Determine the rate of change (slope) and y-intercept (initial value) from tables, graphs, equations, and verbal descriptions of linear relationships. | Grade 8 |
| Arkansas | 8.FN.B.7 | Students understand that a function is a rule that assigns each input exactly one output. Interpret and explain the meaning of the rate of change (slope) and y-intercept (initial value) of a linear relationship in a real-world context. | Grade 8 |
| Arkansas | 8.FN.B.9 | Students understand that a function is a rule that assigns each input exactly one output. Sketch a graph that exhibits qualitative features of a function described verbally. | Grade 8 |
| Arkansas | 8.ALG.A.2 | Students solve linear equations and inequalities. Analyze and solve one-variable linear inequalities with rational coefficients. | Grade 8 |
| Arkansas | 8.GM.A.1 | Students solve problems involving area, volume, and surface area. Apply the formulas for the volume and surface area of cylinders, cones, and spheres to solve real-world and mathematical problems. | Grade 8 |
| Arkansas | 8.GM.B.2 | Students describe cross sections of three-dimensional figures. Describe the two-dimensional figure that results from slicing a three-dimensional figure parallel and perpendicular to the base. Three-dimensional figures include: pyramids, cones, and spheres. | Grade 8 |
| Arkansas | 8.GM.C.4 | Students explore right triangles and apply the Pythagorean Theorem. Apply the Pythagorean Theorem to determine unknown side lengths in right triangles. | Grade 8 |
| Arkansas | 8.GM.C.5 | Students explore right triangles and apply the Pythagorean Theorem. Apply the Pythagorean Theorem to find the distance between two points in a coordinate system. | Grade 8 |
| Arkansas | 8.GM.D.8 | Students use concrete models, diagrams, or geometry to understand congruence and similarity. Given two congruent figures, describe a sequence of transformations that maps one figure to another. | Grade 8 |
| Arkansas | 8.GM.D.9 | Students use concrete models, diagrams, or geometry to understand congruence and similarity. Perform a given sequence of transformations of a figure on the coordinate plane, including rotations, reflections, translations, and dilations. | Grade 8 |
| Arkansas | 8.GM.D.10 | Students use concrete models, diagrams, or geometry to understand congruence and similarity. Describe the effects of rotations, reflections, translations, and dilations on two-dimensional figures using coordinates. | Grade 8 |
| Arkansas | 8.GM.D.11 | Students use concrete models, diagrams, or geometry to understand congruence and similarity. Given two similar two-dimensional figures, describe a sequence of transformations that exhibits similarity, including rotations, reflections, translations, and dilations. | Grade 8 |
| Arkansas | 8.SP.A.1 | Students investigate patterns of association to bivariate data. Construct scatter plots using bivariate data; determine if the data displays a linear or nonlinear pattern and positive, negative, or no association. | Grade 8 |
| Arkansas | 8.SP.A.2 | Students investigate patterns of association to bivariate data. Construct straight lines to approximately fit data displaying a linear association when presented in scatter plots. | Grade 8 |
| Arkansas | A1.FN.A.4 | Students understand the concept of a function, domain and range, and use function notation; students use function notation to solve problems. Evaluate functions expressed in function notation for one or more elements in their domains (inputs); use function notation to describe a contextual situation. | High School |
| Arkansas | A1.LFE.C.11 | Students solve systems of equations and inequalities. Solve systems of linear equations by substitution, elimination, and graphing with and without a real-world context; understand that the solutions will be the same regardless of the method for solving. | High School |
| Arkansas | A1.LFE.D.15 | Students graph linear functions, equations, and inequalities. Write linear equations that model the relationship between two quantities and produce a graph of the equation. | High School |
| Arkansas | A1.QFE.A.2 | Students create and solve equations that model quadratic relationships. Write quadratic equations with real number solutions that model the relationship between two quantities and produce a graph of the equation. | High School |
| Arkansas | A1.QFE.B.6 | Students interpret key features of equations that model quadratic relationships. Interpret the key features of a quadratic function that models a relationship between two quantities in a given context. | High School |
| Arkansas | A1.QFE.B.8 | Students interpret key features of equations that model quadratic relationships. Explain how each form of a quadratic expression (standard, factored, and vertex form) identifies different key attributes, using the different forms to interpret quantities in context. | High School |
| Arkansas | A1.SP.B.3 | Students will investigate patterns of association in bivariate data. Summarize data from two categorical variables in a frequency table; interpret relative frequencies in the context of the data, recognizing data trends and associations. | High School |
| Arkansas | AT.FN.B.3 | Students analyze functions using graphing. Graph functions expressed symbolically and show key features of the graph using technology. Functions include exponential, logarithmic, and trigonometric functions. | High School |
| Arkansas | AT.FN.B.5 | Students analyze functions using graphing. Graph polynomial functions, identifying zeros when suitable factorizations are available and showing end behavior, with or without the appropriate technology. | High School |
| CCSSM | K.CC.A.1 | Count to 100 by ones and by tens. | Kindergarten |
| CCSSM | K.CC.A.2 | Count forward beginning from a given number within the known sequence (instead of having to begin at 1). | Kindergarten |
| CCSSM | K.CC.A.3 | Write numbers from 0 to 20. Represent a number of objects with a written numeral 0-20 (with 0 representing a count of no objects). | Kindergarten |
| CCSSM | K.CC.B.4 | Understand the relationship between numbers and quantities; connect counting to cardinality. | Kindergarten |
| CCSSM | K.CC.B.5 | Count to answer 'how many?' questions about as many as 20 things arranged in a line, a rectangular array, or a circle, or as many as 10 things in a scattered configuration; given a number from 1-20, count out that many objects. | Kindergarten |
| CCSSM | K.CC.C.6 | Identify whether the number of objects in one group is greater than, less than, or equal to the number of objects in another group, e.g., by using matching and counting strategies. | Kindergarten |
| CCSSM | K.CC.C.7 | Compare two numbers between 1 and 10 presented as written numerals. | Kindergarten |
| CCSSM | K.G.A.1 | Describe objects in the environment using names of shapes, and describe the relative positions of these objects using terms such as above, below, beside, in front of, behind, and next to. | Kindergarten |
| CCSSM | K.G.A.2 | Correctly name shapes regardless of their orientations or overall size. | Kindergarten |
| CCSSM | K.G.A.3 | Identify shapes as two-dimensional (lying in a plane, “flat”) or three-dimensional (“solid”). | Kindergarten |
| CCSSM | K.G.B.4 | Analyze and compare two- and three-dimensional shapes, in different sizes and orientations, using informal language to describe their similarities, differences, parts (e.g., number of sides and vertices/'corners') and other attributes (e.g., having sides of equal length). | Kindergarten |
| CCSSM | K.G.B.6 | Compose simple shapes to form larger shapes. | Kindergarten |
| CCSSM | K.MD.A.1 | Describe measurable attributes of objects, such as length or weight. Describe several measurable attributes of a single object. | Kindergarten |
| CCSSM | K.MD.A.2 | Directly compare two objects with a measurable attribute in common, to see which object has “more of”/“less of” the attribute, and describe the difference. | Kindergarten |
| CCSSM | K.MD.B.3 | Classify objects into given categories; count the numbers of objects in each category and sort the categories by count. | Kindergarten |
| CCSSM | K.NBT.A.1 | Compose and decompose numbers from 11 to 19 into ten ones and some further ones, e.g., by using objects or drawings, and record each composition or decomposition by a drawing or equation (such as 18 = 10 + 8); understand that these numbers are composed of ten ones and one, two, three, four, five, six, seven, eight, or nine ones. | Kindergarten |
| CCSSM | K.OA.A.1 | Represent addition and subtraction with objects, fingers, mental images, drawings, sounds (e.g., claps), acting out situations, verbal explanations, expressions, or equations. | Kindergarten |
| CCSSM | K.OA.A.2 | Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem. | Kindergarten |
| CCSSM | K.OA.A.3 | Decompose numbers less than or equal to 10 into pairs in more than one way, e.g., by using objects or drawings, and record each decomposition by a drawing or equation (e.g., 5 = 2 + 3 and 5 = 4 + 1). | Kindergarten |
| CCSSM | K.OA.A.4 | For any number from 1 to 9, find the number that makes 10 when added to the given number, e.g., by using objects or drawings, and record the answer with a drawing or equation. | Kindergarten |
| CCSSM | K.OA.A.5 | Fluently add and subtract within 5. | Kindergarten |
| CCSSM | 1.G.A.1 | Distinguish between defining attributes (e.g., triangles are closed and three-sided) versus non-defining attributes (e.g., color, orientation, overall size); build and draw shapes to possess defining attributes. | Grade 1 |
| CCSSM | 1.G.A.2 | Compose two-dimensional shapes (rectangles, squares, trapezoids, triangles, half-circles, and quarter-circles) or three-dimensional shapes (cubes, right rectangular prisms, right circular cones, and right circular cylinders) to create a composite shape, and compose new shapes from the composite shape. | Grade 1 |
| CCSSM | 1.G.A.3 | Partition circles and rectangles into two and four equal shares, describe the shares using the words halves, fourths, and quarters, and use the phrases half of, fourth of, and quarter of. Describe the whole as two of, or four of the shares. Understand for these examples that decomposing into more equal shares creates smaller shares. | Grade 1 |
| CCSSM | 1.MD.A.1 | Order three objects by length; compare the lengths of two objects indirectly by using a third object. | Grade 1 |
| CCSSM | 1.MD.A.2 | Express the length of an object as a whole number of length units, by laying multiple copies of a shorter object (the length unit) end to end; understand that the length measurement of an object is the number of same-size length units that span it with no gaps or overlaps. | Grade 1 |
| CCSSM | 1.MD.B.3 | Tell and write time in hours and half-hours using analog and digital clocks. | Grade 1 |
| CCSSM | 1.MD.C.4 | Organize, represent, and interpret data with up to three categories; ask and answer questions about the total number of data points, how many in each category, and how many more or less are in one category than in another. | Grade 1 |
| CCSSM | 1.NBT.A.1 | Count to 120, starting at any number less than 120. In this range, read and write numerals and represent a number of objects with a written numeral. | Grade 1 |
| CCSSM | 1.NBT.B.2 | Understand that the two digits of a two-digit number represent amounts of tens and ones. | Grade 1 |
| CCSSM | 1.NBT.B.3 | Compare two two-digit numbers based on meanings of the tens and ones digits, recording the results of comparisons with the symbols >, =, and <. | Grade 1 |
| CCSSM | 1.NBT.C.4 | Add within 100, including adding a two-digit number and a one-digit number, and adding a two-digit number and a multiple of 10, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Understand that in adding two-digit numbers, one adds tens and tens, ones and ones; and sometimes it is necessary to compose a ten. | Grade 1 |
| CCSSM | 1.NBT.C.5 | Given a two-digit number, mentally find 10 more or 10 less than the number, without having to count; explain the reasoning used. | Grade 1 |
| CCSSM | 1.NBT.C.6 | Subtract multiples of 10 in the range 10-90 from multiples of 10 in the range 10-90 (positive or zero differences), using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. | Grade 1 |
| CCSSM | 1.OA.A.1 | Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem. | Grade 1 |
| CCSSM | 1.OA.B.3 | Apply properties of operations as strategies to add and subtract. | Grade 1 |
| CCSSM | 1.OA.B.4 | Understand subtraction as an unknown-addend problem. | Grade 1 |
| CCSSM | 1.OA.C.5 | Relate counting to addition and subtraction (e.g., by counting on 2 to add 2). | Grade 1 |
| CCSSM | 1.OA.C.6 | Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to a ten (e.g., 13 - 4 = 13 - 3 - 1 = 10 - 1 = 9); using the relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 - 8 = 4); and creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13). | Grade 1 |
| CCSSM | 1.OA.D.7 | Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false. For example, which of the following equations are true and which are false? 6 = 6, 7 = 8 - 1, 5 + 2 = 2 + 5, 4 + 1 = 5 + 2. | Grade 1 |
| CCSSM | 1.OA.D.8 | Determine the unknown whole number in an addition or subtraction equation relating three whole numbers. | Grade 1 |
| CCSSM | 2.G.A.1 | Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces. Identify triangles, quadrilaterals, pentagons, hexagons, and cubes. | Grade 2 |
| CCSSM | 2.G.A.2 | Partition a rectangle into rows and columns of same-size squares and count to find the total number of them. | Grade 2 |
| CCSSM | 2.G.A.3 | Partition circles and rectangles into two, three, or four equal shares, describe the shares using the words halves, thirds, half of, a third of, etc., and describe the whole as two halves, three thirds, four fourths. Recognize that equal shares of identical wholes need not have the same shape. | Grade 2 |
| CCSSM | 2.MD.A.1 | Measure the length of an object by selecting and using appropriate tools such as rulers, yardsticks, meter sticks, and measuring tapes. | Grade 2 |
| CCSSM | 2.MD.A.2 | Measure the length of an object twice, using length units of different lengths for the two measurements; describe how the two measurements relate to the size of the unit chosen. | Grade 2 |
| CCSSM | 2.MD.A.4 | Measure to determine how much longer one object is than another, expressing the length difference in terms of a standard length unit. | Grade 2 |
| CCSSM | 2.MD.B.5 | Use addition and subtraction within 100 to solve word problems involving lengths that are given in the same units, e.g., by using drawings (such as drawings of rulers) and equations with a symbol for the unknown number to represent the problem. | Grade 2 |
| CCSSM | 2.MD.C.7 | Tell and write time from analog and digital clocks to the nearest five minutes, using a.m. and p.m. | Grade 2 |
| CCSSM | 2.MD.C.8 | Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies, using $ and ¢ symbols appropriately. | Grade 2 |
| CCSSM | 2.MD.D.9 | Generate measurement data by measuring lengths of several objects to the nearest whole unit, or by making repeated measurements of the same object. Show the measurements by making a line plot, where the horizontal scale is marked off in whole-number units. | Grade 2 |
| CCSSM | 2.MD.D.10 | Draw a picture graph and a bar graph (with single-unit scale) to represent a data set with up to four categories. Solve simple put-together, take-apart, and compare problems using information presented in a bar graph. | Grade 2 |
| CCSSM | 2.NBT.A.1 | Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones. | Grade 2 |
| CCSSM | 2.NBT.A.2 | Count within 1000; skip-count by 5s, 10s, and 100s. | Grade 2 |
| CCSSM | 2.NBT.A.3 | Read and write numbers to 1000 using base-ten numerals, number names, and expanded form. | Grade 2 |
| CCSSM | 2.NBT.A.4 | Compare two three-digit numbers based on meanings of the hundreds, tens, and ones digits, using >, =, and < symbols to record the results of comparisons. | Grade 2 |
| CCSSM | 2.NBT.B.5 | Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction. | Grade 2 |
| CCSSM | 2.NBT.B.6 | Add up to four two-digit numbers using strategies based on place value and properties of operations. | Grade 2 |
| CCSSM | 2.NBT.B.7 | Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method. Understand that in adding or subtracting three-digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds. | Grade 2 |
| CCSSM | 2.NBT.B.8 | Mentally add 10 or 100 to a given number 100-900, and mentally subtract 10 or 100 from a given number 100-900. | Grade 2 |
| CCSSM | 2.OA.A.1 | Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem. | Grade 2 |
| CCSSM | 2.OA.B.2 | Fluently add and subtract within 20 using mental strategies. By end of Grade 2, know from memory all sums of two one-digit numbers. | Grade 2 |
| CCSSM | 2.OA.C.3 | Determine whether a group of objects (up to 20) has an odd or even number of members, e.g., by pairing objects or counting them by 2s; write an equation to express an even number as a sum of two equal addends. | Grade 2 |
| CCSSM | 2.OA.C.4 | Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends. | Grade 2 |
| CCSSM | 3.G.A.1 | Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories. | Grade 3 |
| CCSSM | 3.G.A.2 | Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole. | Grade 3 |
| CCSSM | 3.MD.A.1 | Tell and write time to the nearest minute and measure time intervals in minutes. Solve word problems involving addition and subtraction of time intervals in minutes, e.g., by representing the problem on a number line diagram. | Grade 3 |
| CCSSM | 3.MD.A.2 | Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l). Add, subtract, multiply, or divide to solve one-step word problems involving masses or volumes that are given in the same units, e.g., by using drawings (such as a beaker with a measurement scale) to represent the problem. | Grade 3 |
| CCSSM | 3.MD.B.3 | Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and two-step “how many more” and “how many less” problems using information presented in scaled bar graphs. | Grade 3 |
| CCSSM | 3.MD.B.4 | Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Show the data by making a line plot, where the horizontal scale is marked off in appropriate units-whole numbers, halves, or quarters. | Grade 3 |
| CCSSM | 3.MD.C.5 | Recognize area as an attribute of plane figures and understand concepts of area measurement. | Grade 3 |
| CCSSM | 3.MD.C.6 | Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units). | Grade 3 |
| CCSSM | 3.MD.C.7 | Relate area to the operations of multiplication and addition. | Grade 3 |
| CCSSM | 3.MD.D.8 | Solve real world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters. | Grade 3 |
| CCSSM | 3.NBT.A.1 | Use place value understanding to round whole numbers to the nearest 10 or 100. | Grade 3 |
| CCSSM | 3.NBT.A.2 | Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction. | Grade 3 |
| CCSSM | 3.NBT.A.3 | Multiply one-digit whole numbers by multiples of 10 in the range 10-90 (e.g., 9 × 80, 5 × 60) using strategies based on place value and properties of operations. | Grade 3 |
| CCSSM | 3.NF.A.1 | Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b. | Grade 3 |
| CCSSM | 3.NF.A.2 | Understand a fraction as a number on the number line; represent fractions on a number line diagram. | Grade 3 |
| CCSSM | 3.NF.A.3 | Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size. | Grade 3 |
| CCSSM | 3.OA.A.1 | Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each. | Grade 3 |
| CCSSM | 3.OA.A.2 | Interpret whole-number quotients of whole numbers, e.g., interpret 56 ÷ 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each. | Grade 3 |
| CCSSM | 3.OA.A.3 | Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem. | Grade 3 |
| CCSSM | 3.OA.A.4 | Determine the unknown whole number in a multiplication or division equation relating three whole numbers. | Grade 3 |
| CCSSM | 3.OA.B.5 | Apply properties of operations as strategies to multiply and divide. | Grade 3 |
| CCSSM | 3.OA.B.6 | Understand division as an unknown-factor problem. | Grade 3 |
| CCSSM | 3.OA.C.7 | Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 × 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers. | Grade 3 |
| CCSSM | 3.OA.D.8 | Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. | Grade 3 |
| CCSSM | 3.OA.D.9 | Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations. | Grade 3 |
| CCSSM | 4.G.A.1 | Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures. | Grade 4 |
| CCSSM | 4.G.A.2 | Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles. | Grade 4 |
| CCSSM | 4.G.A.3 | Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify line-symmetric figures and draw lines of symmetry. | Grade 4 |
| CCSSM | 4.MD.A.1 | Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table. | Grade 4 |
| CCSSM | 4.MD.A.2 | Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. | Grade 4 |
| CCSSM | 4.MD.A.3 | Apply the area and perimeter formulas for rectangles in real world and mathematical problems. | Grade 4 |
| CCSSM | 4.MD.B.4 | Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots. | Grade 4 |
| CCSSM | 4.MD.C.5 | Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement. | Grade 4 |
| CCSSM | 4.MD.C.6 | Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure. | Grade 4 |
| CCSSM | 4.MD.C.7 | Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems, e.g., by using an equation with a symbol for the unknown angle measure. | Grade 4 |
| CCSSM | 4.NBT.A.1 | Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. | Grade 4 |
| CCSSM | 4.NBT.A.2 | Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. | Grade 4 |
| CCSSM | 4.NBT.A.3 | Use place value understanding to round multi-digit whole numbers to any place. | Grade 4 |
| CCSSM | 4.NBT.B.4 | Fluently add and subtract multi-digit whole numbers using the standard algorithm. | Grade 4 |
| CCSSM | 4.NBT.B.5 | Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. | Grade 4 |
| CCSSM | 4.NBT.B.6 | Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. | Grade 4 |
| CCSSM | 4.NF.A.1 | Explain why a fraction a/b is equivalent to a fraction (n x a) / (n x b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. | Grade 4 |
| CCSSM | 4.NF.A.2 | Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model. | Grade 4 |
| CCSSM | 4.NF.B.3 | Understand a fraction a/b with a > 1 as a sum of fractions 1/b. | Grade 4 |
| CCSSM | 4.NF.B.4 | Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. | Grade 4 |
| CCSSM | 4.NF.C.5 | Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100. | Grade 4 |
| CCSSM | 4.NF.C.6 | Use decimal notation for fractions with denominators 10 or 100. | Grade 4 |
| CCSSM | 4.NF.C.7 | Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual model. | Grade 4 |
| CCSSM | 4.OA.A.1 | Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 x 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations. | Grade 4 |
| CCSSM | 4.OA.A.2 | Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison. | Grade 4 |
| CCSSM | 4.OA.A.3 | Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. | Grade 4 |
| CCSSM | 4.OA.B.4 | Find all factor pairs for a whole number in the range 1 - 100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1 - 100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1 - 100 is prime or composite. | Grade 4 |
| CCSSM | 4.OA.C.5 | Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. | Grade 4 |
| CCSSM | 5.G.A.1 | Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and the given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate). | Grade 5 |
| CCSSM | 5.G.A.2 | Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. | Grade 5 |
| CCSSM | 5.G.B.3 | Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. | Grade 5 |
| CCSSM | 5.G.B.4 | Classify two-dimensional figures in a hierarchy based on properties. | Grade 5 |
| CCSSM | 5.MD.A.1 | Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. | Grade 5 |
| CCSSM | 5.MD.B.2 | Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. | Grade 5 |
| CCSSM | 5.MD.C.3 | Recognize volume as an attribute of solid figures and understand concepts of volume measurement. | Grade 5 |
| CCSSM | 5.MD.C.4 | Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. | Grade 5 |
| CCSSM | 5.MD.C.5 | Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume. | Grade 5 |
| CCSSM | 5.NBT.A.1 | Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. | Grade 5 |
| CCSSM | 5.NBT.A.2 | Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. | Grade 5 |
| CCSSM | 5.NBT.A.3 | Read, write, and compare decimals to thousandths. | Grade 5 |
| CCSSM | 5.NBT.A.4 | Use place value understanding to round decimals to any place. | Grade 5 |
| CCSSM | 5.NBT.B.5 | Fluently multiply multi-digit whole numbers using the standard algorithm. | Grade 5 |
| CCSSM | 5.NBT.B.6 | Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. | Grade 5 |
| CCSSM | 5.NBT.B.7 | Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. | Grade 5 |
| CCSSM | 5.NF.A.1 | Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. | Grade 5 |
| CCSSM | 5.NF.A.2 | Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators by using visual models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. | Grade 5 |
| CCSSM | 5.NF.B.3 | Interpret a fraction as division of the numerator by the denominator (a/b = a / b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. | Grade 5 |
| CCSSM | 5.NF.B.4 | Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. | Grade 5 |
| CCSSM | 5.NF.B.5 | Interpret multiplication as scaling (resizing). | Grade 5 |
| CCSSM | 5.NF.B.6 | Solve real world problems involving multiplication of fractions and mixed numbers by using visual fraction models or equations to represent the problem. | Grade 5 |
| CCSSM | 5.NF.B.7 | Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. | Grade 5 |
| CCSSM | 5.OA.A.1 | Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. | Grade 5 |
| CCSSM | 5.OA.A.2 | Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. | Grade 5 |
| CCSSM | 5.OA.B.3 | Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. | Grade 5 |
| CCSSM | 6.EE.A.1 | Write and evaluate numerical expressions involving whole-number exponents. | Grade 6 |
| CCSSM | 6.EE.A.2 | Write, read, and evaluate expressions in which letters stand for numbers. | Grade 6 |
| CCSSM | 6.EE.A.3 | Apply the properties of operations to generate equivalent expressions. | Grade 6 |
| CCSSM | 6.EE.A.4 | Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). | Grade 6 |
| CCSSM | 6.EE.B.5 | Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true. | Grade 6 |
| CCSSM | 6.EE.B.6 | Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set. | Grade 6 |
| CCSSM | 6.EE.B.7 | Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers. | Grade 6 |
| CCSSM | 6.EE.B.8 | Write an inequality of the form x > c or x c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams. | Grade 6 |
| CCSSM | 6.EE.C.9 | Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. For example, in a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to represent the relationship between distance and time. | Grade 6 |
| CCSSM | 6.G.A.1 | Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems. | Grade 6 |
| CCSSM | 6.G.A.2 | Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas 𝘝 = 𝘭 𝘸 𝘩 and 𝘝 = 𝘣 𝘩 to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems. | Grade 6 |
| CCSSM | 6.G.A.3 | Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems. | Grade 6 |
| CCSSM | 6.G.A.4 | Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems. | Grade 6 |
| CCSSM | 6.NS.A.1 | Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. | Grade 6 |
| CCSSM | 6.NS.B.2 | Fluently divide multi-digit numbers using the standard algorithm. | Grade 6 |
| CCSSM | 6.NS.B.3 | Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation. | Grade 6 |
| CCSSM | 6.NS.C.5 | Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation. | Grade 6 |
| CCSSM | 6.NS.C.6 | Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates. | Grade 6 |
| CCSSM | 6.NS.C.7 | Understand ordering and absolute value of rational numbers. | Grade 6 |
| CCSSM | 6.NS.C.8 | Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. | Grade 6 |
| CCSSM | 6.RP.A.1 | Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. | Grade 6 |
| CCSSM | 6.RP.A.2 | Understand the concept of a unit rate a/b associated with a ratio a:b with b ≠ 0, and use rate language in the context of a ratio relationship. | Grade 6 |
| CCSSM | 6.RP.A.3 | Use ratio and rate reasoning to solve real-world and mathematical problems, by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams or equations. | Grade 6 |
| CCSSM | 6.SP.B.5 | Summarize numerical data sets in relation to their context. | Grade 6 |
| CCSSM | 7.EE.A.1 | Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients. | Grade 7 |
| CCSSM | 7.EE.A.2 | Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. | Grade 7 |
| CCSSM | 7.EE.B.3 | Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. | Grade 7 |
| CCSSM | 7.EE.B.4 | Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. | Grade 7 |
| CCSSM | 7.G.A.1 | Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale. | Grade 7 |
| CCSSM | 7.G.A.2 | Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle. | Grade 7 |
| CCSSM | 7.G.A.3 | Describe the two-dimensional figures that result from slicing three-dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids. | Grade 7 |
| CCSSM | 7.G.B.4 | Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle. | Grade 7 |
| CCSSM | 7.G.B.5 | Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure. | Grade 7 |
| CCSSM | 7.G.B.6 | Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. | Grade 7 |
| CCSSM | 7.NS.A.1 | Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram. | Grade 7 |
| CCSSM | 7.NS.A.2 | Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers. | Grade 7 |
| CCSSM | 7.NS.A.3 | Solve real-world and mathematical problems involving the four operations with rational numbers. | Grade 7 |
| CCSSM | 7.RP.A.1 | Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. | Grade 7 |
| CCSSM | 7.RP.A.2 | Recognize and represent proportional relationships between quantities. | Grade 7 |
| CCSSM | 7.RP.A.3 | Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error. | Grade 7 |
| CCSSM | 8.EE.A.1 | Know and apply the properties of integer exponents to generate equivalent numerical expressions. | Grade 8 |
| CCSSM | 8.EE.A.2 | Use square root and cube root symbols to represent solutions to equations of the form 𝘹² = 𝘱 and 𝘹³ = 𝘱, where 𝘱 is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that √2 is irrational. | Grade 8 |
| CCSSM | 8.EE.A.3 | Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much ones is than the other. | Grade 8 |
| CCSSM | 8.EE.A.4 | Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities. Interpret scientific notation that has been generated by technology. | Grade 8 |
| CCSSM | 8.EE.B.5 | Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed. | Grade 8 |
| CCSSM | 8.EE.B.6 | Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b. | Grade 8 |
| CCSSM | 8.EE.C.7 | Solve linear equations in one variable. | Grade 8 |
| CCSSM | 8.EE.C.8 | Analyze and solve pairs of simultaneous linear equations. | Grade 8 |
| CCSSM | 8.F.A.1 | Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output. | Grade 8 |
| CCSSM | 8.F.A.2 | Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). | Grade 8 |
| CCSSM | 8.F.A.3 | Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. | Grade 8 |
| CCSSM | 8.F.B.4 | Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values. | Grade 8 |
| CCSSM | 8.F.B.5 | Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally. | Grade 8 |
| CCSSM | 8.G.A.1 | Verify experimentally the properties of rotations, reflections, and translations. | Grade 8 |
| CCSSM | 8.G.A.2 | Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them. | Grade 8 |
| CCSSM | 8.G.A.3 | Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates. | Grade 8 |
| CCSSM | 8.G.A.4 | Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two-dimensional figures, describe a sequence that exhibits the similarity between them. | Grade 8 |
| CCSSM | 8.G.A.5 | Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. | Grade 8 |
| CCSSM | 8.G.B.7 | Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions. | Grade 8 |
| CCSSM | 8.G.B.8 | Apply the Pythagorean Theorem to find the distance between two points in a coordinate system. | Grade 8 |
| CCSSM | 8.G.C.9 | Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems. | Grade 8 |
| CCSSM | 8.NS.A.2 | Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g., π²). | Grade 8 |
| CCSSM | 8.SP.A.1 | Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association. | Grade 8 |
| CCSSM | 8.SP.A.2 | Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line. | Grade 8 |
| CCSSM | A-APR.B.3 | Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial. | Algebra |
| CCSSM | A-CED.A.2 | Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. | Algebra |
| CCSSM | A-CED.A.3 | Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context. | Algebra |
| CCSSM | A-REI.B.3 | Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. | Algebra |
| CCSSM | A-SSE.A.2 | Use the structure of an expression to identify ways to rewrite it. | Algebra |
| CCSSM | A-SSE.B.3 | Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression. | Algebra |
| CCSSM | F-BF.A.1 | Write a function that describes a relationship between two quantities. | Algebra |
| CCSSM | F-IF.A.2 | Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. | Algebra |
| CCSSM | F-IF.B.4 | For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. | Algebra |
| CCSSM | F-IF.C.7 | Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. | Algebra |
| CCSSM | S-ID.B.6 | Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. | Algebra |
| California | K.CC.1 | Count to 100 by ones and by tens. | Kindergarten |
| California | K.CC.2 | Count forward beginning from a given number within the known sequence (instead of having to begin at 1). | Kindergarten |
| California | K.CC.3 | Write numbers from 0 to 20. Represent a number of objects with a written numeral 0-20 (with 0 representing a count of no objects). | Kindergarten |
| California | K.CC.4 | Understand the relationship between numbers and quantities; connect counting to cardinality. | Kindergarten |
| California | K.CC.5 | Count to answer “how many?” questions about as many as 20 things arranged in a line, a rectangular array, or a circle, or as many as 10 things in a scattered configuration; given a number from 1-20, count out that many objects. | Kindergarten |
| California | K.CC.6 | Identify whether the number of objects in one group is greater than, less than, or equal to the number of objects in another group, e.g., by using matching and counting strategies. | Kindergarten |
| California | K.CC.7 | Compare two numbers between 1 and 10 presented as written numerals. | Kindergarten |
| California | K.G.1 | Describe objects in the environment using names of shapes, and describe the relative positions of these objects using terms such as above, below, beside, in front of, behind, and next to. | Kindergarten |
| California | K.G.2 | Correctly name shapes regardless of their orientations or overall size. | Kindergarten |
| California | K.G.3 | Identify shapes as two-dimensional (lying in a plane, “flat”) or three-dimensional (“solid”). | Kindergarten |
| California | K.G.4 | Analyze and compare two- and three-dimensional shapes, in different sizes and orientations, using informal language to describe their similarities, differences, parts (e.g., number of sides and vertices/“corners”) and other attributes (e.g., having sides of equal length). | Kindergarten |
| California | K.G.6 | Compose simple shapes to form larger shapes. | Kindergarten |
| California | K.MD.1 | Describe measurable attributes of objects, such as length or weight. Describe several measurable attributes of a single object. | Kindergarten |
| California | K.MD.2 | Directly compare two objects with a measurable attribute in common, to see which object has “more of”/“less of” the attribute, and describe the difference. | Kindergarten |
| California | K.MD.3 | Classify objects into given categories; count the numbers of objects in each category and sort the categories by count. | Kindergarten |
| California | K.NBT.1 | Compose and decompose numbers from 11 to 19 into ten ones and some further ones, e.g., by using objects or drawings, and record each composition or decomposition by a drawing or equation (e.g., 18 = 10 + 8); understand that these numbers are composed of ten ones and one, two, three, four, five, six, seven, eight, or nine ones. | Kindergarten |
| California | K.OA.1 | Represent addition and subtraction with objects, fingers, mental images, drawings, sounds (e.g., claps), acting out situations, verbal explanations, expressions, or equations. | Kindergarten |
| California | K.OA.2 | Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem. | Kindergarten |
| California | K.OA.3 | Decompose numbers less than or equal to 10 into pairs in more than one way, e.g., by using objects or drawings, and record each decomposition by a drawing or equation (e.g., 5 = 2 + 3 and 5 = 4 + 1). | Kindergarten |
| California | K.OA.4 | For any number from 1 to 9, find the number that makes 10 when added to the given number, e.g., by using objects or drawings, and record the answer with a drawing or equation. | Kindergarten |
| California | K.OA.5 | Fluently add and subtract within 5. | Kindergarten |
| California | 1.G.1 | Distinguish between defining attributes (e.g., triangles are closed and three-sided) versus non-defining attributes (e.g., color, orientation, overall size); build and draw shapes to possess defining attributes. | Grade 1 |
| California | 1.G.2 | Compose two-dimensional shapes (rectangles, squares, trapezoids, triangles, half-circles, and quarter-circles) or three-dimensional shapes (cubes, right rectangular prisms, right circular cones, and right circular cylinders) to create a composite shape, and compose new shapes from the composite shape. | Grade 1 |
| California | 1.G.3 | Partition circles and rectangles into two and four equal shares, describe the shares using the words halves, fourths, and quarters, and use the phrases half of, fourth of, and quarter of. Describe the whole as two of, or four of the shares. Understand for these examples that decomposing into more equal shares creates smaller shares. | Grade 1 |
| California | 1.MD.1 | Order three objects by length; compare the lengths of two objects indirectly by using a third object. | Grade 1 |
| California | 1.MD.2 | Express the length of an object as a whole number of length units, by laying multiple copies of a shorter object (the length unit) end to end; understand that the length measurement of an object is the number of same-size length units that span it with no gaps or overlaps. | Grade 1 |
| California | 1.MD.3 | Tell and write time in hours and half-hours using analog and digital clocks. | Grade 1 |
| California | 1.MD.4 | Organize, represent, and interpret data with up to three categories; ask and answer questions about the total number of data points, how many in each category, and how many more or less are in one category than in another. | Grade 1 |
| California | 1.NBT.1 | Count to 120, starting at any number less than 120. In this range, read and write numerals and represent a number of objects with a written numeral. | Grade 1 |
| California | 1.NBT.2 | Understand that the two digits of a two-digit number represent amounts of tens and ones. Understand the following as special cases: | Grade 1 |
| California | 1.NBT.3 | Compare two two-digit numbers based on meanings of the tens and ones digits, recording the results of comparisons with the symbols >, =, and <. | Grade 1 |
| California | 1.NBT.4 | Add within 100, including adding a two-digit number and a one-digit number, and adding a two-digit number and a multiple of 10, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Understand that in adding two-digit numbers, one adds tens and tens, ones and ones; and sometimes it is necessary to compose a ten. | Grade 1 |
| California | 1.NBT.5 | Given a two-digit number, mentally find 10 more or 10 less than the number, without having to count; explain the reasoning used. | Grade 1 |
| California | 1.NBT.6 | Subtract multiples of 10 in the range 10–90 from multiples of 10 in the range 10–90 (positive or zero differences), using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. | Grade 1 |
| California | 1.OA.1 | Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem. | Grade 1 |
| California | 1.OA.3 | Apply properties of operations as strategies to add and subtract. | Grade 1 |
| California | 1.OA.4 | Understand subtraction as an unknown-addend problem. | Grade 1 |
| California | 1.OA.5 | Relate counting to addition and subtraction (e.g., by counting on 2 to add 2). | Grade 1 |
| California | 1.OA.6 | Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to a ten (e.g., 13 - 4 = 13 - 3 - 1 = 10 - 1 = 9); using the relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 - 8 = 4); and creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13). | Grade 1 |
| California | 1.OA.7 | Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false. | Grade 1 |
| California | 1.OA.8 | Determine the unknown whole number in an addition or subtraction equation relating three whole numbers. | Grade 1 |
| California | 2.G.1 | Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces. Identify triangles, quadrilaterals, pentagons, hexagons, and cubes. | Grade 2 |
| California | 2.G.2 | Partition a rectangle into rows and columns of same-size squares and count to find the total number of them. | Grade 2 |
| California | 2.G.3 | Partition circles and rectangles into two, three, or four equal shares, describe the shares using the words halves, thirds, half of, a third of, etc., and describe the whole as two halves, three thirds, four fourths. Recognize that equal shares of identical wholes need not have the same shape. | Grade 2 |
| California | 2.MD.1 | Measure the length of an object by selecting and using appropriate tools such as rulers, yardsticks, meter sticks, and measuring tapes. | Grade 2 |
| California | 2.MD.2 | Measure the length of an object twice, using length units of different lengths for the two measurements; describe how the two measurements relate to the size of the unit chosen. | Grade 2 |
| California | 2.MD.4 | Measure to determine how much longer one object is than another, expressing the length difference in terms of a standard length unit. | Grade 2 |
| California | 2.MD.5 | Use addition and subtraction within 100 to solve word problems involving lengths that are given in the same units, e.g., by using drawings (such as drawings of rulers) and equations with a symbol for the unknown number to represent the problem. | Grade 2 |
| California | 2.MD.7 | Tell and write time from analog and digital clocks to the nearest five minutes, using a.m. and p.m. Know relationships of time (e.g., minutes in an hour, days in a month, weeks in a year). | Grade 2 |
| California | 2.MD.8 | Solve word problems involving combinations of dollar bills, quarters, dimes, nickels, and pennies, using $ and ¢ symbols appropriately. | Grade 2 |
| California | 2.MD.9 | Generate measurement data by measuring lengths of several objects to the nearest whole unit, or by making repeated measurements of the same object. Show the measurements by making a line plot, where the horizontal scale is marked off in whole-number units. | Grade 2 |
| California | 2.MD.10 | Draw a picture graph and a bar graph (with single-unit scale) to represent a data set with up to four categories. Solve simple put-together, take-apart, and compare problems using information presented in a bar graph. | Grade 2 |
| California | 2.NBT.1 | Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones. Understand the following as special cases: | Grade 2 |
| California | 2.NBT.2 | Count within 1000; skip-count by 2s, 5s, 10s, and 100s. | Grade 2 |
| California | 2.NBT.3 | Read and write numbers to 1000 using base-ten numerals, number names, and expanded form. | Grade 2 |
| California | 2.NBT.4 | Compare two three-digit numbers based on meanings of the hundreds, tens, and ones digits, using >, =, and < symbols to record the results of comparisons. | Grade 2 |
| California | 2.NBT.5 | Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction. | Grade 2 |
| California | 2.NBT.6 | Add up to four two-digit numbers using strategies based on place value and properties of operations. | Grade 2 |
| California | 2.NBT.7 | Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method. Understand that in adding or subtracting three-digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds. | Grade 2 |
| California | 2.NBT.8 | Mentally add 10 or 100 to a given number 100–900, and mentally subtract 10 or 100 from a given number 100–900. | Grade 2 |
| California | 2.OA.1 | Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem. | Grade 2 |
| California | 2.OA.2 | Fluently add and subtract within 20 using mental strategies. By end of Grade 2, know from memory all sums of two one-digit numbers. | Grade 2 |
| California | 2.OA.3 | Determine whether a group of objects (up to 20) has an odd or even number of members, e.g., by pairing objects or counting them by 2s; write an equation to express an even number as a sum of two equal addends. | Grade 2 |
| California | 2.OA.4 | Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends. | Grade 2 |
| California | 3.G.1 | Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories. | Grade 3 |
| California | 3.G.2 | Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole. | Grade 3 |
| California | 3.MD.1 | Tell and write time to the nearest minute and measure time intervals in minutes. Solve word problems involving addition and subtraction of time intervals in minutes, e.g., by representing the problem on a number line diagram. | Grade 3 |
| California | 3.MD.2 | Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l). Add, subtract, multiply, or divide to solve one-step word problems involving masses or volumes that are given in the same units, e.g., by using drawings (such as a beaker with a measurement scale) to represent the problem. | Grade 3 |
| California | 3.MD.3 | Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and two-step “how many more” and “how many less” problems using information presented in scaled bar graphs. | Grade 3 |
| California | 3.MD.4 | Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Show the data by making a line plot, where the horizontal scale is marked off in appropriate units-whole numbers, halves, or quarters. | Grade 3 |
| California | 3.MD.5 | Recognize area as an attribute of plane figures and understand concepts of area measurement. | Grade 3 |
| California | 3.MD.6 | Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units). | Grade 3 |
| California | 3.MD.7 | Relate area to the operations of multiplication and addition. | Grade 3 |
| California | 3.MD.8 | Solve real world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters. | Grade 3 |
| California | 3.NBT.1 | Use place value understanding to round whole numbers to the nearest 10 or 100. | Grade 3 |
| California | 3.NBT.2 | Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction. | Grade 3 |
| California | 3.NBT.3 | Multiply one-digit whole numbers by multiples of 10 in the range 10–90 (e.g., 9 × 80, 5 × 60) using strategies based on place value and properties of operations. | Grade 3 |
| California | 3.NF.1 | Understand a fraction 1/𝘣 as the quantity formed by 1 part when a whole is partitioned into 𝘣 equal parts; understand a fraction 𝘢/𝑏 as the quantity formed by 𝘢 parts of size 1/𝘣. | Grade 3 |
| California | 3.NF.2 | Understand a fraction as a number on the number line; represent fractions on a number line diagram. | Grade 3 |
| California | 3.NF.3 | Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size. | Grade 3 |
| California | 3.OA.1 | Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each. | Grade 3 |
| California | 3.OA.2 | Interpret whole-number quotients of whole numbers, e.g., interpret 56 ÷ 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each. | Grade 3 |
| California | 3.OA.3 | Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem. | Grade 3 |
| California | 3.OA.4 | Determine the unknown whole number in a multiplication or division equation relating three whole numbers. | Grade 3 |
| California | 3.OA.5 | Apply properties of operations as strategies to multiply and divide. | Grade 3 |
| California | 3.OA.6 | Understand division as an unknown-factor problem. | Grade 3 |
| California | 3.OA.7 | Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 × 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers. | Grade 3 |
| California | 3.OA.8 | Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. | Grade 3 |
| California | 3.OA.9 | Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations. | Grade 3 |
| California | 4.G.1 | Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures. | Grade 4 |
| California | 4.G.2 | Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles. (Two-dimensional shapes should include special triangles, e.g., equilateral, isosceles, scalene, and special quadrilaterals, e.g., rhombus, square, rectangle, parallelogram, trapezoid.) | Grade 4 |
| California | 4.G.3 | Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify line-symmetric figures and draw lines of symmetry. | Grade 4 |
| California | 4.MD.1 | Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table. | Grade 4 |
| California | 4.MD.2 | Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. | Grade 4 |
| California | 4.MD.3 | Apply the area and perimeter formulas for rectangles in real-world and mathematical problems. | Grade 4 |
| California | 4.MD.4 | Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots. | Grade 4 |
| California | 4.MD.5 | Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement: | Grade 4 |
| California | 4.MD.6 | Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure. | Grade 4 |
| California | 4.MD.7 | Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real-world and mathematical problems, e.g., by using an equation with a symbol for the unknown angle measure. | Grade 4 |
| California | 4.NBT.1 | Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. | Grade 4 |
| California | 4.NBT.2 | Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. | Grade 4 |
| California | 4.NBT.3 | Use place value understanding to round multi-digit whole numbers to any place. | Grade 4 |
| California | 4.NBT.4 | Fluently add and subtract multi-digit whole numbers using the standard algorithm. | Grade 4 |
| California | 4.NBT.5 | Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. | Grade 4 |
| California | 4.NBT.6 | Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. | Grade 4 |
| California | 4.NF.1 | Explain why a fraction 𝘢/𝘣 is equivalent to a fraction (𝘯 × 𝘢)/(𝘯 × 𝘣) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. | Grade 4 |
| California | 4.NF.2 | Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model. | Grade 4 |
| California | 4.NF.3 | Understand a fraction 𝘢/𝘣 with 𝘢 > 1 as a sum of fractions 1/𝘣. | Grade 4 |
| California | 4.NF.4 | Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. | Grade 4 |
| California | 4.NF.5 | Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100. | Grade 4 |
| California | 4.NF.6 | Use decimal notation for fractions with denominators 10 or 100. | Grade 4 |
| California | 4.NF.7 | Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using the number line or another visual model. | Grade 4 |
| California | 4.OA.1 | Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 × 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations. | Grade 4 |
| California | 4.OA.2 | Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison. | Grade 4 |
| California | 4.OA.3 | Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. | Grade 4 |
| California | 4.OA.4 | Find all factor pairs for a whole number in the range 1-100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1-100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1-100 is prime or composite. | Grade 4 |
| California | 4.OA.5 | Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. | Grade 4 |
| California | 5.G.1 | Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., 𝘹-axis and 𝘹-coordinate, 𝘺-axis and 𝘺-coordinate). | Grade 5 |
| California | 5.G.2 | Represent real-world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. | Grade 5 |
| California | 5.G.3 | Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. | Grade 5 |
| California | 5.G.4 | Classify two-dimensional figures in a hierarchy based on properties. | Grade 5 |
| California | 5.MD.1 | Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real-world problems. | Grade 5 |
| California | 5.MD.2 | Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. | Grade 5 |
| California | 5.MD.3 | Recognize volume as an attribute of solid figures and understand concepts of volume measurement. | Grade 5 |
| California | 5.MD.4 | Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. | Grade 5 |
| California | 5.MD.5 | Relate volume to the operations of multiplication and addition and solve real-world and mathematical problems involving volume. | Grade 5 |
| California | 5.NBT.1 | Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. | Grade 5 |
| California | 5.NBT.2 | Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. | Grade 5 |
| California | 5.NBT.3 | Read, write, and compare decimals to thousandths. | Grade 5 |
| California | 5.NBT.4 | Use place value understanding to round decimals to any place. | Grade 5 |
| California | 5.NBT.5 | Fluently multiply multi-digit whole numbers using the standard algorithm. | Grade 5 |
| California | 5.NBT.6 | Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. | Grade 5 |
| California | 5.NBT.7 | Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. | Grade 5 |
| California | 5.NF.1 | Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. | Grade 5 |
| California | 5.NF.2 | Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. | Grade 5 |
| California | 5.NF.3 | Interpret a fraction as division of the numerator by the denominator (𝘢/𝘣 = 𝘢 ÷ 𝘣). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. | Grade 5 |
| California | 5.NF.4 | Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. | Grade 5 |
| California | 5.NF.5 | Interpret multiplication as scaling (resizing), by: | Grade 5 |
| California | 5.NF.6 | Solve real-world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. | Grade 5 |
| California | 5.NF.7 | Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. | Grade 5 |
| California | 5.OA.1 | Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. | Grade 5 |
| California | 5.OA.2 | Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. | Grade 5 |
| California | 5.OA.3 | Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. | Grade 5 |
| California | 6.EE.1 | Write and evaluate numerical expressions involving whole-number exponents. | Grade 6 |
| California | 6.EE.2 | Write, read, and evaluate expressions in which letters stand for numbers. | Grade 6 |
| California | 6.EE.3 | Apply the properties of operations to generate equivalent expressions. | Grade 6 |
| California | 6.EE.4 | Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). | Grade 6 |
| California | 6.EE.5 | Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true. | Grade 6 |
| California | 6.EE.6 | Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set. | Grade 6 |
| California | 6.EE.7 | Solve real-world and mathematical problems by writing and solving equations of the form 𝘹 + 𝘱 = 𝘲 and 𝘱𝘹 = 𝘲 for cases in which 𝘱, 𝘲 and 𝘹 are all nonnegative rational numbers. | Grade 6 |
| California | 6.EE.8 | Write an inequality of the form 𝘹 > 𝘤 or 𝘹 𝘤 or 𝘹 < 𝘤 have infinitely many solutions; represent solutions of such inequalities on number line diagrams. | Grade 6 |
| California | 6.EE.9 | Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. | Grade 6 |
| California | 6.G.1 | Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems. | Grade 6 |
| California | 6.G.2 | Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas 𝘝 = 𝘭 𝘸 𝘩 and 𝘝 = 𝘣 𝘩 to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems. | Grade 6 |
| California | 6.G.3 | Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems. | Grade 6 |
| California | 6.G.4 | Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems. | Grade 6 |
| California | 6.RP.1 | Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. | Grade 6 |
| California | 6.RP.2 | Understand the concept of a unit rate 𝘢/𝘣 associated with a ratio 𝘢:𝘣 with 𝘣 ≠ 0, and use rate language in the context of a ratio relationship. | Grade 6 |
| California | 6.RP.3 | Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. | Grade 6 |
| California | 6.SP.5 | Summarize numerical data sets in relation to their context, such as by: | Grade 6 |
| California | 6.NS.1 | Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. | Grade 6 |
| California | 6.NS.2 | Fluently divide multi-digit numbers using the standard algorithm. | Grade 6 |
| California | 6.NS.3 | Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation. | Grade 6 |
| California | 6.NS.5 | Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation. | Grade 6 |
| California | 6.NS.6 | Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates. | Grade 6 |
| California | 6.NS.7 | Understand ordering and absolute value of rational numbers. | Grade 6 |
| California | 6.NS.8 | Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. | Grade 6 |
| California | 7.EE.1 | Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients. | Grade 7 |
| California | 7.EE.2 | Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. | Grade 7 |
| California | 7.EE.3 | Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. | Grade 7 |
| California | 7.EE.4 | Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. | Grade 7 |
| California | 7.G.1 | Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale. | Grade 7 |
| California | 7.G.2 | Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle. | Grade 7 |
| California | 7.G.3 | Describe the two-dimensional figures that result from slicing three-dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids. | Grade 7 |
| California | 7.G.4 | Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle. | Grade 7 |
| California | 7.G.5 | Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure. | Grade 7 |
| California | 7.G.6 | Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. | Grade 7 |
| California | 7.RP.1 | Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. | Grade 7 |
| California | 7.RP.2 | Recognize and represent proportional relationships between quantities. | Grade 7 |
| California | 7.RP.3 | Use proportional relationships to solve multistep ratio and percent problems. | Grade 7 |
| California | 7.NS.1 | Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram. | Grade 7 |
| California | 7.NS.2 | Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers. | Grade 7 |
| California | 7.NS.3 | Solve real-world and mathematical problems involving the four operations with rational numbers. | Grade 7 |
| California | 8.EE.1 | Know and apply the properties of integer exponents to generate equivalent numerical expressions. | Grade 8 |
| California | 8.EE.2 | Use square root and cube root symbols to represent solutions to equations of the form 𝘹² = 𝘱 and 𝘹³ = 𝘱, where 𝘱 is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that √2 is irrational. | Grade 8 |
| California | 8.EE.3 | Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other. | Grade 8 |
| California | 8.EE.4 | Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology. | Grade 8 |
| California | 8.EE.5 | Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. | Grade 8 |
| California | 8.EE.6 | Use similar triangles to explain why the slope 𝘮 is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation 𝘺 = 𝘮𝘹 for a line through the origin and the equation 𝘺 = 𝘮𝘹 + 𝘣 for a line intercepting the vertical axis at 𝘣. | Grade 8 |
| California | 8.EE.7 | Solve linear equations in one variable. | Grade 8 |
| California | 8.EE.8 | Analyze and solve pairs of simultaneous linear equations. | Grade 8 |
| California | 8.F.1 | Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output. | Grade 8 |
| California | 8.F.2 | Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). | Grade 8 |
| California | 8.F.3 | Interpret the equation 𝘺 = 𝘮𝘹 + 𝘣 as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. | Grade 8 |
| California | 8.F.4 | Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (𝘹, 𝘺) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values. | Grade 8 |
| California | 8.F.5 | Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally. | Grade 8 |
| California | 8.G.1 | Verify experimentally the properties of rotations, reflections, and translations: | Grade 8 |
| California | 8.G.2 | Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them. | Grade 8 |
| California | 8.G.3 | Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates. | Grade 8 |
| California | 8.G.4 | Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two-dimensional figures, describe a sequence that exhibits the similarity between them. | Grade 8 |
| California | 8.G.5 | Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. | Grade 8 |
| California | 8.G.7 | Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions. | Grade 8 |
| California | 8.G.8 | Apply the Pythagorean Theorem to find the distance between two points in a coordinate system. | Grade 8 |
| California | 8.G.9 | Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems. | Grade 8 |
| California | 8.SP.1 | Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association. | Grade 8 |
| California | 8.SP.2 | Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line. | Grade 8 |
| California | 8.NS.2 | Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g., π²). | Grade 8 |
| California | A-SSE.2 | Use the structure of an expression to identify ways to rewrite it. | Algebra I |
| California | A-SSE.3 | Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression. | Algebra I |
| California | A-CED.2 | Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. | Algebra I |
| California | A-CED.3 | Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context. | Algebra I |
| California | A-REI.3 | Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. | Algebra I |
| California | F-IF.2 | Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. | Algebra I |
| California | F-IF.4 | For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. | Algebra I |
| California | F-IF.7 | Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. | Algebra I |
| California | F-BF.1 | Write a function that describes a relationship between two quantities. | Algebra I |
| California | S-ID.6 | Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. | Algebra I |
| Colorado | K.CC.A.1 | Count to 100 by ones and by tens. | Kindergarten |
| Colorado | K.CC.A.2 | Count forward beginning from a given number within the known sequence (instead of having to begin at 1). | Kindergarten |
| Colorado | K.CC.A.3 | Write numbers from 0 to 20. Represent a number of objects with a written numeral 0–20 (with 0 representing a count of no objects). | Kindergarten |
| Colorado | K.CC.B.4 | Apply the relationship between numbers and quantities and connect counting to cardinality. | Kindergarten |
| Colorado | K.CC.B.5 | Count to answer “how many?” questions about as many as 20 things arranged in a line, a rectangular array, or a circle, or as many as 10 things in a scattered configuration; given a number from 1–20, count out that many objects. | Kindergarten |
| Colorado | K.CC.C.6 | Identify whether the number of objects in one group is greater than, less than, or equal to the number of objects in another group, e.g., by using matching and counting strategies. (Include groups with up to 10 objects.) | Kindergarten |
| Colorado | K.CC.C.7 | Compare two numbers between 1 and 10 presented as written numerals. | Kindergarten |
| Colorado | K.NBT.A.1 | Compose and decompose numbers from 11 to 19 into ten ones and some further ones, e.g., by using objects or drawings, and record each composition or decomposition by a drawing or equation (such as 18 = 10 + 8); understand that these numbers are composed of ten ones and one, two, three, four, five, six, seven, eight, or nine ones. | Kindergarten |
| Colorado | K.OA.A.1 | Represent addition and subtraction with objects, fingers, mental images, drawings (drawings need not show details, but should show the mathematics in the problem), sounds (e.g., claps), acting out situations, verbal explanations, expressions, or equations. | Kindergarten |
| Colorado | K.OA.A.2 | Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem. | Kindergarten |
| Colorado | K.OA.A.3 | Decompose numbers less than or equal to 10 into pairs in more than one way, e.g., by using objects or drawings, and record each decomposition by a drawing or equation (e.g., 5 = 2 + 3 and 5 = 4 + 1). | Kindergarten |
| Colorado | K.OA.A.4 | For any number from 1 to 9, find the number that makes 10 when added to the given number, e.g., by using objects or drawings, and record the answer with a drawing or equation. | Kindergarten |
| Colorado | K.OA.A.5 | Fluently add and subtract within 5. | Kindergarten |
| Colorado | K.MD.A.1 | Describe measurable attributes of objects, such as length or weight. Describe several measurable attributes of a single object. | Kindergarten |
| Colorado | K.MD.A.2 | Directly compare two objects with a measurable attribute in common, to see which object has “more of”/“less of” the attribute, and describe the difference. For example, directly compare the heights of two children and describe one child as taller/shorter. | Kindergarten |
| Colorado | K.MD.B.3 | Classify objects into given categories; count the numbers of objects in each category and sort the categories by count. (Limit category counts to be less than or equal to 10.) | Kindergarten |
| Colorado | K.G.A.1 | Describe objects in the environment using names of shapes, and describe the relative positions of these objects using terms such as above, below, beside, in front of, behind, and next to. | Kindergarten |
| Colorado | K.G.A.2 | Correctly name shapes regardless of their orientations or overall size. | Kindergarten |
| Colorado | K.G.A.3 | Identify shapes as two-dimensional (lying in a plane, “flat”) or threedimensional (“solid”). | Kindergarten |
| Colorado | K.G.B.4 | Analyze and compare two- and three-dimensional shapes, in different sizes and orientations, using informal language to describe their similarities, differences, parts (e.g., number of sides and vertices/“corners”) and other attributes (e.g., having sides of equal length). | Kindergarten |
| Colorado | K.G.B.6 | Compose simple shapes to form larger shapes. For example, “Can you join these two triangles with full sides touching to make a rectangle? | Kindergarten |
| Colorado | 1.NBT.A.1 | Count to 120, starting at any number less than 120. In this range, read and write numerals and represent a number of objects with a written numeral. | Grade 1 |
| Colorado | 1.NBT.B.2 | Understand that the two digits of a two-digit number represent amounts of tens and ones. | Grade 1 |
| Colorado | 1.NBT.B.3 | Compare two two-digit numbers based on meanings of the tens and ones digits, recording the results of comparisons with the symbols >, =, and <. | Grade 1 |
| Colorado | 1.NBT.C.4 | Add within 100, including adding a two-digit number and a one-digit number, and adding a two-digit number and a multiple of 10, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Understand that in adding two-digit numbers, one adds tens and tens, ones and ones; and sometimes it is necessary to compose a ten. | Grade 1 |
| Colorado | 1.NBT.C.5 | Given a two-digit number, mentally find 10 more or 10 less than the number, without having to count; explain the reasoning used. | Grade 1 |
| Colorado | 1.NBT.C.6 | Subtract multiples of 10 in the range 10–90 from multiples of 10 in the range 10–90 (positive or zero differences), using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy toa. written method and explain the reasoning used. | Grade 1 |
| Colorado | 1.OA.A.1 | Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem. | Grade 1 |
| Colorado | 1.OA.B.3 | Apply properties of operations as strategies to add and subtract. (Students need not use formal terms for these properties.) Examples: If 8 + 3 = 11 is known, then 3 + 8 = 11 is also known. (Commutative property of addition.) To add 2 + 6 + 4, the second two numbers can be added to make a ten, so 2 + 6 + 4 = 2 + 10 = 12. (Associative property of addition.) ( | Grade 1 |
| Colorado | 1.OA.B.4 | Understand subtraction as an unknown-addend problem. For example, subtract 10 − 8 by finding the number that makes 10 when added to 8. | Grade 1 |
| Colorado | 1.OA.C.5 | Relate counting to addition and subtraction (e.g., by counting on 2 to add 2). | Grade 1 |
| Colorado | 1.OA.C.6 | Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to a ten (e.g., 13 − 4 = 13 − 3 − 1 = 10 − 1 = 9); using the relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 − 8 = 4); and creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13). | Grade 1 |
| Colorado | 1.OA.D.7 | Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false. For example, which of the following equations are true and which are false? 6 = 6, 7 = 8 − 1, 5 + 2 = 2 + 5, 4 + 1 = 5 + 2 | Grade 1 |
| Colorado | 1.OA.D.8 | Determine the unknown whole number in an addition or subtraction equation relating three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations 8 + ? = 11, 5 = _- 3, 6 + 6 = _. | Grade 1 |
| Colorado | 1.MD.A.1 | Order three objects by length; compare the lengths of two objects indirectly by using a third object. | Grade 1 |
| Colorado | 1.MD.A.2 | Express the length of an object as a whole number of length units, by laying multiple copies of a shorter object (the length unit) end to end; understand that the length measurement of an object is the number of same-size length units that span it with no gaps or overlaps. Limit to contexts where the object being measured is spanned by a whole number of length units with no gaps or overlaps. | Grade 1 |
| Colorado | 1.MD.B.3 | Tell and write time in hours and half-hours using analog and digital clocks. | Grade 1 |
| Colorado | 1.MD.C.4 | Organize, represent, and interpret data with up to three categories; ask and answer questions about the total number of data points, how many in each category, and how many more or less are in one category than in another. | Grade 1 |
| Colorado | 1.G.A.1 | Distinguish between defining attributes (e.g., triangles are closed and threesided) versus non-defining attributes (e.g., color, orientation, overall size); build and draw shapes to possess defining attributes. | Grade 1 |
| Colorado | 1.G.A.2 | Compose two-dimensional shapes (rectangles, squares, trapezoids, triangles, half-circles, and quarter-circles) or three-dimensional shapes (cubes, right rectangular prisms, right circular cones, and right circular cylinders) to create a composite shape, and compose new shapes from the composite shape. (Students do not need to learn formal names, such as “right rectangular prisms.”) | Grade 1 |
| Colorado | 1.G.A.3 | Partition circles and rectangles into two and four equal shares, describe the shares using the words halves, fourths, and quarters, and use the phrases half of, fourth of, and quarter of. Describe the whole as two of, or four of the shares. Understand for these examples that decomposing into more equal shares creates smaller shares. | Grade 1 |
| Colorado | 2.NBT.A.1 | Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones. | Grade 2 |
| Colorado | 2.NBT.A.2 | Count within 1000; skip-count by 5s, 10s, and 100s. | Grade 2 |
| Colorado | 2.NBT.A.3 | Read and write numbers to 1000 using base-ten numerals, number names, and expanded form. | Grade 2 |
| Colorado | 2.NBT.A.4 | Compare two three-digit numbers based on meanings of the hundreds, tens, and ones digits, using >, =, and < symbols to record the results of comparisons. | Grade 2 |
| Colorado | 2.NBT.B.5 | Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction. | Grade 2 |
| Colorado | 2.NBT.B.6 | Add up to four two-digit numbers using strategies based on place value and properties of operations. | Grade 2 |
| Colorado | 2.NBT.B.7 | Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method. Understand that in adding or subtracting three-digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds. | Grade 2 |
| Colorado | 2.NBT.B.8 | Mentally add 10 or 100 to a given number 100–900, and mentally subtract 10 or 100 from a given number 100–900. | Grade 2 |
| Colorado | 2.OA.A.1 | Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem. | Grade 2 |
| Colorado | 2.OA.B.2 | Fluently add and subtract within 20 using mental strategies. (See 1.OA.C.6 for a list of strategies.) By end of Grade 2, know from memory all sums of two one-digit numbers. | Grade 2 |
| Colorado | 2.OA.C.3 | Determine whether a group of objects (up to 20) has an odd or even number of members, e.g., by pairing objects or counting them by 2s; write an equation to express an even number as a sum of two equal addends. | Grade 2 |
| Colorado | 2.OA.C.4 | Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends. | Grade 2 |
| Colorado | 2.MD.A.1 | Measure the length of an object by selecting and using appropriate tools such as rulers, yardsticks, meter sticks, and measuring tapes. | Grade 2 |
| Colorado | 2.MD.A.2 | Measure the length of an object twice, using length units of different lengths for the two measurements; describe how the two measurements relate to the size of the unit chosen. | Grade 2 |
| Colorado | 2.MD.A.4 | Measure to determine how much longer one object is than another, expressing the length difference in terms of a standard length unit. | Grade 2 |
| Colorado | 2.MD.B.5 | Use addition and subtraction within 100 to solve word problems involving lengths that are given in the same units, e.g., by using drawings (such as drawings of rulers) and equations with a symbol for the unknown number to represent the problem. | Grade 2 |
| Colorado | 2.MD.C.7 | Tell and write time from analog and digital clocks to the nearest five minutes, using a.m. and p.m. | Grade 2 |
| Colorado | 2.MD.C.8 | Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies, using $ and ¢ symbols appropriately. | Grade 2 |
| Colorado | 2.MD.D.9 | Generate measurement data by measuring lengths of several objects to the nearest whole unit, or by making repeated measurements of the same object. Show the measurements by making a line plot, where the horizontal scale is marked off in whole-number units. | Grade 2 |
| Colorado | 2.MD.D.10 | Draw a picture graph and a bar graph (with single-unit scale) to represent a data set with up to four categories. Solve simple put-together, take-apart, and compare problems (see Appendix, Table 1) using information presented in a bar graph. | Grade 2 |
| Colorado | 2.G.A.1 | Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces. (Sizes are compared directly or visually, not compared by measuring.) Identify triangles, quadrilaterals, pentagons, hexagons, and cubes. | Grade 2 |
| Colorado | 2.G.A.2 | Partition a rectangle into rows and columns of same-size squares and count to find the total number of them. | Grade 2 |
| Colorado | 2.G.A.3 | Partition circles and rectangles into two, three, or four equal shares, describe the shares using the words halves, thirds, half of, a third of, etc., and describe the whole as two halves, three thirds, four fourths. Recognize that equal shares of identical wholes need not have the same shape. | Grade 2 |
| Colorado | 3.NBT.A.1 | Use place value understanding to round whole numbers to the nearest 10 or 100. | Grade 3 |
| Colorado | 3.NBT.A.2 | Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction. | Grade 3 |
| Colorado | 3.NBT.A.3 | Multiply one-digit whole numbers by multiples of 10 in the range 10-90 (e.g., 9 × 80, 5 × 60) using strategies based on place value and properties of operations. | Grade 3 |
| Colorado | 3.NF.A.1 | Describe a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into 𝑏 equal parts; understand a fraction 𝑎/𝑏 as the quantity formed by 𝑎 parts of size 1 𝑏. | Grade 3 |
| Colorado | 3.NF.A.2 | Describe a fraction as a number on the number line; represent fractions on a number line diagram. | Grade 3 |
| Colorado | 3.NF.A.3 | Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size. | Grade 3 |
| Colorado | 3.OA.A.1 | Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each. For example, describe a context in which a total number of objects can be expressed as 5 × 7. | Grade 3 |
| Colorado | 3.OA.A.2 | Interpret whole-number quotients of whole numbers, e.g., interpret 56 + 8 as the number of objects in each share when 56 objects are partitioned into equal shares of 8 objects each. For example, describe a context in which a number of shares or a number of groups can be expressed as 56 / 8. | Grade 3 |
| Colorado | 3.OA.A.3 | Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem. | Grade 3 |
| Colorado | 3.OA.A.4 | Determine the unknown whole number in a multiplication or division equation relating three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations 8 × ? = 48, 5 = _ ÷ 3, 6 × 6 =? ( | Grade 3 |
| Colorado | 3.OA.B.5 | Apply properties of operations as strategies to multiply and divide. (Students need not use formal terms for these properties.) Examples: If 6 × 4 = 24 is known, then 4 × 6 = 24 is also known. (Commutative property of multiplication.) 3 × 5 × 2 can be found by 3 × 5 = 15, then 15 × 2 = 30, or by 5 × 2 = 10, then 3 × 10 = 30. (Associative property of multiplication.) Knowing that 8 × 5 = 40 and 8 × 2 = 16, one can find 8 × 7 as 8 × (5 + 2) = (8 × 5) + (8 × 2) = 40 + 16 = 56. (Distributive property.) (CCSS: 3.OA.B.5) | Grade 3 |
| Colorado | 3.OA.B.6 | Interpret division as an unknown-factor problem. For example, find 32 ÷ 8 by finding the number that makes 32 when multiplied by 8. | Grade 3 |
| Colorado | 3.OA.C.7 | Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 × 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers. | Grade 3 |
| Colorado | 3.OA.D.8 | Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. (This evidence outcome is limited to problems posed with whole numbers and having whole-number answers; students should know how to perform operations in the conventional order of operations when there are no parentheses to specify a particular order.) | Grade 3 |
| Colorado | 3.OA.D.9 | Identify arithmetic patterns (including patterns in the addition table or multiplication table) and explain them using properties of operations. For example, observe that 4 times a number is always even, and explain why 4 times a number can be decomposed into two equal addends. | Grade 3 |
| Colorado | 3.MD.A.1 | Tell and write time to the nearest minute and measure time intervals in minutes. Solve word problems involving addition and subtraction of time intervals in minutes, e.g., by representing the problem on a number line diagram. | Grade 3 |
| Colorado | 3.MD.A.2 | Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l). (This excludes compound units such as cm3 and finding the geometric volume of a container.) Add, subtract, multiply, or divide to solve one-step word problems involving masses or volumes that are given in the same units, e.g., by using drawings (such as a beaker with a measurement scale) to represent the problem. (This excludes multiplicative comparison problems, such as problems involving notions of “times as much.” See Appendix, Table 2.) | Grade 3 |
| Colorado | 3.MD.B.3 | Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and two-step “how many more” and “how many less” problems using information presented in scaled bar graphs. For example, draw a bar graph in which each square in the bar graph might represent 5 pets. | Grade 3 |
| Colorado | 3.MD.B.4 | Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Show the data by making a line plot, where the horizontal scale is marked off in appropriate units—whole numbers, halves, or quarters. | Grade 3 |
| Colorado | 3.MD.C.5 | Recognize area as an attribute of plane figures and understand concepts of area measurement. | Grade 3 |
| Colorado | 3.MD.C.6 | Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units). | Grade 3 |
| Colorado | 3.MD.C.7 | Use concepts of area and relate area to the operations of multiplication and addition. | Grade 3 |
| Colorado | 3.MD.D.8 | Solve real-world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters. | Grade 3 |
| Colorado | 3.G.A.1 | Explain that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belond to any of these subcategories. | Grade 3 |
| Colorado | 3.G.A.2 | Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole. For example, partition a shape into 4 parts with equal area, and describe the area of each part as 1 4 of the area of the shape. | Grade 3 |
| Colorado | 4.NBT.A.1 | Explain that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. For example, recognize that 700 + 70 = 10 by applying concepts of place value and division. | Grade 4 |
| Colorado | 4.NBT.A.2 | Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. | Grade 4 |
| Colorado | 4.NBT.A.3 | Use place value understanding to round multi-digit whole numbers to any place. | Grade 4 |
| Colorado | 4.NBT.B.4 | Fluently add and subtract multi-digit whole numbers using the standard algorithm. | Grade 4 |
| Colorado | 4.NBT.B.5 | Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. | Grade 4 |
| Colorado | 4.NBT.B.6 | Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. | Grade 4 |
| Colorado | 4.NF.A.1 | Explain why a fraction 𝑎/ 𝑏 is equivalent to a fraction 𝑛×𝑎 𝑛×𝑏 by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. | Grade 4 |
| Colorado | 4.NF.A.2 | Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, and <, and justify the conclisions, e.g., by using a visual fraction model. | Grade 4 |
| Colorado | 4.NF.B.3 | Understand a fraction 𝑎/𝑏 with 𝑎 > 1 as a sum of fractions 1 𝑏 . | Grade 4 |
| Colorado | 4.NF.B.4 | Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. | Grade 4 |
| Colorado | 4.NF.C.5 | Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100. (Students who can generate equivalent fractions can develop strategies for adding fractions with unlike denominators in general. But addition and subtraction with unlike denominators in general is not a requirement at this grade.) For example, express 3/10 as 30/100, and add 3/10 + 4/100 = 34/100. | Grade 4 |
| Colorado | 4.NF.C.6 | Use decimal notation for fractions with denominators 10 or 100. For example, rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram. | Grade 4 |
| Colorado | 4.NF.C.7 | Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual model. | Grade 4 |
| Colorado | 4.OA.A.1 | Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 × 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations | Grade 4 |
| Colorado | 4.OA.A.2 | Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison. | Grade 4 |
| Colorado | 4.OA.A.3 | Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. | Grade 4 |
| Colorado | 4.OA.B.4 | Find all factor pairs for a whole number in the range 1–100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1–100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1–100 is prime or composite. | Grade 4 |
| Colorado | 4.OA.C.5 | Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself | Grade 4 |
| Colorado | 4.MD.A.1 | Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table. For example, know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1,12), (2,24), (3,36), | Grade 4 |
| Colorado | 4.MD.A.2 | Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. | Grade 4 |
| Colorado | 4.MD.A.3 | Apply the area and perimeter formulas for rectangles in real-world and mathematical problems. For example, find the width of a rectangular room given the area of the flooring and the length, by viewing the area formula as a multiplication equation with an unknown factor. | Grade 4 |
| Colorado | 4.MD.B.4 | Make a line plot to display a data set of measurements in fractions of a unit ( 1/2 , 1/4 , 1/8 ). Solve problems involving addition and subtraction of fractions by using information presented in line plots. For example, from a line plot find and interpret the difference in length between the longest and shortest specimens in an insect collection. | Grade 4 |
| Colorado | 4.MD.C.5 | Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement. | Grade 4 |
| Colorado | 4.MD.C.6 | Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure. | Grade 4 |
| Colorado | 4.MD.C.7 | Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real-world and mathematical problems, e.g., by using an equation with a symbol for the unknown angle measure. | Grade 4 |
| Colorado | 4.G.A.1 | Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures. | Grade 4 |
| Colorado | 4.G.A.2 | Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles. | Grade 4 |
| Colorado | 4.G.A.3 | Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify line-symmetric figures and draw lines of symmetry. | Grade 4 |
| Colorado | 5.NBT.A.1 | Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. | Grade 5 |
| Colorado | 5.NBT.A.2 | Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. | Grade 5 |
| Colorado | 5.NBT.A.3 | Read, write, and compare decimals to thousandths. | Grade 5 |
| Colorado | 5.NBT.A.4 | Use place value understanding to round decimals to any place. | Grade 5 |
| Colorado | 5.NBT.B.5 | Fluently multiply multi-digit whole numbers using the standard algorithm. | Grade 5 |
| Colorado | 5.NBT.B.6 | Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. | Grade 5 |
| Colorado | 5.NBT.B.7 | Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. | Grade 5 |
| Colorado | 5.NF.A.1 | Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. | Grade 5 |
| Colorado | 5.NF.A.2 | Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/? by observing that 3/7 < 1/2. | Grade 5 |
| Colorado | 5.NF.B.3 | Interpret a fraction as division of the numerator by the denominator (𝑎/𝑏 = 𝑎 ÷ 𝑏). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4 . If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie? | Grade 5 |
| Colorado | 5.NF.B.4 | Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. | Grade 5 |
| Colorado | 5.NF.B.5 | Interpret multiplication as scaling (resizing) by: a) Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication. b) Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence 𝑎/𝑏 = 𝑛×𝑎 𝑛×𝑏 to the effect of multiplying 𝑎/𝑏 by 1. | Grade 5 |
| Colorado | 5.NF.B.6 | Solve real-world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. | Grade 5 |
| Colorado | 5.NF.B.7 | Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. (Students able to multiply fractions in general can develop strategies to divide fractions in general, by reasoning about the relationship between multiplication and division. But division of a fraction by a fraction is not a requirement at this grade.) | Grade 5 |
| Colorado | 5.OA.A.1 | Use grouping symbols (parentheses, brackets, or braces) in numerical expressions, and evaluate expressions with these symbols. | Grade 5 |
| Colorado | 5.OA.A.2 | Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, express the calculation “add 8 and 7, then multiply by 2” as 2 × (8 + 7). Recognize that 3 × (18932 + 921) is three times as large as 18932 + 921, without having to calculate the indicated sum or product. | Grade 5 |
| Colorado | 5.OA.B.3 | Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. For example, given the rule “Add 3” and the starting number 0, and given the rule “Add 6” and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so. | Grade 5 |
| Colorado | 5.MD.A.1 | Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real-world problems. | Grade 5 |
| Colorado | 5.MD.B.2 | Make a line plot to display a data set of measurements in fractions of a unit ( 1/2 , 1/4 , 1/8 ). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally | Grade 5 |
| Colorado | 5.MD.C.3 | Recognize volume as an attribute of solid figures and understand concepts of volume measurement. | Grade 5 |
| Colorado | 5.MD.C.4 | Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. | Grade 5 |
| Colorado | 5.MD.C.5 | Relate volume to the operations of multiplication and addition and solve real-world and mathematical problems involving volume. | Grade 5 |
| Colorado | 5.G.A.1 | Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., 𝑥𝑥-axis and 𝑥𝑥-coordinate, 𝑦𝑦-axis and 𝑦𝑦- coordinate). | Grade 5 |
| Colorado | 5.G.A.2 | Represent real-world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. | Grade 5 |
| Colorado | 5.G.B.3 | Explain that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. | Grade 5 |
| Colorado | 5.G.B.4 | Classify two-dimensional figures in a hierarchy based on properties. | Grade 5 |
| Colorado | 6.RP.A.1 | Apply the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. For example, “The ratio of wings to beaks in the bird house at the zoo was 2: 1, because for every 2 wings there was 1 beak.” “For every vote Candidate 𝐴 received, Candidate 𝐶 received nearly three votes.” | Grade 6 |
| Colorado | 6.RP.A.2 | Apply the concept of a unit rate 𝑎/𝑏 associated with a ratio 𝑎:𝑏 with 𝑏≠ 0, and use rate language in the context of a ratio relationship. For example, “This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3 4 cup of flour for each cup of sugar.” “We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger.” (Expectations for unit rates in this grade are limited to non-complex fractions.) | Grade 6 |
| Colorado | 6.RP.A.3 | Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. | Grade 6 |
| Colorado | 6.NS.A.1 | Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. For example, create a story context for 2/3 ÷ 3/4 and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that 2/3 ÷ 3/4 = 8/9 because 3/4 of 8/9 is 2/3 . (In general, 𝑎/𝑏 ÷ 𝑐/𝑑 = ad/𝑏c .) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4 -cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi? | Grade 6 |
| Colorado | 6.NS.B.2 | Fluently divide multi-digit numbers using the standard algorithm. | Grade 6 |
| Colorado | 6.NS.B.3 | Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation. | Grade 6 |
| Colorado | 6.NS.C.5 | Explain why positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation. | Grade 6 |
| Colorado | 6.NS.C.6 | Describe a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates. | Grade 6 |
| Colorado | 6.NS.C.7 | Order and find absolute value of rational numbers. | Grade 6 |
| Colorado | 6.NS.C.8 | Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. | Grade 6 |
| Colorado | 6.EE.A.1 | Write and evaluate numerical expressions involving whole-number exponents | Grade 6 |
| Colorado | 6.EE.A.2 | Write, read, and evaluate expressions in which letters stand for numbers. | Grade 6 |
| Colorado | 6.EE.A.3 | Apply the properties of operations to generate equivalent expressions. For example, apply the distributive property to the expression 3(2 + 𝑥) to produce the equivalent expression 6 + 3𝑥; apply the distributive property to the expression 24𝑥 + 18𝑦 to produce the equivalent expression 6(4𝑥 + 3𝑦); apply properties of operations to 𝑦 + 𝑦 + 𝑦 to produce the equivalent expression 3𝑦. | Grade 6 |
| Colorado | 6.EE.A.4 | Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). For example, the expressions 𝑦𝑦 + 𝑦𝑦 + 𝑦𝑦 and 3𝑦𝑦 are equivalent because they name the same number regardless of which number 𝑦𝑦 stands for | Grade 6 |
| Colorado | 6.EE.B.5 | Describe solving an equation or inequality as a process of answering a question: Which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true. | Grade 6 |
| Colorado | 6.EE.B.6 | Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; recognize that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set | Grade 6 |
| Colorado | 6.EE.B.7 | Solve real-world and mathematical problems by writing and solving equations of the form 𝑥 ± 𝑝 = 𝑞 and 𝑝x = 𝑞 for cases in which 𝑝, 𝑞 and 𝑥 are all nonnegative rational numbers | Grade 6 |
| Colorado | 6.EE.B.8 | Write an inequality of the form 𝑥 > 𝑐, 𝑥 ≥ 𝑐, 𝑥 𝑐, 𝑥 ≥ 𝑐, 𝑥 < 𝑐, or 𝑥 ≤ 𝑐 have infinitely many solutions; represent solutions of such inequalities on number line diagrams | Grade 6 |
| Colorado | 6.EE.C.9 | Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. For example, in a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation 𝑑 = 65𝑡 to represent the relationship between distance and time | Grade 6 |
| Colorado | 6.SP.B.5 | Summarize numerical data sets in relation to their context, such as by: a) Reporting the number of observations b) Describing the nature of the attribute under investigation, including how it was measured and its units of measurement c) Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered d) Relating the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered | Grade 6 |
| Colorado | 6.G.A.1 | Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems. | Grade 6 |
| Colorado | 6.G.A.2 | Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas 𝑉𝑉 = 𝑙𝑙𝑙𝑙ℎ and 𝑉𝑉 = 𝑏𝑏ℎ to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems. | Grade 6 |
| Colorado | 6.G.A.3 | Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems. | Grade 6 |
| Colorado | 6.G.A.4 | Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems. | Grade 6 |
| Colorado | 7.RP.A.1 | Compute unit rates associated with ratios of fractions, including ratios of lengths, areas, and other quantities measured in like or different units. For example, if a person walks 1/2 mile in each 1/4 hour, compute the unit rate as the complex fraction 1/2 / 1/4 miles per hour, equivalently 2 miles per hour. | Grade 7 |
| Colorado | 7.RP.A.2 | Identify and represent proportional relationships between quantities. | Grade 7 |
| Colorado | 7.RP.A.3 | Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error. | Grade 7 |
| Colorado | 7.NS.A.1 | Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram | Grade 7 |
| Colorado | 7.NS.A.2 | Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers | Grade 7 |
| Colorado | 7.NS.A.3 | Solve real-world and mathematical problems involving the four operations with rational numbers. (Computations with rational numbers extend the rules for manipulating fractions to complex fractions.) | Grade 7 |
| Colorado | 7.EE.A.1 | Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients | Grade 7 |
| Colorado | 7.EE.A.2 | Demonstrate that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. For example, 𝑎 + 0.05𝑎 = 1.05𝑎 means that “increase by 5%” is the same as “multiply by 1.05.” | Grade 7 |
| Colorado | 7.EE.B.3 | Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. For example: If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation | Grade 7 |
| Colorado | 7.EE.B.4 | Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities | Grade 7 |
| Colorado | 7.G.A.1 | Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale. | Grade 7 |
| Colorado | 7.G.A.2 | Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle | Grade 7 |
| Colorado | 7.G.A.3 | Describe the two-dimensional figures that result from slicing threedimensional figures, as in cross sections of right rectangular prisms and right rectangular pyramids | Grade 7 |
| Colorado | 7.G.B.4 | State the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle. | Grade 7 |
| Colorado | 7.G.B.5 | Use facts about supplementary, complementary, vertical, and adjacent angles in a multistep problem to write and solve simple equations for an unknown angle in a figure. | Grade 7 |
| Colorado | 7.G.B.6 | Solve real-world and mathematical problems involving area, volume, and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. | Grade 7 |
| Colorado | 8.NS.A.2 | Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g., 𝜋2). For example, by truncating the decimal expansion of √2, show that √2 is between 1 and 2, then between 1.4 and 1.5, and explain how to continue on to get better approximations | Grade 8 |
| Colorado | 8.EE.A.1 | Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, 3^2 × 3^−5 = 3^−3 = 1/3^3 = 1/27. | Grade 8 |
| Colorado | 8.EE.A.2 | Use square root and cube root symbols to represent solutions to equations of the form 𝑥2 = 𝑝 and 𝑥3 = 𝑝, where 𝑝 is a positive rational number. Evaluate square roots of small perfect squares (up to 100) and cube roots of small perfect cubes (up to 64). Know that √2 is irrational. | Grade 8 |
| Colorado | 8.EE.A.3 | Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other. For example, estimate the population of the United States as 3 times 10^8 and the population of the world as 7 times 10^9, and determine that the world population is more than 20 times larger | Grade 8 |
| Colorado | 8.EE.A.4 | Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology. | Grade 8 |
| Colorado | 8.EE.B.5 | Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance-time graph to a distancetime equation to determine which of two moving objects has greater speed. | Grade 8 |
| Colorado | 8.EE.B.6 | Use similar triangles to explain why the slope 𝑚𝑚 is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation 𝑦 = 𝑚𝑥 for a line through the origin and the equation 𝑦 = 𝑚x + 𝑏 for a line intercepting the vertical axis at b. | Grade 8 |
| Colorado | 8.EE.C.7 | Solve linear equations in one variable. | Grade 8 |
| Colorado | 8.EE.C.8 | Analyze and solve pairs of simultaneous linear equations. | Grade 8 |
| Colorado | 8.F.A.1 | Define a function as a rule that assigns to each input exactly one output. Show that the graph of a function is the set of ordered pairs consisting of an input and the corresponding output. (Function notation is not required for Grade 8.) | Grade 8 |
| Colorado | 8.F.A.2 | Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a linear function represented by a table of values and a linear function represented by an algebraic expression, determine which function has the greater rate of change. | Grade 8 |
| Colorado | 8.F.A.3 | Interpret the equation 𝑦 = 𝑚x + 𝑏 as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. For example, the function 𝐴 = 𝑠^2 giving the area of a square as a function of its side length is not linear because its graph contains the points (1,1), (2,4) and (3,9), which are not on a straight line. | Grade 8 |
| Colorado | 8.F.B.4 | Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (𝑥, 𝑦) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values. | Grade 8 |
| Colorado | 8.F.B.5 | Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally. | Grade 8 |
| Colorado | 8.SP.A.1 | Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association. | Grade 8 |
| Colorado | 8.SP.A.2 | Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line. | Grade 8 |
| Colorado | 8.G.A.1 | Verify experimentally the properties of rotations, reflections, and translations | Grade 8 |
| Colorado | 8.G.A.2 | Demonstrate that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them | Grade 8 |
| Colorado | 8.G.A.3 | Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates | Grade 8 |
| Colorado | 8.G.A.4 | Demonstrate that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two-dimensional figures, describe a sequence that exhibits the similarity between them. | Grade 8 |
| Colorado | 8.G.A.5 | Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. For example, arrange three copies of the same triangle so that the sum of the three angles appears to form a line, and give an argument in terms of transversals why this is so. | Grade 8 |
| Colorado | 8.G.B.7 | Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions | Grade 8 |
| Colorado | 8.G.B.8 | Apply the Pythagorean Theorem to find the distance between two points in a coordinate system | Grade 8 |
| Colorado | 8.G.C.9 | State the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems. | Grade 8 |
| Colorado | A-SSE.A.2 | Use the structure of an expression to identify ways to rewrite it. For example, see 𝑥^4 − 𝑦^4 as (𝑥^2)2 − (𝑦^2)2, thus recognizing it as a difference of squares that can be factored as (𝑥^2 − 𝑦^2)(𝑥^2 + 𝑦^2). | High School |
| Colorado | A-SSE.B.3 | Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression | High School |
| Colorado | A-APR.B.3 | Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial | High School |
| Colorado | A-CED.A.2 | Create equations in two or more variables to represent relationships between quantities and graph equations on coordinate axes with labels and scales | High School |
| Colorado | A-CED.A.3 | Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. For example, represent inequalities describing nutritional and cost constraints on combinations of different foods | High School |
| Colorado | A-REI.B.3 | Look for and make use of structure. | High School |
| Colorado | F-IF.A.2 | Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. | High School |
| Colorado | F-IF.B.4 | For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity | High School |
| Colorado | F-IF.C.7 | Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases | High School |
| Colorado | F-BF.A.1 | Write a function that describes a relationship between two quantities. | High School |
| Colorado | S-ID.B.6 | Represent data on two quantitative variables on a scatter plot, and describe how the variables are related | High School |
| Connecticut | K.CC.A.1 | Count to 100 by ones and by tens. | Kindergarten |
| Connecticut | K.CC.A.2 | Count forward beginning from a given number within the known sequence (instead of having to begin at 1). | Kindergarten |
| Connecticut | K.CC.A.3 | Write numbers from 0 to 20. Represent a number of objects with a written numeral 0-20 (with 0 representing a count of no objects). | Kindergarten |
| Connecticut | K.CC.B.4 | Understand the relationship between numbers and quantities; connect counting to cardinality. | Kindergarten |
| Connecticut | K.CC.B.5 | Count to answer “how many?” questions about as many as 20 things arranged in a line, a rectangular array, or a circle, or as many as 10 things in a scattered configuration; given a number from 1-20, count out that many objects. | Kindergarten |
| Connecticut | K.CC.C.6 | Identify whether the number of objects in one group is greater than, less than, or equal to the number of objects in another group, e.g., by using matching and counting strategies. | Kindergarten |
| Connecticut | K.CC.C.7 | Compare two numbers between 1 and 10 presented as written numerals. | Kindergarten |
| Connecticut | K.G.A.1 | Describe objects in the environment using names of shapes, and describe the relative positions of these objects using terms such as above, below, beside, in front of, behind, and next to. | Kindergarten |
| Connecticut | K.G.A.2 | Correctly name shapes regardless of their orientations or overall size. | Kindergarten |
| Connecticut | K.G.A.3 | Identify shapes as two-dimensional (lying in a plane, “flat”) or three-dimensional (“solid”). | Kindergarten |
| Connecticut | K.G.B.4 | Analyze and compare two- and three-dimensional shapes, in different sizes and orientations, using informal language to describe their similarities, differences, parts (e.g., number of sides and vertices/“corners”) and other attributes (e.g., having sides of equal length). | Kindergarten |
| Connecticut | K.G.B.6 | Compose simple shapes to form larger shapes. | Kindergarten |
| Connecticut | K.MD.A.1 | Describe measurable attributes of objects, such as length or weight. Describe several measurable attributes of a single object. | Kindergarten |
| Connecticut | K.MD.A.2 | Directly compare two objects with a measurable attribute in common, to see which object has “more of”/“less of” the attribute, and describe the difference. | Kindergarten |
| Connecticut | K.MD.B.3 | Classify objects into given categories; count the numbers of objects in each category and sort the categories by count. | Kindergarten |
| Connecticut | K.NBT.A.1 | Compose and decompose numbers from 11 to 19 into ten ones and some further ones, e.g., by using objects or drawings, and record each composition or decomposition by a drawing or equation (e.g., 18 = 10 + 8); understand that these numbers are composed of ten ones and one, two, three, four, five, six, seven, eight, or nine ones. | Kindergarten |
| Connecticut | K.OA.A.1 | Represent addition and subtraction with objects, fingers, mental images, drawings, sounds (e.g., claps), acting out situations, verbal explanations, expressions, or equations. | Kindergarten |
| Connecticut | K.OA.A.2 | Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem. | Kindergarten |
| Connecticut | K.OA.A.3 | Decompose numbers less than or equal to 10 into pairs in more than one way, e.g., by using objects or drawings, and record each decomposition by a drawing or equation (e.g., 5 = 2 + 3 and 5 = 4 + 1). | Kindergarten |
| Connecticut | K.OA.A.4 | For any number from 1 to 9, find the number that makes 10 when added to the given number, e.g., by using objects or drawings, and record the answer with a drawing or equation. | Kindergarten |
| Connecticut | K.OA.A.5 | Fluently add and subtract within 5. | Kindergarten |
| Connecticut | 1.G.A.1 | Distinguish between defining attributes (e.g., triangles are closed and three-sided) versus non-defining attributes (e.g., color, orientation, overall size); build and draw shapes to possess defining attributes. | Grade 1 |
| Connecticut | 1.G.A.2 | Compose two-dimensional shapes (rectangles, squares, trapezoids, triangles, half-circles, and quarter-circles) or three-dimensional shapes (cubes, right rectangular prisms, right circular cones, and right circular cylinders) to create a composite shape, and compose new shapes from the composite shape. | Grade 1 |
| Connecticut | 1.G.A.3 | Partition circles and rectangles into two and four equal shares, describe the shares using the words halves, fourths, and quarters, and use the phrases half of, fourth of, and quarter of. Describe the whole as two of, or four of the shares. Understand for these examples that decomposing into more equal shares creates smaller shares. | Grade 1 |
| Connecticut | 1.MD.A.1 | Order three objects by length; compare the lengths of two objects indirectly by using a third object. | Grade 1 |
| Connecticut | 1.MD.A.2 | Express the length of an object as a whole number of length units, by laying multiple copies of a shorter object (the length unit) end to end; understand that the length measurement of an object is the number of same-size length units that span it with no gaps or overlaps. | Grade 1 |
| Connecticut | 1.MD.B.3 | Tell and write time in hours and half-hours using analog and digital clocks. | Grade 1 |
| Connecticut | 1.MD.C.4 | Organize, represent, and interpret data with up to three categories; ask and answer questions about the total number of data points, how many in each category, and how many more or less are in one category than in another. | Grade 1 |
| Connecticut | 1.NBT.A.1 | Count to 120, starting at any number less than 120. In this range, read and write numerals and represent a number of objects with a written numeral. | Grade 1 |
| Connecticut | 1.NBT.B.2 | Understand that the two digits of a two-digit number represent amounts of tens and ones. | Grade 1 |
| Connecticut | 1.NBT.B.3 | Compare two two-digit numbers based on meanings of the tens and ones digits, recording the results of comparisons with the symbols >, =, and <. | Grade 1 |
| Connecticut | 1.NBT.C.4 | Add within 100, including adding a two-digit number and a one-digit number, and adding a two-digit number and a multiple of 10, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Understand that in adding two-digit numbers, one adds tens and tens, ones and ones; and sometimes it is necessary to compose a ten. | Grade 1 |
| Connecticut | 1.NBT.C.5 | Given a two-digit number, mentally find 10 more or 10 less than the number, without having to count; explain the reasoning used. | Grade 1 |
| Connecticut | 1.NBT.C.6 | Subtract multiples of 10 in the range 10-90 from multiples of 10 in the range 10-90 (positive or zero differences), using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. | Grade 1 |
| Connecticut | 1.OA.A.1 | Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem. | Grade 1 |
| Connecticut | 1.OA.B.3 | Apply properties of operations as strategies to add and subtract. | Grade 1 |
| Connecticut | 1.OA.B.4 | Understand subtraction as an unknown-addend problem. | Grade 1 |
| Connecticut | 1.OA.C.5 | Relate counting to addition and subtraction (e.g., by counting on 2 to add 2). | Grade 1 |
| Connecticut | 1.OA.C.6 | Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to a ten (e.g., 13 - 4 = 13 - 3 - 1 = 10 - 1 = 9); using the relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 - 8 = 4); and creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13). | Grade 1 |
| Connecticut | 1.OA.D.7 | Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false. | Grade 1 |
| Connecticut | 1.OA.D.8 | Determine the unknown whole number in an addition or subtraction equation relating three whole numbers. | Grade 1 |
| Connecticut | 2.G.A.1 | Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces. Identify triangles, quadrilaterals, pentagons, hexagons, and cubes. | Grade 2 |
| Connecticut | 2.G.A.2 | Partition a rectangle into rows and columns of same-size squares and count to find the total number of them. | Grade 2 |
| Connecticut | 2.G.A.3 | Partition circles and rectangles into two, three, or four equal shares, describe the shares using the words halves, thirds, half of, a third of, etc., and describe the whole as two halves, three thirds, four fourths. Recognize that equal shares of identical wholes need not have the same shape. | Grade 2 |
| Connecticut | 2.MD.A.1 | Measure the length of an object by selecting and using appropriate tools such as rulers, yardsticks, meter sticks, and measuring tapes. | Grade 2 |
| Connecticut | 2.MD.A.2 | Measure the length of an object twice, using length units of different lengths for the two measurements; describe how the two measurements relate to the size of the unit chosen. | Grade 2 |
| Connecticut | 2.MD.A.4 | Measure to determine how much longer one object is than another, expressing the length difference in terms of a standard length unit. | Grade 2 |
| Connecticut | 2.MD.B.5 | Use addition and subtraction within 100 to solve word problems involving lengths that are given in the same units, e.g., by using drawings (such as drawings of rulers) and equations with a symbol for the unknown number to represent the problem. | Grade 2 |
| Connecticut | 2.MD.C.7 | Tell and write time from analog and digital clocks to the nearest five minutes, using a.m. and p.m. | Grade 2 |
| Connecticut | 2.MD.C.8 | Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies, using $ and ¢ symbols appropriately. | Grade 2 |
| Connecticut | 2.MD.D.9 | Generate measurement data by measuring lengths of several objects to the nearest whole unit, or by making repeated measurements of the same object. Show the measurements by making a line plot, where the horizontal scale is marked off in whole-number units. | Grade 2 |
| Connecticut | 2.MD.D.10 | Draw a picture graph and a bar graph (with single-unit scale) to represent a data set with up to four categories. Solve simple put-together, take-apart, and compare problems using information presented in a bar graph. | Grade 2 |
| Connecticut | 2.NBT.A.1 | Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones. | Grade 2 |
| Connecticut | 2.NBT.A.2 | Count within 1000; skip-count by 5s, 10s, and 100s. | Grade 2 |
| Connecticut | 2.NBT.A.3 | Read and write numbers to 1000 using base-ten numerals, number names, and expanded form. | Grade 2 |
| Connecticut | 2.NBT.A.4 | Compare two three-digit numbers based on meanings of the hundreds, tens, and ones digits, using >, =, and < symbols to record the results of comparisons. | Grade 2 |
| Connecticut | 2.NBT.B.5 | Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction. | Grade 2 |
| Connecticut | 2.NBT.B.6 | Add up to four two-digit numbers using strategies based on place value and properties of operations. | Grade 2 |
| Connecticut | 2.NBT.B.7 | Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method. Understand that in adding or subtracting three-digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds. | Grade 2 |
| Connecticut | 2.NBT.B.8 | Mentally add 10 or 100 to a given number 100–900, and mentally subtract 10 or 100 from a given number 100–900. | Grade 2 |
| Connecticut | 2.OA.A.1 | Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem. | Grade 2 |
| Connecticut | 2.OA.B.2 | Fluently add and subtract within 20 using mental strategies. By end of Grade 2, know from memory all sums of two one-digit numbers. | Grade 2 |
| Connecticut | 2.OA.C.3 | Determine whether a group of objects (up to 20) has an odd or even number of members, e.g., by pairing objects or counting them by 2s; write an equation to express an even number as a sum of two equal addends. | Grade 2 |
| Connecticut | 2.OA.C.4 | Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends. | Grade 2 |
| Connecticut | 3.G.A.1 | Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories. | Grade 3 |
| Connecticut | 3.G.A.2 | Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole. | Grade 3 |
| Connecticut | 3.MD.A.1 | Tell and write time to the nearest minute and measure time intervals in minutes. Solve word problems involving addition and subtraction of time intervals in minutes, e.g., by representing the problem on a number line diagram. | Grade 3 |
| Connecticut | 3.MD.A.2 | Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l). Add, subtract, multiply, or divide to solve one-step word problems involving masses or volumes that are given in the same units, e.g., by using drawings (such as a beaker with a measurement scale) to represent the problem. | Grade 3 |
| Connecticut | 3.MD.B.3 | Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and two-step “how many more” and “how many less” problems using information presented in scaled bar graphs. | Grade 3 |
| Connecticut | 3.MD.B.4 | Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Show the data by making a line plot, where the horizontal scale is marked off in appropriate units-whole numbers, halves, or quarters. | Grade 3 |
| Connecticut | 3.MD.C.5 | Recognize area as an attribute of plane figures and understand concepts of area measurement. | Grade 3 |
| Connecticut | 3.MD.C.6 | Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units). | Grade 3 |
| Connecticut | 3.MD.C.7 | Relate area to the operations of multiplication and addition. | Grade 3 |
| Connecticut | 3.MD.D.8 | Solve real world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters. | Grade 3 |
| Connecticut | 3.NBT.A.1 | Use place value understanding to round whole numbers to the nearest 10 or 100. | Grade 3 |
| Connecticut | 3.NBT.A.2 | Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction. | Grade 3 |
| Connecticut | 3.NBT.A.3 | Multiply one-digit whole numbers by multiples of 10 in the range 10–90 (e.g., 9 × 80, 5 × 60) using strategies based on place value and properties of operations. | Grade 3 |
| Connecticut | 3.NF.A.1 | Understand a fraction 1/𝘣 as the quantity formed by 1 part when a whole is partitioned into 𝘣 equal parts; understand a fraction 𝘢/𝑏 as the quantity formed by 𝘢 parts of size 1/𝘣. | Grade 3 |
| Connecticut | 3.NF.A.2 | Understand a fraction as a number on the number line; represent fractions on a number line diagram. | Grade 3 |
| Connecticut | 3.NF.A.3 | Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size. | Grade 3 |
| Connecticut | 3.OA.A.1 | Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each. | Grade 3 |
| Connecticut | 3.OA.A.2 | Interpret whole-number quotients of whole numbers, e.g., interpret 56 ÷ 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each. | Grade 3 |
| Connecticut | 3.OA.A.3 | Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem. | Grade 3 |
| Connecticut | 3.OA.A.4 | Determine the unknown whole number in a multiplication or division equation relating three whole numbers. | Grade 3 |
| Connecticut | 3.OA.B.5 | Apply properties of operations as strategies to multiply and divide. | Grade 3 |
| Connecticut | 3.OA.B.6 | Understand division as an unknown-factor problem. | Grade 3 |
| Connecticut | 3.OA.C.7 | Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 × 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers. | Grade 3 |
| Connecticut | 3.OA.D.8 | Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. | Grade 3 |
| Connecticut | 3.OA.D.9 | Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations. | Grade 3 |
| Connecticut | 4.G.A.1 | Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures. | Grade 4 |
| Connecticut | 4.G.A.2 | Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles. | Grade 4 |
| Connecticut | 4.G.A.3 | Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify line-symmetric figures and draw lines of symmetry. | Grade 4 |
| Connecticut | 4.MD.A.1 | Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table. | Grade 4 |
| Connecticut | 4.MD.A.2 | Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. | Grade 4 |
| Connecticut | 4.MD.A.3 | Apply the area and perimeter formulas for rectangles in real world and mathematical problems. | Grade 4 |
| Connecticut | 4.MD.B.4 | Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots. | Grade 4 |
| Connecticut | 4.MD.C.5 | Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement. | Grade 4 |
| Connecticut | 4.MD.C.6 | Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure. | Grade 4 |
| Connecticut | 4.MD.C.7 | Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems, e.g., by using an equation with a symbol for the unknown angle measure. | Grade 4 |
| Connecticut | 4.NBT.A.1 | Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. | Grade 4 |
| Connecticut | 4.NBT.A.2 | Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. | Grade 4 |
| Connecticut | 4.NBT.A.3 | Use place value understanding to round multi-digit whole numbers to any place. | Grade 4 |
| Connecticut | 4.NBT.B.4 | Fluently add and subtract multi-digit whole numbers using the standard algorithm. | Grade 4 |
| Connecticut | 4.NBT.B.5 | Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. | Grade 4 |
| Connecticut | 4.NBT.B.6 | Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. | Grade 4 |
| Connecticut | 4.NF.A.1 | Explain why a fraction 𝘢/𝘣 is equivalent to a fraction (𝘯 × 𝘢)/(𝘯 × 𝘣) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. | Grade 4 |
| Connecticut | 4.NF.A.2 | Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model. | Grade 4 |
| Connecticut | 4.NF.B.3 | Understand a fraction 𝘢/𝘣 with 𝘢 > 1 as a sum of fractions 1/𝘣. | Grade 4 |
| Connecticut | 4.NF.B.4 | Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. | Grade 4 |
| Connecticut | 4.NF.C.5 | Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100. | Grade 4 |
| Connecticut | 4.NF.C.6 | Use decimal notation for fractions with denominators 10 or 100. | Grade 4 |
| Connecticut | 4.NF.C.7 | Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual model. | Grade 4 |
| Connecticut | 4.OA.A.1 | Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 × 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations. | Grade 4 |
| Connecticut | 4.OA.A.2 | Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison. | Grade 4 |
| Connecticut | 4.OA.A.3 | Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. | Grade 4 |
| Connecticut | 4.OA.B.4 | Find all factor pairs for a whole number in the range 1-100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1-100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1-100 is prime or composite. | Grade 4 |
| Connecticut | 4.OA.C.5 | Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. | Grade 4 |
| Connecticut | 5.G.A.1 | Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., 𝘹-axis and 𝘹-coordinate, 𝘺-axis and 𝘺-coordinate). | Grade 5 |
| Connecticut | 5.G.A.2 | Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. | Grade 5 |
| Connecticut | 5.G.B.3 | Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. | Grade 5 |
| Connecticut | 5.G.B.4 | Classify two-dimensional figures in a hierarchy based on properties. | Grade 5 |
| Connecticut | 5.MD.A.1 | Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. | Grade 5 |
| Connecticut | 5.MD.B.2 | Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. | Grade 5 |
| Connecticut | 5.MD.C.3 | Recognize volume as an attribute of solid figures and understand concepts of volume measurement. | Grade 5 |
| Connecticut | 5.MD.C.4 | Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. | Grade 5 |
| Connecticut | 5.MD.C.5 | Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume. | Grade 5 |
| Connecticut | 5.NBT.A.1 | Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. | Grade 5 |
| Connecticut | 5.NBT.A.2 | Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. | Grade 5 |
| Connecticut | 5.NBT.A.3 | Read, write, and compare decimals to thousandths. | Grade 5 |
| Connecticut | 5.NBT.A.4 | Use place value understanding to round decimals to any place. | Grade 5 |
| Connecticut | 5.NBT.B.5 | Fluently multiply multi-digit whole numbers using the standard algorithm. | Grade 5 |
| Connecticut | 5.NBT.B.6 | Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. | Grade 5 |
| Connecticut | 5.NBT.B.7 | Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. | Grade 5 |
| Connecticut | 5.NF.A.1 | Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. | Grade 5 |
| Connecticut | 5.NF.A.2 | Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. | Grade 5 |
| Connecticut | 5.NF.B.3 | Interpret a fraction as division of the numerator by the denominator (𝘢/𝘣 = 𝘢 ÷ 𝘣). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. | Grade 5 |
| Connecticut | 5.NF.B.4 | Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. | Grade 5 |
| Connecticut | 5.NF.B.5 | Interpret multiplication as scaling (resizing). | Grade 5 |
| Connecticut | 5.NF.B.6 | Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. | Grade 5 |
| Connecticut | 5.NF.B.7 | Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. | Grade 5 |
| Connecticut | 5.OA.A.1 | Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. | Grade 5 |
| Connecticut | 5.OA.A.2 | Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. | Grade 5 |
| Connecticut | 5.OA.B.3 | Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. | Grade 5 |
| Connecticut | 6.EE.A.1 | Write and evaluate numerical expressions involving whole-number exponents. | Grade 6 |
| Connecticut | 6.EE.A.2 | Write, read, and evaluate expressions in which letters stand for numbers. | Grade 6 |
| Connecticut | 6.EE.A.3 | Apply the properties of operations to generate equivalent expressions. | Grade 6 |
| Connecticut | 6.EE.A.4 | Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). | Grade 6 |
| Connecticut | 6.EE.B.5 | Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true. | Grade 6 |
| Connecticut | 6.EE.B.6 | Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set. | Grade 6 |
| Connecticut | 6.EE.B.7 | Solve real-world and mathematical problems by writing and solving equations of the form 𝘹 + 𝘱 = 𝘲 and 𝘱𝘹 = 𝘲 for cases in which 𝘱, 𝘲 and 𝘹 are all nonnegative rational numbers. | Grade 6 |
| Connecticut | 6.EE.B.8 | Write an inequality of the form 𝘹 > 𝘤 or 𝘹 𝘤 or 𝘹 < 𝘤 have infinitely many solutions; represent solutions of such inequalities on number line diagrams. | Grade 6 |
| Connecticut | 6.EE.C.9 | Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. | Grade 6 |
| Connecticut | 6.G.A.1 | Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems. | Grade 6 |
| Connecticut | 6.G.A.2 | Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas 𝘝 = 𝘭 𝘸 𝘩 and 𝘝 = 𝘣 𝘩 to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems. | Grade 6 |
| Connecticut | 6.G.A.3 | Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems. | Grade 6 |
| Connecticut | 6.G.A.4 | Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems. | Grade 6 |
| Connecticut | 6.RP.A.1 | Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. | Grade 6 |
| Connecticut | 6.RP.A.2 | Understand the concept of a unit rate 𝘢/𝘣 associated with a ratio 𝘢:𝘣 with 𝘣 ≠ 0, and use rate language in the context of a ratio relationship. | Grade 6 |
| Connecticut | 6.RP.A.3 | Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. | Grade 6 |
| Connecticut | 6.SP.B.5 | Summarize numerical data sets in relation to their context, such as by: | Grade 6 |
| Connecticut | 6.NS.A.1 | Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. | Grade 6 |
| Connecticut | 6.NS.B.2 | Fluently divide multi-digit numbers using the standard algorithm. | Grade 6 |
| Connecticut | 6.NS.B.3 | Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation. | Grade 6 |
| Connecticut | 6.NS.C.5 | Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation. | Grade 6 |
| Connecticut | 6.NS.C.6 | Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates. | Grade 6 |
| Connecticut | 6.NS.C.7 | Understand ordering and absolute value of rational numbers. | Grade 6 |
| Connecticut | 6.NS.C.8 | Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. | Grade 6 |
| Connecticut | 7.EE.A.1 | Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients. | Grade 7 |
| Connecticut | 7.EE.A.2 | Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. | Grade 7 |
| Connecticut | 7.EE.B.3 | Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. | Grade 7 |
| Connecticut | 7.EE.B.4 | Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. | Grade 7 |
| Connecticut | 7.G.A.1 | Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale. | Grade 7 |
| Connecticut | 7.G.A.2 | Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle. | Grade 7 |
| Connecticut | 7.G.A.3 | Describe the two-dimensional figures that result from slicing three-dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids. | Grade 7 |
| Connecticut | 7.G.B.4 | Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle. | Grade 7 |
| Connecticut | 7.G.B.5 | Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure. | Grade 7 |
| Connecticut | 7.G.B.6 | Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. | Grade 7 |
| Connecticut | 7.RP.A.1 | Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. | Grade 7 |
| Connecticut | 7.RP.A.2 | Recognize and represent proportional relationships between quantities. | Grade 7 |
| Connecticut | 7.RP.A.3 | Use proportional relationships to solve multistep ratio and percent problems. | Grade 7 |
| Connecticut | 7.NS.A.1 | Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram. | Grade 7 |
| Connecticut | 7.NS.A.2 | Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers. | Grade 7 |
| Connecticut | 7.NS.A.3 | Solve real-world and mathematical problems involving the four operations with rational numbers. | Grade 7 |
| Connecticut | 8.EE.A.1 | Know and apply the properties of integer exponents to generate equivalent numerical expressions. | Grade 8 |
| Connecticut | 8.EE.A.2 | Use square root and cube root symbols to represent solutions to equations of the form 𝘹² = 𝘱 and 𝘹³ = 𝘱, where 𝘱 is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that √2 is irrational. | Grade 8 |
| Connecticut | 8.EE.A.3 | Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other. | Grade 8 |
| Connecticut | 8.EE.A.4 | Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology. | Grade 8 |
| Connecticut | 8.EE.B.5 | Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. | Grade 8 |
| Connecticut | 8.EE.B.6 | Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation 𝘺 = 𝘮𝘹 for a line through the origin and the equation 𝘺 = 𝘮𝘹 + 𝘣 for a line intercepting the vertical axis at 𝘣. | Grade 8 |
| Connecticut | 8.EE.C.7 | Solve linear equations in one variable. | Grade 8 |
| Connecticut | 8.EE.C.8 | Analyze and solve pairs of simultaneous linear equations. | Grade 8 |
| Connecticut | 8.F.A.1 | Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output. | Grade 8 |
| Connecticut | 8.F.A.2 | Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). | Grade 8 |
| Connecticut | 8.F.A.3 | Interpret the equation 𝘺 = 𝘮𝘹 + 𝘣 as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. | Grade 8 |
| Connecticut | 8.F.B.4 | Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (𝘹, 𝘺) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values. | Grade 8 |
| Connecticut | 8.F.B.5 | Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally. | Grade 8 |
| Connecticut | 8.G.A.1 | Verify experimentally the properties of rotations, reflections, and translations. | Grade 8 |
| Connecticut | 8.G.A.2 | Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them. | Grade 8 |
| Connecticut | 8.G.A.3 | Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates. | Grade 8 |
| Connecticut | 8.G.A.4 | Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two-dimensional figures, describe a sequence that exhibits the similarity between them. | Grade 8 |
| Connecticut | 8.G.A.5 | Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. | Grade 8 |
| Connecticut | 8.G.B.7 | Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions. | Grade 8 |
| Connecticut | 8.G.B.8 | Apply the Pythagorean Theorem to find the distance between two points in a coordinate system. | Grade 8 |
| Connecticut | 8.G.C.9 | Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems. | Grade 8 |
| Connecticut | 8.SP.A.1 | Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association. | Grade 8 |
| Connecticut | 8.SP.A.2 | Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line. | Grade 8 |
| Connecticut | 8.NS.A.2 | Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g., π²). | Grade 8 |
| Connecticut | A-APR.B.3 | Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial. | High School |
| Connecticut | A-CED.A.2 | Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. | High School |
| Connecticut | A-CED.A.3 | Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context. | High School |
| Connecticut | A-REI.B.3 | Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. | High School |
| Connecticut | A-SSE.A.2 | Use the structure of an expression to identify ways to rewrite it. | High School |
| Connecticut | A-SSE.B.3 | Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression. | High School |
| Connecticut | F-BF.A.1 | Write a function that describes a relationship between two quantities. | High School |
| Connecticut | F-IF.A.2 | Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. | High School |
| Connecticut | F-IF.B.4 | For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. | High School |
| Connecticut | F-IF.C.7 | Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. | High School |
| Connecticut | S-ID.B.6 | Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. | High School |
| Delaware | K.CC.A.1 | Count to 100 by ones and by tens. | Kindergarten |
| Delaware | K.CC.A.2 | Count forward beginning from a given number within the known sequence (instead of having to begin at 1). | Kindergarten |
| Delaware | K.CC.A.3 | Write numbers from 0 to 20. Represent a number of objects with a written numeral 0-20 (with 0 representing a count of no objects). | Kindergarten |
| Delaware | K.CC.B.4 | Understand the relationship between numbers and quantities; connect counting to cardinality. | Kindergarten |
| Delaware | K.CC.B.5 | Count to answer “how many?” questions about as many as 20 things arranged in a line, a rectangular array, or a circle, or as many as 10 things in a scattered configuration; given a number from 1-20, count out that many objects. | Kindergarten |
| Delaware | K.CC.C.6 | Identify whether the number of objects in one group is greater than, less than, or equal to the number of objects in another group, e.g., by using matching and counting strategies. | Kindergarten |
| Delaware | K.CC.C.7 | Compare two numbers between 1 and 10 presented as written numerals. | Kindergarten |
| Delaware | K.G.A.1 | Describe objects in the environment using names of shapes, and describe the relative positions of these objects using terms such as above, below, beside, in front of, behind, and next to. | Kindergarten |
| Delaware | K.G.A.2 | Correctly name shapes regardless of their orientations or overall size. | Kindergarten |
| Delaware | K.G.A.3 | Identify shapes as two-dimensional (lying in a plane, “flat”) or three-dimensional (“solid”). | Kindergarten |
| Delaware | K.G.B.4 | Analyze and compare two- and three-dimensional shapes, in different sizes and orientations, using informal language to describe their similarities, differences, parts (e.g., number of sides and vertices/“corners”) and other attributes (e.g., having sides of equal length). | Kindergarten |
| Delaware | K.G.B.6 | Compose simple shapes to form larger shapes. | Kindergarten |
| Delaware | K.MD.A.1 | Describe measurable attributes of objects, such as length or weight. Describe several measurable attributes of a single object. | Kindergarten |
| Delaware | K.MD.A.2 | Directly compare two objects with a measurable attribute in common, to see which object has “more of”/“less of” the attribute, and describe the difference. | Kindergarten |
| Delaware | K.MD.B.3 | Classify objects into given categories; count the numbers of objects in each category and sort the categories by count. | Kindergarten |
| Delaware | K.NBT.A.1 | Compose and decompose numbers from 11 to 19 into ten ones and some further ones, e.g., by using objects or drawings, and record each composition or decomposition by a drawing or equation (e.g., 18 = 10 + 8); understand that these numbers are composed of ten ones and one, two, three, four, five, six, seven, eight, or nine ones. | Kindergarten |
| Delaware | K.OA.A.1 | Represent addition and subtraction with objects, fingers, mental images, drawings, sounds (e.g., claps), acting out situations, verbal explanations, expressions, or equations. | Kindergarten |
| Delaware | K.OA.A.2 | Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem. | Kindergarten |
| Delaware | K.OA.A.3 | Decompose numbers less than or equal to 10 into pairs in more than one way, e.g., by using objects or drawings, and record each decomposition by a drawing or equation (e.g., 5 = 2 + 3 and 5 = 4 + 1). | Kindergarten |
| Delaware | K.OA.A.4 | For any number from 1 to 9, find the number that makes 10 when added to the given number, e.g., by using objects or drawings, and record the answer with a drawing or equation. | Kindergarten |
| Delaware | K.OA.A.5 | Fluently add and subtract within 5. | Kindergarten |
| Delaware | 1.G.A.1 | Distinguish between defining attributes (e.g., triangles are closed and three-sided) versus non-defining attributes (e.g., color, orientation, overall size); build and draw shapes to possess defining attributes. | Grade 1 |
| Delaware | 1.G.A.2 | Compose two-dimensional shapes (rectangles, squares, trapezoids, triangles, half-circles, and quarter-circles) or three-dimensional shapes (cubes, right rectangular prisms, right circular cones, and right circular cylinders) to create a composite shape, and compose new shapes from the composite shape. | Grade 1 |
| Delaware | 1.G.A.3 | Partition circles and rectangles into two and four equal shares, describe the shares using the words halves, fourths, and quarters, and use the phrases half of, fourth of, and quarter of. Describe the whole as two of, or four of the shares. Understand for these examples that decomposing into more equal shares creates smaller shares. | Grade 1 |
| Delaware | 1.MD.A.1 | Order three objects by length; compare the lengths of two objects indirectly by using a third object. | Grade 1 |
| Delaware | 1.MD.A.2 | Express the length of an object as a whole number of length units, by laying multiple copies of a shorter object (the length unit) end to end; understand that the length measurement of an object is the number of same-size length units that span it with no gaps or overlaps. | Grade 1 |
| Delaware | 1.MD.B.3 | Tell and write time in hours and half-hours using analog and digital clocks. | Grade 1 |
| Delaware | 1.MD.C.4 | Organize, represent, and interpret data with up to three categories; ask and answer questions about the total number of data points, how many in each category, and how many more or less are in one category than in another. | Grade 1 |
| Delaware | 1.NBT.A.1 | Count to 120, starting at any number less than 120. In this range, read and write numerals and represent a number of objects with a written numeral. | Grade 1 |
| Delaware | 1.NBT.B.2 | Understand that the two digits of a two-digit number represent amounts of tens and ones. | Grade 1 |
| Delaware | 1.NBT.B.3 | Compare two two-digit numbers based on meanings of the tens and ones digits, recording the results of comparisons with the symbols >, =, and <. | Grade 1 |
| Delaware | 1.NBT.C.4 | Add within 100, including adding a two-digit number and a one-digit number, and adding a two-digit number and a multiple of 10, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Understand that in adding two-digit numbers, one adds tens and tens, ones and ones; and sometimes it is necessary to compose a ten. | Grade 1 |
| Delaware | 1.NBT.C.5 | Given a two-digit number, mentally find 10 more or 10 less than the number, without having to count; explain the reasoning used. | Grade 1 |
| Delaware | 1.NBT.C.6 | Subtract multiples of 10 in the range 10-90 from multiples of 10 in the range 10-90 (positive or zero differences), using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. | Grade 1 |
| Delaware | 1.OA.A.1 | Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem. | Grade 1 |
| Delaware | 1.OA.B.3 | Apply properties of operations as strategies to add and subtract. | Grade 1 |
| Delaware | 1.OA.B.4 | Understand subtraction as an unknown-addend problem. | Grade 1 |
| Delaware | 1.OA.C.5 | Relate counting to addition and subtraction (e.g., by counting on 2 to add 2). | Grade 1 |
| Delaware | 1.OA.C.6 | Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to a ten (e.g., 13 - 4 = 13 - 3 - 1 = 10 - 1 = 9); using the relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 - 8 = 4); and creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13). | Grade 1 |
| Delaware | 1.OA.D.7 | Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false. | Grade 1 |
| Delaware | 1.OA.D.8 | Determine the unknown whole number in an addition or subtraction equation relating three whole numbers. | Grade 1 |
| Delaware | 2.G.A.1 | Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces. Identify triangles, quadrilaterals, pentagons, hexagons, and cubes. | Grade 2 |
| Delaware | 2.G.A.2 | Partition a rectangle into rows and columns of same-size squares and count to find the total number of them. | Grade 2 |
| Delaware | 2.G.A.3 | Partition circles and rectangles into two, three, or four equal shares, describe the shares using the words halves, thirds, half of, a third of, etc., and describe the whole as two halves, three thirds, four fourths. Recognize that equal shares of identical wholes need not have the same shape. | Grade 2 |
| Delaware | 2.MD.A.1 | Measure the length of an object by selecting and using appropriate tools such as rulers, yardsticks, meter sticks, and measuring tapes. | Grade 2 |
| Delaware | 2.MD.A.2 | Measure the length of an object twice, using length units of different lengths for the two measurements; describe how the two measurements relate to the size of the unit chosen. | Grade 2 |
| Delaware | 2.MD.A.4 | Measure to determine how much longer one object is than another, expressing the length difference in terms of a standard length unit. | Grade 2 |
| Delaware | 2.MD.B.5 | Use addition and subtraction within 100 to solve word problems involving lengths that are given in the same units, e.g., by using drawings (such as drawings of rulers) and equations with a symbol for the unknown number to represent the problem. | Grade 2 |
| Delaware | 2.MD.C.7 | Tell and write time from analog and digital clocks to the nearest five minutes, using a.m. and p.m. | Grade 2 |
| Delaware | 2.MD.C.8 | Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies, using $ and ¢ symbols appropriately. | Grade 2 |
| Delaware | 2.MD.D.9 | Generate measurement data by measuring lengths of several objects to the nearest whole unit, or by making repeated measurements of the same object. Show the measurements by making a line plot, where the horizontal scale is marked off in whole-number units. | Grade 2 |
| Delaware | 2.MD.D.10 | Draw a picture graph and a bar graph (with single-unit scale) to represent a data set with up to four categories. Solve simple put-together, take-apart, and compare problems using information presented in a bar graph. | Grade 2 |
| Delaware | 2.NBT.A.1 | Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones. | Grade 2 |
| Delaware | 2.NBT.A.2 | Count within 1000; skip-count by 5s, 10s, and 100s. | Grade 2 |
| Delaware | 2.NBT.A.3 | Read and write numbers to 1000 using base-ten numerals, number names, and expanded form. | Grade 2 |
| Delaware | 2.NBT.A.4 | Compare two three-digit numbers based on meanings of the hundreds, tens, and ones digits, using >, =, and < symbols to record the results of comparisons. | Grade 2 |
| Delaware | 2.NBT.B.5 | Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction. | Grade 2 |
| Delaware | 2.NBT.B.6 | Add up to four two-digit numbers using strategies based on place value and properties of operations. | Grade 2 |
| Delaware | 2.NBT.B.7 | Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method. Understand that in adding or subtracting three-digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds. | Grade 2 |
| Delaware | 2.NBT.B.8 | Mentally add 10 or 100 to a given number 100–900, and mentally subtract 10 or 100 from a given number 100–900. | Grade 2 |
| Delaware | 2.OA.A.1 | Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem. | Grade 2 |
| Delaware | 2.OA.B.2 | Fluently add and subtract within 20 using mental strategies. By end of Grade 2, know from memory all sums of two one-digit numbers. | Grade 2 |
| Delaware | 2.OA.C.3 | Determine whether a group of objects (up to 20) has an odd or even number of members, e.g., by pairing objects or counting them by 2s; write an equation to express an even number as a sum of two equal addends. | Grade 2 |
| Delaware | 2.OA.C.4 | Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends. | Grade 2 |
| Delaware | 3.G.A.1 | Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories. | Grade 3 |
| Delaware | 3.G.A.2 | Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole. | Grade 3 |
| Delaware | 3.MD.A.1 | Tell and write time to the nearest minute and measure time intervals in minutes. Solve word problems involving addition and subtraction of time intervals in minutes, e.g., by representing the problem on a number line diagram. | Grade 3 |
| Delaware | 3.MD.A.2 | Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l). Add, subtract, multiply, or divide to solve one-step word problems involving masses or volumes that are given in the same units, e.g., by using drawings (such as a beaker with a measurement scale) to represent the problem. | Grade 3 |
| Delaware | 3.MD.B.3 | Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and two-step “how many more” and “how many less” problems using information presented in scaled bar graphs. | Grade 3 |
| Delaware | 3.MD.B.4 | Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Show the data by making a line plot, where the horizontal scale is marked off in appropriate units-whole numbers, halves, or quarters. | Grade 3 |
| Delaware | 3.MD.C.5 | Recognize area as an attribute of plane figures and understand concepts of area measurement. | Grade 3 |
| Delaware | 3.MD.C.6 | Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units). | Grade 3 |
| Delaware | 3.MD.C.7 | Relate area to the operations of multiplication and addition. | Grade 3 |
| Delaware | 3.MD.D.8 | Solve real world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters. | Grade 3 |
| Delaware | 3.NBT.A.1 | Use place value understanding to round whole numbers to the nearest 10 or 100. | Grade 3 |
| Delaware | 3.NBT.A.2 | Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction. | Grade 3 |
| Delaware | 3.NBT.A.3 | Multiply one-digit whole numbers by multiples of 10 in the range 10–90 (e.g., 9 × 80, 5 × 60) using strategies based on place value and properties of operations. | Grade 3 |
| Delaware | 3.NF.A.1 | Understand a fraction 1/𝘣 as the quantity formed by 1 part when a whole is partitioned into 𝘣 equal parts; understand a fraction 𝘢/𝑏 as the quantity formed by 𝘢 parts of size 1/𝘣. | Grade 3 |
| Delaware | 3.NF.A.2 | Understand a fraction as a number on the number line; represent fractions on a number line diagram. | Grade 3 |
| Delaware | 3.NF.A.3 | Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size. | Grade 3 |
| Delaware | 3.OA.A.1 | Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each. | Grade 3 |
| Delaware | 3.OA.A.2 | Interpret whole-number quotients of whole numbers, e.g., interpret 56 ÷ 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each. | Grade 3 |
| Delaware | 3.OA.A.3 | Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem. | Grade 3 |
| Delaware | 3.OA.A.4 | Determine the unknown whole number in a multiplication or division equation relating three whole numbers. | Grade 3 |
| Delaware | 3.OA.B.5 | Apply properties of operations as strategies to multiply and divide. | Grade 3 |
| Delaware | 3.OA.B.6 | Understand division as an unknown-factor problem. | Grade 3 |
| Delaware | 3.OA.C.7 | Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 × 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers. | Grade 3 |
| Delaware | 3.OA.D.8 | Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. | Grade 3 |
| Delaware | 3.OA.D.9 | Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations. | Grade 3 |
| Delaware | 4.G.A.1 | Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures. | Grade 4 |
| Delaware | 4.G.A.2 | Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles. | Grade 4 |
| Delaware | 4.G.A.3 | Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify line-symmetric figures and draw lines of symmetry. | Grade 4 |
| Delaware | 4.MD.A.1 | Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table. | Grade 4 |
| Delaware | 4.MD.A.2 | Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. | Grade 4 |
| Delaware | 4.MD.A.3 | Apply the area and perimeter formulas for rectangles in real world and mathematical problems. | Grade 4 |
| Delaware | 4.MD.B.4 | Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots. | Grade 4 |
| Delaware | 4.MD.C.5 | Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement. | Grade 4 |
| Delaware | 4.MD.C.6 | Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure. | Grade 4 |
| Delaware | 4.MD.C.7 | Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems, e.g., by using an equation with a symbol for the unknown angle measure. | Grade 4 |
| Delaware | 4.NBT.A.1 | Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. | Grade 4 |
| Delaware | 4.NBT.A.2 | Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. | Grade 4 |
| Delaware | 4.NBT.A.3 | Use place value understanding to round multi-digit whole numbers to any place. | Grade 4 |
| Delaware | 4.NBT.B.4 | Fluently add and subtract multi-digit whole numbers using the standard algorithm. | Grade 4 |
| Delaware | 4.NBT.B.5 | Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. | Grade 4 |
| Delaware | 4.NBT.B.6 | Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. | Grade 4 |
| Delaware | 4.NF.A.1 | Explain why a fraction 𝘢/𝘣 is equivalent to a fraction (𝘯 × 𝘢)/(𝘯 × 𝘣) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. | Grade 4 |
| Delaware | 4.NF.A.2 | Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model. | Grade 4 |
| Delaware | 4.NF.B.3 | Understand a fraction 𝘢/𝘣 with 𝘢 > 1 as a sum of fractions 1/𝘣. | Grade 4 |
| Delaware | 4.NF.B.4 | Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. | Grade 4 |
| Delaware | 4.NF.C.5 | Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100. | Grade 4 |
| Delaware | 4.NF.C.6 | Use decimal notation for fractions with denominators 10 or 100. | Grade 4 |
| Delaware | 4.NF.C.7 | Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual model. | Grade 4 |
| Delaware | 4.OA.A.1 | Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 × 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations. | Grade 4 |
| Delaware | 4.OA.A.2 | Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison. | Grade 4 |
| Delaware | 4.OA.A.3 | Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. | Grade 4 |
| Delaware | 4.OA.B.4 | Find all factor pairs for a whole number in the range 1-100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1-100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1-100 is prime or composite. | Grade 4 |
| Delaware | 4.OA.C.5 | Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. | Grade 4 |
| Delaware | 5.G.A.1 | Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., 𝘹-axis and 𝘹-coordinate, 𝘺-axis and 𝘺-coordinate). | Grade 5 |
| Delaware | 5.G.A.2 | Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. | Grade 5 |
| Delaware | 5.G.B.3 | Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. | Grade 5 |
| Delaware | 5.G.B.4 | Classify two-dimensional figures in a hierarchy based on properties. | Grade 5 |
| Delaware | 5.MD.A.1 | Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. | Grade 5 |
| Delaware | 5.MD.B.2 | Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. | Grade 5 |
| Delaware | 5.MD.C.3 | Recognize volume as an attribute of solid figures and understand concepts of volume measurement. | Grade 5 |
| Delaware | 5.MD.C.4 | Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. | Grade 5 |
| Delaware | 5.MD.C.5 | Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume. | Grade 5 |
| Delaware | 5.NBT.A.1 | Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. | Grade 5 |
| Delaware | 5.NBT.A.2 | Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. | Grade 5 |
| Delaware | 5.NBT.A.3 | Read, write, and compare decimals to thousandths. | Grade 5 |
| Delaware | 5.NBT.A.4 | Use place value understanding to round decimals to any place. | Grade 5 |
| Delaware | 5.NBT.B.5 | Fluently multiply multi-digit whole numbers using the standard algorithm. | Grade 5 |
| Delaware | 5.NBT.B.6 | Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. | Grade 5 |
| Delaware | 5.NBT.B.7 | Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. | Grade 5 |
| Delaware | 5.NF.A.1 | Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. | Grade 5 |
| Delaware | 5.NF.A.2 | Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. | Grade 5 |
| Delaware | 5.NF.B.3 | Interpret a fraction as division of the numerator by the denominator (𝘢/𝘣 = 𝘢 ÷ 𝘣). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. | Grade 5 |
| Delaware | 5.NF.B.4 | Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. | Grade 5 |
| Delaware | 5.NF.B.5 | Interpret multiplication as scaling (resizing). | Grade 5 |
| Delaware | 5.NF.B.6 | Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. | Grade 5 |
| Delaware | 5.NF.B.7 | Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. | Grade 5 |
| Delaware | 5.OA.A.1 | Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. | Grade 5 |
| Delaware | 5.OA.A.2 | Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. | Grade 5 |
| Delaware | 5.OA.B.3 | Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. | Grade 5 |
| Delaware | 6.EE.A.1 | Write and evaluate numerical expressions involving whole-number exponents. | Grade 6 |
| Delaware | 6.EE.A.2 | Write, read, and evaluate expressions in which letters stand for numbers. | Grade 6 |
| Delaware | 6.EE.A.3 | Apply the properties of operations to generate equivalent expressions. | Grade 6 |
| Delaware | 6.EE.A.4 | Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). | Grade 6 |
| Delaware | 6.EE.B.5 | Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true. | Grade 6 |
| Delaware | 6.EE.B.6 | Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set. | Grade 6 |
| Delaware | 6.EE.B.7 | Solve real-world and mathematical problems by writing and solving equations of the form 𝘹 + 𝘱 = 𝘲 and 𝘱𝘹 = 𝘲 for cases in which 𝘱, 𝘲 and 𝘹 are all nonnegative rational numbers. | Grade 6 |
| Delaware | 6.EE.B.8 | Write an inequality of the form 𝘹 > 𝘤 or 𝘹 𝘤 or 𝘹 < 𝘤 have infinitely many solutions; represent solutions of such inequalities on number line diagrams. | Grade 6 |
| Delaware | 6.EE.C.9 | Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. | Grade 6 |
| Delaware | 6.G.A.1 | Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems. | Grade 6 |
| Delaware | 6.G.A.2 | Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas 𝘝 = 𝘭 𝘸 𝘩 and 𝘝 = 𝘣 𝘩 to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems. | Grade 6 |
| Delaware | 6.G.A.3 | Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems. | Grade 6 |
| Delaware | 6.G.A.4 | Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems. | Grade 6 |
| Delaware | 6.RP.A.1 | Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. | Grade 6 |
| Delaware | 6.RP.A.2 | Understand the concept of a unit rate 𝘢/𝘣 associated with a ratio 𝘢:𝘣 with 𝘣 ≠ 0, and use rate language in the context of a ratio relationship. | Grade 6 |
| Delaware | 6.RP.A.3 | Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. | Grade 6 |
| Delaware | 6.SP.B.5 | Summarize numerical data sets in relation to their context, such as by: | Grade 6 |
| Delaware | 6.NS.A.1 | Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. | Grade 6 |
| Delaware | 6.NS.B.2 | Fluently divide multi-digit numbers using the standard algorithm. | Grade 6 |
| Delaware | 6.NS.B.3 | Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation. | Grade 6 |
| Delaware | 6.NS.C.5 | Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation. | Grade 6 |
| Delaware | 6.NS.C.6 | Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates. | Grade 6 |
| Delaware | 6.NS.C.7 | Understand ordering and absolute value of rational numbers. | Grade 6 |
| Delaware | 6.NS.C.8 | Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. | Grade 6 |
| Delaware | 7.EE.A.1 | Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients. | Grade 7 |
| Delaware | 7.EE.A.2 | Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. | Grade 7 |
| Delaware | 7.EE.B.3 | Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. | Grade 7 |
| Delaware | 7.EE.B.4 | Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. | Grade 7 |
| Delaware | 7.G.A.1 | Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale. | Grade 7 |
| Delaware | 7.G.A.2 | Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle. | Grade 7 |
| Delaware | 7.G.A.3 | Describe the two-dimensional figures that result from slicing three-dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids. | Grade 7 |
| Delaware | 7.G.B.4 | Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle. | Grade 7 |
| Delaware | 7.G.B.5 | Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure. | Grade 7 |
| Delaware | 7.G.B.6 | Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. | Grade 7 |
| Delaware | 7.RP.A.1 | Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. | Grade 7 |
| Delaware | 7.RP.A.2 | Recognize and represent proportional relationships between quantities. | Grade 7 |
| Delaware | 7.RP.A.3 | Use proportional relationships to solve multistep ratio and percent problems. | Grade 7 |
| Delaware | 7.NS.A.1 | Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram. | Grade 7 |
| Delaware | 7.NS.A.2 | Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers. | Grade 7 |
| Delaware | 7.NS.A.3 | Solve real-world and mathematical problems involving the four operations with rational numbers. | Grade 7 |
| Delaware | 8.EE.A.1 | Know and apply the properties of integer exponents to generate equivalent numerical expressions. | Grade 8 |
| Delaware | 8.EE.A.2 | Use square root and cube root symbols to represent solutions to equations of the form 𝘹² = 𝘱 and 𝘹³ = 𝘱, where 𝘱 is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that √2 is irrational. | Grade 8 |
| Delaware | 8.EE.A.3 | Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other. | Grade 8 |
| Delaware | 8.EE.A.4 | Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology. | Grade 8 |
| Delaware | 8.EE.B.5 | Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. | Grade 8 |
| Delaware | 8.EE.B.6 | Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation 𝘺 = 𝘮𝘹 for a line through the origin and the equation 𝘺 = 𝘮𝘹 + 𝘣 for a line intercepting the vertical axis at 𝘣. | Grade 8 |
| Delaware | 8.EE.C.7 | Solve linear equations in one variable. | Grade 8 |
| Delaware | 8.EE.C.8 | Analyze and solve pairs of simultaneous linear equations. | Grade 8 |
| Delaware | 8.F.A.1 | Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output. | Grade 8 |
| Delaware | 8.F.A.2 | Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). | Grade 8 |
| Delaware | 8.F.A.3 | Interpret the equation 𝘺 = 𝘮𝘹 + 𝘣 as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. | Grade 8 |
| Delaware | 8.F.B.4 | Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (𝘹, 𝘺) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values. | Grade 8 |
| Delaware | 8.F.B.5 | Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally. | Grade 8 |
| Delaware | 8.G.A.1 | Verify experimentally the properties of rotations, reflections, and translations. | Grade 8 |
| Delaware | 8.G.A.2 | Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them. | Grade 8 |
| Delaware | 8.G.A.3 | Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates. | Grade 8 |
| Delaware | 8.G.A.4 | Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two-dimensional figures, describe a sequence that exhibits the similarity between them. | Grade 8 |
| Delaware | 8.G.A.5 | Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. | Grade 8 |
| Delaware | 8.G.B.7 | Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions. | Grade 8 |
| Delaware | 8.G.B.8 | Apply the Pythagorean Theorem to find the distance between two points in a coordinate system. | Grade 8 |
| Delaware | 8.G.C.9 | Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems. | Grade 8 |
| Delaware | 8.SP.A.1 | Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association. | Grade 8 |
| Delaware | 8.SP.A.2 | Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line. | Grade 8 |
| Delaware | 8.NS.A.2 | Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g., π²). | Grade 8 |
| Delaware | A-APR.B.3 | Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial. | High School |
| Delaware | A-CED.A.2 | Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. | High School |
| Delaware | A-CED.A.3 | Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context. | High School |
| Delaware | A-REI.B.3 | Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. | High School |
| Delaware | A-SSE.A.2 | Use the structure of an expression to identify ways to rewrite it. | High School |
| Delaware | A-SSE.B.3 | Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression. | High School |
| Delaware | F-BF.A.1 | Write a function that describes a relationship between two quantities. | High School |
| Delaware | F-IF.A.2 | Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. | High School |
| Delaware | F-IF.B.4 | For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. | High School |
| Delaware | F-IF.C.7 | Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. | High School |
| Delaware | S-ID.B.6 | Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. | High School |
| Florida | MA.K.NSO.1.1 | Given a group of 20 objects, count a number of objects in that group and represent the number of objects with a written numeral. State the number of objects in a rearrangement of that group without recounting. | Kindergarten |
| Florida | MA.K.NSO.1.2 | Given a number from 0 to 20, count out that many objects. | Kindergarten |
| Florida | MA.K.NSO.1.3 | Identify positions of objects within a sequence using the words first, second, third, fourth‚ or fifth. | Kindergarten |
| Florida | MA.K.NSO.1.4 | Compare the number of objects from 0 to 20 in two groups using the terms less than, equal to or greater than. | Kindergarten |
| Florida | MA.K.NSO.2.1 | Recite the number names to 100 by ones and by tens. Starting at a given number, count forward within 100 and backward within 20. | Kindergarten |
| Florida | MA.K.NSO.2.2 | Represent whole numbers from 10 to 20, using a unit of ten and a group of ones, with objects, drawing and expressions or equations. | Kindergarten |
| Florida | MA.K.NSO.2.3 | Locate, order and compare numbers from 0 to 20 using the number line and terms less than, equal to or greater than. | Kindergarten |
| Florida | MA.K.NSO.3.1 | Explore addition of two whole numbers from 0 to 10, and related subtraction facts. | Kindergarten |
| Florida | MA.K.NSO.3.2 | Add two one-digit whole numbers with sums from 0 to 10 and subtract using related facts with procedural reliability. | Kindergarten |
| Florida | MA.K.AR.1.1 | For any number from 1 to 9, find the number that makes 10 when added to the given number. | Kindergarten |
| Florida | MA.K.AR.1.2 | Given a number from 0 to 10, find the different ways it can be represented as the sum of two numbers. | Kindergarten |
| Florida | MA.K.AR.1.3 | Solve addition and subtraction real-world problems using objects, drawings or equations to represent the problem. | Kindergarten |
| Florida | MA.K.AR.2.1 | Explain why addition or subtraction equations are true using objects or drawings. | Kindergarten |
| Florida | MA.K.M.1.1 | Identify the attributes of a single object that can be measured such as length, volume or weight. | Kindergarten |
| Florida | MA.K.M.1.2 | Directly compare two objects that have an attribute which can be measured in common. Express the comparison using language to describe the difference. | Kindergarten |
| Florida | MA.K.M.1.3 | Express the length of an object, up to 20 units long, as a whole of lengths by laying non-standard objects end to end with no gaps or overlaps. | Kindergarten |
| Florida | MA.K.GR.1.1 | Identify two- and three-dimensional figures regardless of their size or orientation. Figures are limited to circles, triangles, rectangles, squares, spheres, cubes, cones and cylinders. | Kindergarten |
| Florida | MA.K.GR.1.2 | Compare two-dimensional figures based on their similarities, differences and positions. Sort two-dimensional figures based on their similarities and differences. Figures are limited to circles, triangles, rectangles and squares. | Kindergarten |
| Florida | MA.K.GR.1.3 | Compare three-dimensional figures based in their similarities, differences and positions. Sort three-dimensional figures based on their similarities and differences. Figures are limited to spheres, cubes, cones and cylinders. | Kindergarten |
| Florida | MA.K.GR.1.4 | Find real-world objects that can be modeled by a given two- or three-dimensional figure. Figures are limited to circles, triangles, rectangles, squares, spheres, cubes, cones and cylinders. | Kindergarten |
| Florida | MA.K.GR.1.5 | Combine two-dimensional figures to form a given composite figure. Figures used to form a composite shape are limited to triangles, rectangles and squares. | Kindergarten |
| Florida | MA.K.DP.1.1 | Collect and sort objects into categories and compare the categories by counting the objects in each category. Report the results verbally, with a written numeral or with drawings. | Kindergarten |
| Florida | MA.1.NSO.1.1 | Starting at a given number, count forward and backwards within 120 by ones. Skip count by 2s to 20 and by 5s to 100. | Grade 1 |
| Florida | MA.1.NSO.1.2 | Read numbers from 0 to 100 written in standard form, expanded form and word form. Write numbers from 0 to 100 using standard form and expanded form. | Grade 1 |
| Florida | MA.1.NSO.1.3 | Compose and decompose two-digit numbers in multiple ways using tens and ones. Demonstrate each composition or decomposition with objects, drawings and expressions or equations. | Grade 1 |
| Florida | MA.1.NSO.1.4 | Plot, order and compare whole numbers up to 100. | Grade 1 |
| Florida | MA.1.NSO.2.1 | Recall addition facts with sums to 10 and related subtraction facts with automaticity. | Grade 1 |
| Florida | MA.1.NSO.2.2 | Add two whole numbers with sums from 0 to 20, and subtract using related facts with procedural reliability. | Grade 1 |
| Florida | MA.1.NSO.2.3 | Identify the number that is one more, one less, ten more and ten less than a given two-digit number. | Grade 1 |
| Florida | MA.1.NSO.2.4 | Explore the addition of a two-digit number and a one-digit number with sums to 100. | Grade 1 |
| Florida | MA.1.NSO.2.5 | Explore subtraction of a one-digit number from a two-digit number. | Grade 1 |
| Florida | MA.1.FR.1.1 | Partition circles and rectangles into two and four equal-sized parts. Name the parts of the whole using appropriate language including halves or fourths. | Grade 1 |
| Florida | MA.1.AR.1.1 | Apply properties of addition to find a sum of three or more whole numbers. | Grade 1 |
| Florida | MA.1.AR.1.2 | Solve addition and subtraction real-world problems using objects, drawings or equations to represent the problem. | Grade 1 |
| Florida | MA.1.AR.2.1 | Restate a subtraction problem as a missing addend problem using the relationship between addition and subtraction. | Grade 1 |
| Florida | MA.1.AR.2.2 | Determine and explain if equations involving addition or subtraction are true or false. | Grade 1 |
| Florida | MA.1.AR.2.3 | Determine the unknown whole number in an addition or subtraction equation, relating three whole numbers, with the unknown in any position. | Grade 1 |
| Florida | MA.1.M.1.1 | Estimate the length of an object to the nearest inch. Measure the length of an object to the nearest inch or centimeter. | Grade 1 |
| Florida | MA.1.M.1.2 | Compare and order the length of up to three objects using direct and indirect comparison. | Grade 1 |
| Florida | MA.1.M.2.1 | Using analog and digital clocks, tell and write time in hours and half hours. | Grade 1 |
| Florida | MA.1.M.2.2 | Identify pennies, nickels, dimes and quarters, and express their values using the ¢ symbol. State how many of each coin equal a dollar. | Grade 1 |
| Florida | MA.1.M.2.3 | Find the value of combinations of pennies, nickels and dimes up to one dollar, and the value of combinations of one, five and ten dollar bills up to $100. Use the ¢ and $ symbols appropriately. | Grade 1 |
| Florida | MA.1.GR.1.1 | Identify, compare and sort two- and three-dimensional figures based on their defining attributes. Figures are limited to circles, semi-circles, triangles, rectangles, squares, trapezoids, hexagons, spheres, cubes, rectangular prisms, cones and cylinders. | Grade 1 |
| Florida | MA.1.GR.1.2 | Sketch two-dimensional figures when given defining attributes. Figures are limited to triangles, rectangles, squares and hexagons. | Grade 1 |
| Florida | MA.1.GR.1.3 | Compose and decompose two- and three-dimensional figures. Figures are limited to semi-circles, triangles, rectangles, squares, trapezoids, hexagons, cubes, rectangular prisms, cones and cylinders. | Grade 1 |
| Florida | MA.1.GR.1.4 | Given a real-world object, identify parts that are modeled by two- and three-dimensional figures. Figures are limited to semi-circles, triangles, rectangles, squares and hexagons, spheres, cubes, rectangular prisms, cones and cylinders. | Grade 1 |
| Florida | MA.1.DP.1.1 | Collect data into categories and represent the results using tally marks or pictographs. | Grade 1 |
| Florida | MA.1.DP.1.2 | Interpret data represented with tally marks or pictographs by calculating the total number of data points and comparing the totals of different categories. | Grade 1 |
| Florida | MA.2.NSO.1.1 | Read and write numbers from 0 to 1,000 using standard form, expanded form and word form. | Grade 2 |
| Florida | MA.2.NSO.1.2 | Compose and decompose three-digit numbers in multiple ways using hundreds, tens and ones. Demonstrate each composition or decomposition with objects, drawings and expressions or equations. | Grade 2 |
| Florida | MA.2.NSO.1.3 | Plot, order and compare whole numbers up to 1,000. | Grade 2 |
| Florida | MA.2.NSO.1.4 | Round whole numbers from 0 to 100 to the nearest 10. | Grade 2 |
| Florida | MA.2.NSO.2.1 | Recall addition facts with sums to 20 and related subtraction facts with automaticity. | Grade 2 |
| Florida | MA.2.NSO.2.2 | Identify the number that is ten more, ten less, one hundred more and one hundred less than a given three-digit number. | Grade 2 |
| Florida | MA.2.NSO.2.3 | Add two whole numbers with sums up to 100 with procedural reliability. Subtract a whole number from a whole number, each no larger than 100, with procedural reliability. | Grade 2 |
| Florida | MA.2.NSO.2.4 | Explore the addition of two whole numbers with sums up to 1,000. Explore the subtraction of a whole number from a whole number, each no larger than 1,000. | Grade 2 |
| Florida | MA.2.FR.1.1 | Partition circles and rectangles into two, three or four equal-sized parts. Name the parts using appropriate language, and describe the whole as two halves, three thirds or four fourths. | Grade 2 |
| Florida | MA.2.FR.1.2 | Partition rectangles into two, three or four equal-sized parts in two different ways showing that equal-sized parts of the same whole may have different shapes. | Grade 2 |
| Florida | MA.2.AR.1.1 | Solve one- and two-step addition and subtraction real-world problems. | Grade 2 |
| Florida | MA.2.AR.2.1 | Determine and explain whether equations involving addition and subtraction are true or false. | Grade 2 |
| Florida | MA.2.AR.2.2 | Determine the unknown whole number in an addition or subtraction equation, relating three or four whole numbers, with the unknown in any position. | Grade 2 |
| Florida | MA.2.AR.3.1 | Represent an even number using two equal groups or two equal addends. Represent an odd number using two equal groups with one left over or two equals addends plus 1. | Grade 2 |
| Florida | MA.2.AR.3.2 | Use repeated addition to find the total number of objects in a collection of equal groups. Represent the total number of objects using rectangular arrays and equations. | Grade 2 |
| Florida | MA.2.M.1.1 | Estimate and measure the length of an object to the nearest inch, foot, yard, centimeter or meter by selecting and using an appropriate tool. | Grade 2 |
| Florida | MA.2.M.1.2 | Measure the lengths of two objects using the same unit and determine the difference between their measurements. | Grade 2 |
| Florida | MA.2.M.1.3 | Solve one-and two-step real-world measurement problems involving addition and subtraction of lengths given the same units. | Grade 2 |
| Florida | MA.2.M.2.1 | Using analog and digital clocks, tell and write time to the nearest five minutes using a.m. and p.m. appropriately. Express portions of an hour using the fractional terms half an hour, half past, quarter of an hour, quarter after and quarter til. | Grade 2 |
| Florida | MA.2.M.2.2 | Solve one- and two-step addition and subtraction real-world problems involving either dollar bills within $100 or coins within 100¢ using $ and ¢ symbols appropriately. | Grade 2 |
| Florida | MA.2.GR.1.1 | Identify and draw two-dimensional figures based on their defining attributes. Figures are limited to triangles, rectangles, squares, pentagons, hexagons and octagons. | Grade 2 |
| Florida | MA.2.GR.1.2 | Categorize two-dimensional figures based on the number and length of sides, number of vertices, whether they are closed or not and whether the edges are curved or straight. | Grade 2 |
| Florida | MA.2.GR.1.3 | Identify line(s) of symmetry for a two-dimensional figure. | Grade 2 |
| Florida | MA.2.GR.2.1 | Explore perimeter as an attribute of a figure by placing unit segments along the boundary without gaps or overlaps. Find perimeters of rectangles by counting unit segments. | Grade 2 |
| Florida | MA.2.GR.2.2 | Find the perimeter of a polygon with whole-number side lengths. Polygons are limited to triangles, rectangles, squares and pentagons. | Grade 2 |
| Florida | MA.2.DP.1.1 | Collect, categorize and represent data using tally marks, tables, pictographs or bar graphs. Use appropriate titles, labels and units. | Grade 2 |
| Florida | MA.2.DP.1.2 | Interpret data represented with tally marks, tables, pictographs or bar graphs including solving addition and subtraction problems. | Grade 2 |
| Florida | MA.3.NSO.1.1 | Read and write numbers from 0 to 10,000 using standard form, expanded form and word form. | Grade 3 |
| Florida | MA.3.NSO.1.2 | Compose and decompose four-digit numbers in multiple ways using thousands, hundreds, tens and ones. Demonstrate each composition or decomposition using objects, drawings and expressions or equations. | Grade 3 |
| Florida | MA.3.NSO.1.3 | Plot, order and compare whole numbers up to 10,000. | Grade 3 |
| Florida | MA.3.NSO.1.4 | Round whole numbers from 0 to 1,000 to the nearest 10 or 100. | Grade 3 |
| Florida | MA.3.NSO.2.1 | Add and subtract multi-digit whole numbers including using a standard algorithm with procedural fluency. | Grade 3 |
| Florida | MA.3.NSO.2.2 | Explore multiplication of two whole numbers with products from 0 to 144, and related division facts. | Grade 3 |
| Florida | MA.3.NSO.2.3 | Multiply a one-digit whole number by a multiple of 10, up to 90, or a multiple of 100, up to 900, with procedural reliability. | Grade 3 |
| Florida | MA.3.NSO.2.4 | Multiply two whole numbers from 0 to 12 and divide using related facts with procedural reliability. | Grade 3 |
| Florida | MA.3.FR.1.1 | Represent and interpret unit fractions in the form 1/n as the quantity formed by one part when a whole is partitioned into n equal parts. | Grade 3 |
| Florida | MA.3.FR.1.2 | Represent and interpret fractions, including fractions greater than one, in the form of m/n as the result of adding the unit fraction 1/n to itself m times. | Grade 3 |
| Florida | MA.3.FR.1.3 | Read and write fractions, including fractions greater than one, using standard form, numeral-word form and word form. | Grade 3 |
| Florida | MA.3.FR.2.1 | Plot, order and compare fractional numbers with the same numerator or the same denominator. | Grade 3 |
| Florida | MA.3.FR.2.2 | Identify equivalent fractions and explain why they are equivalent. | Grade 3 |
| Florida | MA.3.AR.1.1 | Apply the distributive property to multiply a one-digit number and two-digit number. Apply properties of multiplication to find a product of one-digit whole numbers. | Grade 3 |
| Florida | MA.3.AR.1.2 | Solve one- and two-step real-world problems involving any of four operations with whole numbers. | Grade 3 |
| Florida | MA.3.AR.2.1 | Restate a division problem as a missing factor problem using the relationship between multiplication and division. | Grade 3 |
| Florida | MA.3.AR.2.2 | Determine and explain whether an equation involving multiplication or division is true or false. | Grade 3 |
| Florida | MA.3.AR.2.3 | Determine the unknown whole number in a multiplication or division equation, relating three whole numbers, with the unknown in any position. | Grade 3 |
| Florida | MA.3.AR.3.1 | Determine and explain whether a whole number from 1 to 1,000 is even or odd. | Grade 3 |
| Florida | MA.3.AR.3.2 | Determine whether a whole number from 1 to 144 is a multiple of a given one-digit number. | Grade 3 |
| Florida | MA.3.AR.3.3 | Identify, create and extend numerical patterns. | Grade 3 |
| Florida | MA.3.M.1.1 | Select and use appropriate tools to measure the length of an object, the volume of liquid within a beaker and temperature. | Grade 3 |
| Florida | MA.3.M.1.2 | Solve real-world problems involving any of the four operations with whole-number lengths, masses, weights, temperatures or liquid volumes. | Grade 3 |
| Florida | MA.3.M.2.1 | Using analog and digital clocks tell and write time to the nearest minute using a.m. and p.m. appropriately. | Grade 3 |
| Florida | MA.3.M.2.2 | Solve one- and two-step real-world problems involving elapsed time. | Grade 3 |
| Florida | MA.3.GR.1.1 | Describe and draw points, lines, line segments, rays, intersecting lines, perpendicular lines and parallel lines. Identify these in two-dimensional figures. | Grade 3 |
| Florida | MA.3.GR.1.2 | Identify and draw quadrilaterals based on their defining attributes. Quadrilaterals include parallelograms, rhombi, rectangles, squares and trapezoids. | Grade 3 |
| Florida | MA.3.GR.1.3 | Draw line(s) of symmetry in a two-dimensional figure and identify line-symmetric two-dimensional figures. | Grade 3 |
| Florida | MA.3.GR.2.1 | Explore area as an attribute of a two-dimensional figure by covering the figure with unit squares without gaps or overlaps. Find areas of rectangles by counting unit squares. | Grade 3 |
| Florida | MA.3.GR.2.2 | Find the area of a rectangle with whole-number side lengths using a visual model and a multiplication formula. | Grade 3 |
| Florida | MA.3.GR.2.3 | Solve mathematical and real-world problems involving the perimeter and area of rectangles with whole-number side lengths using a visual model and a formula. | Grade 3 |
| Florida | MA.3.GR.2.4 | Solve mathematical and real-world problems involving the perimeter and area of composite figures composed of non-overlapping rectangles with whole-number side lengths. | Grade 3 |
| Florida | MA.3.DP.1.1 | Collect and represent numerical and categorical data with whole-number values using tables, scaled pictographs, scaled bar graphs or line plots. Use appropriate titles, labels and units. | Grade 3 |
| Florida | MA.3.DP.1.2 | Interpret data with whole-number values represented with tables, scaled pictographs, circle graphs, scaled bar graphs or line plots by solving one- and two-step problems. | Grade 3 |
| Florida | MA.4.NSO.1.1 | Express how the value of a digit in a multi-digit whole number changes if the digit moves one place to the left or right. | Grade 4 |
| Florida | MA.4.NSO.1.2 | Read and write multi-digit whole numbers from 0 to 1,000,000 using standard form, expanded form and word form. | Grade 4 |
| Florida | MA.4.NSO.1.3 | Plot, order and compare multi-digit whole numbers up to 1,000,000. | Grade 4 |
| Florida | MA.4.NSO.1.4 | Round whole numbers from 0 to 10,000 to the nearest 10, 100 or 1,000. | Grade 4 |
| Florida | MA.4.NSO.1.5 | Plot, order and compare decimals up to the hundredths. | Grade 4 |
| Florida | MA.4.NSO.2.1 | Recall multiplication facts with factors up to 12 and related division facts with automaticity. | Grade 4 |
| Florida | MA.4.NSO.2.2 | Multiply two whole numbers, up to three digits by up to two digits, with procedural reliability. | Grade 4 |
| Florida | MA.4.NSO.2.3 | Multiply two whole numbers, each up to two digits, including using a standard algorithm with procedural fluency. | Grade 4 |
| Florida | MA.4.NSO.2.4 | Divide a whole number up to four digits by a one-digit whole number with procedural reliability. Represent remainders as fractional parts of the divisor. | Grade 4 |
| Florida | MA.4.NSO.2.5 | Explore the multiplication and division of multi-digit whole numbers using estimation, rounding and place value. | Grade 4 |
| Florida | MA.4.NSO.2.6 | Identify the number that is one-tenth more, one-tenth less, one-hundredth more and one-hundredth less than a given number. | Grade 4 |
| Florida | MA.4.NSO.2.7 | Explore the addition and subtraction of multi-digit numbers with decimals to the hundredths. | Grade 4 |
| Florida | MA.4.FR.1.1 | Model and express a fraction, including mixed numbers and fractions greater than one, with the denominator 10 as an equivalent fraction with the denominator 100. | Grade 4 |
| Florida | MA.4.FR.1.2 | Use decimal notation to represent fractions with denominators of 10 or 100, including mixed numbers and fractions greater than 1, and use fractional notation with denominators of 10 or 100 to represent decimals. | Grade 4 |
| Florida | MA.4.FR.1.3 | Identify and generate equivalent fractions, including fractions greater than one. Describe how the numerator and denominator are affected when the equivalent fraction is created. | Grade 4 |
| Florida | MA.4.FR.1.4 | Plot, order and compare fractions, including mixed numbers and fractions greater than one, with different numerators and different denominators. | Grade 4 |
| Florida | MA.4.FR.2.1 | Decompose a fraction, including mixed numbers and fractions greater than one, into a sum of fractions with the same denominator in multiple ways. Demonstrate each decomposition with objects, drawings and equations. | Grade 4 |
| Florida | MA.4.FR.2.2 | Add and subtract fractions with like denominators, including mixed numbers and fractions greater than one, with procedural reliability. | Grade 4 |
| Florida | MA.4.FR.2.3 | Explore the addition of a fraction with denominator of 10 to a fraction with denominator of 100 using equivalent fractions. | Grade 4 |
| Florida | MA.4.FR.2.4 | Extend previous understanding of multiplication to explore the multiplication of a fraction by a whole number or a whole number by a fraction. | Grade 4 |
| Florida | MA.4.AR.1.1 | Solve real-world problems involving multiplication and division of whole numbers including problems in which remainders must be interpreted within the context. | Grade 4 |
| Florida | MA.4.AR.1.2 | Solve real-world problems involving addition and subtraction of fractions with like denominators, including mixed numbers and fractions greater than one. | Grade 4 |
| Florida | MA.4.AR.1.3 | Solve real-world problems involving multiplication of a fraction by a whole number or a whole number by a fraction. | Grade 4 |
| Florida | MA.4.AR.2.1 | Determine and explain whether an equation involving any of the four operations with whole numbers is true or false. | Grade 4 |
| Florida | MA.4.AR.2.2 | Given a mathematical or real-world context, write an equation involving multiplication or division to determine the unknown whole number with the unknown in any position. | Grade 4 |
| Florida | MA.4.AR.3.1 | Determine factor pairs for a whole number from 0 to 144. Determine whether a whole number from 0 to 144 is prime, composite or neither. | Grade 4 |
| Florida | MA.4.AR.3.2 | Generate, describe and extend a numerical pattern that follows a given rule. | Grade 4 |
| Florida | MA.4.M.1.1 | Select and use appropriate tools to measure attributes of objects. | Grade 4 |
| Florida | MA.4.M.1.2 | Convert within a single system of measurement using the units: yards, feet, inches; kilometers, meters, centimeters, millimeters; pounds, ounces; kilograms, grams; gallons, quarts, pints, cups; liter, milliliter; and hours, minutes, seconds. | Grade 4 |
| Florida | MA.4.M.2.1 | Solve two-step real-world problems involving distances and intervals of time using any combination of the four operations. | Grade 4 |
| Florida | MA.4.M.2.2 | Solve one- and two-step addition and subtraction real-world problems involving money using decimal notation. | Grade 4 |
| Florida | MA.4.GR.1.1 | Informally explore angles as an attribute of two-dimensional figures. Identify and classify angles as acute, right, obtuse, straight or reflex. | Grade 4 |
| Florida | MA.4.GR.1.2 | Estimate angle measures. Using a protractor, measure angles in whole-number degrees and draw angles of specified measure in whole-number degrees. Demonstrate that angle measure is additive. | Grade 4 |
| Florida | MA.4.GR.1.3 | Solve real-world and mathematical problems involving unknown whole-number angle measures. Write an equation to represent the unknown. | Grade 4 |
| Florida | MA.4.GR.2.1 | Solve perimeter and area mathematical and real-world problems, including problems with unknown sides, for rectangles with whole-number side lengths. | Grade 4 |
| Florida | MA.4.GR.2.2 | Solve problems involving rectangles with the same perimeter and different areas or with the same area and different perimeters. | Grade 4 |
| Florida | MA.4.DP.1.1 | Collect and represent numerical data, including fractional values, using tables, stem-and-leaf plots or line plots. | Grade 4 |
| Florida | MA.4.DP.1.2 | Determine the mode, median or range to interpret numerical data including fractional values, represented with tables, stem-and-leaf plots or line plots. | Grade 4 |
| Florida | MA.4.DP.1.3 | Solve real-world problems involving numerical data. | Grade 4 |
| Florida | MA.5.NSO.1.1 | Express how the value of a digit in a multi-digit number with decimals to the thousandths changes if the digit moves one or more places to the left or right. | Grade 5 |
| Florida | MA.5.NSO.1.2 | Read and write multi-digit numbers with decimals to the thousandths using standard form, word form and expanded form. | Grade 5 |
| Florida | MA.5.NSO.1.3 | Compose and decompose multi-digit numbers with decimals to the thousandths in multiple ways using the values of the digits in each place. Demonstrate the compositions or decompositions using objects, drawings and expressions and equations. | Grade 5 |
| Florida | MA.5.NSO.1.4 | Plot, order and compare multi-digit numbers with decimals up to the thousandths. | Grade 5 |
| Florida | MA.5.NSO.1.5 | Round multi-digit numbers with decimals to the thousandths to the nearest hundredth, tenth or whole number. | Grade 5 |
| Florida | MA.5.NSO.2.1 | Multiply multi-digit whole numbers including using standard algorithm with procedural fluency. | Grade 5 |
| Florida | MA.5.NSO.2.2 | Divide multi-digit whole numbers, up to five digits by two digits, including using a standard algorithm with procedural fluency. Represent remainders as fractions. | Grade 5 |
| Florida | MA.5.NSO.2.3 | Add and subtract multi-digit numbers with decimals to the thousandths, including using a standard algorithm with procedural fluency. | Grade 5 |
| Florida | MA.5.NSO.2.4 | Explore the multiplication and division of multi-digit numbers with decimals to the hundredths using estimation, rounding and place value. | Grade 5 |
| Florida | MA.5.NSO.2.5 | Multiply and divide a multi-digit number with decimals to the tenths by on- tenth and one-hundredth with procedural reliability. | Grade 5 |
| Florida | MA.5.FR.1.1 | Given a mathematical or real-world problem, represent the division of two whole numbers as a fraction. | Grade 5 |
| Florida | MA.5.FR.2.1 | Add and subtract fractions with unlike denominators, including mixed numbers and fractions greater than 1, with procedural reliability. | Grade 5 |
| Florida | MA.5.FR.2.2 | Extend previous understanding of multiplication to multiply a fraction by a fraction, including mixed numbers and fractions greater than 1, with procedural reliability. | Grade 5 |
| Florida | MA.5.FR.2.3 | When multiplying a given number by a fraction less than 1 or a fraction greater than 1, predict and explain the relative size of the product to the given number without calculating. | Grade 5 |
| Florida | MA.5.FR.2.4 | Extend previous understanding of division to explore the division of a unit fraction by a whole number and a whole number by a unit fraction. | Grade 5 |
| Florida | MA.5.AR.1.1 | Solve multi-step real-world problems involving any combination of the four operations with whole numbers, including problems in which remainders must be interpreted within the context. | Grade 5 |
| Florida | MA.5.AR.1.2 | Solve real-world problems involving the addition, subtraction or multiplication of fractions, including mixed numbers and fractions greater than 1. | Grade 5 |
| Florida | MA.5.AR.1.3 | Solve real-world problems involving division of a unit fraction by a whole number and a whole number by a unit fraction. | Grade 5 |
| Florida | MA.5.AR.2.1 | Translate written real-world and mathematical descriptions into numerical expressions and numerical expressions into written mathematical descriptions. | Grade 5 |
| Florida | MA.5.AR.2.2 | Evaluate multi-step numerical expressions using order of operations. | Grade 5 |
| Florida | MA.5.AR.2.3 | Determine and explain whether an equation involving any of the four operations is true or false. | Grade 5 |
| Florida | MA.5.AR.2.4 | Given a mathematical or real-world context, write an equation involving any of the four operations to determine the unknown whole number with the unknown in any position. | Grade 5 |
| Florida | MA.5.AR.3.1 | Given a numerical pattern, identify and write a rule that can describe the pattern as an expression. | Grade 5 |
| Florida | MA.5.AR.3.2 | Given a rule for a numerical pattern, use a two-column table to record the inputs and outputs. | Grade 5 |
| Florida | MA.5.M.1.1 | Solve multi-step real-world problems that involve converting measurement units to equivalent measurements within a single system of measurement. | Grade 5 |
| Florida | MA.5.M.2.1 | Solve multi-step real-world problems involving money using decimal notation. | Grade 5 |
| Florida | MA.5.GR.1.1 | Classify triangles or quadrilaterals into different categories based on shared defining attributes. Explain why a triangle or quadrilateral would or would not belong to a category. | Grade 5 |
| Florida | MA.5.GR.1.2 | Identify and classify three-dimensional figures into categories based on their defining attributes. Figures are limited to right pyramids, right prisms, right circular cylinders, right circular cones and spheres. | Grade 5 |
| Florida | MA.5.GR.2.1 | Find the perimeter and area of a rectangle with fractional or decimal side lengths using visual models and formulas. | Grade 5 |
| Florida | MA.5.GR.3.1 | Explore volume as an attribute of three-dimensional figures by packing them with unit cubes without gaps. Find the volume of a right rectangular prism with whole-number side lengths by counting unit cubes. | Grade 5 |
| Florida | MA.5.GR.3.2 | Find the volume of a right rectangular prism with whole-number side lengths using a visual model and a formula. | Grade 5 |
| Florida | MA.5.GR.3.3 | Solve real-world problems involving the volume of right rectangular prisms, including problems with an unknown edge length, with whole-number edge lengths using a visual model or a formula. Write an equation with a variable for the unknown to represent the problem. | Grade 5 |
| Florida | MA.5.GR.4.1 | Identify the origin and axes in the coordinate system. Plot and label ordered pairs in the first quadrant of the coordinate plane. | Grade 5 |
| Florida | MA.5.GR.4.2 | Represent mathematical and real-world problems by plotting points in the first quadrant of the coordinate plane and interpret coordinate values of points in the context of the situation. | Grade 5 |
| Florida | MA.5.DP.2.1 | Collect and represent numerical data, including fractional and decimal values, using tables, line graphs or line plots. | Grade 5 |
| Florida | MA.5.DP.2.2 | Interpret numerical data, with whole-number values, represented with tables or line plots by determining the mean, mode, median or range. | Grade 5 |
| Florida | MA.6.NSO.1.1 | Extend previous understanding of numbers to define rational numbers. Plot, order and compare rational numbers. | Grade 6 |
| Florida | MA.6.NSO.1.2 | Given a mathematical or real-world context, represent quantities that have opposite direction using rational numbers. Compare them on a number line and explain the meaning of zero within its context. | Grade 6 |
| Florida | MA.6.NSO.1.3 | Given a mathematical or real-world context, interpret the absolute value of a number as the distance from zero on a number line. Find the absolute value of rational numbers. | Grade 6 |
| Florida | MA.6.NSO.1.4 | Solve mathematical and real-world problems involving absolute value, including the comparison of absolute value. | Grade 6 |
| Florida | MA.6.NSO.2.1 | Multiply and divide positive multi-digit numbers with decimals to the thousandths, including using a standard algorithm with procedural fluency. | Grade 6 |
| Florida | MA.6.NSO.2.2 | Extend previous understanding of multiplication and division to compute products and quotients of positive fractions by positive fractions, including mixed numbers, with procedural fluency. | Grade 6 |
| Florida | MA.6.NSO.2.3 | Solve multi-step real-world problems involving any of the four operations with positive multi-digit decimals or positive fractions, including mixed numbers. | Grade 6 |
| Florida | MA.6.NSO.3.3 | Evaluate positive rational numbers and integers with natural number exponents. | Grade 6 |
| Florida | MA.6.NSO.3.4 | Express composite whole numbers as a product of prime factors with natural number exponents. | Grade 6 |
| Florida | MA.6.NSO.3.5 | Rewrite positive rational numbers in different but equivalent forms including fractions, terminating decimals and percentages. | Grade 6 |
| Florida | MA.6.NSO.4.1 | Apply and extend previous understandings of operations with whole numbers to add and subtract integers with procedural fluency. | Grade 6 |
| Florida | MA.6.NSO.4.2 | Apply and extend previous understandings of operations with whole numbers to multiply and divide integers with procedural fluency. | Grade 6 |
| Florida | MA.6.AR.1.1 | Given a mathematical or real-world context, translate written descriptions into algebraic expressions and translate algebraic expressions into written descriptions. | Grade 6 |
| Florida | MA.6.AR.1.2 | Translate a real-world written description into an algebraic inequality in the form of x > a, x < a, x ≥ a or x ≤ a. Represent the inequality on a number line. | Grade 6 |
| Florida | MA.6.AR.1.3 | Evaluate algebraic expressions using substitution and order of operations. | Grade 6 |
| Florida | MA.6.AR.1.4 | Apply the properties of operations to generate equivalent algebraic expressions with integer coefficients. | Grade 6 |
| Florida | MA.6.AR.2.1 | Given an equation or inequality and a specified set of integer values, determine which values make the equation or inequality true or false. | Grade 6 |
| Florida | MA.6.AR.2.2 | Write and solve one-step equations in one variable within a mathematical or real-world context using addition and subtraction, where all terms and solutions are integers. | Grade 6 |
| Florida | MA.6.AR.2.3 | Write and solve one-step equations in one variable within a mathematical or real-world context using multiplication and division, where all terms and solutions are integers. | Grade 6 |
| Florida | MA.6.AR.2.4 | Determine the unknown decimal or fraction in an equation involving any of the four operations, relating three numbers, with the unknown in any position. | Grade 6 |
| Florida | MA.6.AR.3.1 | Given a real-world context, write and interpret ratios to show the relative sizes of two quantities using appropriate notation: a/b, a to b, or a : b where b ≠ 0. | Grade 6 |
| Florida | MA.6.AR.3.2 | Given a real-world context, determine a rate for a ratio of quantities with different units. Calculate and interpret the corresponding unit rate. | Grade 6 |
| Florida | MA.6.AR.3.3 | Extend previous understanding of fractions and numerical patterns to generate or complete a two- or three-column table to display equivalent part-to-part ratios and part-to-part-to-whole ratios. | Grade 6 |
| Florida | MA.6.AR.3.4 | Apply ratio relationships to solve mathematical and real-world problems involving percentages using the relationship between two quantities. | Grade 6 |
| Florida | MA.6.AR.3.5 | Solve mathematical and real-world problems involving ratios, rates and unit rates, including comparisons, mixtures, ratios of lengths and conversions within the same measurement system. | Grade 6 |
| Florida | MA.6.GR.1.1 | Extend previous understanding of the coordinate plane to plot rational number ordered pairs in all four quadrants and on both axes. Identify the x- or y- axis as the line of reflection when two ordered pairs have an opposite x- or y- coordinate. | Grade 6 |
| Florida | MA.6.GR.1.2 | Find distances between ordered pairs, limited to the same x-coordinate or the same y-coordinate, represented on the coordinate plane. | Grade 6 |
| Florida | MA.6.GR.1.3 | Solve mathematical and real-world problems by plotting points on a coordinate plane, including finding the perimeter or area of a rectangle. | Grade 6 |
| Florida | MA.6.GR.2.1 | Derive a formula for the area of a right triangle using a rectangle. Apply a formula to find the area of a triangle. | Grade 6 |
| Florida | MA.6.GR.2.2 | Solve mathematical and real-world problems involving the area of quadrilaterals and composite figures by decomposing them into triangles or rectangles. | Grade 6 |
| Florida | MA.6.GR.2.3 | Solve mathematical and real-world problems involving the volume of right rectangular prisms with positive rational number edge lengths using a visual model and a formula. | Grade 6 |
| Florida | MA.6.GR.2.4 | Given a mathematical or real-world context, find the surface area of right rectangular prisms and right rectangular pyramids using the figure's net. | Grade 6 |
| Florida | MA.7.NSO.1.1 | Know and apply the Laws of Exponents to evaluate numerical expressions and generate equivalent numerical expressions, limited to whole-number exponents and rational number bases. | Grade 7 |
| Florida | MA.7.NSO.1.2 | Rewrite rational numbers in different but equivalent forms including fractions, mixed numbers, repeating decimals and percentages to solve mathematical and real-world problems. | Grade 7 |
| Florida | MA.7.NSO.2.1 | Solve mathematical problems using multi-step order of operations with rational numbers including grouping symbols, whole-number exponents and absolute value. | Grade 7 |
| Florida | MA.7.NSO.2.2 | Add, subtract, multiply and divide rational numbers with procedural fluency. | Grade 7 |
| Florida | MA.7.NSO.2.3 | Solve real-world problems involving any of the four operations with rational numbers. | Grade 7 |
| Florida | MA.7.AR.1.1 | Apply properties of operations to add and subtract linear expressions with rational coefficients. | Grade 7 |
| Florida | MA.7.AR.1.2 | Determine whether two linear expressions are equivalent. | Grade 7 |
| Florida | MA.7.AR.2.1 | Write and solve one-step inequalities in one variable within a mathematical context and represent solutions algebraically or graphically. | Grade 7 |
| Florida | MA.7.AR.2.2 | Write and solve two-step equations in one variable within a mathematical or real-world context, where all terms are rational numbers. | Grade 7 |
| Florida | MA.7.AR.3.1 | Apply previous understanding of percentages and ratios to solve multi-step real-world percent problems. | Grade 7 |
| Florida | MA.7.AR.3.2 | Apply previous understanding of ratios to solve real-world problems involving proportions. | Grade 7 |
| Florida | MA.7.AR.3.3 | Solve mathematical and real-world problems involving the conversion of units across different measurement systems. | Grade 7 |
| Florida | MA.7.AR.4.1 | Determine whether two quantities have a proportional relationship by examining a table, graph or written description. | Grade 7 |
| Florida | MA.7.AR.4.2 | Determine the constant of proportionality within a mathematical or real-world context given a table, graph or written description of a proportional relationship. | Grade 7 |
| Florida | MA.7.AR.4.3 | Given a mathematical or real-world context, graph proportional relationships from a table, equation or a written description. | Grade 7 |
| Florida | MA.7.AR.4.4 | Given any representation of a proportional relationship, translate the representation to a written description, table or equation. | Grade 7 |
| Florida | MA.7.AR.4.5 | Solve real-world problems involving proportional relationships. | Grade 7 |
| Florida | MA.7.GR.1.1 | Apply formulas to find the areas of trapezoids, parallelograms and rhombi. | Grade 7 |
| Florida | MA.7.GR.1.2 | Solve mathematical or real-world problems involving the area of polygons or composite figures by decomposing them into triangles or quadrilaterals. | Grade 7 |
| Florida | MA.7.GR.1.3 | Explore the proportional relationship between circumferences and diameters of circles. Apply a formula for the circumference of a circle to solve mathematical and real-world problems. | Grade 7 |
| Florida | MA.7.GR.1.4 | Explore and apply a formula to find the area of a circle to solve mathematical and real-world problems. | Grade 7 |
| Florida | MA.7.GR.1.5 | Solve mathematical and real-world problems involving dimensions and areas of geometric figures, including scale drawings and scale factors. | Grade 7 |
| Florida | MA.7.GR.2.1 | Given a mathematical or real-world context, find the surface area of a right circular cylinder using the figure's net. | Grade 7 |
| Florida | MA.7.GR.2.2 | Solve real-world problems involving surface area of right circular cylinders. | Grade 7 |
| Florida | MA.7.GR.2.3 | Solve mathematical and real-world problems involving volume of right circular cylinders. | Grade 7 |
| Florida | MA.8.NSO.1.1 | Extend previous understanding of rational numbers to define irrational numbers within the real number system. Locate an approximate value of a numerical expression involving irrational numbers on a number line. | Grade 8 |
| Florida | MA.8.NSO.1.2 | Plot, order and compare rational and irrational numbers, represented in various forms. | Grade 8 |
| Florida | MA.8.NSO.1.3 | Extend previous understanding of the Laws of Exponents to include integer exponents. Apply the Laws of Exponents to evaluate numerical expressions and generate equivalent numerical expressions, limited to integer exponents and rational number bases, with procedural fluency. | Grade 8 |
| Florida | MA.8.NSO.1.4 | Express numbers in scientific notation to represent and approximate very large or very small quantities. Determine how many times larger or smaller one number is compared to a second number | Grade 8 |
| Florida | MA.8.NSO.1.5 | Add, subtract, multiply and divide numbers expressed in scientific notation with procedural fluency | Grade 8 |
| Florida | MA.8.NSO.1.6 | Solve real-world problems involving operations with numbers expressed in scientific notation. | Grade 8 |
| Florida | MA.8.NSO.1.7 | Solve multi-step mathematical and real-world problems involving the order of operations with rational numbers including exponents and radicals. | Grade 8 |
| Florida | MA.8.AR.1.1 | Apply the Laws of Exponents to generate equivalent algebraic expressions, limited to integer exponents and monomial bases. | Grade 8 |
| Florida | MA.8.AR.1.2 | Apply properties of operations to multiply two linear expressions with rational coefficients. | Grade 8 |
| Florida | MA.8.AR.1.3 | Rewrite the sum of two algebraic expressions having a common monomial factor as a common factor multiplied by the sum of two algebraic expressions. | Grade 8 |
| Florida | MA.8.AR.2.1 | Solve multi-step linear equations in one variable, with rational number coefficients. Include equations with variables on both sides. | Grade 8 |
| Florida | MA.8.AR.2.2 | Solve two-step linear inequalities in one variable and represent solutions algebraically and graphically. | Grade 8 |
| Florida | MA.8.AR.2.3 | Given an equation in the form of x²=p and x³=q, where p is a whole number and q is an integer, determine the real solutions. | Grade 8 |
| Florida | MA.8.AR.3.1 | Determine if a linear relationship is also a proportional relationship. | Grade 8 |
| Florida | MA.8.AR.3.2 | Given a table, graph or written description of a linear relationship, determine the slope. | Grade 8 |
| Florida | MA.8.AR.3.3 | Given a table, graph or written description of a linear relationship, write an equation in slope-intercept form. | Grade 8 |
| Florida | MA.8.AR.3.4 | Given a mathematical or real-world context, graph a two-variable linear equation from a written description, a table or an equation in slope-intercept form. | Grade 8 |
| Florida | MA.8.AR.3.5 | Given a real-world context, determine and interpret the slope and y-intercept of a two-variable linear equation from a written description, a table, a graph or an equation in slope-intercept form. | Grade 8 |
| Florida | MA.8.AR.4.1 | Given a system of two linear equations and a specified set of possible solutions, determine which ordered pairs satisfy the system of linear equations. | Grade 8 |
| Florida | MA.8.AR.4.2 | Given a system of two linear equations represented graphically on the same coordinate plane, determine whether there is one solution, no solution or infinitely many solutions. | Grade 8 |
| Florida | MA.8.AR.4.3 | Given a mathematical or real-world context, solve systems of two linear equations by graphing. | Grade 8 |
| Florida | MA.8.F.1.1 | Given a set of ordered pairs, a table, a graph or mapping diagram, determine whether the relationship is a function. Identify the domain and range of the relation. | Grade 8 |
| Florida | MA.8.F.1.2 | Given a function defined by a graph or an equation, determine whether the function is a linear function. Given an input-output table, determine whether it could represent a linear function. | Grade 8 |
| Florida | MA.8.F.1.3 | Analyze a real-world written description or graphical representation of a functional relationship between two quantities and identify where the function is increasing, decreasing or constant. | Grade 8 |
| Florida | MA.8.GR.1.1 | Apply the Pythagorean Theorem to solve mathematical and real-world problems involving unknown side lengths in right triangles. | Grade 8 |
| Florida | MA.8.GR.1.2 | Apply the Pythagorean Theorem to solve mathematical and real-world problems involving the distance between two points in a coordinate plane. | Grade 8 |
| Florida | MA.8.GR.1.3 | Use the Triangle Inequality Theorem to determine if a triangle can be formed from a given set of sides. Use the converse of the Pythagorean Theorem to determine if a right triangle can be formed from a given set of sides. | Grade 8 |
| Florida | MA.8.GR.1.4 | Solve mathematical problems involving the relationships between supplementary, complementary, vertical or adjacent angles. | Grade 8 |
| Florida | MA.8.GR.1.5 | Solve problems involving the relationships of interior and exterior angles of a triangle. | Grade 8 |
| Florida | MA.8.GR.1.6 | Develop and use formulas for the sums of the interior angles of regular polygons by decomposing them into triangles. | Grade 8 |
| Florida | MA.8.GR.2.1 | Given a preimage and image generated by a single transformation, identify the transformation that describes the relationship. | Grade 8 |
| Florida | MA.8.GR.2.2 | Given a preimage and image generated by a single dilation, identify the scale factor that describes the relationship. | Grade 8 |
| Florida | MA.8.GR.2.3 | Describe and apply the effect of a single transformation on two-dimensional figures using coordinates and the coordinate plane. | Grade 8 |
| Florida | MA.8.DP.1.1 | Given a set of real-world bivariate numerical data, construct a scatter plot or a line graph as appropriate for the context. | Grade 8 |
| Florida | MA.8.DP.1.2 | Given a scatter plot within a real-world context, describe patterns of association. | Grade 8 |
| Florida | MA.8.DP.1.3 | Given a scatter plot with a linear association, informally fit a straight line. | Grade 8 |
| Florida | MA.912.AR.2.1 | Given a real-world context, write and solve one-variable multi-step linear equations. | Algebra I |
| Florida | MA.912.AR.9.6 | Given a real-world context, represent constraints as systems of linear equations or inequalities. Interpret solutions to problems as viable or nonviable options. | Algebra I |
| Florida | MA.912.GR.4.5 | Solve mathematical and real-world problems involving the volume of three-dimensional figures limited to cylinders, pyramids, prisms, cones and spheres. | Algebra I |
| Florida | MA.912.GR.4.6 | Solve mathematical and real-world problems involving the surface area of three-dimensional figures limited to cylinders, pyramids, prisms, cones and spheres. | Algebra I |
| Georgia | K.NR.1.1 | Count up to 20 objects in a variety of structured arrangements and up to 10 objects in a scattered arrangement. | Kindergarten |
| Georgia | K.NR.1.2 | When counting objects, explain that the last number counted represents the total quantity in a set (cardinality), regardless of the arrangement and order. | Kindergarten |
| Georgia | K.NR.1.3 | Given a number from 1-20, identify the number that is one more or one less. | Kindergarten |
| Georgia | K.NR.2.1 | Count forward to 100 by tens and ones and backward from 20 by ones. | Kindergarten |
| Georgia | K.NR.2.2 | Count forward beginning from any number within 100 and count backward from any number within 20. | Kindergarten |
| Georgia | K.NR.3.1 | Describe numbers from 11 to 19 by composing (putting together) and decomposing (breaking apart) the numbers into ten ones and some more ones. | Kindergarten |
| Georgia | K.NR.4.1 | Identify written numerals 0-20 and represent a number of objects with a written numeral 0-20 (with 0 representing a count of no objects). | Kindergarten |
| Georgia | K.NR.4.2 | Compare two sets of up to 10 objects and identify whether the number of objects in one group is more or less than the other group, using the words “greater than,” “less than,” or “the same as”. | Kindergarten |
| Georgia | K.NR.5.1 | Compose (put together) and decompose (break apart) numbers up to 10 using objects and drawings. | Kindergarten |
| Georgia | K.NR.5.2 | Represent addition and subtraction within 10 from a given authentic situation using a variety of representations and strategies. | Kindergarten |
| Georgia | K.NR.5.3 | Use a variety of strategies to solve addition and subtraction problems within 10. | Kindergarten |
| Georgia | K.NR.5.4 | Fluently add and subtract within 5 using a variety of strategies to solve practical, mathematical problems. | Kindergarten |
| Georgia | K.PAR.6.1 | Create, extend, and describe repeating patterns with numbers and shapes, and explain the rationale for the pattern. | Kindergarten |
| Georgia | K.MDR.7.1 | Directly compare, describe, and order common objects, using measurable attributes (length, height, width, or weight) and describe the difference. | Kindergarten |
| Georgia | K.MDR.7.2 | Classify and sort up to ten objects into categories by an attribute; count the number of objects in each category and sort the categories by count. | Kindergarten |
| Georgia | K.GSR.8.1 | Identify, sort, classify, analyze, and compare two-dimensional shapes and three-dimensional figures, in different sizes and orientations, using informal language to describe their similarities, differences, number of sides and vertices, and other attributes. | Kindergarten |
| Georgia | K.GSR.8.2 | Describe the relative location of an object using positional words. | Kindergarten |
| Georgia | K.GSR.8.4 | Use two or more basic shapes to form larger shapes. | Kindergarten |
| Georgia | 1.NR.1.1 | Count within 120, forward and backward, starting at any number. In this range, read and write numerals and represent a number of objects with a written numeral. | Grade 1 |
| Georgia | 1.NR.1.2 | Explain that the two digits of a 2-digit number represent the amounts of tens and ones. | Grade 1 |
| Georgia | 1.NR.1.3 | Compare and order whole numbers up to 100 using concrete models, drawings, and the symbols >, =, and <. | Grade 1 |
| Georgia | 1.NR.2.1 | Use a variety of strategies to solve addition and subtraction problems within 20. | Grade 1 |
| Georgia | 1.NR.2.2 | Use pictures, drawings, and equations to develop strategies for addition and subtraction within 20 by exploring strings of related problems. | Grade 1 |
| Georgia | 1.NR.2.3 | Recognize the inverse relationship between subtraction and addition within 20 and use this inverse relationship to solve authentic problems. | Grade 1 |
| Georgia | 1.NR.2.4 | Fluently add and subtract within 10 using a variety of strategies. | Grade 1 |
| Georgia | 1.NR.2.5 | Use the meaning of the equal sign to determine whether equations involving addition and subtraction are true or false. | Grade 1 |
| Georgia | 1.NR.2.6 | Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers. | Grade 1 |
| Georgia | 1.NR.2.7 | Apply properties of operations as strategies to solve addition and subtraction problem situations within 20. | Grade 1 |
| Georgia | 1.PAR.3.1 | Investigate, create, and make predictions about repeating patterns with a core of up to 3 elements resulting from repeating an operation, as a series of shapes, or a number string. | Grade 1 |
| Georgia | 1.PAR.3.2 | Identify, describe, and create growing, shrinking, and repeating patterns based on the repeated addition or subtraction of 1s, 2s, 5s, and 10s. | Grade 1 |
| Georgia | 1.GSR.4.1 | Identify common two-dimensional shapes and three-dimensional figures, sort and classify them by their attributes and build and draw shapes that possess defining attributes. | Grade 1 |
| Georgia | 1.GSR.4.2 | Compose two-dimensional shapes (rectangles, squares, triangles, half-circles, and quarter-circles) and three-dimensional figures (cubes, rectangular prisms, cones, and cylinders) to create a shape formed of two or more common shapes and compose new shapes from the composite shape. | Grade 1 |
| Georgia | 1.GSR.4.3 | Partition circles and rectangles into two and four equal shares. | Grade 1 |
| Georgia | 1.NR.5.1 | Use a variety of strategies to solve applicable, mathematical addition and subtraction problems with one- and two-digit whole numbers. | Grade 1 |
| Georgia | 1.NR.5.2 | Given a two-digit number, mentally find 10 more or 10 less than the number, without having to count; explain the reasoning used. | Grade 1 |
| Georgia | 1.NR.5.3 | Add and subtract multiples of 10 within 100. | Grade 1 |
| Georgia | 1.MDR.6.1 | Estimate, measure, and record lengths of objects using non-standard units, and compare and order up to three objects using the recorded measurements. Describe the objects compared. | Grade 1 |
| Georgia | 1.MDR.6.2 | Tell and write time in hours and half-hours using analog and digital clocks, and measure elapsed time to the hour on the hour using a predetermined number line. | Grade 1 |
| Georgia | 1.MDR.6.3 | Identify the value of quarters and compare the values of pennies, nickels, dimes, and quarters. | Grade 1 |
| Georgia | 1.MDR.6.4 | Ask questions and answer them based on gathered information, observations, and appropriate graphical displays to compare and order whole numbers. | Grade 1 |
| Georgia | 2.NR.1.1 | Explain the value of a three- digit number using hundreds, tens, and ones in a variety of ways. | Grade 2 |
| Georgia | 2.NR.1.2 | Count forward and backward by ones from any number within 1000. Count forward by fives from multiples of 5 within 1000. Count forward and backward by 10s and 100s from any number within 1000. Count forward by 25s from 0. | Grade 2 |
| Georgia | 2.NR.1.3 | Represent, compare, and order whole numbers to 1000 with an emphasis on place value and equality. Use >, =, and < symbols to record the results of comparisons. | Grade 2 |
| Georgia | 2.NR.2.1 | Fluently add and subtract within 20 using a variety of mental, part-whole strategies. | Grade 2 |
| Georgia | 2.NR.2.2 | Find 10 more or 10 less than a given three-digit number and find 100 more or 100 less than a given three-digit number. | Grade 2 |
| Georgia | 2.NR.2.3 | Solve problems involving the addition and subtraction of two-digit numbers using part- whole strategies. | Grade 2 |
| Georgia | 2.NR.2.4 | Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction. | Grade 2 |
| Georgia | 2.NR.3.1 | Determine whether a group (up to 20) has an odd or even number of objects. Write an equation to express an even number as a sum of two equal addends. | Grade 2 |
| Georgia | 2.NR.3.2 | Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; the total as a sum of equal addends. write an equation to express | Grade 2 |
| Georgia | 2.PAR.4.1 | Identify, describe, and create a numerical pattern resulting from repeating an operation such as addition and subtraction. | Grade 2 |
| Georgia | 2.PAR.4.2 | Identify, describe, and create growing patterns and shrinking patterns involving addition and subtraction up to 20. | Grade 2 |
| Georgia | 2.MDR.5.1 | Construct simple measuring instruments using unit models. Compare unit models to rulers. | Grade 2 |
| Georgia | 2.MDR.5.2 | Estimate and measure the length of an object or distance to the nearest whole unit using appropriate units and standard measuring tools. | Grade 2 |
| Georgia | 2.MDR.5.3 | Measure to determine how much longer one object is than another and express the length difference in terms of a standard-length unit. | Grade 2 |
| Georgia | 2.MDR.5.4 | Ask questions and answer them based on gathered information, observations, and appropriate graphical displays to solve problems relevant to everyday life. | Grade 2 |
| Georgia | 2.MDR.5.5 | Represent whole-number sums and differences within a standard unit of measurement on a number line diagram. | Grade 2 |
| Georgia | 2.MDR.6.1 | Tell and write time from analog and digital clocks to the nearest five minutes, and estimate and measure elapsed time using a timeline, to the hour or half hour on the hour or half hour. | Grade 2 |
| Georgia | 2.MDR.6.2 | Find the value of a group of coins and determine combinations of coins that equal a given amount that is less than one hundred cents, and solve problems involving dollar bills, quarters, dimes, nickels, and pennies, using $ and ¢ symbols appropriately. | Grade 2 |
| Georgia | 2.GSR.7.1 | Describe, compare and sort 2-D shapes including polygons, triangles, quadrilaterals, pentagons, hexagons, and 3-D shapes including rectangular prisms and cones, given a set of attributes. | Grade 2 |
| Georgia | 2.GSR.7.3 | Partition circles and rectangles into two, three, or four equal shares. Identify and describe equal-sized parts of the whole using fractional names (“halves,” “thirds,” “fourths”, “half of,” “third of,” “quarter of,” etc.). | Grade 2 |
| Georgia | 2.GSR.7.4 | Recognize that equal shares of identical wholes may be different shapes within the same whole. | Grade 2 |
| Georgia | 3.NR.1.1 | Read and write multi-digit whole numbers up to 10,000 using base-ten numerals and expanded form. | Grade 3 |
| Georgia | 3.NR.1.2 | Use place value reasoning to compare multi-digit numbers up to 10,000, using >, =, and < symbols to record the results of comparisons. | Grade 3 |
| Georgia | 3.NR.1.3 | Use place value understanding to round whole numbers up to 1000 to the nearest 10 or 100. | Grade 3 |
| Georgia | 3.PAR.2.1 | Fluently add and subtract within 1000 to solve problems. | Grade 3 |
| Georgia | 3.PAR.2.2 | Apply part-whole strategies, properties of operations and place value understanding, to solve problems involving addition and subtraction within 10,000. Represent these problems using equations with a letter standing for the unknown quantity. Justify solutions. | Grade 3 |
| Georgia | 3.PAR.3.1 | Describe, extend, and create numeric patterns related to multiplication. Make predictions related to the patterns. | Grade 3 |
| Georgia | 3.PAR.3.2 | Represent single digit multiplication and division facts using a variety of strategies. Explain the relationship between multiplication and division. | Grade 3 |
| Georgia | 3.PAR.3.3 | Apply properties of operations (i.e., commutative property, associative property, distributive property) to multiply and divide within 100. | Grade 3 |
| Georgia | 3.PAR.3.5 | Use place value reasoning and properties of operations to multiply one-digit whole numbers by multiples of 10, in the range 10-90. | Grade 3 |
| Georgia | 3.PAR.3.6 | Solve practical, relevant problems involving multiplication and division within 100 using part-whole strategies, visual representations, and/or concrete models. | Grade 3 |
| Georgia | 3.PAR.3.7 | Use multiplication and division to solve problems involving whole numbers to 100. Represent these problems using equations with a letter standing for the unknown quantity. Justify solutions. | Grade 3 |
| Georgia | 3.NR.4.1 | Describe a unit fraction and explain how multiple copies of a unit fraction form a non-unit fraction. Use parts of a whole, parts of a set, points on a number line, distances on a number line and area models. | Grade 3 |
| Georgia | 3.NR.4.2 | Compare two unit fractions by flexibly using a variety of tools and strategies. | Grade 3 |
| Georgia | 3.NR.4.3 | Represent fractions, including fractions greater than one, in multiple ways. | Grade 3 |
| Georgia | 3.NR.4.4 | Recognize and generate simple equivalent fractions. | Grade 3 |
| Georgia | 3.MDR.5.1 | Ask questions and answer them based on gathered information, observations, and appropriate graphical displays to solve problems relevant to everyday life. | Grade 3 |
| Georgia | 3.MDR.5.2 | Tell and write time to the nearest minute and estimate time to the nearest fifteen minutes (quarter hour) from the analysis of an analog clock. | Grade 3 |
| Georgia | 3.MDR.5.3 | Solve meaningful problems involving elapsed time, including intervals of time to the hour, half hour, and quarter hour where the times presented are only on the hour, half hour, or quarter hour within a.m. or p.m. only. | Grade 3 |
| Georgia | 3.MDR.5.4 | Use rulers to measure lengths in halves and fourths (quarters) of an inch and a whole inch. | Grade 3 |
| Georgia | 3.MDR.5.5 | Estimate and measure liquid volumes, lengths and masses of objects using customary units. Solve problems involving mass, length, and volume given in the same unit, and reason about the relative sizes of measurement units within the customary system. | Grade 3 |
| Georgia | 3.GSR.6.1 | Identify perpendicular line segments, parallel line segments, and right angles, identify these in polygons, and solve problems involving parallel line segments, perpendicular line segments, and right angles. | Grade 3 |
| Georgia | 3.GSR.6.2 | Classify, compare, and contrast polygons, with a focus on quadrilaterals, based on properties. Analyze specific 3-dimensional figures to identify and describe quadrilaterals as faces of these figures. | Grade 3 |
| Georgia | 3.GSR.6.3 | Identify lines of symmetry in polygons. | Grade 3 |
| Georgia | 3.GSR.7.1 | Investigate area by covering the space of rectangles presented in realistic situations using multiple copies of the same unit, with no gaps or overlaps, and determine the total area (total number of units that covered the space). | Grade 3 |
| Georgia | 3.GSR.7.2 | Determine the area of rectangles (or shapes composed of rectangles) presented in relevant problems by tiling and counting. | Grade 3 |
| Georgia | 3.GSR.7.3 | Discover and explain how area can be found by multiplying the dimensions of a rectangle. | Grade 3 |
| Georgia | 3.GSR.8.1 | Determine the perimeter of a polygon and explain that the perimeter represents the distance around a polygon. Solve problems involving perimeters of polygons. | Grade 3 |
| Georgia | 3.GSR.8.2 | Investigate and describe how rectangles with the same perimeter can have different areas or how rectangles with the same area can have different perimeters. | Grade 3 |
| Georgia | 4.NR.1.1 | Read and write multi-digit whole numbers to the hundred-thousands place using base-ten numerals and expanded form. | Grade 4 |
| Georgia | 4.NR.1.2 | Recognize and show that a digit in one place has a value ten times greater than what it represents in the place to its right and extend this understanding to determine the value of a digit when it is shifted to the left or right, based on the relationship between multiplication and division. | Grade 4 |
| Georgia | 4.NR.1.3 | Use place value reasoning to represent, compare, and order multi-digit numbers, using >, =, and < symbols to record the results of comparisons. | Grade 4 |
| Georgia | 4.NR.1.4 | Use place value understanding to round multi-digit whole numbers. | Grade 4 |
| Georgia | 4.NR.2.1 | Fluently add and subtract multi-digit numbers to solve practical, mathematical problems using place value understanding, properties of operations, and relationships between operations. | Grade 4 |
| Georgia | 4.NR.2.2 | Interpret, model, and solve problems involving multiplicative comparison. | Grade 4 |
| Georgia | 4.NR.2.3 | Solve relevant problems involving multiplication of a number with up to four digits by a 1-digit whole number or involving multiplication of two two-digit numbers using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. | Grade 4 |
| Georgia | 4.NR.2.4 | Solve authentic division problems involving up to 4-digit dividends and 1- digit divisors (including whole number quotients with remainders) using strategies based on place-value understanding, properties of operations, and the relationships between operations. | Grade 4 |
| Georgia | 4.NR.2.5 | Solve multi-step problems using addition, subtraction, multiplication, and division involving whole numbers. Use mental computation and estimation strategies to justify the reasonableness of solutions. | Grade 4 |
| Georgia | 4.PAR.3.1 | Generate both number and shape patterns that follow a provided rule. | Grade 4 |
| Georgia | 4.PAR.3.2 | Use input-output rules, tables, and charts to represent and describe patterns, find relationships, and solve problems. | Grade 4 |
| Georgia | 4.PAR.3.3 | Find factor pairs in the range 1–100 and find multiples of single-digit numbers up to 100. | Grade 4 |
| Georgia | 4.PAR.3.4 | Identify composite numbers and prime numbers and explain the relationship with the factor pairs. | Grade 4 |
| Georgia | 4.NR.4.1 | Using concrete materials, drawings, and number lines, demonstrate and explain the relationship between equivalent fractions, including fractions greater than one, and explain the identity property of multiplication as it relates to equivalent fractions. Generate equivalent fractions using these relationships. | Grade 4 |
| Georgia | 4.NR.4.2 | Compare two fractions with the same numerator or the same denominator by reasoning about their size and recognize that comparisons are valid only when the two fractions refer to the same whole. | Grade 4 |
| Georgia | 4.NR.4.3 | Compare two fractions with different numerators and/or different denominators by flexibly using a variety of tools and strategies and recognize that comparisons are valid only when the two fractions refer to the same whole. | Grade 4 |
| Georgia | 4.NR.4.4 | Represent whole numbers and fractions as the sum of unit fractions. | Grade 4 |
| Georgia | 4.NR.4.5 | Represent a fraction as a sum of fractions with the same denominator in more than one way, recording with an equation. | Grade 4 |
| Georgia | 4.NR.4.6 | Add and subtract fractions and mixed numbers with like denominators using a variety of tools. | Grade 4 |
| Georgia | 4.NR.5.1 | Demonstrate and explain the concept of equivalent fractions with denominators of 10 and 100, using concrete materials and visual models. Add two fractions with denominators of 10 and 100. | Grade 4 |
| Georgia | 4.NR.5.2 | Represent, read, and write fractions with denominators of 10 or 100 using decimal notation, and decimal numbers to the hundredths place as fractions, using concrete materials and drawings. | Grade 4 |
| Georgia | 4.NR.5.3 | Compare two decimal numbers to the hundredths place by reasoning about their size. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions. | Grade 4 |
| Georgia | 4.MDR.6.1 | Use the four operations to solve problems involving elapsed time to the nearest minute, intervals of time, metric measurements of liquid volumes, lengths, distances, and masses of objects, including problems involving fractions with like denominators, and also problems that require expressing measurements given in a larger unit in terms of a smaller unit, and expressing a smaller unit in terms of a larger unit based on the idea of equivalence. | Grade 4 |
| Georgia | 4.MDR.6.3 | Create dot plots to display a distribution of numerical (quantitative) measurement data. | Grade 4 |
| Georgia | 4.GSR.7.1 | Recognize angles as geometric shapes formed when two rays share a common endpoint. Draw right, acute, and obtuse angles based on the relationship of the angle measure to 90 degrees. | Grade 4 |
| Georgia | 4.GSR.7.2 | Measure angles in reference to a circle with the center at the common endpoint of two rays. Determine an angle’s measure in relation to the 360 degrees in a circle through division or as a missing factor problem. | Grade 4 |
| Georgia | 4.GSR.8.1 | Explore, investigate, and draw points, lines, line segments, rays, angles (right, acute, obtuse), perpendicular lines, parallel lines, and lines of symmetry. Identify these in two-dimensional figures. | Grade 4 |
| Georgia | 4.GSR.8.2 | Classify, compare, and contrast polygons based on lines of symmetry, the presence or absence of parallel or perpendicular line segments, or the presence or absence of angles of a specified size and based on side lengths. | Grade 4 |
| Georgia | 4.GSR.8.3 | Solve problems involving area and perimeter of composite rectangles involving whole numbers with known side lengths. | Grade 4 |
| Georgia | 5.NR.1.1 | Explain that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. | Grade 5 |
| Georgia | 5.NR.1.2 | Explain patterns in the placement of digits when multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10, up to 103. | Grade 5 |
| Georgia | 5.NR.2.1 | Fluently multiply multi-digit (up to 3- digit by 2-digit) whole numbers to solve authentic problems. | Grade 5 |
| Georgia | 5.NR.2.2 | Fluently divide multi-digit whole numbers (up to 4-digit dividends and 2-digit divisors no greater than 25) to solve practical problems. | Grade 5 |
| Georgia | 5.NR.3.1 | Explain the meaning of a fraction as division of the numerator by the denominator. Solve problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers. | Grade 5 |
| Georgia | 5.NR.3.2 | Compare and order up to three fractions with different numerators and/or different denominators by flexibly using a variety of tools and strategies. | Grade 5 |
| Georgia | 5.NR.3.3 | Model and solve problems involving addition and subtraction of fractions and mixed numbers with unlike denominators. | Grade 5 |
| Georgia | 5.NR.3.4 | Model and solve problems involving multiplication of a fraction and a whole number. | Grade 5 |
| Georgia | 5.NR.3.5 | Explain why multiplying a whole number by a fraction greater than one results in a product greater than the whole number, and why multiplying a whole number by a fraction less than one results in a product less than the whole number and multiplying a whole number by a fraction equal to one results in a product equal to the whole number. | Grade 5 |
| Georgia | 5.NR.3.6 | Model and solve problems involving division of a unit fraction by a whole number and a whole number by a unit fraction. | Grade 5 |
| Georgia | 5.NR.4.1 | Read and write decimal numbers to the thousandths place using base- ten numerals written in standard form and expanded form. | Grade 5 |
| Georgia | 5.NR.4.2 | Represent, compare, and order decimal numbers to the thousandths place based on the meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. | Grade 5 |
| Georgia | 5.NR.4.3 | Use place value understanding to round decimal numbers to the hundredths place. | Grade 5 |
| Georgia | 5.NR.4.4 | Solve problems involving addition and subtraction of decimal numbers to the hundredths place using a variety of strategies. | Grade 5 |
| Georgia | 5.NR.5.1 | Write, interpret, and evaluate simple numerical expressions involving whole numbers with or without grouping symbols to represent actual situations. | Grade 5 |
| Georgia | 5.PAR.6.1 | Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms by completing a table. | Grade 5 |
| Georgia | 5.PAR.6.2 | Represent problems by plotting ordered pairs and explain coordinate values of points in the first quadrant of the coordinate plane. | Grade 5 |
| Georgia | 5.MDR.7.1 | Explore realistic problems involving different units of measurement, including distance, mass, weight, volume, and time. | Grade 5 |
| Georgia | 5.MDR.7.2 | Ask questions and answer them based on gathered information, observations, and appropriate graphical displays to solve problems relevant to everyday life. | Grade 5 |
| Georgia | 5.MDR.7.3 | Convert among units within the metric system and then apply these conversions to solve multi- step, practical problems. | Grade 5 |
| Georgia | 5.MDR.7.4 | Convert among units within relative sizes of measurement units within the customary measurement system. | Grade 5 |
| Georgia | 5.GSR.8.1 | Classify, compare, and contrast polygons based on properties. | Grade 5 |
| Georgia | 5.GSR.8.2 | Determine, through exploration and investigation, that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. | Grade 5 |
| Georgia | 5.GSR.8.3 | Investigate volume of right rectangular prisms by packing them with unit cubes without gaps or overlaps. Then, determine the total volume to solve problems. | Grade 5 |
| Georgia | 5.GSR.8.4 | Discover and explain how the volume of a right rectangular prism can be found by multiplying the area of the base times the height to solve authentic, mathematical problems. | Grade 5 |
| Georgia | 6.NR.1.1 | Fluently add and subtract any combination of fractions to solve problems. | Grade 6 |
| Georgia | 6.NR.1.2 | Multiply and divide any combination of whole numbers, fractions, and mixed numbers using a student-selected strategy. Interpret products and quotients of fractions and solve word problems. | Grade 6 |
| Georgia | 6.NR.1.3 | Perform operations with multi-digit decimal numbers fluently using models and student-selected strategies. | Grade 6 |
| Georgia | 6.NR.2.2 | Summarize categorical and quantitative (numerical) data sets in relation to the context: display the distributions of quantitative (numerical) data in plots on a number line, including dot plots, histograms, and box plots and display the distribution of categorical data using bar graphs. | Grade 6 |
| Georgia | 6.NR.2.4 | Design simple experiments and collect data. Use data gathered from realistic scenarios and simulations to determine quantitative measures of center (median and/or mean) and variability (interquartile range and range). Use these quantities to draw conclusions about the data, compare different numerical data sets, and make predictions. | Grade 6 |
| Georgia | 6.NR.3.1 | Identify and compare integers and explain the meaning of zero based on multiple authentic situations. | Grade 6 |
| Georgia | 6.NR.3.2 | Order and plot integers on a number line and use distance from zero to discover the connection between integers and their opposites. | Grade 6 |
| Georgia | 6.NR.3.3 | Recognize and explain that opposite signs of integers indicate locations on opposite sides of zero on the number line; recognize and explain that the opposite of the opposite of a number is the number itself. | Grade 6 |
| Georgia | 6.NR.3.4 | Write, interpret, and explain statements of order for rational numbers in authentic, mathematical situations. Compare rational numbers, including integers, using equality and inequality symbols. | Grade 6 |
| Georgia | 6.NR.3.5 | Explain the absolute value of a rational number as its distance from zero on the number line; interpret absolute value as distance for a positive or negative quantity in a relevant situation. | Grade 6 |
| Georgia | 6.NR.3.6 | Distinguish comparisons of absolute value from statements about order. | Grade 6 |
| Georgia | 6.NR.4.1 | Explain the concept of a ratio, represent ratios, and use ratio language to describe a relationship between two quantities. | Grade 6 |
| Georgia | 6.NR.4.2 | Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios. | Grade 6 |
| Georgia | 6.NR.4.3 | Solve problems involving proportions using a variety of student-selected strategies. | Grade 6 |
| Georgia | 6.NR.4.4 | Describe the concept of rates and unit rate in the context of a ratio relationship. | Grade 6 |
| Georgia | 6.NR.4.5 | Solve unit rate problems including those involving unit pricing and constant speed. | Grade 6 |
| Georgia | 6.NR.4.6 | Calculate a percent of a quantity as a rate per 100 and solve everyday problems given a percent. | Grade 6 |
| Georgia | 6.NR.4.7 | Use ratios to convert within measurement systems (customary and metric) to solve authentic problems that exist in everyday life. | Grade 6 |
| Georgia | 6.GSR.5.1 | Explore area as a measurable attribute of triangles, quadrilaterals, and other polygons conceptually by composing or decomposing into rectangles, triangles, and other shapes. Find the area of these geometric figures to solve problems. | Grade 6 |
| Georgia | 6.GSR.5.2 | Given the net of three-dimensional figures with rectangular and triangular faces, determine the surface area of these figures. | Grade 6 |
| Georgia | 6.GSR.5.3 | Calculate the volume of right rectangular prisms with fractional edge lengths by applying the formula, V = (area of base) x (height). | Grade 6 |
| Georgia | 6.PAR.6.1 | Write and evaluate numerical expressions involving rational bases and whole-number exponents. | Grade 6 |
| Georgia | 6.PAR.6.3 | Write and read expressions that represent operations with numbers and variables in realistic situations. | Grade 6 |
| Georgia | 6.PAR.6.4 | Evaluate expressions when given values for the variables, including expressions that arise in everyday situations. | Grade 6 |
| Georgia | 6.PAR.6.5 | Apply the properties of operations to identify and generate equivalent expressions. | Grade 6 |
| Georgia | 6.PAR.7.1 | Solve one-step equations and inequalities involving variables when values for the variables are given. Determine whether an equation and inequality involving a variable is true or false for a given value of the variable. | Grade 6 |
| Georgia | 6.PAR.7.2 | Write one-step equations and inequalities to represent and solve problems; explain that a variable can represent an unknown number or any number in a specified set. | Grade 6 |
| Georgia | 6.PAR.7.3 | Solve problems by writing and solving equations of the form x +- p = q, px = q, and x/p = q for cases in which p, q, and x are all nonnegative rational numbers. | Grade 6 |
| Georgia | 6.PAR.7.4 | Recognize and generate inequalities of the form x > c, x ≥ c, x < c, or x ≤ c to explain situations that have infinitely many solutions; represent solutions of such inequalities on a number line. | Grade 6 |
| Georgia | 6.PAR.8.1 | Locate and position rational numbers on a horizontal or vertical number line; find and position pairs of integers and other rational numbers on a coordinate plane. | Grade 6 |
| Georgia | 6.PAR.8.2 | Show and explain that signs of numbers in ordered pairs indicate locations in quadrants of the coordinate plane and determine how two ordered pairs may differ based only on the signs. | Grade 6 |
| Georgia | 6.PAR.8.3 | Solve problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same x- coordinate or the same y-coordinate. | Grade 6 |
| Georgia | 6.PAR.8.4 | Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same x-coordinate or the same y- coordinate. | Grade 6 |
| Georgia | 7.NR.1.1 | Show that a number and its opposite have a sum of 0 (are additive inverses). Describe situations in which opposite quantities combine to make 0. | Grade 7 |
| Georgia | 7.NR.1.2 | Show and explain p + q as the number located a distance |q| from p, in the positive or negative direction, depending on whether q is positive or negative. Interpret sums of rational numbers by describing applicable situations. | Grade 7 |
| Georgia | 7.NR.1.3 | Represent addition and subtraction with rational numbers on a horizontal or a vertical number line diagram to solve authentic problems. | Grade 7 |
| Georgia | 7.NR.1.4 | Show and explain subtraction of rational numbers as adding the additive inverse, p – q = p + (–q). Show that the distance between two rational numbers on the number line is the absolute value of their difference and apply this principle in contextual situations. | Grade 7 |
| Georgia | 7.NR.1.5 | Apply properties of operations, including part-whole reasoning, as strategies to add and subtract rational numbers. | Grade 7 |
| Georgia | 7.NR.1.6 | Make sense of multiplication of rational numbers using realistic applications. | Grade 7 |
| Georgia | 7.NR.1.7 | Show and explain that integers can be divided, assuming the divisor is not zero, and every quotient of integers is a rational number. | Grade 7 |
| Georgia | 7.NR.1.8 | Represent the multiplication and division of integers using a variety of strategies and interpret products and quotients of rational numbers by describing them based on the relevant situation. | Grade 7 |
| Georgia | 7.NR.1.9 | Apply properties of operations as strategies to solve multiplication and division problems involving rational numbers represented in an applicable scenario. | Grade 7 |
| Georgia | 7.NR.1.10 | Convert rational numbers between forms to include fractions, decimal numbers and percentages, using understanding of the part divided by the whole. Know that the decimal form of a rational number terminates in 0s or eventually repeats. | Grade 7 |
| Georgia | 7.NR.1.11 | Solve multi-step, contextual problems involving rational numbers, converting between forms as appropriate, and assessing the reasonableness of answers using mental computation and estimation strategies. | Grade 7 |
| Georgia | 7.PAR.2.1 | Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients. | Grade 7 |
| Georgia | 7.PAR.2.2 | Rewrite an expression in different forms from a contextual problem to clarify the problem and show how the quantities in it are related. | Grade 7 |
| Georgia | 7.PAR.3.1 | Construct algebraic equations to solve practical problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Interpret the solution based on the situation. | Grade 7 |
| Georgia | 7.PAR.3.2 | Construct algebraic inequalities to solve problems, leading to inequalities of the form px + q > r, px + q < r, px + q ≤ r, or px + q ≥ r, where p, q, and r are specific rational numbers. Graph and interpret the solution based on the realistic situation that the inequalities represent. | Grade 7 |
| Georgia | 7.PAR.4.1 | Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units presented in realistic problems. | Grade 7 |
| Georgia | 7.PAR.4.2 | Determine the unit rate (constant of proportionality) in tables, graphs (1, r), equations, diagrams, and verbal descriptions of proportional relationships to solve realistic problems. | Grade 7 |
| Georgia | 7.PAR.4.3 | Determine whether two quantities presented in authentic problems are in a proportional relationship. | Grade 7 |
| Georgia | 7.PAR.4.4 | Identify, represent, and use proportional relationships. | Grade 7 |
| Georgia | 7.PAR.4.5 | Use context to explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r) where r is the unit rate. | Grade 7 |
| Georgia | 7.PAR.4.6 | Solve everyday problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale. | Grade 7 |
| Georgia | 7.PAR.4.7 | Use similar triangles to explain why the slope, m, is the same between any two distinct points on a non- vertical line in the coordinate plane. | Grade 7 |
| Georgia | 7.PAR.4.8 | Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. | Grade 7 |
| Georgia | 7.PAR.4.9 | Use proportional relationships to solve multi-step ratio and percent problems presented in applicable situations. | Grade 7 |
| Georgia | 7.GSR.5.1 | Measure angles in whole non- standard units. | Grade 7 |
| Georgia | 7.GSR.5.2 | Measure angles in whole number degrees using a protractor. | Grade 7 |
| Georgia | 7.GSR.5.3 | Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve equations for an unknown angle in a figure. | Grade 7 |
| Georgia | 7.GSR.5.4 | Explore and describe the relationship between pi, radius, diameter, circumference, and area of a circle to derive the formulas for the circumference and area of a circle. | Grade 7 |
| Georgia | 7.GSR.5.5 | Given the formula for the area and circumference of a circle, solve problems that exist in everyday life. | Grade 7 |
| Georgia | 7.GSR.5.6 | Solve realistic problems involving surface area of right prisms and cylinders. | Grade 7 |
| Georgia | 7.GSR.5.7 | Describe the two-dimensional figures (cross sections) that result from slicing three-dimensional figures, as in the plane sections of right rectangular prisms, right rectangular pyramids, cones, cylinders, and spheres. | Grade 7 |
| Georgia | 7.GSR.5.8 | Explore volume as a measurable attribute of cylinders and right prisms. Find the volume of these geometric figures using concrete problems. | Grade 7 |
| Georgia | 8.NR.1.2 | Approximate irrational numbers to compare the size of irrational numbers, locate them approximately on a number line, and estimate the value of expressions. | Grade 8 |
| Georgia | 8.NR.2.1 | Apply the properties of integer exponents to generate equivalent numerical expressions. | Grade 8 |
| Georgia | 8.NR.2.2 | Use square root and cube root symbols to represent solutions to equations. Recognize that x² = p (where p is a positive rational number and |x| ≤ 25) has two solutions and x³ = p (where p is a negative or positive rational number and |x| ≤ 10) has one solution. Evaluate square roots of perfect squares ≤ 625 and cube roots of perfect cubes ≥ -1000 and ≤ 1000. | Grade 8 |
| Georgia | 8.NR.2.3 | Use numbers expressed in scientific notation to estimate very large or very small quantities, and to express how many times as much one is than the other. | Grade 8 |
| Georgia | 8.NR.2.4 | Add, subtract, multiply and divide numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Interpret scientific notation that has been generated by technology (e.g., calculators or online technology tools). | Grade 8 |
| Georgia | 8.PAR.3.2 | Describe and solve linear equations in one variable with one solution (x = a), infinitely many solutions (a = a), or no solutions (a = b). Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x = a, a = a, or a = b results (where a and b are different numbers). | Grade 8 |
| Georgia | 8.PAR.3.3 | Create and solve linear equations and inequalities in one variable within a relevant application. | Grade 8 |
| Georgia | 8.PAR.3.5 | Solve linear equations and inequalities in one variable with coefficients represented by letters and explain the solution based on the contextual, mathematical situation. | Grade 8 |
| Georgia | 8.PAR.4.1 | Use the equation y = mx (proportional) for a line through the origin to derive the equation y = mx + b (non-proportional) for a line intersecting the vertical axis at b. | Grade 8 |
| Georgia | 8.PAR.4.2 | Show and explain that the graph of an equation representing an applicable situation in two variables is the set of all its solutions plotted in the coordinate plane. | Grade 8 |
| Georgia | 8.FGR.5.1 | Show and explain that a function is a rule that assigns to each input exactly one output. | Grade 8 |
| Georgia | 8.FGR.5.2 | Within realistic situations, identify and describe examples of functions that are linear or nonlinear. Sketch a graph that exhibits the qualitative features of a function that has been described verbally. | Grade 8 |
| Georgia | 8.FGR.5.3 | Relate the domain of a linear function to its graph and where applicable to the quantitative relationship it describes. | Grade 8 |
| Georgia | 8.FGR.5.4 | Compare properties (rate of change and initial value) of two functions used to model an authentic situation each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). | Grade 8 |
| Georgia | 8.FGR.5.5 | Write and explain the equations y = mx + b (slope-intercept form), Ax + By = C (standard form), and (y - y1) = m(x-x1) (point-slope form) as defining a linear function whose graph is a straight line to reveal and explain different properties of the function. | Grade 8 |
| Georgia | 8.FGR.5.7 | Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x,y) values, including reading these from a table or from a graph. | Grade 8 |
| Georgia | 8.FGR.5.8 | Explain the meaning of the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values. | Grade 8 |
| Georgia | 8.FGR.6.1 | Show that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, visually fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line of best fit. | Grade 8 |
| Georgia | 8.FGR.7.1 | Interpret and solve relevant mathematical problems leading to two linear equations in two variables. | Grade 8 |
| Georgia | 8.FGR.7.2 | Show and explain that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because the points of intersection satisfy both equations simultaneously. | Grade 8 |
| Georgia | 8.FGR.7.3 | Approximate solutions of two linear equations in two variables by graphing the equations and solving simple cases by inspection. | Grade 8 |
| Georgia | 8.FGR.7.4 | Analyze and solve systems of two linear equations in two variables algebraically to find exact solutions. | Grade 8 |
| Georgia | 8.FGR.7.5 | Create and compare the equations of two lines that are either parallel to each other, perpendicular to each other, or neither parallel nor perpendicular. | Grade 8 |
| Georgia | 8.GSR.8.2 | Apply the Pythagorean Theorem to determine unknown side lengths in right triangles within authentic, mathematical problems in two and three dimensions. | Grade 8 |
| Georgia | 8.GSR.8.3 | Apply the Pythagorean Theorem to find the distance between two points in a coordinate system in practical, mathematical problems. | Grade 8 |
| Georgia | 8.GSR.8.4 | Apply the formulas for the volume of cones, cylinders, and spheres and use them to solve in relevant problems. | Grade 8 |
| Hawaii | K.CC.1 | Count to 100 by ones and by tens. | Kindergarten |
| Hawaii | K.CC.2 | Count forward beginning from a given number within the known sequence (instead of having to begin at 1). | Kindergarten |
| Hawaii | K.CC.3 | Write numbers from 0 to 20. Represent a number of objects with a written numeral 0-20 (with 0 representing a count of no objects). | Kindergarten |
| Hawaii | K.CC.4 | Understand the relationship between numbers and quantities; connect counting to cardinality. | Kindergarten |
| Hawaii | K.CC.5 | Count to answer “how many?” questions about as many as 20 things arranged in a line, a rectangular array, or a circle, or as many as 10 things in a scattered configuration; given a number from 1-20, count out that many objects. | Kindergarten |
| Hawaii | K.CC.6 | Identify whether the number of objects in one group is greater than, less than, or equal to the number of objects in another group, e.g., by using matching and counting strategies. | Kindergarten |
| Hawaii | K.CC.7 | Compare two numbers between 1 and 10 presented as written numerals. | Kindergarten |
| Hawaii | K.G.1 | Describe objects in the environment using names of shapes, and describe the relative positions of these objects using terms such as above, below, beside, in front of, behind, and next to. | Kindergarten |
| Hawaii | K.G.2 | Correctly name shapes regardless of their orientations or overall size. | Kindergarten |
| Hawaii | K.G.3 | Identify shapes as two-dimensional (lying in a plane, “flat”) or three-dimensional (“solid”). | Kindergarten |
| Hawaii | K.G.4 | Analyze and compare two- and three-dimensional shapes, in different sizes and orientations, using informal language to describe their similarities, differences, parts (e.g., number of sides and vertices/“corners”) and other attributes (e.g., having sides of equal length). | Kindergarten |
| Hawaii | K.G.6 | Compose simple shapes to form larger shapes. | Kindergarten |
| Hawaii | K.MD.1 | Describe measurable attributes of objects, such as length or weight. Describe several measurable attributes of a single object. | Kindergarten |
| Hawaii | K.MD.2 | Directly compare two objects with a measurable attribute in common, to see which object has “more of”/“less of” the attribute, and describe the difference. | Kindergarten |
| Hawaii | K.MD.3 | Classify objects into given categories; count the numbers of objects in each category and sort the categories by count. | Kindergarten |
| Hawaii | K.NBT.1 | Compose and decompose numbers from 11 to 19 into ten ones and some further ones, e.g., by using objects or drawings, and record each composition or decomposition by a drawing or equation (e.g., 18 = 10 + 8); understand that these numbers are composed of ten ones and one, two, three, four, five, six, seven, eight, or nine ones. | Kindergarten |
| Hawaii | K.OA.1 | Represent addition and subtraction with objects, fingers, mental images, drawings, sounds (e.g., claps), acting out situations, verbal explanations, expressions, or equations. | Kindergarten |
| Hawaii | K.OA.2 | Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem. | Kindergarten |
| Hawaii | K.OA.3 | Decompose numbers less than or equal to 10 into pairs in more than one way, e.g., by using objects or drawings, and record each decomposition by a drawing or equation (e.g., 5 = 2 + 3 and 5 = 4 + 1). | Kindergarten |
| Hawaii | K.OA.4 | For any number from 1 to 9, find the number that makes 10 when added to the given number, e.g., by using objects or drawings, and record the answer with a drawing or equation. | Kindergarten |
| Hawaii | K.OA.5 | Fluently add and subtract within 5. | Kindergarten |
| Hawaii | 1.G.1 | Distinguish between defining attributes (e.g., triangles are closed and three-sided) versus non-defining attributes (e.g., color, orientation, overall size); build and draw shapes to possess defining attributes. | Grade 1 |
| Hawaii | 1.G.2 | Compose two-dimensional shapes (rectangles, squares, trapezoids, triangles, half-circles, and quarter-circles) or three-dimensional shapes (cubes, right rectangular prisms, right circular cones, and right circular cylinders) to create a composite shape, and compose new shapes from the composite shape. | Grade 1 |
| Hawaii | 1.G.3 | Partition circles and rectangles into two and four equal shares, describe the shares using the words halves, fourths, and quarters, and use the phrases half of, fourth of, and quarter of. Describe the whole as two of, or four of the shares. Understand for these examples that decomposing into more equal shares creates smaller shares. | Grade 1 |
| Hawaii | 1.MD.1 | Order three objects by length; compare the lengths of two objects indirectly by using a third object. | Grade 1 |
| Hawaii | 1.MD.2 | Express the length of an object as a whole number of length units, by laying multiple copies of a shorter object (the length unit) end to end; understand that the length measurement of an object is the number of same-size length units that span it with no gaps or overlaps. | Grade 1 |
| Hawaii | 1.MD.3 | Tell and write time in hours and half-hours using analog and digital clocks. | Grade 1 |
| Hawaii | 1.MD.4 | Organize, represent, and interpret data with up to three categories; ask and answer questions about the total number of data points, how many in each category, and how many more or less are in one category than in another. | Grade 1 |
| Hawaii | 1.NBT.1 | Count to 120, starting at any number less than 120. In this range, read and write numerals and represent a number of objects with a written numeral. | Grade 1 |
| Hawaii | 1.NBT.2 | Understand that the two digits of a two-digit number represent amounts of tens and ones. | Grade 1 |
| Hawaii | 1.NBT.3 | Compare two two-digit numbers based on meanings of the tens and ones digits, recording the results of comparisons with the symbols >, =, and <. | Grade 1 |
| Hawaii | 1.NBT.4 | Add within 100, including adding a two-digit number and a one-digit number, and adding a two-digit number and a multiple of 10, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Understand that in adding two-digit numbers, one adds tens and tens, ones and ones; and sometimes it is necessary to compose a ten. | Grade 1 |
| Hawaii | 1.NBT.5 | Given a two-digit number, mentally find 10 more or 10 less than the number, without having to count; explain the reasoning used. | Grade 1 |
| Hawaii | 1.NBT.6 | Subtract multiples of 10 in the range 10-90 from multiples of 10 in the range 10-90 (positive or zero differences), using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. | Grade 1 |
| Hawaii | 1.OA.1 | Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem. | Grade 1 |
| Hawaii | 1.OA.3 | Apply properties of operations as strategies to add and subtract. | Grade 1 |
| Hawaii | 1.OA.4 | Understand subtraction as an unknown-addend problem. | Grade 1 |
| Hawaii | 1.OA.5 | Relate counting to addition and subtraction (e.g., by counting on 2 to add 2). | Grade 1 |
| Hawaii | 1.OA.6 | Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to a ten (e.g., 13 - 4 = 13 - 3 - 1 = 10 - 1 = 9); using the relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 - 8 = 4); and creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13). | Grade 1 |
| Hawaii | 1.OA.7 | Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false. | Grade 1 |
| Hawaii | 1.OA.8 | Determine the unknown whole number in an addition or subtraction equation relating three whole numbers. | Grade 1 |
| Hawaii | 2.G.1 | Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces. Identify triangles, quadrilaterals, pentagons, hexagons, and cubes. | Grade 2 |
| Hawaii | 2.G.2 | Partition a rectangle into rows and columns of same-size squares and count to find the total number of them. | Grade 2 |
| Hawaii | 2.G.3 | Partition circles and rectangles into two, three, or four equal shares, describe the shares using the words halves, thirds, half of, a third of, etc., and describe the whole as two halves, three thirds, four fourths. Recognize that equal shares of identical wholes need not have the same shape. | Grade 2 |
| Hawaii | 2.MD.1 | Measure the length of an object by selecting and using appropriate tools such as rulers, yardsticks, meter sticks, and measuring tapes. | Grade 2 |
| Hawaii | 2.MD.2 | Measure the length of an object twice, using length units of different lengths for the two measurements; describe how the two measurements relate to the size of the unit chosen. | Grade 2 |
| Hawaii | 2.MD.4 | Measure to determine how much longer one object is than another, expressing the length difference in terms of a standard length unit. | Grade 2 |
| Hawaii | 2.MD.5 | Use addition and subtraction within 100 to solve word problems involving lengths that are given in the same units, e.g., by using drawings (such as drawings of rulers) and equations with a symbol for the unknown number to represent the problem. | Grade 2 |
| Hawaii | 2.MD.7 | Tell and write time from analog and digital clocks to the nearest five minutes, using a.m. and p.m. | Grade 2 |
| Hawaii | 2.MD.8 | Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies, using $ and ¢ symbols appropriately. | Grade 2 |
| Hawaii | 2.MD.9 | Generate measurement data by measuring lengths of several objects to the nearest whole unit, or by making repeated measurements of the same object. Show the measurements by making a line plot, where the horizontal scale is marked off in whole-number units. | Grade 2 |
| Hawaii | 2.MD.10 | Draw a picture graph and a bar graph (with single-unit scale) to represent a data set with up to four categories. Solve simple put-together, take-apart, and compare problems using information presented in a bar graph. | Grade 2 |
| Hawaii | 2.NBT.1 | Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones. | Grade 2 |
| Hawaii | 2.NBT.2 | Count within 1000; skip-count by 5s, 10s, and 100s. | Grade 2 |
| Hawaii | 2.NBT.3 | Read and write numbers to 1000 using base-ten numerals, number names, and expanded form. | Grade 2 |
| Hawaii | 2.NBT.4 | Compare two three-digit numbers based on meanings of the hundreds, tens, and ones digits, using >, =, and < symbols to record the results of comparisons. | Grade 2 |
| Hawaii | 2.NBT.5 | Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction. | Grade 2 |
| Hawaii | 2.NBT.6 | Add up to four two-digit numbers using strategies based on place value and properties of operations. | Grade 2 |
| Hawaii | 2.NBT.7 | Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method. Understand that in adding or subtracting three-digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds. | Grade 2 |
| Hawaii | 2.NBT.8 | Mentally add 10 or 100 to a given number 100–900, and mentally subtract 10 or 100 from a given number 100–900. | Grade 2 |
| Hawaii | 2.OA.1 | Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem. | Grade 2 |
| Hawaii | 2.OA.2 | Fluently add and subtract within 20 using mental strategies. By end of Grade 2, know from memory all sums of two one-digit numbers. | Grade 2 |
| Hawaii | 2.OA.3 | Determine whether a group of objects (up to 20) has an odd or even number of members, e.g., by pairing objects or counting them by 2s; write an equation to express an even number as a sum of two equal addends. | Grade 2 |
| Hawaii | 2.OA.4 | Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends. | Grade 2 |
| Hawaii | 3.G.1 | Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories. | Grade 3 |
| Hawaii | 3.G.2 | Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole. | Grade 3 |
| Hawaii | 3.MD.1 | Tell and write time to the nearest minute and measure time intervals in minutes. Solve word problems involving addition and subtraction of time intervals in minutes, e.g., by representing the problem on a number line diagram. | Grade 3 |
| Hawaii | 3.MD.2 | Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l). Add, subtract, multiply, or divide to solve one-step word problems involving masses or volumes that are given in the same units, e.g., by using drawings (such as a beaker with a measurement scale) to represent the problem. | Grade 3 |
| Hawaii | 3.MD.3 | Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and two-step “how many more” and “how many less” problems using information presented in scaled bar graphs. | Grade 3 |
| Hawaii | 3.MD.4 | Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Show the data by making a line plot, where the horizontal scale is marked off in appropriate units-whole numbers, halves, or quarters. | Grade 3 |
| Hawaii | 3.MD.5 | Recognize area as an attribute of plane figures and understand concepts of area measurement. | Grade 3 |
| Hawaii | 3.MD.6 | Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units). | Grade 3 |
| Hawaii | 3.MD.7 | Relate area to the operations of multiplication and addition. | Grade 3 |
| Hawaii | 3.MD.8 | Solve real world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters. | Grade 3 |
| Hawaii | 3.NBT.1 | Use place value understanding to round whole numbers to the nearest 10 or 100. | Grade 3 |
| Hawaii | 3.NBT.2 | Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction. | Grade 3 |
| Hawaii | 3.NBT.3 | Multiply one-digit whole numbers by multiples of 10 in the range 10–90 (e.g., 9 × 80, 5 × 60) using strategies based on place value and properties of operations. | Grade 3 |
| Hawaii | 3.NF.1 | Understand a fraction 1/𝘣 as the quantity formed by 1 part when a whole is partitioned into 𝘣 equal parts; understand a fraction 𝘢/𝑏 as the quantity formed by 𝘢 parts of size 1/𝘣. | Grade 3 |
| Hawaii | 3.NF.2 | Understand a fraction as a number on the number line; represent fractions on a number line diagram. | Grade 3 |
| Hawaii | 3.NF.3 | Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size. | Grade 3 |
| Hawaii | 3.OA.1 | Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each. | Grade 3 |
| Hawaii | 3.OA.2 | Interpret whole-number quotients of whole numbers, e.g., interpret 56 ÷ 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each. | Grade 3 |
| Hawaii | 3.OA.3 | Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem. | Grade 3 |
| Hawaii | 3.OA.4 | Determine the unknown whole number in a multiplication or division equation relating three whole numbers. | Grade 3 |
| Hawaii | 3.OA.5 | Apply properties of operations as strategies to multiply and divide. | Grade 3 |
| Hawaii | 3.OA.6 | Understand division as an unknown-factor problem. | Grade 3 |
| Hawaii | 3.OA.7 | Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 × 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers. | Grade 3 |
| Hawaii | 3.OA.8 | Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. | Grade 3 |
| Hawaii | 3.OA.9 | Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations. | Grade 3 |
| Hawaii | 4.G.1 | Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures. | Grade 4 |
| Hawaii | 4.G.2 | Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles. | Grade 4 |
| Hawaii | 4.G.3 | Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify line-symmetric figures and draw lines of symmetry. | Grade 4 |
| Hawaii | 4.MD.1 | Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table. | Grade 4 |
| Hawaii | 4.MD.2 | Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. | Grade 4 |
| Hawaii | 4.MD.3 | Apply the area and perimeter formulas for rectangles in real world and mathematical problems. | Grade 4 |
| Hawaii | 4.MD.4 | Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots. | Grade 4 |
| Hawaii | 4.MD.5 | Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement. | Grade 4 |
| Hawaii | 4.MD.6 | Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure. | Grade 4 |
| Hawaii | 4.MD.7 | Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems, e.g., by using an equation with a symbol for the unknown angle measure. | Grade 4 |
| Hawaii | 4.NBT.1 | Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. | Grade 4 |
| Hawaii | 4.NBT.2 | Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. | Grade 4 |
| Hawaii | 4.NBT.3 | Use place value understanding to round multi-digit whole numbers to any place. | Grade 4 |
| Hawaii | 4.NBT.4 | Fluently add and subtract multi-digit whole numbers using the standard algorithm. | Grade 4 |
| Hawaii | 4.NBT.5 | Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. | Grade 4 |
| Hawaii | 4.NBT.6 | Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. | Grade 4 |
| Hawaii | 4.NF.1 | Explain why a fraction 𝘢/𝘣 is equivalent to a fraction (𝘯 × 𝘢)/(𝘯 × 𝘣) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. | Grade 4 |
| Hawaii | 4.NF.2 | Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model. | Grade 4 |
| Hawaii | 4.NF.3 | Understand a fraction 𝘢/𝘣 with 𝘢 > 1 as a sum of fractions 1/𝘣. | Grade 4 |
| Hawaii | 4.NF.4 | Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. | Grade 4 |
| Hawaii | 4.NF.5 | Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100. | Grade 4 |
| Hawaii | 4.NF.6 | Use decimal notation for fractions with denominators 10 or 100. | Grade 4 |
| Hawaii | 4.NF.7 | Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual model. | Grade 4 |
| Hawaii | 4.OA.1 | Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 × 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations. | Grade 4 |
| Hawaii | 4.OA.2 | Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison. | Grade 4 |
| Hawaii | 4.OA.3 | Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. | Grade 4 |
| Hawaii | 4.OA.4 | Find all factor pairs for a whole number in the range 1-100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1-100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1-100 is prime or composite. | Grade 4 |
| Hawaii | 4.OA.5 | Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. | Grade 4 |
| Hawaii | 5.G.1 | Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., 𝘹-axis and 𝘹-coordinate, 𝘺-axis and 𝘺-coordinate). | Grade 5 |
| Hawaii | 5.G.2 | Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. | Grade 5 |
| Hawaii | 5.G.3 | Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. | Grade 5 |
| Hawaii | 5.G.4 | Classify two-dimensional figures in a hierarchy based on properties. | Grade 5 |
| Hawaii | 5.MD.1 | Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. | Grade 5 |
| Hawaii | 5.MD.2 | Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. | Grade 5 |
| Hawaii | 5.MD.3 | Recognize volume as an attribute of solid figures and understand concepts of volume measurement. | Grade 5 |
| Hawaii | 5.MD.4 | Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. | Grade 5 |
| Hawaii | 5.MD.5 | Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume. | Grade 5 |
| Hawaii | 5.NBT.1 | Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. | Grade 5 |
| Hawaii | 5.NBT.2 | Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. | Grade 5 |
| Hawaii | 5.NBT.3 | Read, write, and compare decimals to thousandths. | Grade 5 |
| Hawaii | 5.NBT.4 | Use place value understanding to round decimals to any place. | Grade 5 |
| Hawaii | 5.NBT.5 | Fluently multiply multi-digit whole numbers using the standard algorithm. | Grade 5 |
| Hawaii | 5.NBT.6 | Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. | Grade 5 |
| Hawaii | 5.NBT.7 | Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. | Grade 5 |
| Hawaii | 5.NF.1 | Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. | Grade 5 |
| Hawaii | 5.NF.2 | Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. | Grade 5 |
| Hawaii | 5.NF.3 | Interpret a fraction as division of the numerator by the denominator (𝘢/𝘣 = 𝘢 ÷ 𝘣). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. | Grade 5 |
| Hawaii | 5.NF.4 | Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. | Grade 5 |
| Hawaii | 5.NF.5 | Interpret multiplication as scaling (resizing). | Grade 5 |
| Hawaii | 5.NF.6 | Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. | Grade 5 |
| Hawaii | 5.NF.7 | Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. | Grade 5 |
| Hawaii | 5.OA.1 | Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. | Grade 5 |
| Hawaii | 5.OA.2 | Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. | Grade 5 |
| Hawaii | 5.OA.3 | Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. | Grade 5 |
| Hawaii | 6.EE.1 | Write and evaluate numerical expressions involving whole-number exponents. | Grade 6 |
| Hawaii | 6.EE.2 | Write, read, and evaluate expressions in which letters stand for numbers. | Grade 6 |
| Hawaii | 6.EE.3 | Apply the properties of operations to generate equivalent expressions. | Grade 6 |
| Hawaii | 6.EE.4 | Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). | Grade 6 |
| Hawaii | 6.EE.5 | Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true. | Grade 6 |
| Hawaii | 6.EE.6 | Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set. | Grade 6 |
| Hawaii | 6.EE.7 | Solve real-world and mathematical problems by writing and solving equations of the form 𝘹 + 𝘱 = 𝘲 and 𝘱𝘹 = 𝘲 for cases in which 𝘱, 𝘲 and 𝘹 are all nonnegative rational numbers. | Grade 6 |
| Hawaii | 6.EE.8 | Write an inequality of the form 𝘹 > 𝘤 or 𝘹 𝘤 or 𝘹 < 𝘤 have infinitely many solutions; represent solutions of such inequalities on number line diagrams. | Grade 6 |
| Hawaii | 6.EE.9 | Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. | Grade 6 |
| Hawaii | 6.G.1 | Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems. | Grade 6 |
| Hawaii | 6.G.2 | Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas 𝘝 = 𝘭 𝘸 𝘩 and 𝘝 = 𝘣 𝘩 to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems. | Grade 6 |
| Hawaii | 6.G.3 | Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems. | Grade 6 |
| Hawaii | 6.G.4 | Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems. | Grade 6 |
| Hawaii | 6.RP.1 | Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. | Grade 6 |
| Hawaii | 6.RP.2 | Understand the concept of a unit rate 𝘢/𝘣 associated with a ratio 𝘢:𝘣 with 𝘣 ≠ 0, and use rate language in the context of a ratio relationship. | Grade 6 |
| Hawaii | 6.RP.3 | Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. | Grade 6 |
| Hawaii | 6.SP.5 | Summarize numerical data sets in relation to their context, such as by: | Grade 6 |
| Hawaii | 6.NS.1 | Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. | Grade 6 |
| Hawaii | 6.NS.2 | Fluently divide multi-digit numbers using the standard algorithm. | Grade 6 |
| Hawaii | 6.NS.3 | Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation. | Grade 6 |
| Hawaii | 6.NS.5 | Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation. | Grade 6 |
| Hawaii | 6.NS.6 | Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates. | Grade 6 |
| Hawaii | 6.NS.7 | Understand ordering and absolute value of rational numbers. | Grade 6 |
| Hawaii | 6.NS.8 | Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. | Grade 6 |
| Hawaii | 7.EE.1 | Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients. | Grade 7 |
| Hawaii | 7.EE.2 | Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. | Grade 7 |
| Hawaii | 7.EE.3 | Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. | Grade 7 |
| Hawaii | 7.EE.4 | Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. | Grade 7 |
| Hawaii | 7.G.1 | Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale. | Grade 7 |
| Hawaii | 7.G.2 | Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle. | Grade 7 |
| Hawaii | 7.G.3 | Describe the two-dimensional figures that result from slicing three-dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids. | Grade 7 |
| Hawaii | 7.G.4 | Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle. | Grade 7 |
| Hawaii | 7.G.5 | Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure. | Grade 7 |
| Hawaii | 7.G.6 | Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. | Grade 7 |
| Hawaii | 7.RP.1 | Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. | Grade 7 |
| Hawaii | 7.RP.2 | Recognize and represent proportional relationships between quantities. | Grade 7 |
| Hawaii | 7.RP.3 | Use proportional relationships to solve multistep ratio and percent problems. | Grade 7 |
| Hawaii | 7.NS.1 | Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram. | Grade 7 |
| Hawaii | 7.NS.2 | Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers. | Grade 7 |
| Hawaii | 7.NS.3 | Solve real-world and mathematical problems involving the four operations with rational numbers. | Grade 7 |
| Hawaii | 8.EE.1 | Know and apply the properties of integer exponents to generate equivalent numerical expressions. | Grade 8 |
| Hawaii | 8.EE.2 | Use square root and cube root symbols to represent solutions to equations of the form 𝘹² = 𝘱 and 𝘹³ = 𝘱, where 𝘱 is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that √2 is irrational. | Grade 8 |
| Hawaii | 8.EE.3 | Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other. | Grade 8 |
| Hawaii | 8.EE.4 | Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology. | Grade 8 |
| Hawaii | 8.EE.5 | Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. | Grade 8 |
| Hawaii | 8.EE.6 | Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation 𝘺 = 𝘮𝘹 for a line through the origin and the equation 𝘺 = 𝘮𝘹 + 𝘣 for a line intercepting the vertical axis at 𝘣. | Grade 8 |
| Hawaii | 8.EE.7 | Solve linear equations in one variable. | Grade 8 |
| Hawaii | 8.EE.8 | Analyze and solve pairs of simultaneous linear equations. | Grade 8 |
| Hawaii | 8.F.1 | Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output. | Grade 8 |
| Hawaii | 8.F.2 | Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). | Grade 8 |
| Hawaii | 8.F.3 | Interpret the equation 𝘺 = 𝘮𝘹 + 𝘣 as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. | Grade 8 |
| Hawaii | 8.F.4 | Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (𝘹, 𝘺) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values. | Grade 8 |
| Hawaii | 8.F.5 | Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally. | Grade 8 |
| Hawaii | 8.G.1 | Verify experimentally the properties of rotations, reflections, and translations. | Grade 8 |
| Hawaii | 8.G.2 | Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them. | Grade 8 |
| Hawaii | 8.G.3 | Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates. | Grade 8 |
| Hawaii | 8.G.4 | Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two-dimensional figures, describe a sequence that exhibits the similarity between them. | Grade 8 |
| Hawaii | 8.G.5 | Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. | Grade 8 |
| Hawaii | 8.G.7 | Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions. | Grade 8 |
| Hawaii | 8.G.8 | Apply the Pythagorean Theorem to find the distance between two points in a coordinate system. | Grade 8 |
| Hawaii | 8.G.9 | Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems. | Grade 8 |
| Hawaii | 8.SP.1 | Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association. | Grade 8 |
| Hawaii | 8.SP.2 | Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line. | Grade 8 |
| Hawaii | 8.NS.2 | Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g., π²). | Grade 8 |
| Hawaii | A.SSE.2 | Use the structure of an expression to identify ways to rewrite it. | High School |
| Hawaii | A.SSE.3 | Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression. | High School |
| Hawaii | A.APR.3 | Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial. | High School |
| Hawaii | A.CED.2 | Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. | High School |
| Hawaii | A.CED.3 | Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context. | High School |
| Hawaii | A.REI.3 | Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. | High School |
| Hawaii | F.IF.2 | Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. | High School |
| Hawaii | F.IF.4 | For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. | High School |
| Hawaii | F.IF.7 | Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. | High School |
| Hawaii | F.BF.1 | Write a function that describes a relationship between two quantities. | High School |
| Hawaii | S.ID.6 | Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. | High School |
| Idaho | K.CC.1 | Count to 100 by ones and by tens. | Kindergarten |
| Idaho | K.CC.2 | Count forward beginning from a given number within the known sequence (instead of having to begin at 1). | Kindergarten |
| Idaho | K.CC.3 | Write numbers from 0 to 20. Represent a number of objects with a written numeral 0-20 (with 0 representing a count of no objects). | Kindergarten |
| Idaho | K.CC.4 | Understand the relationship between numbers and quantities; connect counting to cardinality. | Kindergarten |
| Idaho | K.CC.5 | Count to answer “how many?” questions about as many as 20 things arranged in a line, a rectangular array, or a circle, or as many as 10 things in a scattered configuration; given a number from 1–20, count out that many objects. | Kindergarten |
| Idaho | K.CC.6 | Identify whether the number of objects in one group is greater than, less than, or equal to the number of objects in another group, e.g., by using matching and counting strategies. | Kindergarten |
| Idaho | K.CC.7 | Compare two numbers between 1 and 10 presented as written numerals. | Kindergarten |
| Idaho | K.G.1 | Describe objects in the environment using names of shapes, and describe the relative positions of these objects using terms such as above, below, beside, in front of, behind, and next to. | Kindergarten |
| Idaho | K.G.2 | Correctly name shapes regardless of their orientations or overall size. | Kindergarten |
| Idaho | K.G.3 | Identify shapes as two-dimensional (lying in a plane, “flat”) or three-dimensional (“solid”). | Kindergarten |
| Idaho | K.G.4 | Analyze and compare two- and three-dimensional shapes, in different sizes and orientations, using informal language to describe their similarities, differences, parts (e.g., number of sides and vertices/“corners”) and other attributes (e.g., having sides of equal length). | Kindergarten |
| Idaho | K.G.6 | Compose simple shapes to form larger shapes. | Kindergarten |
| Idaho | K.MD.1 | Describe measurable attributes of objects, such as length or weight. Describe several measurable attributes of a single object. | Kindergarten |
| Idaho | K.MD.2 | Directly compare two objects with a measurable attribute in common, to see which object has “more of”/“less of” the attribute, and describe the difference. | Kindergarten |
| Idaho | K.MD.3 | Classify objects into given categories; count the numbers of objects in each category and sort the categories by count. | Kindergarten |
| Idaho | K.NBT.1 | Compose and decompose numbers from 11 to 19 into ten ones and some further ones, e.g., by using objects or drawings, and record each composition or decomposition by a drawing or equation (e.g., 18 = 10 + 8); understand that these numbers are composed of ten ones and one, two, three, four, five, six, seven, eight, or nine ones. | Kindergarten |
| Idaho | K.OA.1 | Represent addition and subtraction with objects, fingers, mental images, drawings, sounds (e.g., claps), acting out situations, verbal explanations, expressions, or equations. | Kindergarten |
| Idaho | K.OA.2 | Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem. | Kindergarten |
| Idaho | K.OA.3 | Decompose numbers less than or equal to 10 into pairs in more than one way, e.g., by using objects or drawings, and record each decomposition by a drawing or equation (e.g., 5 = 2 + 3 and 5 = 4 + 1). | Kindergarten |
| Idaho | K.OA.4 | For any number from 1 to 9, find the number that makes 10 when added to the given number, e.g., by using objects or drawings, and record the answer with a drawing or equation. | Kindergarten |
| Idaho | K.OA.5 | Fluently add and subtract within 5. | Kindergarten |
| Idaho | 1.G.1 | Distinguish between defining attributes (e.g., triangles are closed and three-sided) versus non-defining attributes (e.g., color, orientation, overall size); build and draw shapes to possess defining attributes. | Grade 1 |
| Idaho | 1.G.2 | Compose two-dimensional shapes (rectangles, squares, trapezoids, triangles, half-circles, and quarter-circles) or three-dimensional shapes (cubes, right rectangular prisms, right circular cones, and right circular cylinders) to create a composite shape, and compose new shapes from the composite shape. | Grade 1 |
| Idaho | 1.G.3 | Partition circles and rectangles into two and four equal shares, describe the shares using the words halves, fourths, and quarters, and use the phrases half of, fourth of, and quarter of. Describe the whole as two of, or four of the shares. Understand for these examples that decomposing into more equal shares creates smaller shares. | Grade 1 |
| Idaho | 1.MD.1 | Order three objects by length; compare the lengths of two objects indirectly by using a third object. | Grade 1 |
| Idaho | 1.MD.2 | Express the length of an object as a whole number of length units, by laying multiple copies of a shorter object (the length unit) end to end; understand that the length measurement of an object is the number of same-size length units that span it with no gaps or overlaps. | Grade 1 |
| Idaho | 1.MD.3 | Tell and write time in hours and half-hours using analog and digital clocks. | Grade 1 |
| Idaho | 1.MD.4 | Organize, represent, and interpret data with up to three categories; ask and answer questions about the total number of data points, how many in each category, and how many more or less are in one category than in another. | Grade 1 |
| Idaho | 1.NBT.1 | Count to 120, starting at any number less than 120. In this range, read and write numerals and represent a number of objects with a written numeral. | Grade 1 |
| Idaho | 1.NBT.2 | Understand that the two digits of a two-digit number represent amounts of tens and ones. | Grade 1 |
| Idaho | 1.NBT.3 | Compare two two-digit numbers based on meanings of the tens and ones digits, recording the results of comparisons with the symbols >, =, and <. | Grade 1 |
| Idaho | 1.NBT.4 | Add within 100, including adding a two-digit number and a one-digit number, and adding a two-digit number and a multiple of 10, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Understand that in adding two-digit numbers, one adds tens and tens, ones and ones; and sometimes it is necessary to compose a ten. | Grade 1 |
| Idaho | 1.NBT.5 | Given a two-digit number, mentally find 10 more or 10 less than the number, without having to count; explain the reasoning used. | Grade 1 |
| Idaho | 1.NBT.6 | Subtract multiples of 10 in the range 10-90 from multiples of 10 in the range 10-90 (positive or zero differences), using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. | Grade 1 |
| Idaho | 1.OA.1 | Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem. | Grade 1 |
| Idaho | 1.OA.3 | Apply properties of operations as strategies to add and subtract. | Grade 1 |
| Idaho | 1.OA.4 | Understand subtraction as an unknown-addend problem. | Grade 1 |
| Idaho | 1.OA.5 | Relate counting to addition and subtraction (e.g., by counting on 2 to add 2). | Grade 1 |
| Idaho | 1.OA.6 | Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to a ten (e.g., 13 – 4 = 13 – 3 – 1 = 10 – 1 = 9); using the relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 – 8 = 4); and creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13). | Grade 1 |
| Idaho | 1.OA.7 | Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false. | Grade 1 |
| Idaho | 1.OA.8 | Determine the unknown whole number in an addition or subtraction equation relating three whole numbers. | Grade 1 |
| Idaho | 2.G.1 | Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces. Identify triangles, quadrilaterals, pentagons, hexagons, and cubes. | Grade 2 |
| Idaho | 2.G.2 | Partition a rectangle into rows and columns of same-size squares and count to find the total number of them. | Grade 2 |
| Idaho | 2.G.3 | Partition circles and rectangles into two, three, or four equal shares, describe the shares using the words halves, thirds, half of, a third of, etc., and describe the whole as two halves, three thirds, four fourths. Recognize that equal shares of identical wholes need not have the same shape. | Grade 2 |
| Idaho | 2.MD.1 | Measure the length of an object by selecting and using appropriate tools such as rulers, yardsticks, meter sticks, and measuring tapes. | Grade 2 |
| Idaho | 2.MD.2 | Measure the length of an object twice, using length units of different lengths for the two measurements; describe how the two measurements relate to the size of the unit chosen. | Grade 2 |
| Idaho | 2.MD.4 | Measure to determine how much longer one object is than another, expressing the length difference in terms of a standard length unit. | Grade 2 |
| Idaho | 2.MD.5 | Use addition and subtraction within 100 to solve word problems involving lengths that are given in the same units, e.g., by using drawings (such as drawings of rulers) and equations with a symbol for the unknown number to represent the problem. | Grade 2 |
| Idaho | 2.MD.7 | Tell and write time from analog and digital clocks to the nearest five minutes, using a.m. and p.m. | Grade 2 |
| Idaho | 2.MD.8 | Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies, using $ and ¢ symbols appropriately. | Grade 2 |
| Idaho | 2.MD.9 | Generate measurement data by measuring lengths of several objects to the nearest whole unit, or by making repeated measurements of the same object. Show the measurements by making a line plot, where the horizontal scale is marked off in whole-number units. | Grade 2 |
| Idaho | 2.MD.10 | Draw a picture graph and a bar graph (with single-unit scale) to represent a data set with up to four categories. Solve simple put-together, take-apart, and compare problems 4 using information presented in a bar graph. | Grade 2 |
| Idaho | 2.NBT.1 | Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones. | Grade 2 |
| Idaho | 2.NBT.2 | Count within 1000; skip-count by 5s, 10s, and 100s. | Grade 2 |
| Idaho | 2.NBT.3 | Read and write numbers to 1000 using base-ten numerals, number names, and expanded form. | Grade 2 |
| Idaho | 2.NBT.4 | Compare two three-digit numbers based on meanings of the hundreds, tens, and ones digits, using >, =, and < symbols to record the results of comparisons. | Grade 2 |
| Idaho | 2.NBT.5 | Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction. | Grade 2 |
| Idaho | 2.NBT.6 | Add up to four two-digit numbers using strategies based on place value and properties of operations. | Grade 2 |
| Idaho | 2.NBT.7 | Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method. Understand that in adding or subtracting three-digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds. | Grade 2 |
| Idaho | 2.NBT.8 | Mentally add 10 or 100 to a given number 100–900, and mentally subtract 10 or 100 from a given number 100–900. | Grade 2 |
| Idaho | 2.OA.1 | Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem. | Grade 2 |
| Idaho | 2.OA.2 | Fluently add and subtract within 20 using mental strategies. By end of Grade 2, know from memory all sums of two one-digit numbers. | Grade 2 |
| Idaho | 2.OA.3 | Determine whether a group of objects (up to 20) has an odd or even number of members, e.g., by pairing objects or counting them by 2s; write an equation to express an even number as a sum of two equal addends. | Grade 2 |
| Idaho | 2.OA.4 | Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends. | Grade 2 |
| Idaho | 3.G.1 | Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories. | Grade 3 |
| Idaho | 3.G.2 | Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole. | Grade 3 |
| Idaho | 3.MD.1 | Tell and write time to the nearest minute and measure time intervals in minutes. Solve word problems involving addition and subtraction of time intervals in minutes, e.g., by representing the problem on a number line diagram. | Grade 3 |
| Idaho | 3.MD.2 | Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l). Add, subtract, multiply, or divide to solve one-step word problems involving masses or volumes that are given in the same units, e.g., by using drawings (such as a beaker with a measurement scale) to represent the problem. | Grade 3 |
| Idaho | 3.MD.3 | Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and two-step “how many more” and “how many less” problems using information presented in scaled bar graphs. | Grade 3 |
| Idaho | 3.MD.4 | Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Show the data by making a line plot, where the horizontal scale is marked off in appropriate units—whole numbers, halves, or quarters. | Grade 3 |
| Idaho | 3.MD.5 | Recognize area as an attribute of plane figures and understand concepts of area measurement. | Grade 3 |
| Idaho | 3.MD.6 | Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units). | Grade 3 |
| Idaho | 3.MD.7 | Relate area to the operations of multiplication and addition. | Grade 3 |
| Idaho | 3.MD.8 | Solve real world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters. | Grade 3 |
| Idaho | 3.NBT.1 | Use place value understanding to round whole numbers to the nearest 10 or 100. | Grade 3 |
| Idaho | 3.NBT.2 | Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction. | Grade 3 |
| Idaho | 3.NBT.3 | Multiply one-digit whole numbers by multiples of 10 in the range 10–90 (e.g., 9 × 80, 5 × 60) using strategies based on place value and properties of operations. | Grade 3 |
| Idaho | 3.NF.1 | Understand a fraction 1/𝑏 as the quantity formed by 1 part when a whole is partitioned into 𝑏 equal parts; understand a fraction 𝑎/𝑏 as the quantity formed by a parts of size 1/𝑏. | Grade 3 |
| Idaho | 3.NF.2 | Understand a fraction as a number on the number line; represent fractions on a number line diagram. | Grade 3 |
| Idaho | 3.NF.3 | Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size. | Grade 3 |
| Idaho | 3.OA.1 | Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each. | Grade 3 |
| Idaho | 3.OA.2 | Interpret whole-number quotients of whole numbers, e.g., interpret 56 ÷ 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each. | Grade 3 |
| Idaho | 3.OA.3 | Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem. | Grade 3 |
| Idaho | 3.OA.4 | Determine the unknown whole number in a multiplication or division equation relating three whole numbers. | Grade 3 |
| Idaho | 3.OA.5 | Apply properties of operations as strategies to multiply and divide. | Grade 3 |
| Idaho | 3.OA.6 | Understand division as an unknown-factor problem. | Grade 3 |
| Idaho | 3.OA.7 | Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 × 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers. | Grade 3 |
| Idaho | 3.OA.8 | Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. | Grade 3 |
| Idaho | 3.OA.9 | Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations. | Grade 3 |
| Idaho | 4.G.1 | Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures. | Grade 4 |
| Idaho | 4.G.2 | Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles. | Grade 4 |
| Idaho | 4.G.3 | Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify line-symmetric figures and draw lines of symmetry. | Grade 4 |
| Idaho | 4.MD.1 | Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table. | Grade 4 |
| Idaho | 4.MD.2 | Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. | Grade 4 |
| Idaho | 4.MD.3 | Apply the area and perimeter formulas for rectangles in real world and mathematical problems. | Grade 4 |
| Idaho | 4.MD.4 | Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots. | Grade 4 |
| Idaho | 4.MD.5 | Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement. | Grade 4 |
| Idaho | 4.MD.6 | Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure. | Grade 4 |
| Idaho | 4.MD.7 | Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems, e.g., by using an equation with a symbol for the unknown angle measure. | Grade 4 |
| Idaho | 4.NBT.1 | Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. | Grade 4 |
| Idaho | 4.NBT.2 | Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. | Grade 4 |
| Idaho | 4.NBT.3 | Use place value understanding to round multi-digit whole numbers to anyplace. | Grade 4 |
| Idaho | 4.NBT.4 | Fluently add and subtract multi-digit whole numbers using the standard algorithm. | Grade 4 |
| Idaho | 4.NBT.5 | Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. | Grade 4 |
| Idaho | 4.NBT.6 | Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. | Grade 4 |
| Idaho | 4.NF.1 | Explain why a fraction 𝑎/𝑏 is equivalent to a fraction (𝑛 × 𝑎)/(𝑛 × 𝑏) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. | Grade 4 |
| Idaho | 4.NF.2 | Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model. | Grade 4 |
| Idaho | 4.NF.3 | Understand a fraction 𝑎/𝑏 with 𝑎 > 1 as a sum of fractions 1/𝑏. | Grade 4 |
| Idaho | 4.NF.4 | Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. | Grade 4 |
| Idaho | 4.NF.5 | Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100. | Grade 4 |
| Idaho | 4.NF.6 | Use decimal notation for fractions with denominators 10 or 100. | Grade 4 |
| Idaho | 4.NF.7 | Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual model. | Grade 4 |
| Idaho | 4.OA.1 | Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 × 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations. | Grade 4 |
| Idaho | 4.OA.2 | Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison. | Grade 4 |
| Idaho | 4.OA.3 | Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. | Grade 4 |
| Idaho | 4.OA.4 | Find all factor pairs for a whole number in the range 1–100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1–100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1–100 is prime or composite. | Grade 4 |
| Idaho | 4.OA.5 | Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. | Grade 4 |
| Idaho | 5.G.1 | Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., 𝑥-axis and 𝑥-coordinate, 𝑦-axis and 𝑦-coordinate). | Grade 5 |
| Idaho | 5.G.2 | Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. | Grade 5 |
| Idaho | 5.G.3 | Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. | Grade 5 |
| Idaho | 5.G.4 | Classify two-dimensional figures in a hierarchy based on properties. | Grade 5 |
| Idaho | 5.MD.1 | Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. | Grade 5 |
| Idaho | 5.MD.2 | Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. | Grade 5 |
| Idaho | 5.MD.3 | Recognize volume as an attribute of solid figures and understand concepts of volume measurement. | Grade 5 |
| Idaho | 5.MD.4 | Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. | Grade 5 |
| Idaho | 5.MD.5 | Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume. | Grade 5 |
| Idaho | 5.NBT.1 | Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. | Grade 5 |
| Idaho | 5.NBT.2 | Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. | Grade 5 |
| Idaho | 5.NBT.3 | Read, write, and compare decimals to thousandths. | Grade 5 |
| Idaho | 5.NBT.4 | Use place value understanding to round decimals to any place. | Grade 5 |
| Idaho | 5.NBT.5 | Fluently multiply multi-digit whole numbers using the standard algorithm. | Grade 5 |
| Idaho | 5.NBT.6 | Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. | Grade 5 |
| Idaho | 5.NBT.7 | Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. | Grade 5 |
| Idaho | 5.NF.1 | Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. | Grade 5 |
| Idaho | 5.NF.2 | Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. | Grade 5 |
| Idaho | 5.NF.3 | Interpret a fraction as division of the numerator by the denominator (𝑎/𝑏 = 𝑎 ÷ 𝑏). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. | Grade 5 |
| Idaho | 5.NF.4 | Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. | Grade 5 |
| Idaho | 5.NF.5 | Interpret multiplication as scaling (resizing). | Grade 5 |
| Idaho | 5.NF.6 | Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. | Grade 5 |
| Idaho | 5.NF.7 | Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. | Grade 5 |
| Idaho | 5.OA.1 | Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. | Grade 5 |
| Idaho | 5.OA.2 | Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. | Grade 5 |
| Idaho | 5.OA.3 | Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. | Grade 5 |
| Idaho | 6.EE.1 | Write and evaluate numerical expressions involving whole-number exponents. | Grade 6 |
| Idaho | 6.EE.2 | Write, read, and evaluate expressions in which letters stand for numbers. | Grade 6 |
| Idaho | 6.EE.3 | Apply the properties of operations to generate equivalent expressions. | Grade 6 |
| Idaho | 6.EE.4 | Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). | Grade 6 |
| Idaho | 6.EE.5 | Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true. | Grade 6 |
| Idaho | 6.EE.6 | Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set. | Grade 6 |
| Idaho | 6.EE.7 | Solve real-world and mathematical problems by writing and solving equations of the form 𝑥 + 𝑝 = 𝑞 and 𝑝𝑥 = 𝑞 for cases in which 𝑝, 𝑞 and 𝑥 are all nonnegative rational numbers. | Grade 6 |
| Idaho | 6.EE.8 | Write an inequality of the form 𝑥 > 𝑐 or 𝑥 𝑐 or 𝑥 < 𝑐 have infinitely many solutions; represent solutions of such inequalities on number line diagrams. | Grade 6 |
| Idaho | 6.EE.9 | Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. | Grade 6 |
| Idaho | 6.G.1 | Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems. | Grade 6 |
| Idaho | 6.G.2 | Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas 𝑉 = 𝑙 × 𝑤 × 𝘩 and 𝑉 = 𝑏 × 𝘩 to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems. | Grade 6 |
| Idaho | 6.G.3 | Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems. | Grade 6 |
| Idaho | 6.G.4 | Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems. | Grade 6 |
| Idaho | 6.RP.1 | Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. | Grade 6 |
| Idaho | 6.RP.2 | Understand the concept of a unit rate 𝑎/𝑏 associated with a ratio 𝑎:𝑏 with 𝑏 ≠ 0, and use rate language in the context of a ratio relationship. | Grade 6 |
| Idaho | 6.RP.3 | Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. | Grade 6 |
| Idaho | 6.SP.5 | Summarize numerical data sets in relation to their context, such as by: | Grade 6 |
| Idaho | 6.NS.1 | Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. | Grade 6 |
| Idaho | 6.NS.2 | Fluently divide multi-digit numbers using the standard algorithm. | Grade 6 |
| Idaho | 6.NS.3 | Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation. | Grade 6 |
| Idaho | 6.NS.5 | Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation. | Grade 6 |
| Idaho | 6.NS.6 | Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates. | Grade 6 |
| Idaho | 6.NS.7 | Understand ordering and absolute value of rational numbers. | Grade 6 |
| Idaho | 6.NS.8 | Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. | Grade 6 |
| Idaho | 7.EE.1 | Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients. | Grade 7 |
| Idaho | 7.EE.2 | Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. | Grade 7 |
| Idaho | 7.EE.3 | Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. | Grade 7 |
| Idaho | 7.EE.4 | Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. | Grade 7 |
| Idaho | 7.G.1 | Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale. | Grade 7 |
| Idaho | 7.G.2 | Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle. | Grade 7 |
| Idaho | 7.G.3 | Describe the two-dimensional figures that result from slicing three-dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids. | Grade 7 |
| Idaho | 7.G.4 | Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle. | Grade 7 |
| Idaho | 7.G.5 | Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure. | Grade 7 |
| Idaho | 7.G.6 | Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. | Grade 7 |
| Idaho | 7.RP.1 | Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. | Grade 7 |
| Idaho | 7.RP.2 | Recognize and represent proportional relationships between quantities. | Grade 7 |
| Idaho | 7.RP.3 | Use proportional relationships to solve multistep ratio and percent problems. | Grade 7 |
| Idaho | 7.NS.1 | Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram. | Grade 7 |
| Idaho | 7.NS.2 | Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers. | Grade 7 |
| Idaho | 7.NS.3 | Solve real-world and mathematical problems involving the four operations with rational numbers. | Grade 7 |
| Idaho | 8.EE.1 | Know and apply the properties of integer exponents to generate equivalent numerical expressions. | Grade 8 |
| Idaho | 8.EE.2 | Use square root and cube root symbols to represent solutions to equations of the form 𝑥² = 𝑝 and 𝑥³ = 𝑝, where 𝑝 is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that √2 is irrational. | Grade 8 |
| Idaho | 8.EE.3 | Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other. | Grade 8 |
| Idaho | 8.EE.4 | Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology. | Grade 8 |
| Idaho | 8.EE.5 | Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. | Grade 8 |
| Idaho | 8.EE.6 | Use similar triangles to explain why the slope 𝑚 is the same bet ween any two distinct points on a non-vertical line in the coordinate plane; derive the equation 𝑦 = 𝑚𝑥 for a line through the origin and the equation 𝑦 = 𝑚𝑥 + 𝑏 for a line intercepting the vertical axis at 𝑏. | Grade 8 |
| Idaho | 8.EE.7 | Solve linear equations in one variable. | Grade 8 |
| Idaho | 8.EE.8 | Analyze and solve pairs of simultaneous linear equations. | Grade 8 |
| Idaho | 8.F.1 | Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output. | Grade 8 |
| Idaho | 8.F.2 | Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). | Grade 8 |
| Idaho | 8.F.3 | Interpret the equation 𝑦 = 𝑚𝑥 + 𝑏 as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. | Grade 8 |
| Idaho | 8.F.4 | Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (𝑥, 𝑦) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values. | Grade 8 |
| Idaho | 8.F.5 | Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally. | Grade 8 |
| Idaho | 8.G.1 | Verify experimentally the properties of rotations, reflections, and translations. | Grade 8 |
| Idaho | 8.G.2 | Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them. | Grade 8 |
| Idaho | 8.G.3 | Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates. | Grade 8 |
| Idaho | 8.G.4 | Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two-dimensional figures, describe a sequence that exhibits the similarity between them. | Grade 8 |
| Idaho | 8.G.5 | Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. | Grade 8 |
| Idaho | 8.G.7 | Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions. | Grade 8 |
| Idaho | 8.G.8 | Apply the Pythagorean Theorem to find the distance between two points in a coordinate system. | Grade 8 |
| Idaho | 8.G.9 | Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems. | Grade 8 |
| Idaho | 8.SP.1 | Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association. | Grade 8 |
| Idaho | 8.SP.2 | Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line. | Grade 8 |
| Idaho | 8.NS.2 | Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g., π²). | Grade 8 |
| Idaho | A-APR.3 | Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial. | High School |
| Idaho | A-CED.2 | Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. | High School |
| Idaho | A-CED.3 | Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context. | High School |
| Idaho | A-REI.3 | Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. | High School |
| Idaho | A-SSE.2 | Use the structure of an expression to identify ways to rewrite it. | High School |
| Idaho | A-SSE.3 | Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression. | High School |
| Idaho | F-BF.1 | Write a function that describes a relationship between two quantities. | High School |
| Idaho | F-IF.2 | Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. | High School |
| Idaho | F-IF.4 | For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. | High School |
| Idaho | F-IF.7 | Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. | High School |
| Idaho | S-ID.6 | Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. | High School |
| Illinois | K.CC.A.1 | Count to 100 by ones and by tens. | Kindergarten |
| Illinois | K.CC.A.2 | Count forward beginning from a given number within the known sequence (instead of having to begin at 1). | Kindergarten |
| Illinois | K.CC.A.3 | Write numbers from 0 to 20. Represent a number of objects with a written numeral 0-20 (with 0 representing a count of no objects). | Kindergarten |
| Illinois | K.CC.B.4 | Understand the relationship between numbers and quantities; connect counting to cardinality. | Kindergarten |
| Illinois | K.CC.B.5 | Count to answer “how many?” questions about as many as 20 things arranged in a line, a rectangular array, or a circle, or as many as 10 things in a scattered configuration; given a number from 1-20, count out that many objects. | Kindergarten |
| Illinois | K.CC.C.6 | Identify whether the number of objects in one group is greater than, less than, or equal to the number of objects in another group, e.g., by using matching and counting strategies. | Kindergarten |
| Illinois | K.CC.C.7 | Compare two numbers between 1 and 10 presented as written numerals. | Kindergarten |
| Illinois | K.G.A.1 | Describe objects in the environment using names of shapes, and describe the relative positions of these objects using terms such as above, below, beside, in front of, behind, and next to. | Kindergarten |
| Illinois | K.G.A.2 | Correctly name shapes regardless of their orientations or overall size. | Kindergarten |
| Illinois | K.G.A.3 | Identify shapes as two-dimensional (lying in a plane, “flat”) or three-dimensional (“solid”). | Kindergarten |
| Illinois | K.G.B.4 | Analyze and compare two- and three-dimensional shapes, in different sizes and orientations, using informal language to describe their similarities, differences, parts (e.g., number of sides and vertices/“corners”) and other attributes (e.g., having sides of equal length). | Kindergarten |
| Illinois | K.G.B.6 | Compose simple shapes to form larger shapes. | Kindergarten |
| Illinois | K.MD.A.1 | Describe measurable attributes of objects, such as length or weight. Describe several measurable attributes of a single object. | Kindergarten |
| Illinois | K.MD.A.2 | Directly compare two objects with a measurable attribute in common, to see which object has “more of”/“less of” the attribute, and describe the difference. | Kindergarten |
| Illinois | K.MD.B.3 | Classify objects into given categories; count the numbers of objects in each category and sort the categories by count. | Kindergarten |
| Illinois | K.NBT.A.1 | Compose and decompose numbers from 11 to 19 into ten ones and some further ones, e.g., by using objects or drawings, and record each composition or decomposition by a drawing or equation (e.g., 18 = 10 + 8); understand that these numbers are composed of ten ones and one, two, three, four, five, six, seven, eight, or nine ones. | Kindergarten |
| Illinois | K.OA.A.1 | Represent addition and subtraction with objects, fingers, mental images, drawings, sounds (e.g., claps), acting out situations, verbal explanations, expressions, or equations. | Kindergarten |
| Illinois | K.OA.A.2 | Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem. | Kindergarten |
| Illinois | K.OA.A.3 | Decompose numbers less than or equal to 10 into pairs in more than one way, e.g., by using objects or drawings, and record each decomposition by a drawing or equation (e.g., 5 = 2 + 3 and 5 = 4 + 1). | Kindergarten |
| Illinois | K.OA.A.4 | For any number from 1 to 9, find the number that makes 10 when added to the given number, e.g., by using objects or drawings, and record the answer with a drawing or equation. | Kindergarten |
| Illinois | K.OA.A.5 | Fluently add and subtract within 5. | Kindergarten |
| Illinois | 1.G.A.1 | Distinguish between defining attributes (e.g., triangles are closed and three-sided) versus non-defining attributes (e.g., color, orientation, overall size); build and draw shapes to possess defining attributes. | Grade 1 |
| Illinois | 1.G.A.2 | Compose two-dimensional shapes (rectangles, squares, trapezoids, triangles, half-circles, and quarter-circles) or three-dimensional shapes (cubes, right rectangular prisms, right circular cones, and right circular cylinders) to create a composite shape, and compose new shapes from the composite shape. | Grade 1 |
| Illinois | 1.G.A.3 | Partition circles and rectangles into two and four equal shares, describe the shares using the words halves, fourths, and quarters, and use the phrases half of, fourth of, and quarter of. Describe the whole as two of, or four of the shares. Understand for these examples that decomposing into more equal shares creates smaller shares. | Grade 1 |
| Illinois | 1.MD.A.1 | Order three objects by length; compare the lengths of two objects indirectly by using a third object. | Grade 1 |
| Illinois | 1.MD.A.2 | Express the length of an object as a whole number of length units, by laying multiple copies of a shorter object (the length unit) end to end; understand that the length measurement of an object is the number of same-size length units that span it with no gaps or overlaps. | Grade 1 |
| Illinois | 1.MD.B.3 | Tell and write time in hours and half-hours using analog and digital clocks. | Grade 1 |
| Illinois | 1.MD.C.4 | Organize, represent, and interpret data with up to three categories; ask and answer questions about the total number of data points, how many in each category, and how many more or less are in one category than in another. | Grade 1 |
| Illinois | 1.NBT.A.1 | Count to 120, starting at any number less than 120. In this range, read and write numerals and represent a number of objects with a written numeral. | Grade 1 |
| Illinois | 1.NBT.B.2 | Understand that the two digits of a two-digit number represent amounts of tens and ones. Understand the following as special cases: | Grade 1 |
| Illinois | 1.NBT.B.3 | Compare two two-digit numbers based on meanings of the tens and ones digits, recording the results of comparisons with the symbols >, =, and <. | Grade 1 |
| Illinois | 1.NBT.C.4 | Add within 100, including adding a two-digit number and a one-digit number, and adding a two-digit number and a multiple of 10, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Understand that in adding two-digit numbers, one adds tens and tens, ones and ones; and sometimes it is necessary to compose a ten. | Grade 1 |
| Illinois | 1.NBT.C.5 | Given a two-digit number, mentally find 10 more or 10 less than the number, without having to count; explain the reasoning used. | Grade 1 |
| Illinois | 1.NBT.C.6 | Subtract multiples of 10 in the range 10-90 from multiples of 10 in the range 10-90 (positive or zero differences), using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. | Grade 1 |
| Illinois | 1.OA.A.1 | Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem. | Grade 1 |
| Illinois | 1.OA.B.3 | Apply properties of operations as strategies to add and subtract. | Grade 1 |
| Illinois | 1.OA.B.4 | Understand subtraction as an unknown-addend problem. | Grade 1 |
| Illinois | 1.OA.C.5 | Relate counting to addition and subtraction (e.g., by counting on 2 to add 2). | Grade 1 |
| Illinois | 1.OA.C.6 | Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to a ten (e.g., 13 - 4 = 13 - 3 - 1 = 10 - 1 = 9); using the relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 - 8 = 4); and creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13). | Grade 1 |
| Illinois | 1.OA.D.7 | Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false. | Grade 1 |
| Illinois | 1.OA.D.8 | Determine the unknown whole number in an addition or subtraction equation relating three whole numbers. | Grade 1 |
| Illinois | 2.G.A.1 | Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces. Identify triangles, quadrilaterals, pentagons, hexagons, and cubes. | Grade 2 |
| Illinois | 2.G.A.2 | Partition a rectangle into rows and columns of same-size squares and count to find the total number of them. | Grade 2 |
| Illinois | 2.G.A.3 | Partition circles and rectangles into two, three, or four equal shares, describe the shares using the words halves, thirds, half of, a third of, etc., and describe the whole as two halves, three thirds, four fourths. Recognize that equal shares of identical wholes need not have the same shape. | Grade 2 |
| Illinois | 2.MD.A.1 | Measure the length of an object by selecting and using appropriate tools such as rulers, yardsticks, meter sticks, and measuring tapes. | Grade 2 |
| Illinois | 2.MD.A.2 | Measure the length of an object twice, using length units of different lengths for the two measurements; describe how the two measurements relate to the size of the unit chosen. | Grade 2 |
| Illinois | 2.MD.A.4 | Measure to determine how much longer one object is than another, expressing the length difference in terms of a standard length unit. | Grade 2 |
| Illinois | 2.MD.B.5 | Use addition and subtraction within 100 to solve word problems involving lengths that are given in the same units, e.g., by using drawings (such as drawings of rulers) and equations with a symbol for the unknown number to represent the problem. | Grade 2 |
| Illinois | 2.MD.C.7 | Tell and write time from analog and digital clocks to the nearest five minutes, using a.m. and p.m. | Grade 2 |
| Illinois | 2.MD.C.8 | Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies, using $ and ¢ symbols appropriately. | Grade 2 |
| Illinois | 2.MD.D.9 | Generate measurement data by measuring lengths of several objects to the nearest whole unit, or by making repeated measurements of the same object. Show the measurements by making a line plot, where the horizontal scale is marked off in whole-number units. | Grade 2 |
| Illinois | 2.MD.D.10 | Draw a picture graph and a bar graph (with single-unit scale) to represent a data set with up to four categories. Solve simple put-together, take-apart, and compare problems using information presented in a bar graph. | Grade 2 |
| Illinois | 2.NBT.A.1 | Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones. Understand the following as special cases: | Grade 2 |
| Illinois | 2.NBT.A.2 | Count within 1000; skip-count by 5s, 10s, and 100s. | Grade 2 |
| Illinois | 2.NBT.A.3 | Read and write numbers to 1000 using base-ten numerals, number names, and expanded form. | Grade 2 |
| Illinois | 2.NBT.A.4 | Compare two three-digit numbers based on meanings of the hundreds, tens, and ones digits, using >, =, and < symbols to record the results of comparisons. | Grade 2 |
| Illinois | 2.NBT.B.5 | Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction. | Grade 2 |
| Illinois | 2.NBT.B.6 | Add up to four two-digit numbers using strategies based on place value and properties of operations. | Grade 2 |
| Illinois | 2.NBT.B.7 | Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method. Understand that in adding or subtracting three-digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds. | Grade 2 |
| Illinois | 2.NBT.B.8 | Mentally add 10 or 100 to a given number 100–900, and mentally subtract 10 or 100 from a given number 100–900. | Grade 2 |
| Illinois | 2.OA.A.1 | Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem. | Grade 2 |
| Illinois | 2.OA.B.2 | Fluently add and subtract within 20 using mental strategies. By end of Grade 2, know from memory all sums of two one-digit numbers. | Grade 2 |
| Illinois | 2.OA.C.3 | Determine whether a group of objects (up to 20) has an odd or even number of members, e.g., by pairing objects or counting them by 2s; write an equation to express an even number as a sum of two equal addends. | Grade 2 |
| Illinois | 2.OA.C.4 | Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends. | Grade 2 |
| Illinois | 3.G.A.1 | Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories. | Grade 3 |
| Illinois | 3.G.A.2 | Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole. | Grade 3 |
| Illinois | 3.MD.A.1 | Tell and write time to the nearest minute and measure time intervals in minutes. Solve word problems involving addition and subtraction of time intervals in minutes, e.g., by representing the problem on a number line diagram. | Grade 3 |
| Illinois | 3.MD.A.2 | Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l). Add, subtract, multiply, or divide to solve one-step word problems involving masses or volumes that are given in the same units, e.g., by using drawings (such as a beaker with a measurement scale) to represent the problem. | Grade 3 |
| Illinois | 3.MD.B.3 | Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and two-step “how many more” and “how many less” problems using information presented in scaled bar graphs. | Grade 3 |
| Illinois | 3.MD.B.4 | Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Show the data by making a line plot, where the horizontal scale is marked off in appropriate units-whole numbers, halves, or quarters. | Grade 3 |
| Illinois | 3.MD.C.5 | Recognize area as an attribute of plane figures and understand concepts of area measurement. | Grade 3 |
| Illinois | 3.MD.C.6 | Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units). | Grade 3 |
| Illinois | 3.MD.C.7 | Relate area to the operations of multiplication and addition. | Grade 3 |
| Illinois | 3.MD.D.8 | Solve real world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters. | Grade 3 |
| Illinois | 3.NBT.A.1 | Use place value understanding to round whole numbers to the nearest 10 or 100. | Grade 3 |
| Illinois | 3.NBT.A.2 | Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction. | Grade 3 |
| Illinois | 3.NBT.A.3 | Multiply one-digit whole numbers by multiples of 10 in the range 10–90 (e.g., 9 × 80, 5 × 60) using strategies based on place value and properties of operations. | Grade 3 |
| Illinois | 3.NF.A.1 | Understand a fraction 1/𝘣 as the quantity formed by 1 part when a whole is partitioned into 𝘣 equal parts; understand a fraction 𝘢/𝑏 as the quantity formed by 𝘢 parts of size 1/𝘣. | Grade 3 |
| Illinois | 3.NF.A.2 | Understand a fraction as a number on the number line; represent fractions on a number line diagram. | Grade 3 |
| Illinois | 3.NF.A.3 | Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size. | Grade 3 |
| Illinois | 3.OA.A.1 | Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each. | Grade 3 |
| Illinois | 3.OA.A.2 | Interpret whole-number quotients of whole numbers, e.g., interpret 56 ÷ 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each. | Grade 3 |
| Illinois | 3.OA.A.3 | Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem. | Grade 3 |
| Illinois | 3.OA.A.4 | Determine the unknown whole number in a multiplication or division equation relating three whole numbers. | Grade 3 |
| Illinois | 3.OA.B.5 | Apply properties of operations as strategies to multiply and divide. | Grade 3 |
| Illinois | 3.OA.B.6 | Understand division as an unknown-factor problem. | Grade 3 |
| Illinois | 3.OA.C.7 | Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 × 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers. | Grade 3 |
| Illinois | 3.OA.D.8 | Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. | Grade 3 |
| Illinois | 3.OA.D.9 | Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations. | Grade 3 |
| Illinois | 4.G.A.1 | Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures. | Grade 4 |
| Illinois | 4.G.A.2 | Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles. | Grade 4 |
| Illinois | 4.G.A.3 | Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify line-symmetric figures and draw lines of symmetry. | Grade 4 |
| Illinois | 4.MD.A.1 | Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table. | Grade 4 |
| Illinois | 4.MD.A.2 | Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. | Grade 4 |
| Illinois | 4.MD.A.3 | Apply the area and perimeter formulas for rectangles in real world and mathematical problems. | Grade 4 |
| Illinois | 4.MD.B.4 | Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots. | Grade 4 |
| Illinois | 4.MD.C.5 | Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement: | Grade 4 |
| Illinois | 4.MD.C.6 | Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure. | Grade 4 |
| Illinois | 4.MD.C.7 | Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems, e.g., by using an equation with a symbol for the unknown angle measure. | Grade 4 |
| Illinois | 4.NBT.A.1 | Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. | Grade 4 |
| Illinois | 4.NBT.A.2 | Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. | Grade 4 |
| Illinois | 4.NBT.A.3 | Use place value understanding to round multi-digit whole numbers to any place. | Grade 4 |
| Illinois | 4.NBT.B.4 | Fluently add and subtract multi-digit whole numbers using the standard algorithm. | Grade 4 |
| Illinois | 4.NBT.B.5 | Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. | Grade 4 |
| Illinois | 4.NBT.B.6 | Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. | Grade 4 |
| Illinois | 4.NF.A.1 | Explain why a fraction 𝘢/𝘣 is equivalent to a fraction (𝘯 × 𝘢)/(𝘯 × 𝘣) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. | Grade 4 |
| Illinois | 4.NF.A.2 | Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model. | Grade 4 |
| Illinois | 4.NF.B.3 | Understand a fraction 𝘢/𝘣 with 𝘢 > 1 as a sum of fractions 1/𝘣. | Grade 4 |
| Illinois | 4.NF.B.4 | Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. | Grade 4 |
| Illinois | 4.NF.C.5 | Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100. | Grade 4 |
| Illinois | 4.NF.C.6 | Use decimal notation for fractions with denominators 10 or 100. | Grade 4 |
| Illinois | 4.NF.C.7 | Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual model. | Grade 4 |
| Illinois | 4.OA.A.1 | Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 × 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations. | Grade 4 |
| Illinois | 4.OA.A.2 | Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison. | Grade 4 |
| Illinois | 4.OA.A.3 | Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. | Grade 4 |
| Illinois | 4.OA.B.4 | Find all factor pairs for a whole number in the range 1-100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1-100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1-100 is prime or composite. | Grade 4 |
| Illinois | 4.OA.C.5 | Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. | Grade 4 |
| Illinois | 5.G.A.1 | Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., 𝘹-axis and 𝘹-coordinate, 𝘺-axis and 𝘺-coordinate). | Grade 5 |
| Illinois | 5.G.A.2 | Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. | Grade 5 |
| Illinois | 5.G.B.3 | Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. | Grade 5 |
| Illinois | 5.G.B.4 | Classify two-dimensional figures in a hierarchy based on properties. | Grade 5 |
| Illinois | 5.MD.A.1 | Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. | Grade 5 |
| Illinois | 5.MD.B.2 | Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. | Grade 5 |
| Illinois | 5.MD.C.3 | Recognize volume as an attribute of solid figures and understand concepts of volume measurement. | Grade 5 |
| Illinois | 5.MD.C.4 | Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. | Grade 5 |
| Illinois | 5.MD.C.5 | Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume. | Grade 5 |
| Illinois | 5.NBT.A.1 | Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. | Grade 5 |
| Illinois | 5.NBT.A.2 | Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. | Grade 5 |
| Illinois | 5.NBT.A.3 | Read, write, and compare decimals to thousandths. | Grade 5 |
| Illinois | 5.NBT.A.4 | Use place value understanding to round decimals to any place. | Grade 5 |
| Illinois | 5.NBT.B.5 | Fluently multiply multi-digit whole numbers using the standard algorithm. | Grade 5 |
| Illinois | 5.NBT.B.6 | Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. | Grade 5 |
| Illinois | 5.NBT.B.7 | Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. | Grade 5 |
| Illinois | 5.NF.A.1 | Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. | Grade 5 |
| Illinois | 5.NF.A.2 | Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. | Grade 5 |
| Illinois | 5.NF.B.3 | Interpret a fraction as division of the numerator by the denominator (𝘢/𝘣 = 𝘢 ÷ 𝘣). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. | Grade 5 |
| Illinois | 5.NF.B.4 | Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. | Grade 5 |
| Illinois | 5.NF.B.5 | Interpret multiplication as scaling (resizing), by: | Grade 5 |
| Illinois | 5.NF.B.6 | Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. | Grade 5 |
| Illinois | 5.NF.B.7 | Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. | Grade 5 |
| Illinois | 5.OA.A.1 | Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. | Grade 5 |
| Illinois | 5.OA.A.2 | Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. | Grade 5 |
| Illinois | 5.OA.B.3 | Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. | Grade 5 |
| Illinois | 6.EE.A.1 | Write and evaluate numerical expressions involving whole-number exponents. | Grade 6 |
| Illinois | 6.EE.A.2 | Write, read, and evaluate expressions in which letters stand for numbers. | Grade 6 |
| Illinois | 6.EE.A.3 | Apply the properties of operations to generate equivalent expressions. | Grade 6 |
| Illinois | 6.EE.A.4 | Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). | Grade 6 |
| Illinois | 6.EE.B.5 | Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true. | Grade 6 |
| Illinois | 6.EE.B.6 | Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set. | Grade 6 |
| Illinois | 6.EE.B.7 | Solve real-world and mathematical problems by writing and solving equations of the form 𝘹 + 𝘱 = 𝘲 and 𝘱𝘹 = 𝘲 for cases in which 𝘱, 𝘲 and 𝘹 are all nonnegative rational numbers. | Grade 6 |
| Illinois | 6.EE.B.8 | Write an inequality of the form 𝘹 > 𝘤 or 𝘹 𝘤 or 𝘹 < 𝘤 have infinitely many solutions; represent solutions of such inequalities on number line diagrams. | Grade 6 |
| Illinois | 6.EE.C.9 | Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. | Grade 6 |
| Illinois | 6.G.A.1 | Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems. | Grade 6 |
| Illinois | 6.G.A.2 | Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas 𝘝 = 𝘭 𝘸 𝘩 and 𝘝 = 𝘣 𝘩 to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems. | Grade 6 |
| Illinois | 6.G.A.3 | Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems. | Grade 6 |
| Illinois | 6.G.A.4 | Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems. | Grade 6 |
| Illinois | 6.RP.A.1 | Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. | Grade 6 |
| Illinois | 6.RP.A.2 | Understand the concept of a unit rate 𝘢/𝘣 associated with a ratio 𝘢:𝘣 with 𝘣 ≠ 0, and use rate language in the context of a ratio relationship. | Grade 6 |
| Illinois | 6.RP.A.3 | Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. | Grade 6 |
| Illinois | 6.SP.B.5 | Summarize numerical data sets in relation to their context, such as by: | Grade 6 |
| Illinois | 6.NS.A.1 | Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. | Grade 6 |
| Illinois | 6.NS.B.2 | Fluently divide multi-digit numbers using the standard algorithm. | Grade 6 |
| Illinois | 6.NS.B.3 | Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation. | Grade 6 |
| Illinois | 6.NS.C.5 | Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation. | Grade 6 |
| Illinois | 6.NS.C.6 | Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates. | Grade 6 |
| Illinois | 6.NS.C.7 | Understand ordering and absolute value of rational numbers. | Grade 6 |
| Illinois | 6.NS.C.8 | Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. | Grade 6 |
| Illinois | 7.EE.A.1 | Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients. | Grade 7 |
| Illinois | 7.EE.A.2 | Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. | Grade 7 |
| Illinois | 7.EE.B.3 | Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. | Grade 7 |
| Illinois | 7.EE.B.4 | Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. | Grade 7 |
| Illinois | 7.G.A.1 | Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale. | Grade 7 |
| Illinois | 7.G.A.2 | Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle. | Grade 7 |
| Illinois | 7.G.A.3 | Describe the two-dimensional figures that result from slicing three-dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids. | Grade 7 |
| Illinois | 7.G.B.4 | Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle. | Grade 7 |
| Illinois | 7.G.B.5 | Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure. | Grade 7 |
| Illinois | 7.G.B.6 | Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. | Grade 7 |
| Illinois | 7.RP.A.1 | Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. | Grade 7 |
| Illinois | 7.RP.A.2 | Recognize and represent proportional relationships between quantities. | Grade 7 |
| Illinois | 7.RP.A.3 | Use proportional relationships to solve multistep ratio and percent problems. | Grade 7 |
| Illinois | 7.NS.A.1 | Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram. | Grade 7 |
| Illinois | 7.NS.A.2 | Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers. | Grade 7 |
| Illinois | 7.NS.A.3 | Solve real-world and mathematical problems involving the four operations with rational numbers. | Grade 7 |
| Illinois | 8.EE.A.1 | Know and apply the properties of integer exponents to generate equivalent numerical expressions. | Grade 8 |
| Illinois | 8.EE.A.2 | Use square root and cube root symbols to represent solutions to equations of the form 𝘹² = 𝘱 and 𝘹³ = 𝘱, where 𝘱 is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that √2 is irrational. | Grade 8 |
| Illinois | 8.EE.A.3 | Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other. | Grade 8 |
| Illinois | 8.EE.A.4 | Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology. | Grade 8 |
| Illinois | 8.EE.B.5 | Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. | Grade 8 |
| Illinois | 8.EE.B.6 | Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation 𝘺 = 𝘮𝘹 for a line through the origin and the equation 𝘺 = 𝘮𝘹 + 𝘣 for a line intercepting the vertical axis at 𝘣. | Grade 8 |
| Illinois | 8.EE.C.7 | Solve linear equations in one variable. | Grade 8 |
| Illinois | 8.EE.C.8 | Analyze and solve pairs of simultaneous linear equations. | Grade 8 |
| Illinois | 8.F.A.1 | Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output. | Grade 8 |
| Illinois | 8.F.A.2 | Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). | Grade 8 |
| Illinois | 8.F.A.3 | Interpret the equation 𝘺 = 𝘮𝘹 + 𝘣 as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. | Grade 8 |
| Illinois | 8.F.B.4 | Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (𝘹, 𝘺) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values. | Grade 8 |
| Illinois | 8.F.B.5 | Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally. | Grade 8 |
| Illinois | 8.G.A.1 | Verify experimentally the properties of rotations, reflections, and translations: | Grade 8 |
| Illinois | 8.G.A.2 | Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them. | Grade 8 |
| Illinois | 8.G.A.3 | Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates. | Grade 8 |
| Illinois | 8.G.A.4 | Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two-dimensional figures, describe a sequence that exhibits the similarity between them. | Grade 8 |
| Illinois | 8.G.A.5 | Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. | Grade 8 |
| Illinois | 8.G.B.7 | Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions. | Grade 8 |
| Illinois | 8.G.B.8 | Apply the Pythagorean Theorem to find the distance between two points in a coordinate system. | Grade 8 |
| Illinois | 8.G.C.9 | Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems. | Grade 8 |
| Illinois | 8.SP.A.1 | Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association. | Grade 8 |
| Illinois | 8.SP.A.2 | Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line. | Grade 8 |
| Illinois | 8.NS.A.2 | Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g., π²). | Grade 8 |
| Illinois | HSA-APR.B.3 | Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial. | High School - Algebra |
| Illinois | HSA-CED.A.2 | Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. | High School - Algebra |
| Illinois | HSA-CED.A.3 | Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context. | High School - Algebra |
| Illinois | HSA-REI.B.3 | Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. | High School - Algebra |
| Illinois | HSA-SSE.A.2 | Use the structure of an expression to identify ways to rewrite it. | High School - Algebra |
| Illinois | HSA-SSE.B.3 | Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression. | High School - Algebra |
| Illinois | HSF-BF.A.1 | Write a function that describes a relationship between two quantities. | High School - Functions |
| Illinois | HSF-IF.A.2 | Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. | High School - Functions |
| Illinois | HSF-IF.B.4 | For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. | High School - Functions |
| Illinois | HSF-IF.C.7 | Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. | High School - Functions |
| Illinois | HSS-ID.B.6 | Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. | High School - Statistics and Probability |
| Indiana | K.NS.1 | Count to at least 100 by ones and tens. Count by one from any given number. | Kindergarten |
| Indiana | K.NS.2 | Write whole numbers from 0 to 20 and identify number words from 0 to 10. Represent a number of objects with a written numeral 0-20 (with 0 representing a count of no objects). | Kindergarten |
| Indiana | K.NS.3 | Say the number names in standard order when counting objects, pairing each object with one and only one number name and each number name with one and only one object. Understand that the last number name said describes the number of objects counted and that the number of objects is the same regardless of their arrangement or the order in which they were counted. Count out the number of objects, given a number from 1 to 20. | Kindergarten |
| Indiana | K.NS.4 | Identify sets of 1 to 10 objects in patterned arrangements and tell how many without counting. | Kindergarten |
| Indiana | K.NS.5 | Identify whether the number of objects in one group is greater than, less than, or equal to the number of objects in another group (e.g., by using matching and counting strategies). | Kindergarten |
| Indiana | K.NS.6 | Compare the values of two numbers from 1 to 20 presented as written numerals. | Kindergarten |
| Indiana | K.NS.7 | Define and model a ten as a group of ten ones. Model equivalent forms of whole numbers from 10 to 20 as groups of tens and ones using objects and drawings. | Kindergarten |
| Indiana | K.CA.1 | Solve real-world problems that involve addition and subtraction within 10 using modeling with objects or drawings. | Kindergarten |
| Indiana | K.CA.2 | Use objects or drawings to model the decomposition of numbers less than 10 into pairs in more than one way. Identify corresponding equations. | Kindergarten |
| Indiana | K.CA.3 | Find the number that makes 10 when added to the given number for any number from 1 to 9 (e.g., by using objects or drawings), and record the answer with a drawing or an equation. | Kindergarten |
| Indiana | K.G.1 | Compare two- and three-dimensional shapes in different sizes and orientations, using informal language to describe their similarities, differences, parts (e.g., number of sides and vertices/corners), and other attributes (e.g., having sides of equal length). | Kindergarten |
| Indiana | K.M.1 | Make direct comparisons of the length, capacity, weight, and temperature of objects, and identify which object is shorter, longer, taller, lighter, heavier, warmer, cooler, or holds more. | Kindergarten |
| Indiana | 1.NS.1 | Count to at least 120 by ones, fives, and tens from any given number. In this range, read and write numerals and represent a number of objects with a written numeral. | Grade 1 |
| Indiana | 1.NS.2 | Model place value concepts of two-digit numbers, multiples of 10, and equivalent forms of whole numbers using objects and drawings. | Grade 1 |
| Indiana | 1.NS.4 | Use place value understanding to compare two two-digit numbers based on meanings of the tens and ones digits, recording the results of comparisons with the symbols > , = , and <. | Grade 1 |
| Indiana | 1.CA.1 | Demonstrate fluency with addition facts and the corresponding subtraction facts within 20. Use strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to a 10 (e.g., 13 - 4 = 13 - 3 - 1 = 10 - 1 = 9); using the relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 - 8 = 4); and creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13). Model the role of 0 and the equal sign in addition and subtraction using objects or drawings. | Grade 1 |
| Indiana | 1.CA.2 | Solve real-world problems involving addition and subtraction within 20 in situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all parts of the addition or subtraction problem (e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem). | Grade 1 |
| Indiana | 1.CA.3 | Using number sense and place value strategies, add within 100, including adding a two-digit number and a one-digit number, and adding a two-digit number and a multiple of 10. Use models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; describe the strategy and explain the reasoning used. | Grade 1 |
| Indiana | 1.CA.4 | Create, extend, and give an appropriate rule for number patterns using addition within 100. | Grade 1 |
| Indiana | 1.G.1 | Distinguish between defining attributes of two- and three-dimensional shapes (e.g., triangles are closed and three-sided) versus non-defining attributes (e.g., color, orientation, overall size). Create and draw two-dimensional shapes with defining attributes. | Grade 1 |
| Indiana | 1.G.2 | Use two-dimensional shapes (e.g., rectangles, squares, trapezoids, triangles, half-circles, quarter-circles) or three-dimensional shapes (e.g., cubes, right rectangular prisms, right circular cones, and right circular cylinders) to create a composite shape, and compose new shapes from the composite shape. [In grade 1, students do not need to learn formal names such as right rectangular prism.] | Grade 1 |
| Indiana | 1.G.3 | Partition circles and rectangles into two and four equal parts; describe the parts using the words halves, fourths, and quarters; and use the phrases half of, fourth of, and quarter of. Describe the whole as two of, or four of, the parts. Understand for partitioning circles and rectangles into two and four equal parts that decomposing into equal parts creates smaller parts. | Grade 1 |
| Indiana | 1.M.1 | Use direct comparison or a nonstandard unit to compare and order objects according to length, area, capacity, weight, and temperature. | Grade 1 |
| Indiana | 1.M.2 | Tell and write time to the nearest half-hour and relate time to events (before/after, shorter/longer) using analog clocks. Explain how to read hours and minutes using digital clocks. | Grade 1 |
| Indiana | 1.M.3 | Identify the value of a penny, nickel, dime, and a collection of pennies, nickels, and dimes. | Grade 1 |
| Indiana | 1.DA.1 | With guidance, collect data from a simple survey or collaborative investigation; organize data into appropriate single-unit bar graphs, pictographs, and/or tables and draw conclusions based on mathematical observations, comparisons, and grade-level computation strategies. | Grade 1 |
| Indiana | 2.NS.1 | Count by ones, twos, fives, tens, and hundreds up to at least 1,000 from any given number. | Grade 2 |
| Indiana | 2.NS.2 | Read and write whole numbers up to 1,000. Use words, models, standard form, and expanded form to represent and show equivalent forms of whole numbers up to 1,000. | Grade 2 |
| Indiana | 2.NS.3 | Determine whether a group of objects (up to 20) has an odd or even number of members (e.g., by placing that number of objects in two groups of the same size and recognizing that for even numbers no object will be left over and for odd numbers one object will be left over, or by pairing objects or counting them by twos). | Grade 2 |
| Indiana | 2.NS.4 | Define and model a hundred as a group of ten tens. Model place value concepts of three-digit numbers, multiples of 100, and equivalent forms of whole numbers using objects and drawings. | Grade 2 |
| Indiana | 2.NS.5 | Use place value understanding to compare two three-digit numbers based on meanings of the hundreds, tens, and ones digits, using > , = , and < symbols to record the results of comparisons. | Grade 2 |
| Indiana | 2.CA.1 | Solve real-world problems involving addition and subtraction within 100 in situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all parts of the addition or subtraction problem (e.g., by using drawings and equations with a symbol for the unknown number to represent the problem). Use estimation to decide whether answers are reasonable in addition problems. | Grade 2 |
| Indiana | 2.CA.2 | Using number sense and place value strategies, add and subtract within 1,000, including composing and decomposing tens and hundreds. Use models, drawings, and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; describe the strategy and explain the reasoning used. | Grade 2 |
| Indiana | 2.CA.3 | Show that the order in which two numbers are added (commutative property) and how the numbers are grouped in addition (associative property) will not change the sum. These properties can be used to show that numbers can be added in any order. | Grade 2 |
| Indiana | 2.CA.4 | Create, extend, and give an appropriate rule for number patterns using addition and subtraction within 1,000. | Grade 2 |
| Indiana | 2.G.1 | Identify, describe, and classify two- and three-dimensional shapes (i.e., triangle, square, rectangle, cube, right rectangular prism) according to the number and shape of faces and the number of sides and/or vertices. Draw two-dimensional shapes. | Grade 2 |
| Indiana | 2.G.2 | Investigate and predict the result of composing and decomposing two- and three-dimensional shapes. | Grade 2 |
| Indiana | 2.G.3 | Partition a rectangle into rows and columns of same-size (unit) squares and count to find the total number of same-size squares. | Grade 2 |
| Indiana | 2.G.4 | Partition circles and rectangles into two, three, or four equal parts; describe the shares using the words halves, thirds, half of, a third of, etc.; and describe the whole as two halves, three thirds, or four fourths. Recognize that equal parts of identical wholes need not have the same shape. | Grade 2 |
| Indiana | 2.M.1 | Describe the relationships among an inch, foot, and yard. Describe the relationship between a centimeter and meter. | Grade 2 |
| Indiana | 2.M.2 | Estimate and measure the length of an object by selecting and using appropriate tools, such as rulers, yardsticks, meter sticks, and measuring tapes to the nearest inch, foot, yard, centimeter, and meter. | Grade 2 |
| Indiana | 2.M.3 | Estimate and measure volume (capacity) using cups and pints. Add and subtract to solve real-world problems involving capacities that are given in the same units or obtained through investigations. | Grade 2 |
| Indiana | 2.M.4 | Tell and write time to the nearest five minutes from analog clocks, using a.m. and p.m. Solve real-world problems involving addition and subtraction of time intervals on the hour or half hour. | Grade 2 |
| Indiana | 2.M.6 | Find the value of a collection of pennies, nickels, dimes, quarters, and dollars. | Grade 2 |
| Indiana | 2.DA.1 | Collect, organize, and graph data from observations, surveys, and investigations using scaled bar graphs and pictographs (limit scale to 2s, 5s, 10s, and 100s); interpret mathematical relationships within the data using grade-level addition, subtraction, and comparison strategies. | Grade 2 |
| Indiana | 3.NS.2 | Model unit fractions as the quantity formed by 1 part when a whole is partitioned into equal parts; model non-unit fractions as the quantity formed by iterations of unit fractions. [In grade 3, limit denominators of fractions to 2, 3, 4, 6, 8.] | Grade 3 |
| Indiana | 3.NS.3 | Model a non-unit fraction on a number line by marking equal lengths from 0, identifying each part as a unit fraction and locating the non-unit fraction as the endpoint on the number line. | Grade 3 |
| Indiana | 3.NS.4 | Use fraction models to represent two simple equivalent fractions with attention to how the number and size of the parts differ even though the quantities are the same. Use this principle to generate simple equivalent fractions (e.g., 1/2 = 2/4, 4/6 = 2/3). | Grade 3 |
| Indiana | 3.NS.5 | Compare two fractions with the same numerator or the same denominator by reasoning about their size based on the same whole. Record the results of comparisons with the symbols > , = , or < , and justify the conclusions (e.g., by using a visual fraction model). | Grade 3 |
| Indiana | 3.NS.6 | Use place value understanding to round two- and three-digit whole numbers to the nearest 10 or 100. | Grade 3 |
| Indiana | 3.CA.1 | Fluently add and subtract multi-digit whole numbers using strategies and algorithms based on place value, properties of operations, and relationships between addition and subtraction. | Grade 3 |
| Indiana | 3.CA.2 | Solve real-world problems involving addition and subtraction of multi-digit whole numbers (e.g., by using drawings and equations with a symbol for the unknown number to represent the problem). | Grade 3 |
| Indiana | 3.CA.3 | Model the concept of multiplication of whole numbers using equal-sized groups, arrays, area models, and equal intervals on a number line. Model the properties of 0 and 1 in multiplication using objects or drawings. | Grade 3 |
| Indiana | 3.CA.4 | Model the concept of division of whole numbers with the following models: partitioning, sharing, and an inverse of multiplication. Model the properties of 0 and 1 in division using objects or drawings. | Grade 3 |
| Indiana | 3.CA.5 | Multiply and divide within 100 using strategies such as the relationship between multiplication and division (e.g., knowing that 8 x 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. | Grade 3 |
| Indiana | 3.CA.6 | Demonstrate fluency with mastery of multiplication facts and corresponding division facts of 0 to 10. | Grade 3 |
| Indiana | 3.CA.7 | Solve real-world problems involving whole number multiplication and division within 100 in situations involving equal groups, arrays, and measurement quantities (e.g., by using drawings and equations with a symbol for the unknown number to represent the problem). | Grade 3 |
| Indiana | 3.CA.8 | Create, extend, and give an appropriate rule for number patterns within 100 (including patterns in the addition table or multiplication table). | Grade 3 |
| Indiana | 3.G.1 | Define, identify, and classify four-sided shapes such as rhombuses, rectangles, and squares as quadrilaterals. Identify and draw examples and non-examples of quadrilaterals. | Grade 3 |
| Indiana | 3.G.2 | Identify, describe, and draw points, lines, and line segments using appropriate tools (e.g., ruler, straightedge, and technology), and use these terms when describing two-dimensional shapes. | Grade 3 |
| Indiana | 3.G.3 | Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole (i.e., 1/2, 1/3, 1/4, 1/6, 1/8). | Grade 3 |
| Indiana | 3.M.1 | Estimate and measure the mass of objects in grams (g) and kilograms (kg) and the volume of objects in quarts (qt), gallons (gal), and liters (l). Add, subtract, multiply, or divide to solve one-step, real-world problems involving masses or volumes that are given in the same units or obtained through investigation. | Grade 3 |
| Indiana | 3.M.3 | Tell and write time to the nearest minute and measure time intervals in minutes. Solve word problems involving addition and subtraction of time intervals in minutes (e.g., by representing the problem on a number line diagram). | Grade 3 |
| Indiana | 3.M.5 | Find the area of a rectangle with whole-number side lengths by modeling with unit squares, and show that the area is the same as would be found by multiplying the side lengths. Identify and draw rectangles with the same perimeter and different areas or with the same area and different perimeters. | Grade 3 |
| Indiana | 3.M.6 | Find perimeters of polygons given the side lengths or given an unknown side length. | Grade 3 |
| Indiana | 3.DA.1 | Collect, organize, and graph data from observations, surveys, and experiments using scaled bar graphs and pictographs. Solve real-world problems by analyzing and interpreting the data using grade-level computation and comparison strategies. | Grade 3 |
| Indiana | 4.NS.1 | Read and write whole numbers up to 1,000,000. Use words, models, standard form, and expanded form to represent and show equivalent forms of whole numbers up to 1,000,000. | Grade 4 |
| Indiana | 4.NS.2 | Model mixed numbers and improper fractions using visual fraction models such as number lines and area models. Use a visual fraction model to show the equivalency between whole numbers and whole numbers as fractions. | Grade 4 |
| Indiana | 4.NS.3 | Use fraction models to represent two equivalent fractions with attention to how the number and size of the parts differ even though the fractions themselves are the same size. Use this principle to generate equivalent fractions. [In grade 4, limit denominators of fractions to 2, 3, 4, 5, 6, 8, 10, 25, 100.] | Grade 4 |
| Indiana | 4.NS.4 | Compare two fractions with different numerators and different denominators (e.g., by creating common denominators or numerators, or by comparing to a benchmark, such as 0, 1/2, and 1). Explain why comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols > , = , or < , and justify the conclusions (e.g., by using a visual fraction model). | Grade 4 |
| Indiana | 4.NS.5 | Write tenths and hundredths in decimal and fraction notations. Use words, models, standard form, and expanded form to represent decimal numbers to hundredths. Mentally calculate fraction and decimal equivalents for halves and fourths (e.g., 1/2 = 0.5 = 0.50, 7/4 = 1 3/4 = 1.75). | Grade 4 |
| Indiana | 4.NS.6 | Compare two decimals to hundredths by reasoning about their size based on the same whole. Record the results of comparisons with the symbols > , = , or < , and justify the conclusions (e.g., by using a visual model). | Grade 4 |
| Indiana | 4.NS.7 | Use place value understanding to round multi-digit whole numbers to any given place value. | Grade 4 |
| Indiana | 4.CA.1 | Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Describe the strategy and explain the reasoning. | Grade 4 |
| Indiana | 4.CA.2 | Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Describe the strategy and explain the reasoning. | Grade 4 |
| Indiana | 4.CA.4 | Investigate the mathematical relationship between factors and multiples for whole numbers from 1-100, including the set of factors and multiples for given numbers. Identify sets of factors and multiples for any given whole number up to 100. | Grade 4 |
| Indiana | 4.CA.5 | Solve real-world problems with whole numbers involving multiplicative comparison (e.g., by using drawings and equations with a symbol for the unknown number to represent the problem), distinguishing multiplicative comparison from additive comparison. [In grade 4, division problems should not include a remainder.] | Grade 4 |
| Indiana | 4.CA.6 | Add and subtract fractions with common denominators using visual fraction models. Decompose non-unit fractions to represent them as iterations of unit fractions. | Grade 4 |
| Indiana | 4.CA.7 | Add and subtract mixed numbers with common denominators (e.g., by replacing each mixed number with an equivalent fraction and/or by using properties of operations and the relationship between addition and subtraction). | Grade 4 |
| Indiana | 4.CA.8 | Solve real-world problems involving addition and subtraction of fractions referring to the same whole and having common denominators (e.g., by using visual fraction models and equations to represent the problem). | Grade 4 |
| Indiana | 4.CA.9 | Describe the relationship between two terms and use it to find a second number when a first number is given. Generate a number pattern that follows a given rule. | Grade 4 |
| Indiana | 4.G.1 | Identify, describe, and draw parallelograms, rhombuses, and trapezoids using appropriate tools (e.g., ruler, straightedge, and technology). | Grade 4 |
| Indiana | 4.G.2 | Identify, describe, and draw rays, angles (right, acute, obtuse), and perpendicular and parallel lines using appropriate tools (e.g., ruler, straightedge, and technology). Identify these in two-dimensional figures. | Grade 4 |
| Indiana | 4.G.3 | Classify triangles and quadrilaterals based on the presence or absence of parallel or perpendicular lines, or right, acute, or obtuse angles. | Grade 4 |
| Indiana | 4.M.1 | Measure length to the nearest quarter-inch, eighth-inch, and millimeter. | Grade 4 |
| Indiana | 4.M.2 | Within given measurement systems, convert larger units to smaller units, including km, m, cm; kg, g; lb, oz; l, ml; hr, min, sec., and use these conversions to solve real-world problems. | Grade 4 |
| Indiana | 4.M.3 | Use the four operations to solve real-world problems involving distances, intervals of time, volumes, masses of objects, and money. Include addition and subtraction problems involving simple fractions and problems that require expressing measurements given in a larger unit in terms of a smaller unit. | Grade 4 |
| Indiana | 4.M.4 | Apply the area and perimeter formulas for rectangles to solve real-world and other mathematical problems. Investigate the area of complex shapes composed of rectangles by decomposing them into non-overlapping rectangles and adding the areas of the non-overlapping parts; apply this technique to solve real-world problems and other mathematical problems. | Grade 4 |
| Indiana | 4.DA.2 | Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using data displayed in line plots. | Grade 4 |
| Indiana | 5.NS.1 | Use a number line to compare and order fractions, mixed numbers, and decimals to thousandths. Write the results using > , = , and < symbols. | Grade 5 |
| Indiana | 5.NS.3 | Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. | Grade 5 |
| Indiana | 5.CA.1 | Find whole-number quotients and remainders with up to four-digit dividends and two-digit divisors using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Describe the strategy and explain the reasoning used. | Grade 5 |
| Indiana | 5.CA.2 | Solve real-world problems involving multiplication and division of whole numbers (e.g., by using equations to represent the problem). In division problems that involve a remainder, explain how the remainder affects the solution to the problem. | Grade 5 |
| Indiana | 5.CA.3 | Add and subtract fractions and mixed numbers with unlike denominators using strategies or the standard algorithm. | Grade 5 |
| Indiana | 5.CA.4 | Solve real-world problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators (e.g., by using visual fraction models and equations to represent the problem). Use benchmark fractions and number sense of fractions to estimate mentally and assess whether the answer is reasonable. | Grade 5 |
| Indiana | 5.CA.5 | Use visual fraction models to multiply a fraction by a fraction or a whole number. | Grade 5 |
| Indiana | 5.CA.6 | Use visual fraction models and numbers to divide a fraction by a fraction or a whole number. | Grade 5 |
| Indiana | 5.CA.7 | Solve real-world problems involving multiplication of fractions, including mixed numbers (e.g., by using visual fraction models and equations to represent the problem). | Grade 5 |
| Indiana | 5.CA.8 | Solve real-world problems involving division of fractions and mixed numbers (e.g., by using visual fraction models and equations to represent the problem). | Grade 5 |
| Indiana | 5.CA.9 | Add, subtract, multiply, and divide decimals to hundredths, using models or drawings and strategies based on place value or the properties of operations. Describe the strategy and explain the reasoning. | Grade 5 |
| Indiana | 5.CA.10 | Solve real-world problems involving addition, subtraction, multiplication, and division with decimals to hundredths including problems that involve money in decimal notation (e.g., by using equations, models or drawings, and strategies based on place value or properties of operations to represent the problem). | Grade 5 |
| Indiana | 5.CA.11 | Represent real-world problems and equations by graphing ordered pairs in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. | Grade 5 |
| Indiana | 5.M.1 | Convert among different-sized standard measurement units within a given measurement system and use these conversions in solving multi-step, real-world problems. | Grade 5 |
| Indiana | 5.M.4 | Find the volume of a right rectangular prism with whole-number side lengths by packing it with unit cubes, and show that the volume is the same as would be found by multiplying the edge lengths or multiplying the height by the area of the base. | Grade 5 |
| Indiana | 5.M.5 | Apply the formulas V = l × w × h and V = B × h for right rectangular prisms to find volumes of right rectangular prisms with whole-number edge lengths to solve real-world problems and other mathematical problems. | Grade 5 |
| Indiana | 5.DA.1 | Formulate questions that can be addressed with categorical and numerical data and make predictions about the data. Collect, organize, and graph data from observations, surveys, and experiments using line plots with fractional intervals, histograms, or other graphical representations that appropriately represent the data set. | Grade 5 |
| Indiana | 6.NS.1 | Use positive and negative numbers to represent and compare quantities in real-world contexts, explaining the meaning of 0 in each situation. | Grade 6 |
| Indiana | 6.NS.2 | Explain how opposite signs of numbers indicate locations on opposite sides of 0 on the number line; identify the opposite of the opposite of a number. | Grade 6 |
| Indiana | 6.NS.3 | Compare and order rational numbers and plot them on a number line. Write, interpret, and explain statements of order for rational numbers in real-world contexts. | Grade 6 |
| Indiana | 6.NS.4 | Solve real-world problems with positive fractions and decimals by using one or two operations. | Grade 6 |
| Indiana | 6.NS.7 | Apply the properties of operations (i.e., identity, inverse, commutative, associative, distributive properties) to create equivalent linear expressions and to justify whether two linear expressions are equivalent when the two expressions name the same number regardless of which value is substituted into them. | Grade 6 |
| Indiana | 6.NS.8 | Evaluate positive rational numbers with whole number exponents. | Grade 6 |
| Indiana | 6.RP.2 | Understand the concept of a unit rate and use terms related to rate in the context of a ratio relationship. | Grade 6 |
| Indiana | 6.RP.3 | Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. | Grade 6 |
| Indiana | 6.RP.4 | Solve real-world and other mathematical problems involving rates and ratios using models and strategies such as reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. | Grade 6 |
| Indiana | 6.RP.5 | Use variables to represent two quantities in a proportional relationship in a real-world problem; write an equation to express one quantity, the dependent variable, in terms of the other quantity, the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. | Grade 6 |
| Indiana | 6.AF.1 | Define and use multiple variables when writing expressions to represent real-world and other mathematical problems, and evaluate them for given values. | Grade 6 |
| Indiana | 6.AF.2 | Demonstrate which values from a specified set, if any, make the equation or inequality true. Use substitution to determine whether a given number in a specified set makes an equation or inequality true. | Grade 6 |
| Indiana | 6.AF.3 | Solve equations of the form x + p = q, x - p = q, px = q , and x/p = q fluently for cases in which p, q and x are all nonnegative rational numbers. Represent real-world problems using equations of these forms and solve such problems. | Grade 6 |
| Indiana | 6.AF.4 | Write an inequality of the form x > c, x ≥ c, x < c, or x ≤ c , where c is a rational number, to represent a constraint or condition in a real-world or other mathematical problem. Explain that inequalities have infinitely many solutions and how to represent solutions on a number line diagram. | Grade 6 |
| Indiana | 6.AF.5 | Solve real-world and other mathematical problems by graphing points with rational number coordinates on a coordinate plane. Include the use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. | Grade 6 |
| Indiana | 6.GM.2 | Apply the sums of interior angles of triangles and quadrilaterals to solve real-world and mathematical problems. | Grade 6 |
| Indiana | 6.GM.3 | Find the area of complex shapes composed of polygons by composing or decomposing into simple shapes; apply this technique to solve real-world and other mathematical problems. | Grade 6 |
| Indiana | 6.GM.4 | Find the volume of a right rectangular prism with fractional edge lengths using unit cubes of the appropriate unit fraction edge lengths (e.g., using technology or concrete materials) and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas V = lwh and V = Bh to find volumes of right rectangular prisms with fractional edge lengths to solve real-world and other mathematical problems. | Grade 6 |
| Indiana | 6.DS.3 | Summarize numerical data sets in relation to their context in multiple ways, such as: a. Report the number of observations; b. Describe the nature of the attribute under investigation, including how it was measured and its units of measurement; c. Determine quantitative measures of center (mean and/or median) and spread (range and interquartile range); d. Describe any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered; and e. Relate the choice of measures of center and spread to the shape of the data distribution and the context in which the data were gathered. | Grade 6 |
| Indiana | 7.NS.1 | Show on a number line that a number and its opposite have a sum of 0 (are additive inverses). Find and interpret sums of rational numbers in real-world contexts. | Grade 7 |
| Indiana | 7.NS.2 | Show that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in real-world contexts. | Grade 7 |
| Indiana | 7.NS.3 | Use the properties of operations, particularly the distributive property, leading to products such as (-1)(-1) = 1 and the rules for multiplying signed numbers. | Grade 7 |
| Indiana | 7.NS.6 | Apply the inverse relationship between squaring and finding the square root of a perfect square whole number. Find square roots of perfect square whole numbers. | Grade 7 |
| Indiana | 7.NS.7 | Compute fluently with rational numbers using an algorithmic approach. | Grade 7 |
| Indiana | 7.RP.1 | Identify the unit rate or constant of proportionality in tables, graphs, equations, and verbal descriptions of proportional relationships. | Grade 7 |
| Indiana | 7.RP.2 | Use proportional relationships to solve ratio and percent problems with multiple operations (e.g., simple interest, tax, markups, markdowns, gratuities, conversions within and across measurement systems, and percent increase and decrease). | Grade 7 |
| Indiana | 7.RP.3 | Represent real-world and other mathematical situations that involve proportional relationships. Write equations and draw graphs to represent these proportional relationships. Apply the definition of unit rate to y = mx . | Grade 7 |
| Indiana | 7.AF.1 | Apply the properties of operations (e.g., identity, inverse, commutative, associative, distributive properties) to create equivalent linear expressions, including situations that involve factoring out a common number (e.g., given 2x - 10 , create an equivalent expression 2(x - 5) ). Justify each step in the process. | Grade 7 |
| Indiana | 7.AF.2 | Solve real-world problems with rational numbers by using one or two operations. | Grade 7 |
| Indiana | 7.AF.3 | Solve equations of the form px + q = r and p(x + q) = r fluently, where p, q , and r are specific rational numbers. Represent real-world problems using equations of these forms and solve such problems. | Grade 7 |
| Indiana | 7.AF.4 | Solve inequalities of the form px + q (> or ≥) r or px + q (< or ≤) r , where p, q , and r are specific rational numbers. Represent real-world problems using inequalities of these forms and solve such problems. Graph the solution set of the inequality and interpret it in the context of the problem. | Grade 7 |
| Indiana | 7.AF.5 | Define slope as vertical change for each unit of horizontal change, and apply that a constant rate of change or constant slope describes a linear function. Identify and describe situations with constant or varying rates of change. | Grade 7 |
| Indiana | 7.AF.6 | Graph a line given its slope and a point on the line. Find the slope of a line given its graph. | Grade 7 |
| Indiana | 7.GM.1 | Solve real-world and other mathematical problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing. Create a scale drawing by using proportional reasoning. | Grade 7 |
| Indiana | 7.GM.2 | Understand the formulas for area and circumference of a circle and use them to solve real-world and other mathematical problems; give an informal derivation of the relationship between circumference and area of a circle. | Grade 7 |
| Indiana | 7.GM.3 | Solve real-world and other mathematical problems involving volume of cylinders and three-dimensional objects composed of right rectangular prisms. | Grade 7 |
| Indiana | 8.NS.2 | Use rational approximations of irrational numbers to compare the size of irrational numbers, plot them approximately on a number line, and estimate the value of expressions involving irrational numbers. | Grade 8 |
| Indiana | 8.NS.3 | Given a numeric expression with common rational number bases and integer exponents, apply the properties of exponents to generate equivalent expressions. | Grade 8 |
| Indiana | 8.NS.4 | Solve real-world problems with rational numbers by using multiple operations. | Grade 8 |
| Indiana | 8.AF.1 | Solve linear equations and inequalities with rational number coefficients fluently, including those whose solutions require expanding expressions using the distributive property and collecting like terms. Represent real-world problems using linear equations and inequalities in one variable and solve such problems. | Grade 8 |
| Indiana | 8.AF.2 | Generate linear equations in one variable with one solution, infinitely many solutions, or no solutions. Justify the classification given. | Grade 8 |
| Indiana | 8.AF.3 | Understand that a function assigns to each x-value (independent variable) exactly one y-value (dependent variable), and that the graph of a function is the set of ordered pairs (x,y). | Grade 8 |
| Indiana | 8.AF.4 | Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear, has a maximum or minimum value). Sketch a graph that exhibits the qualitative features of a function that has been verbally described. | Grade 8 |
| Indiana | 8.AF.5 | Interpret the equation y = mx + b as defining a linear function whose graph is a straight line; give examples of functions that are not linear. Describe similarities and differences between linear and nonlinear functions from tables, graphs, verbal descriptions, and equations. | Grade 8 |
| Indiana | 8.AF.6 | Construct a function to model a linear relationship between two quantities given a verbal description, table of values, or graph. Within the context of a problem, describe the meaning of m (rate of change) and b (y-intercept) in y = mx + b . | Grade 8 |
| Indiana | 8.AF.7 | Compare properties of two linear functions given in different forms, such as a table of values, equation, verbal description, and graph (e.g., compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed). | Grade 8 |
| Indiana | 8.AF.8 | Approximate the solution of a system of equations by graphing and interpreting the reasonableness of the approximation. | Grade 8 |
| Indiana | 8.GM.1 | Explore dilations, translations, rotations, and reflections on two-dimensional figures in the coordinate plane. | Grade 8 |
| Indiana | 8.GM.2 | Solve real-world and other mathematical problems involving volume of cones, spheres, and pyramids and surface area of spheres. | Grade 8 |
| Indiana | 8.GM.3 | Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and other mathematical problems in two dimensions. | Grade 8 |
| Indiana | 8.DSP.1 | Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantitative variables. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association. | Grade 8 |
| Indiana | AI.NF.4 | Evaluate functions for given elements of the domain, and interpret statements in function notation in terms of a context. | Algebra I |
| Indiana | AI.NF.5 | Describe, qualitatively, the functional relationship between two quantities by analyzing key features of a graph. Sketch a graph that exhibits given key features of a function that has been verbally described, including intercepts, where the function is increasing or decreasing, where the function is positive or negative, and any relative maximum or minimum values. Identify the independent and dependent variables. | Algebra I |
| Indiana | AI.L.1 | Represent real-world problems using linear equations and inequalities in one variable, including those with rational number coefficients and variables on both sides of the equal sign. Solve them fluently, explaining the process used and justify the choice of a solution method. | Algebra I |
| Indiana | AI.L.2 | Represent linear functions as graphs from equations (with emphasis on technology), equations from graphs, and equations from tables and other given information (e.g., from a given point on a line and the slope of the line). Find the equations of a line in a slope-intercept, point-slope, and standard forms. Reveal more or less information about a given situation based on the form used. | Algebra I |
| Indiana | AI.SEI.1 | Represent real-world problems using linear inequalities in two variables and solve such problems; interpret the solution set, and determine whether it is reasonable. Graph the solutions to a linear inequality in two variables as a half-plane. | Algebra I |
| Indiana | AI.QE.4 | Represent real-world problems using quadratic equations in one or two variables and solve such problems with technology. Interpret the solution(s), and determine whether they are reasonable. | Algebra I |
| Indiana | AI.QE.5 | Graph exponential and quadratic functions with and without technology. Identify and describe key features, such as zeros, lines of symmetry, and extreme values in real-world and other mathematical problems involving quadratic functions with and without technology; interpret the results in the real-world contexts. | Algebra I |
| Indiana | AI.QE.6 | Describe the relationships among a solution of a quadratic equation, a zero of the function, an x-intercept of the graph, and the factors of the expression. Explain that every quadratic has two complex solutions, which may or may not be real solutions. | Algebra I |
| Indiana | AI.DS.1 | Interpret statistics as a process for making inferences about a population based on a random sample from that population. Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each. | Algebra I |
| Indiana | AI.DS.2 | Understand that statistics and data are non-neutral and designed to serve a particular interest. Analyze the possibilities for whose interest might be served and how the representations might be misleading. | Algebra I |
| Iowa | K.CC.A.1 | Count to 100 by ones and by tens. | Kindergarten |
| Iowa | K.CC.A.2 | Count forward beginning from a given number within the known sequence (instead of having to begin at 1). | Kindergarten |
| Iowa | K.CC.A.3 | Write numbers from 0 to 20. Represent a number of objects with a written numeral 0-20 (with 0 representing a count of no objects). | Kindergarten |
| Iowa | K.CC.B.4 | Understand the relationship between numbers and quantities; connect counting to cardinality. | Kindergarten |
| Iowa | K.CC.B.5 | Count to answer “how many?” questions about as many as 20 things arranged in a line, a rectangular array, or a circle, or as many as 10 things in a scattered configuration; given a number from 1-20, count out that many objects. | Kindergarten |
| Iowa | K.CC.C.6 | Identify whether the number of objects in one group is greater than, less than, or equal to the number of objects in another group, e.g., by using matching and counting strategies. | Kindergarten |
| Iowa | K.CC.C.7 | Compare two numbers between 1 and 10 presented as written numerals. | Kindergarten |
| Iowa | K.G.A.1 | Describe objects in the environment using names of shapes, and describe the relative positions of these objects using terms such as above, below, beside, in front of, behind, and next to. | Kindergarten |
| Iowa | K.G.A.2 | Correctly name shapes regardless of their orientations or overall size. | Kindergarten |
| Iowa | K.G.A.3 | Identify shapes as two-dimensional (lying in a plane, “flat”) or three-dimensional (“solid”). | Kindergarten |
| Iowa | K.G.B.4 | Analyze and compare two- and three-dimensional shapes, in different sizes and orientations, using informal language to describe their similarities, differences, parts (e.g., number of sides and vertices/“corners”) and other attributes (e.g., having sides of equal length). | Kindergarten |
| Iowa | K.G.B.6 | Compose simple shapes to form larger shapes. | Kindergarten |
| Iowa | K.MD.A.1 | Describe measurable attributes of objects, such as length or weight. Describe several measurable attributes of a single object. | Kindergarten |
| Iowa | K.MD.A.2 | Directly compare two objects with a measurable attribute in common, to see which object has “more of”/“less of” the attribute, and describe the difference. | Kindergarten |
| Iowa | K.MD.B.3 | Classify objects into given categories; count the numbers of objects in each category and sort the categories by count. | Kindergarten |
| Iowa | K.NBT.A.1 | Compose and decompose numbers from 11 to 19 into ten ones and some further ones, e.g., by using objects or drawings, and record each composition or decomposition by a drawing or equation (e.g., 18 = 10 + 8); understand that these numbers are composed of ten ones and one, two, three, four, five, six, seven, eight, or nine ones. | Kindergarten |
| Iowa | K.OA.A.1 | Represent addition and subtraction with objects, fingers, mental images, drawings, sounds (e.g., claps), acting out situations, verbal explanations, expressions, or equations. | Kindergarten |
| Iowa | K.OA.A.2 | Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem. | Kindergarten |
| Iowa | K.OA.A.3 | Decompose numbers less than or equal to 10 into pairs in more than one way, e.g., by using objects or drawings, and record each decomposition by a drawing or equation (e.g., 5 = 2 + 3 and 5 = 4 + 1). | Kindergarten |
| Iowa | K.OA.A.4 | For any number from 1 to 9, find the number that makes 10 when added to the given number, e.g., by using objects or drawings, and record the answer with a drawing or equation. | Kindergarten |
| Iowa | K.OA.A.5 | Fluently add and subtract within 5. | Kindergarten |
| Iowa | 1.G.A.1 | Distinguish between defining attributes (e.g., triangles are closed and three-sided) versus non-defining attributes (e.g., color, orientation, overall size); build and draw shapes to possess defining attributes. | Grade 1 |
| Iowa | 1.G.A.2 | Compose two-dimensional shapes (rectangles, squares, trapezoids, triangles, half-circles, and quarter-circles) or three-dimensional shapes (cubes, right rectangular prisms, right circular cones, and right circular cylinders) to create a composite shape, and compose new shapes from the composite shape. | Grade 1 |
| Iowa | 1.G.A.3 | Partition circles and rectangles into two and four equal shares, describe the shares using the words halves, fourths, and quarters, and use the phrases half of, fourth of, and quarter of. Describe the whole as two of, or four of the shares. Understand for these examples that decomposing into more equal shares creates smaller shares. | Grade 1 |
| Iowa | 1.MD.A.1 | Order three objects by length; compare the lengths of two objects indirectly by using a third object. | Grade 1 |
| Iowa | 1.MD.A.2 | Express the length of an object as a whole number of length units, by laying multiple copies of a shorter object (the length unit) end to end; understand that the length measurement of an object is the number of same-size length units that span it with no gaps or overlaps. | Grade 1 |
| Iowa | 1.MD.B.3 | Tell and write time in hours and half-hours using analog and digital clocks. | Grade 1 |
| Iowa | 1.MD.C.4 | Organize, represent, and interpret data with up to three categories; ask and answer questions about the total number of data points, how many in each category, and how many more or less are in one category than in another. | Grade 1 |
| Iowa | 1.NBT.A.1 | Count to 120, starting at any number less than 120. In this range, read and write numerals and represent a number of objects with a written numeral. | Grade 1 |
| Iowa | 1.NBT.B.2 | Understand that the two digits of a two-digit number represent amounts of tens and ones. | Grade 1 |
| Iowa | 1.NBT.B.3 | Compare two two-digit numbers based on meanings of the tens and ones digits, recording the results of comparisons with the symbols >, =, and <. | Grade 1 |
| Iowa | 1.NBT.C.4 | Add within 100, including adding a two-digit number and a one-digit number, and adding a two-digit number and a multiple of 10, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Understand that in adding two-digit numbers, one adds tens and tens, ones and ones; and sometimes it is necessary to compose a ten. | Grade 1 |
| Iowa | 1.NBT.C.5 | Given a two-digit number, mentally find 10 more or 10 less than the number, without having to count; explain the reasoning used. | Grade 1 |
| Iowa | 1.NBT.C.6 | Subtract multiples of 10 in the range 10-90 from multiples of 10 in the range 10-90 (positive or zero differences), using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. | Grade 1 |
| Iowa | 1.OA.A.1 | Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem. | Grade 1 |
| Iowa | 1.OA.B.3 | Apply properties of operations as strategies to add and subtract. | Grade 1 |
| Iowa | 1.OA.B.4 | Understand subtraction as an unknown-addend problem. | Grade 1 |
| Iowa | 1.OA.C.5 | Relate counting to addition and subtraction (e.g., by counting on 2 to add 2). | Grade 1 |
| Iowa | 1.OA.C.6 | Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to a ten (e.g., 13 - 4 = 13 - 3 - 1 = 10 - 1 = 9); using the relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 - 8 = 4); and creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13). | Grade 1 |
| Iowa | 1.OA.D.7 | Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false. | Grade 1 |
| Iowa | 1.OA.D.8 | Determine the unknown whole number in an addition or subtraction equation relating three whole numbers. | Grade 1 |
| Iowa | 2.G.A.1 | Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces. Identify triangles, quadrilaterals, pentagons, hexagons, and cubes. | Grade 2 |
| Iowa | 2.G.A.2 | Partition a rectangle into rows and columns of same-size squares and count to find the total number of them. | Grade 2 |
| Iowa | 2.G.A.3 | Partition circles and rectangles into two, three, or four equal shares, describe the shares using the words halves, thirds, half of, a third of, etc., and describe the whole as two halves, three thirds, four fourths. Recognize that equal shares of identical wholes need not have the same shape. | Grade 2 |
| Iowa | 2.MD.A.1 | Measure the length of an object by selecting and using appropriate tools such as rulers, yardsticks, meter sticks, and measuring tapes. | Grade 2 |
| Iowa | 2.MD.A.2 | Measure the length of an object twice, using length units of different lengths for the two measurements; describe how the two measurements relate to the size of the unit chosen. | Grade 2 |
| Iowa | 2.MD.A.4. | Measure to determine how much longer one object is than another, expressing the length difference in terms of a standard length unit. | Grade 2 |
| Iowa | 2.MD.B.5 | Use addition and subtraction within 100 to solve word problems involving lengths that are given in the same units, e.g., by using drawings (such as drawings of rulers) and equations with a symbol for the unknown number to represent the problem. | Grade 2 |
| Iowa | 2.MD.C.7 | Tell and write time from analog and digital clocks to the nearest five minutes, using a.m. and p.m. | Grade 2 |
| Iowa | 2.MD.C.8 | Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies, using $ and ¢ symbols appropriately. | Grade 2 |
| Iowa | 2.MD.D.9 | Generate measurement data by measuring lengths of several objects to the nearest whole unit, or by making repeated measurements of the same object. Show the measurements by making a line plot, where the horizontal scale is marked off in whole-number units. | Grade 2 |
| Iowa | 2.MD.D.IA.2 | Use interviews, surveys, and observations to collect data that answer questions about students' interests and/or their environment. | Grade 2 |
| Iowa | 2.MD.D.10 | Draw a picture graph and a bar graph (with single-unit scale) to represent a data set with up to four categories. Solve simple put-together, take-apart, and compare problems using information presented in a bar graph. | Grade 2 |
| Iowa | 2.NBT.A.1 | Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones. | Grade 2 |
| Iowa | 2.NBT.A.2 | Count within 1000; skip-count by 5s, 10s, and 100s. | Grade 2 |
| Iowa | 2.NBT.A.3 | Read and write numbers to 1000 using base-ten numerals, number names, and expanded form. | Grade 2 |
| Iowa | 2.NBT.A.4 | Compare two three-digit numbers based on meanings of the hundreds, tens, and ones digits, using >, =, and < symbols to record the results of comparisons. | Grade 2 |
| Iowa | 2.NBT.B.5 | Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction. | Grade 2 |
| Iowa | 2.NBT.B.6 | Add up to four two-digit numbers using strategies based on place value and properties of operations. | Grade 2 |
| Iowa | 2.NBT.B.7 | Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method. Understand that in adding or subtracting three-digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds. | Grade 2 |
| Iowa | 2.NBT.B.8 | Mentally add 10 or 100 to a given number 100–900, and mentally subtract 10 or 100 from a given number 100–900. | Grade 2 |
| Iowa | 2.OA.A.1 | Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem. | Grade 2 |
| Iowa | 2.OA.B.2 | Fluently add and subtract within 20 using mental strategies. By end of Grade 2, know from memory all sums of two one-digit numbers. | Grade 2 |
| Iowa | 2.OA.C.3 | Determine whether a group of objects (up to 20) has an odd or even number of members, e.g., by pairing objects or counting them by 2s; write an equation to express an even number as a sum of two equal addends. | Grade 2 |
| Iowa | 2.OA.C.4 | Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends. | Grade 2 |
| Iowa | 3.G.A.1 | Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories. | Grade 3 |
| Iowa | 3.G.A.2 | Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole. | Grade 3 |
| Iowa | 3.MD.A.1 | Tell and write time to the nearest minute and measure time intervals in minutes. Solve word problems involving addition and subtraction of time intervals in minutes, e.g., by representing the problem on a number line diagram. | Grade 3 |
| Iowa | 3.MD.A.2 | Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l). Add, subtract, multiply, or divide to solve one-step word problems involving masses or volumes that are given in the same units, e.g., by using drawings (such as a beaker with a measurement scale) to represent the problem. | Grade 3 |
| Iowa | 3.MD.B.3 | Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and two-step “how many more” and “how many less” problems using information presented in scaled bar graphs. | Grade 3 |
| Iowa | 3.MD.B.4 | Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Show the data by making a line plot, where the horizontal scale is marked off in appropriate units-whole numbers, halves, or quarters. | Grade 3 |
| Iowa | 3.MD.C.5 | Recognize area as an attribute of plane figures and understand concepts of area measurement. | Grade 3 |
| Iowa | 3.MD.C.6 | Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units). | Grade 3 |
| Iowa | 3.MD.C.7 | Relate area to the operations of multiplication and addition. | Grade 3 |
| Iowa | 3.MD.D.8 | Solve real world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters. | Grade 3 |
| Iowa | 3.NBT.A.1 | Use place value understanding to round whole numbers to the nearest 10 or 100. | Grade 3 |
| Iowa | 3.NBT.A.2 | Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction. | Grade 3 |
| Iowa | 3.NBT.A.3 | Multiply one-digit whole numbers by multiples of 10 in the range 10–90 (e.g., 9 × 80, 5 × 60) using strategies based on place value and properties of operations. | Grade 3 |
| Iowa | 3.NF.A.1 | Understand a fraction 1/𝘣 as the quantity formed by 1 part when a whole is partitioned into 𝘣 equal parts; understand a fraction 𝘢/𝑏 as the quantity formed by 𝘢 parts of size 1/𝘣. | Grade 3 |
| Iowa | 3.NF.A.2 | Understand a fraction as a number on the number line; represent fractions on a number line diagram. | Grade 3 |
| Iowa | 3.NF.A.3 | Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size. | Grade 3 |
| Iowa | 3.OA.A.1 | Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each. | Grade 3 |
| Iowa | 3.OA.A.2 | Interpret whole-number quotients of whole numbers, e.g., interpret 56 ÷ 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each. | Grade 3 |
| Iowa | 3.OA.A.3 | Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem. | Grade 3 |
| Iowa | 3.OA.A.4 | Determine the unknown whole number in a multiplication or division equation relating three whole numbers. | Grade 3 |
| Iowa | 3.OA.B.5 | Apply properties of operations as strategies to multiply and divide. | Grade 3 |
| Iowa | 3.OA.B.6 | Understand division as an unknown-factor problem. | Grade 3 |
| Iowa | 3.OA.C.7 | Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 × 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers. | Grade 3 |
| Iowa | 3.OA.D.8 | Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. | Grade 3 |
| Iowa | 3.OA.D.9 | Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations. | Grade 3 |
| Iowa | 4.G.A.1 | Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures. | Grade 4 |
| Iowa | 4.G.A.2 | Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles. | Grade 4 |
| Iowa | 4.G.A.3 | Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify line-symmetric figures and draw lines of symmetry. | Grade 4 |
| Iowa | 4.MD.A.1 | Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table. | Grade 4 |
| Iowa | 4.MD.A.2 | Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. | Grade 4 |
| Iowa | 4.MD.A.3 | Apply the area and perimeter formulas for rectangles in real world and mathematical problems. | Grade 4 |
| Iowa | 4.MD.B.4 | Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots. | Grade 4 |
| Iowa | 4.MD.C.5 | Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement. | Grade 4 |
| Iowa | 4.MD.C.6 | Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure. | Grade 4 |
| Iowa | 4.MD.C.7 | Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems, e.g., by using an equation with a symbol for the unknown angle measure. | Grade 4 |
| Iowa | 4.NBT.A.1 | Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. | Grade 4 |
| Iowa | 4.NBT.A.2 | Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. | Grade 4 |
| Iowa | 4.NBT.A.3 | Use place value understanding to round multi-digit whole numbers to any place. | Grade 4 |
| Iowa | 4.NBT.B.4 | Fluently add and subtract multi-digit whole numbers using the standard algorithm. | Grade 4 |
| Iowa | 4.NBT.B.5 | Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. | Grade 4 |
| Iowa | 4.NBT.B.6 | Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. | Grade 4 |
| Iowa | 4.NF.A.1 | Explain why a fraction 𝘢/𝘣 is equivalent to a fraction (𝘯 × 𝘢)/(𝘯 × 𝘣) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. | Grade 4 |
| Iowa | 4.NF.A.2 | Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model. | Grade 4 |
| Iowa | 4.NF.B.3 | Understand a fraction 𝘢/𝘣 with 𝘢 > 1 as a sum of fractions 1/𝘣. | Grade 4 |
| Iowa | 4.NF.B.4 | Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. | Grade 4 |
| Iowa | 4.NF.C.5 | Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100. | Grade 4 |
| Iowa | 4.NF.C.6 | Use decimal notation for fractions with denominators 10 or 100. | Grade 4 |
| Iowa | 4.NF.C.7 | Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual model. | Grade 4 |
| Iowa | 4.OA.A.1 | Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 × 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations. | Grade 4 |
| Iowa | 4.OA.A.2 | Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison. | Grade 4 |
| Iowa | 4.OA.A.3 | Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. | Grade 4 |
| Iowa | 4.OA.B.4 | Find all factor pairs for a whole number in the range 1-100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1-100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1-100 is prime or composite. | Grade 4 |
| Iowa | 4.OA.C.5 | Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. | Grade 4 |
| Iowa | 5.G.A.1 | Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., 𝘹-axis and 𝘹-coordinate, 𝘺-axis and 𝘺-coordinate). | Grade 5 |
| Iowa | 5.G.A.2 | Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. | Grade 5 |
| Iowa | 5.G.B.3 | Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. | Grade 5 |
| Iowa | 5.G.B.4 | Classify two-dimensional figures in a hierarchy based on properties. | Grade 5 |
| Iowa | 5.MD.A.1 | Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. | Grade 5 |
| Iowa | 5.MD.B.2 | Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. | Grade 5 |
| Iowa | 5.MD.C.3 | Recognize volume as an attribute of solid figures and understand concepts of volume measurement. | Grade 5 |
| Iowa | 5.MD.C.4 | Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. | Grade 5 |
| Iowa | 5.MD.C.5 | Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume. | Grade 5 |
| Iowa | 5.NBT.A.1 | Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. | Grade 5 |
| Iowa | 5.NBT.A.2 | Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. | Grade 5 |
| Iowa | 5.NBT.A.3 | Read, write, and compare decimals to thousandths. | Grade 5 |
| Iowa | 5.NBT.A.4 | Use place value understanding to round decimals to any place. | Grade 5 |
| Iowa | 5.NBT.B.5 | Fluently multiply multi-digit whole numbers using the standard algorithm. | Grade 5 |
| Iowa | 5.NBT.B.6 | Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. | Grade 5 |
| Iowa | 5.NBT.B.7 | Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. | Grade 5 |
| Iowa | 5.NF.A.1 | Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. | Grade 5 |
| Iowa | 5.NF.A.2 | Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. | Grade 5 |
| Iowa | 5.NF.B.3 | Interpret a fraction as division of the numerator by the denominator (𝘢/𝘣 = 𝘢 ÷ 𝘣). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. | Grade 5 |
| Iowa | 5.NF.B.4 | Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. | Grade 5 |
| Iowa | 5.NF.B.5 | Interpret multiplication as scaling (resizing). | Grade 5 |
| Iowa | 5.NF.B.6 | Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. | Grade 5 |
| Iowa | 5.NF.B.7 | Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. | Grade 5 |
| Iowa | 5.OA.A.1 | Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. | Grade 5 |
| Iowa | 5.OA.A.2 | Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. | Grade 5 |
| Iowa | 5.OA.B.3 | Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. | Grade 5 |
| Iowa | 6.EE.A.1 | Write and evaluate numerical expressions involving whole-number exponents. | Grade 6 |
| Iowa | 6.EE.A.2 | Write, read, and evaluate expressions in which letters stand for numbers. | Grade 6 |
| Iowa | 6.EE.A.3 | Apply the properties of operations to generate equivalent expressions. | Grade 6 |
| Iowa | 6.EE.A.4 | Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). | Grade 6 |
| Iowa | 6.EE.B.5 | Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true. | Grade 6 |
| Iowa | 6.EE.B.6 | Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set. | Grade 6 |
| Iowa | 6.EE.B.7 | Solve real-world and mathematical problems by writing and solving equations of the form 𝘹 + 𝘱 = 𝘲 and 𝘱𝘹 = 𝘲 for cases in which 𝘱, 𝘲 and 𝘹 are all nonnegative rational numbers. | Grade 6 |
| Iowa | 6.EE.B.8 | Write an inequality of the form 𝘹 > 𝘤 or 𝘹 𝘤 or 𝘹 < 𝘤 have infinitely many solutions; represent solutions of such inequalities on number line diagrams. | Grade 6 |
| Iowa | 6.EE.C.9 | Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. | Grade 6 |
| Iowa | 6.G.A.1 | Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems. | Grade 6 |
| Iowa | 6.G.A.2 | Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas 𝘝 = 𝘭 𝘸 𝘩 and 𝘝 = 𝘣 𝘩 to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems. | Grade 6 |
| Iowa | 6.G.A.3 | Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems. | Grade 6 |
| Iowa | 6.G.A.4 | Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems. | Grade 6 |
| Iowa | 6.RP.A.1 | Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. | Grade 6 |
| Iowa | 6.RP.A.2 | Understand the concept of a unit rate 𝘢/𝘣 associated with a ratio 𝘢:𝘣 with 𝘣 ≠ 0, and use rate language in the context of a ratio relationship. | Grade 6 |
| Iowa | 6.RP.A.3 | Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. | Grade 6 |
| Iowa | 6.SP.B.5 | Summarize numerical data sets in relation to their context, such as by: | Grade 6 |
| Iowa | 6.NS.A.1 | Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. | Grade 6 |
| Iowa | 6.NS.B.2 | Fluently divide multi-digit numbers using the standard algorithm. | Grade 6 |
| Iowa | 6.NS.B.3 | Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation. | Grade 6 |
| Iowa | 6.NS.C.5 | Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation. | Grade 6 |
| Iowa | 6.NS.C.6 | Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates. | Grade 6 |
| Iowa | 6.NS.C.7 | Understand ordering and absolute value of rational numbers. | Grade 6 |
| Iowa | 6.NS.C.8 | Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. | Grade 6 |
| Iowa | 7.EE.A.1 | Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients. | Grade 7 |
| Iowa | 7.EE.A.2 | Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. | Grade 7 |
| Iowa | 7.EE.B.3 | Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. | Grade 7 |
| Iowa | 7.EE.B.4 | Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. | Grade 7 |
| Iowa | 7.G.A.1 | Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale. | Grade 7 |
| Iowa | 7.G.A.2 | Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle. | Grade 7 |
| Iowa | 7.G.A.3 | Describe the two-dimensional figures that result from slicing three-dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids. | Grade 7 |
| Iowa | 7.G.B.4 | Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle. | Grade 7 |
| Iowa | 7.G.B.5 | Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure. | Grade 7 |
| Iowa | 7.G.B.6 | Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. | Grade 7 |
| Iowa | 7.RP.A.1 | Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. | Grade 7 |
| Iowa | 7.RP.A.2 | Recognize and represent proportional relationships between quantities. | Grade 7 |
| Iowa | 7.RP.A.3 | Use proportional relationships to solve multistep ratio and percent problems. | Grade 7 |
| Iowa | 7.NS.A.1 | Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram. | Grade 7 |
| Iowa | 7.NS.A.2 | Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers. | Grade 7 |
| Iowa | 7.NS.A.3 | Solve real-world and mathematical problems involving the four operations with rational numbers. | Grade 7 |
| Iowa | 8.EE.A.1 | Know and apply the properties of integer exponents to generate equivalent numerical expressions. | Grade 8 |
| Iowa | 8.EE.A.2 | Use square root and cube root symbols to represent solutions to equations of the form 𝘹² = 𝘱 and 𝘹³ = 𝘱, where 𝘱 is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that √2 is irrational. | Grade 8 |
| Iowa | 8.EE.A.3 | Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other. | Grade 8 |
| Iowa | 8.EE.A.4 | Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology. | Grade 8 |
| Iowa | 8.EE.B.5 | Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. | Grade 8 |
| Iowa | 8.EE.B.6 | Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation 𝘺 = 𝘮𝘹 for a line through the origin and the equation 𝘺 = 𝘮𝘹 + 𝘣 for a line intercepting the vertical axis at 𝘣. | Grade 8 |
| Iowa | 8.EE.C.7 | Solve linear equations in one variable. | Grade 8 |
| Iowa | 8.EE.C.8 | Analyze and solve pairs of simultaneous linear equations. | Grade 8 |
| Iowa | 8.F.A.1 | Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output. | Grade 8 |
| Iowa | 8.F.A.2 | Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). | Grade 8 |
| Iowa | 8.F.A.3 | Interpret the equation 𝘺 = 𝘮𝘹 + 𝘣 as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. | Grade 8 |
| Iowa | 8.F.B.4 | Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (𝘹, 𝘺) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values. | Grade 8 |
| Iowa | 8.F.B.5 | Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally. | Grade 8 |
| Iowa | 8.G.A.1 | Verify experimentally the properties of rotations, reflections, and translations. | Grade 8 |
| Iowa | 8.G.A.2 | Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them. | Grade 8 |
| Iowa | 8.G.A.3 | Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates. | Grade 8 |
| Iowa | 8.G.A.4 | Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two-dimensional figures, describe a sequence that exhibits the similarity between them. | Grade 8 |
| Iowa | 8.G.A.5 | Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. | Grade 8 |
| Iowa | 8.G.B.7 | Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions. | Grade 8 |
| Iowa | 8.G.B.8 | Apply the Pythagorean Theorem to find the distance between two points in a coordinate system. | Grade 8 |
| Iowa | 8.G.C.9 | Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems. | Grade 8 |
| Iowa | 8.SP.A.1 | Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association. | Grade 8 |
| Iowa | 8.SP.A.2 | Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line. | Grade 8 |
| Iowa | 8.NS.A.2 | Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g., π²). | Grade 8 |
| Iowa | A-APR.B.3 | Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial. | High School |
| Iowa | A-CED.A.2 | Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. | High School |
| Iowa | A-CED.A.3 | Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context. | High School |
| Iowa | A-REI.B.3 | Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. | High School |
| Iowa | A-SSE.A.2 | Use the structure of an expression to identify ways to rewrite it. | High School |
| Iowa | A-SSE.B.3 | Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression. | High School |
| Iowa | F-BF.A.1 | Write a function that describes a relationship between two quantities. | High School |
| Iowa | F-IF.A.2 | Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. | High School |
| Iowa | F-IF.B.4 | For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. | High School |
| Iowa | F-IF.C.7 | Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. | High School |
| Iowa | S-ID.B.6 | Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. | High School |
| Kansas | K.CC.1 | Count to 100 by ones and by tens and identify as a growth pattern. | Kindergarten |
| Kansas | K.CC.2 | Count forward beginning from a given number within the known sequence (instead of having to begin at 1). | Kindergarten |
| Kansas | K.CC.3 | Read and write numerals from 0 to 20. | Kindergarten |
| Kansas | K.CC.4 | Understand the relationship between numbers and quantities; connect counting to cardinality. | Kindergarten |
| Kansas | K.CC.5 | Count to answer “how many?” up to 20 concrete or pictorial objects arranged in a line, a rectangular array, or a circle, or as many as 10 objects in a scattered configuration (subitizing); given a number from 1 to 20, count out that many objects. | Kindergarten |
| Kansas | K.CC.6 | Identify whether the number of objects in one group is greater than, less than, or equal to the number of objects in another group, (e.g., by using matching and counting strategies.) Include groups with up to ten objects. | Kindergarten |
| Kansas | K.CC.7 | Compare two numbers between 1 and 10 presented as written numerals. | Kindergarten |
| Kansas | K.G.1 | Describe objects in the environment using names of shapes, and describe the relative positions of these objects using terms such as above, below, beside, in front of, behind, and next to. | Kindergarten |
| Kansas | K.G.2 | Correctly gives most precise name of shapes regardless of their orientations (position and direction in space) or overall size. | Kindergarten |
| Kansas | K.G.3 | Identify shapes as two-dimensional (lying in a plane, “flat”) or three-dimensional (“solid”). | Kindergarten |
| Kansas | K.G.4 | Analyze and compare two- and three-dimensional shapes, in different sizes and orientations (position and direction in space), using informal language to describe their similarities, differences, parts (e.g., number of sides and vertices/“corners”) and other attributes (e.g., having sides of equal length). | Kindergarten |
| Kansas | K.MD.1 | Describe measurable attributes of objects, such as length or weight. Describe several measurable attributes of a single object. | Kindergarten |
| Kansas | K.MD.2 | Directly compare two objects, with a measurable attribute in common, to see which object has “more of”/”less of” the attribute, and describe the difference. | Kindergarten |
| Kansas | K.MD.3 | Classify objects into given categories; count the numbers of objects in each category and sort the categories by count (Limit category counts to be less than or equal to 10). | Kindergarten |
| Kansas | K.NBT.1 | Compose and decompose numbers from 11 to 19 into ten ones and some further ones, (e.g., by using objects or drawings, and record each composition or decomposition by a drawing or equation (e.g., 10 + 8 = 18 𝑎𝑛𝑑 19 = 10 + 9)); understand that these numbers are composed of ten ones and one, two, three, four, five, six, seven, eight, or nine ones. | Kindergarten |
| Kansas | K.OA.1 | Represent addition and subtraction with objects, fingers, mental images, drawings, sounds (e.g., claps), acting out situations, verbal explanations, expressions, or equations. | Kindergarten |
| Kansas | K.OA.2 | Solve addition and subtraction word problems, and add and subtract within 10, (e.g. by using objects or drawings to represent the problem). | Kindergarten |
| Kansas | K.OA.3 | Decompose numbers less than or equal to 10 into pairs in more than one way, (e.g., by using objects or drawings, and record each decomposition by a drawing or equation (e.g., 5 = 2 + 3 𝑎𝑛𝑑 5 = 4 + 1)). | Kindergarten |
| Kansas | K.OA.4 | For any number from 1 to 9, find the number that makes 10 when added to the given number, (e.g., by using objects or drawings, and record the answer with a drawing or equation.). | Kindergarten |
| Kansas | K.OA.5 | Fluently (efficiently, accurately, and flexibly) add and subtract within 5. | Kindergarten |
| Kansas | 1.G.1 | Distinguish between defining attributes (e.g. triangles are closed and three-sided) versus non-defining attributes (e.g. color, orientation, overall size); build and draw shapes that possess defining attributes. | Grade 1 |
| Kansas | 1.G.2 | Compose two-dimensional shapes (rectangles, squares, trapezoids, triangles, half-circles, and quarter-circles) or three-dimensional shapes (cubes, right rectangular prisms, right circular cones, and right circular cylinders) to create a composite shape, and compose new shapes from the composite shape. Students do not need to learn formal names such as “right rectangular prism”. | Grade 1 |
| Kansas | 1.G.3 | Partition circles and rectangles into two and four equal shares, describe the shares using the words halves, fourths, and quarters, and use the phrases half of, fourth of, and quarter of. | Grade 1 |
| Kansas | 1.MD.1 | Order three objects by length; compare the lengths of two objects indirectly by using a third object. | Grade 1 |
| Kansas | 1.MD.2 | Express the length of an object as a whole number of length units, by laying multiple copies of a shorter object (the length unit) end to end; understand that the length measurement of an object is the number of same-size length units that span it with no gaps or overlaps. Limit to contexts where the object being measured is spanned by a whole number of length units with no gaps or overlaps. | Grade 1 |
| Kansas | 1.MD.3 | Tell and write time in hours and half-hours using analog and digital clocks. | Grade 1 |
| Kansas | 1.MD.4 | Organize, represent, and interpret data with up to three categories; ask and answer questions about the total number of data points, how many in each category, and how many more or less are in one category than in another. | Grade 1 |
| Kansas | 1.NBT.1 | Count to 120 (recognizing growth and repeating patterns), starting at any number less than 120. In this range, read and write numerals and represent a number of objects with a written numeral. | Grade 1 |
| Kansas | 1.NBT.2 | Understand that the two digits of a two-digit number represent amounts of tens and ones. Understand the following as special cases: | Grade 1 |
| Kansas | 1.NBT.3 | Compare two two-digit numbers based on meanings of the tens and ones digits, recording the results of comparisons with the relational symbols >, <, =, and ≠. | Grade 1 |
| Kansas | 1.NBT.4 | Add within 100 using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used including: | Grade 1 |
| Kansas | 1.NBT.5 | Given a two-digit number, mentally find 10 more or 10 less than the number, without having to count; explain the reasoning used. | Grade 1 |
| Kansas | 1.NBT.6 | Subtract multiples of 10 in the range 10 to 90 from multiples of 10 in the range 10 to 90 (positive or zero differences), using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. | Grade 1 |
| Kansas | 1.OA.1 | Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, (e.g., by using objects, drawings, and situation equations and/or solution equations with a symbol for the unknown number to represent the problem.) | Grade 1 |
| Kansas | 1.OA.3 | Apply (not necessary to name) properties of operations as strategies to add and subtract. | Grade 1 |
| Kansas | 1.OA.4 | Understand subtraction as an unknown-addend problem. | Grade 1 |
| Kansas | 1.OA.5 | Relate counting to addition and subtraction (e.g. by counting on 2 to add 2, counting back 1 to subtract 1). | Grade 1 |
| Kansas | 1.OA.6 | Add and subtract within 20, demonstrating fluency (efficiently, accurately, and flexibly) for addition and subtraction within 10. Use mental strategies such as counting on; making ten (e.g. 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to a ten (e.g. 13 − 4 = 13 − 3 − 1 = 10 − 1 = 9); using the relationship between addition and subtraction (e.g. knowing that 8 + 4 = 12, one knows 12 − 8 = 4); and creating equivalent but easier or known sums (e.g. adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13). | Grade 1 |
| Kansas | 1.OA.7 | Understand the meaning of the equal sign (the value is the same on both sides of the equal sign), and determine if equations involving addition and subtraction are true or false. | Grade 1 |
| Kansas | 1.OA.8 | Using related equations, determine the unknown whole number in an addition or subtraction equation. | Grade 1 |
| Kansas | 2.G.1 | Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces. Identify triangles, quadrilaterals, pentagons, hexagons, and cubes. | Grade 2 |
| Kansas | 2.G.2 | Partition a rectangle into rows and columns of same-size squares and count to find the total number of them. | Grade 2 |
| Kansas | 2.G.3 | Partition circles and rectangles into two, three, or four equal shares, describe the shares using the words halves, thirds, half of, a third of, etc., and describe the whole as two halves, three thirds, four fourths. Note: Fraction notation ½, ⅓, ¼ is not expected at this grade level. Recognize that equal shares of identical wholes need not have the same shape. | Grade 2 |
| Kansas | 2.MD.1 | Measure the length of an object by selecting and using appropriate tools such as rulers, yardsticks, meter sticks, and measuring tapes. | Grade 2 |
| Kansas | 2.MD.2 | Measure the length of an object twice, using length units of different lengths for the two measurements; describe how the two measurements relate to the size of the unit chosen. | Grade 2 |
| Kansas | 2.MD.4 | Measure to determine how much longer one object is than another, expressing the length difference in terms of a standard length unit (inches, feet, centimeters, and meters). | Grade 2 |
| Kansas | 2.MD.5 | Use addition and subtraction within 100 to solve one- and two-step word problems involving lengths that are given in the same units, e.g., by using drawings (such as drawings of rulers) and equations with a symbol for the unknown number to represent the problem. | Grade 2 |
| Kansas | 2.MD.7 | Tell and write time from analog and digital clocks to the nearest five minutes. | Grade 2 |
| Kansas | 2.MD.8 | Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies, using $ and ¢ symbols appropriately. (Do not use decimal point, if showing 25 cents, use the word cents or ¢.) | Grade 2 |
| Kansas | 2.MD.10 | Generate measurement data by measuring lengths of several objects to the nearest whole unit, or by making repeated measurements of the same object using different units. Show the measurements by making a line plot, where the horizontal scale is marked off in whole-number units. | Grade 2 |
| Kansas | 2.MD.11 | Draw a picture graph and a bar graph (with single-unit scale) to represent a data set with up to four categories. Solve simple put-together, take-apart, and compare problems using information presented in a bar graph. | Grade 2 |
| Kansas | 2.NBT.1 | Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones; (e.g., 706 equals 7 hundreds, 0 tens, and 6 ones.) Understand the following as special cases: | Grade 2 |
| Kansas | 2.NBT.2 | Count within 1000; skip-count by 2s, 5s, 10s, and 100s; explain and generalize the patterns. | Grade 2 |
| Kansas | 2.NBT.3 | Read and write numbers within 1000 using base-ten numerals, number names, expanded form, and unit form. | Grade 2 |
| Kansas | 2.NBT.4 | Compare two three-digit numbers based on meanings of the hundreds, tens, and ones digits, using >, <, =, and ≠ relational symbols to record the results of comparisons. | Grade 2 |
| Kansas | 2.NBT.5 | Fluently (efficiently, accurately, and flexibly) add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction (e.g., composing/decomposing by like base-10 units, using friendly or benchmark numbers, using related equations, compensation, number line, etc.). | Grade 2 |
| Kansas | 2.NBT.6 | Add up to four two-digit numbers using strategies based on place value and properties of operations. | Grade 2 |
| Kansas | 2.NBT.7 | Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method. Understand that in adding or subtracting three-digit numbers, like base-ten units such as hundreds and hundreds, tens and tens, ones and ones are used; and sometimes it is necessary to compose or decompose tens or hundreds. | Grade 2 |
| Kansas | 2.NBT.8 | Mentally add 10 or 100 to a given number 100 - 900, and mentally subtract 10 or 100 from a given number 100 - 900. | Grade 2 |
| Kansas | 2.OA.1 | Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, (e.g., by using drawings and situation equations and/or solution equations with a symbol for the unknown number to represent the problem). | Grade 2 |
| Kansas | 2.OA.2 | Fluently (efficiently, accurately, and flexibly) add and subtract within 20 using mental strategies (counting on, making a ten, decomposing a number, creating an equivalent but easier and known sum, and using the relationship between addition and subtraction) Work with equal groups of objects to gain foundations for multiplication. | Grade 2 |
| Kansas | 2.OA.3 | Determine whether a group of objects (up to 20) has an odd or even number of members, (e.g., by pairing objects or counting them by 2s); write an equation to express an even number as a sum of two equal addends. | Grade 2 |
| Kansas | 2.OA.4 | Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends. | Grade 2 |
| Kansas | 3.G.1 | Understand that shapes in different categories (e.g., rhombuses, rectangles, trapezoids, kites and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories. | Grade 3 |
| Kansas | 3.G.2 | Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole. | Grade 3 |
| Kansas | 3.MD.1 | Tell and write time to the nearest minute using a.m. and p.m. and measure time intervals in minutes. Solve word problems involving addition and subtraction of time intervals in minutes, (e.g., by representing the problem on a number line diagram). | Grade 3 |
| Kansas | 3.MD.2 | Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l). (Excludes cubed units such as 𝑐𝑚³ and finding the geometric volume of a container.) | Grade 3 |
| Kansas | 3.MD.3 | Add, subtract, multiply, or divide to solve one-step word problems involving masses or volumes that are given in the same units (e.g., by using drawings (such as a beaker with a measurement scale) to represent the problem). (Excludes multiplicative comparison problems.) | Grade 3 |
| Kansas | 3.MD.4 | Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and two-step “how many more” and “how many less” problems using information presented in scaled bar graphs. | Grade 3 |
| Kansas | 3.MD.5 | Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Show the data by making a line plot, where the horizontal scale is marked off in appropriate units - whole numbers, halves, or quarters. | Grade 3 |
| Kansas | 3.MD.6 | Recognize area as an attribute of plane figures and understand concepts of area measurement. | Grade 3 |
| Kansas | 3.MD.7 | Measure areas by counting unit squares (square cm, square m, square in., square ft., and non-standard square units). | Grade 3 |
| Kansas | 3.MD.8 | Relate area to the operations of multiplication and addition. | Grade 3 |
| Kansas | 3.MD.9 | Solve real world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters. | Grade 3 |
| Kansas | 3.NBT.1 | Use place value understanding to round whole numbers to the nearest 10 or 100. | Grade 3 |
| Kansas | 3.NBT.2 | Fluently (efficiently, accurately, & flexibly) add and subtract within 1000 using strategies (e.g., composing/decomposing by like base-10 units, using friendly or benchmark numbers, using related equations, compensation, number line, etc.) and algorithms (including, but not limited to: traditional, partial-sums, etc.) based on place value, properties of operations, and/or the relationship between addition and subtraction. | Grade 3 |
| Kansas | 3.NBT.3 | Multiply one-digit whole numbers by multiples of 10 in the range 10 to 90 (e.g., 9 ⋅ 80, 5 ⋅ 60) using strategies based on place value and properties of operations. | Grade 3 |
| Kansas | 3.NF.1 | Understand a fraction 1/𝑏 as the quantity formed by 1 part when a whole is partitioned into 𝑏 equal parts; understand a fraction 𝑎/𝑏 as the quantity formed by 𝑎 parts of size 1/𝑏. | Grade 3 |
| Kansas | 3.NF.2 | Understand a fraction as a number on the number line; represent fractions on a number line diagram. | Grade 3 |
| Kansas | 3.NF.3 | Explain equivalence of fractions, and compare fractions by reasoning about their size. (It is a mathematical convention that when comparing fractions, the whole is the same size.) | Grade 3 |
| Kansas | 3.OA.1 | Interpret products of whole numbers, (e.g., interpret 5 ⋅ 7 as the total number of objects in 5 groups of 7 objects each). | Grade 3 |
| Kansas | 3.OA.2 | Interpret whole-number quotients of whole numbers, (e.g., interpret 56 ÷ 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each). | Grade 3 |
| Kansas | 3.OA.3 | Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, (e.g., by using drawings and equations with a symbol for the unknown number to represent the problem). | Grade 3 |
| Kansas | 3.OA.4 | Determine the unknown whole number in a multiplication or division equation by using related equations. | Grade 3 |
| Kansas | 3.OA.5 | Apply properties of operations as strategies to multiply and divide. | Grade 3 |
| Kansas | 3.OA.6 | Understand division as an unknown-factor problem. | Grade 3 |
| Kansas | 3.OA.7 | Fluently (efficiently, accurately, and flexibly) multiply and divide with single digit multiplications and related divisions using strategies (e.g., relationship between multiplication and division, doubles, double and double again, half and then double, etc.) or properties of operations. | Grade 3 |
| Kansas | 3.OA.8 | Solve two-step word problems using any of the four operations. Represent these problems using both situation equations and/or solution equations with a letter or symbol standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. This standard is limited to problems posed with whole numbers and having whole-number answers. | Grade 3 |
| Kansas | 3.OA.9 | Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations. | Grade 3 |
| Kansas | 4.G.1 | Draw points, lines, line segments, rays, angles (right, acute, obtuse, straight, reflex), and perpendicular and parallel lines. Identify these in two-dimensional figures. | Grade 4 |
| Kansas | 4.G.2 | Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles (right, acute, obtuse, straight, reflex). Recognize and categorize triangles based on angles (right, acute, obtuse, and equiangular) and/or sides (scalene, isosceles, and equilateral). | Grade 4 |
| Kansas | 4.G.3 | Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify line-symmetric figures and draw lines of symmetry. | Grade 4 |
| Kansas | 4.MD.1 | Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb., oz.; l, ml; hr., min., sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table. | Grade 4 |
| Kansas | 4.MD.2 | Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. | Grade 4 |
| Kansas | 4.MD.3 | Apply the area and perimeter formulas for rectangles in real world and mathematical problems explaining and justifying the appropriate unit of measure. | Grade 4 |
| Kansas | 4.MD.4 | Make a data display (line plot, bar graph, pictograph) to show a set of measurements in fractions of a unit (1/2,1/4,1/8). Solve problems involving addition and subtraction of fractions by using information presented in the data display. | Grade 4 |
| Kansas | 4.NBT.1 | Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. | Grade 4 |
| Kansas | 4.NBT.2 | Read and write multi-digit whole numbers using base-ten numerals, number names, expanded form, and unit form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, <, =, and ≠ symbols to record the results of comparisons. | Grade 4 |
| Kansas | 4.NBT.3 | Use place value understanding to round multi-digit whole numbers to any place. | Grade 4 |
| Kansas | 4.NBT.4 | Fluently (efficiently, accurately, and flexibly) add and subtract multi-digit whole numbers using an efficient algorithm (including, but not limited to: traditional, partial-sums, etc.), based on place value understanding and the properties of operations. | Grade 4 |
| Kansas | 4.NBT.5 | Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. | Grade 4 |
| Kansas | 4.NBT.6 | Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. | Grade 4 |
| Kansas | 4.NF.1 | Explain why a fraction 𝑎/𝑏 is equivalent to a fraction (𝑛⋅𝑎)/(𝑛⋅𝑏) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. | Grade 4 |
| Kansas | 4.NF.2 | Compare two fractions with different numerators and different denominators, (e.g., by creating common numerators or denominators, or by comparing to a benchmark fraction such as 1/2.) Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with relational symbols >, <, =, or ≠, and justify the conclusions, (e.g., by using visual fraction models.). | Grade 4 |
| Kansas | 4.NF.3 | Understand a fraction 𝑎/𝑏 with a > 1 as a sum of fractions 1/𝑏. | Grade 4 |
| Kansas | 4.NF.5 | Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100. | Grade 4 |
| Kansas | 4.NF.6 | Use decimal notation for fractions with denominators 10 or 100. | Grade 4 |
| Kansas | 4.NF.7 | Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the relational symbols >, <, =, or ≠, and justify the conclusions, (e.g., by using a visual model.). | Grade 4 |
| Kansas | 4.OA.1 | Interpret a multiplication equation as a comparison, (e.g., interpret 35 = 5 ⋅ 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5.) Represent verbal statements of multiplicative comparisons as multiplication equations. | Grade 4 |
| Kansas | 4.OA.2 | Multiply or divide to solve word problems involving multiplicative comparison, (e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison). | Grade 4 |
| Kansas | 4.OA.3 | Solve multi-step word problem posed with whole numbers and having whole number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using situation equations and/or solution equations with a letter or symbol standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. | Grade 4 |
| Kansas | 4.OA.4 | Find all factor pairs for a whole number in the range 1 to 100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1 to 100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1 to 100 is prime or composite. | Grade 4 |
| Kansas | 4.OA.5 | Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. For example, given the rule “Add 3” and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way. | Grade 4 |
| Kansas | 5.G.1 | Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., 𝑥-axis and 𝑥-coordinate, 𝑦-axis and 𝑦-coordinate). | Grade 5 |
| Kansas | 5.G.2 | Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation (e.g., plotting the relationship between two positive quantities such as maps, coordinate grid games (such as Battleship), time/temperature, time/distance, cost/quantity, etc.). | Grade 5 |
| Kansas | 5.G.3 | Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. | Grade 5 |
| Kansas | 5.G.4 | Classify two-dimensional figures in a hierarchy based on properties. | Grade 5 |
| Kansas | 5.MD.1 | Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. | Grade 5 |
| Kansas | 5.MD.2 | Make a data display (line plot, bar graph, pictograph) to show a data set of measurements in fractions of a unit (1/2,1/4,1/8). Use operations (add, subtract, multiply) on fractions for this grade to solve problems involving information presented in the data display. | Grade 5 |
| Kansas | 5.MD.3 | Recognize volume as an attribute of solid figures and understand concepts of volume measurement. | Grade 5 |
| Kansas | 5.MD.4 | Measure volumes by counting unit cubes such as cubic cm, cubic in., cubic ft. or non-standard cubic units. | Grade 5 |
| Kansas | 5.MD.5 | Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume. | Grade 5 |
| Kansas | 5.NBT.1 | Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. | Grade 5 |
| Kansas | 5.NBT.2 | Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. | Grade 5 |
| Kansas | 5.NBT.3 | Read, write, and compare decimals to thousandths. | Grade 5 |
| Kansas | 5.NBT.4 | Use place value understanding to round decimals to any place. | Grade 5 |
| Kansas | 5.NBT.5 | Fluently (efficiently, accurately, and flexibly) multiply multi-digit whole numbers using an efficient algorithm (ex., traditional, partial products, etc.) based on place value understanding and the properties of operations. | Grade 5 |
| Kansas | 5.NBT.6 | Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. | Grade 5 |
| Kansas | 5.NBT.7 | Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. | Grade 5 |
| Kansas | 5.NF.1 | Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. | Grade 5 |
| Kansas | 5.NF.2 | Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, (e.g., by using visual fraction models or equations to represent the problem.) Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. | Grade 5 |
| Kansas | 5.NF.3 | Interpret a fraction as division of the numerator by the denominator (𝑎/𝑏 = 𝑎 ÷ 𝑏). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. | Grade 5 |
| Kansas | 5.NF.6 | Solve real world problems involving multiplication of fractions and mixed numbers, (e.g., by using visual fraction models or equations to represent the problem). | Grade 5 |
| Kansas | 5.NF.7 | Apply and extend previous understandings of division (3.OA.2, 3.OA.5), to divide unit fractions by whole numbers and whole numbers by unit fractions. Division of a fraction by a fraction is not a requirement at this grade. | Grade 5 |
| Kansas | 5.OA.1 | Use parentheses in numerical expressions and evaluate expressions with these symbols. | Grade 5 |
| Kansas | 5.OA.2 | Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. | Grade 5 |
| Kansas | 6.EE.1 | Write and evaluate numerical expressions involving whole-number exponents. | Grade 6 |
| Kansas | 6.EE.2 | Write, read, and evaluate expressions in which letters stand for numbers. | Grade 6 |
| Kansas | 6.EE.3 | Apply the properties of operations and combine like terms, with the conventions of algebraic notation, to identify and generate equivalent expressions. | Grade 6 |
| Kansas | 6.EE.4 | Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true. | Grade 6 |
| Kansas | 6.EE.5 | Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set. | Grade 6 |
| Kansas | 6.EE.6 | Solve one-step equations involving non-negative rational numbers using addition, subtraction, multiplication and division. | Grade 6 |
| Kansas | 6.EE.7 | Write an inequality of the form 𝑥 > 𝑐 𝑜𝑟 𝑥 𝑐 or 𝑥 < 𝑐 have infinitely many solutions; represent solutions of such inequalities on number line diagrams. | Grade 6 |
| Kansas | 6.G.1 | Find the area of all triangles, special quadrilaterals (including parallelograms, kites and trapezoids), and polygons whose edges meet at right angles (rectilinear figure polygons) by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems. | Grade 6 |
| Kansas | 6.G.2 | Find the volume of a right rectangular prism with fractional edge lengths by applying the formulas 𝑉 = 𝑙𝑤ℎ and 𝑉 = 𝐵ℎ (𝐵 is the area of the base and ℎ is the height) to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems. (Builds on the 5th grade concept of packing unit cubes to find the volume of a rectangular prism with whole number edge lengths.) | Grade 6 |
| Kansas | 6.G.3 | Draw polygons whose edges meet at right angles (rectilinear figure polygons) in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems. | Grade 6 |
| Kansas | 6.G.4 | Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems. | Grade 6 |
| Kansas | 6.RP.1 | Use ratio language to describe a relationship between two quantities. Distinguish between part-to-part and part-to-whole relationships. | Grade 6 |
| Kansas | 6.RP.2 | Use unit rate language (“for each one”, “for every one” and “per”) and unit rate notation to demonstrate understanding the concept of a unit rate 𝑎/𝑏 associated with a ratio 𝑎:𝑏 𝑤𝑖𝑡ℎ 𝑏 ≠ 0. | Grade 6 |
| Kansas | 6.RP.3 | Use ratio and rate reasoning to solve real-world and mathematical problems, (e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagram, or using calculations). | Grade 6 |
| Kansas | 6.NS.1 | Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, requiring multiple exposures connecting various concrete and abstract models. | Grade 6 |
| Kansas | 6.NS.2 | Fluently (efficiently, accurately, and flexibly) divide multi-digit numbers using an efficient algorithm. | Grade 6 |
| Kansas | 6.NS.3 | Fluently (efficiently, accurately, and flexibly) add, subtract, multiply, and divide multi-digit decimals using an efficient algorithm for each operation. | Grade 6 |
| Kansas | 6.NS.6 | Understand a rational number as a point on the number line and a coordinate pair as a location on a coordinate plane. | Grade 6 |
| Kansas | 6.NS.7 | Understand ordering and absolute value of rational numbers. | Grade 6 |
| Kansas | 6.NS.8 | Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. | Grade 6 |
| Kansas | 7.EE.1 | Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with integer coefficients. | Grade 7 |
| Kansas | 7.EE.2 | Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. | Grade 7 |
| Kansas | 7.EE.3 | Solve multi-step real-life and mathematical problems with rational numbers. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. | Grade 7 |
| Kansas | 7.G.1 | Solve problems involving scale drawings of geometric figures, such as computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale. | Grade 7 |
| Kansas | 7.G.3 | Describe the two-dimensional figures that result from slicing three-dimensional figures, as in plane sections of right rectangular prisms and right cylinder. | Grade 7 |
| Kansas | 7.G.4 | Use the formulas for the area and circumference of a circle and solve problems; give an informal derivation of the relationship between the circumference and area of a circle. | Grade 7 |
| Kansas | 7.G.6 | Solve real-world and mathematical problems involving area of two-dimensional objects and volume and surface area of three-dimensional objects including cylinders and right prisms. (Solutions should not require students to take square roots or cube roots. For example, given the volume of a cylinder and the area of the base, students would identify the height.) | Grade 7 |
| Kansas | 7.RP.1 | Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. | Grade 7 |
| Kansas | 7.RP.2 | Recognize and represent proportional relationships between quantities: | Grade 7 |
| Kansas | 7.RP.3 | Use proportional relationships to solve multistep ratio and percent problems. | Grade 7 |
| Kansas | 7.NS.1 | Represent addition and subtraction on a horizontal or vertical number line diagram. | Grade 7 |
| Kansas | 7.NS.2 | Apply and extend previous understandings of multiplication and division of positive rational numbers to multiply and divide all rational numbers. | Grade 7 |
| Kansas | 7.NS.3 | Solve and interpret real-world and mathematical problems involving the four operations with rational numbers. (Computations with rational numbers extend the rules for manipulating fractions to complex fractions.) | Grade 7 |
| Kansas | 8.EE.1 | Use square root and cube root symbols to represent solutions to equations of the form 𝑥² = 𝑝 and 𝑥³ = 𝑝, where 𝑝 is a positive rational number. Evaluate square roots of whole number perfect squares with solutions between 0 and 15 and cube roots of whole number perfect cubes with solutions between 0 and 5. Know that √2 is irrational. | Grade 8 |
| Kansas | 8.EE.2 | Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other. | Grade 8 |
| Kansas | 8.EE.3 | Read and write numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology. | Grade 8 |
| Kansas | 8.EE.4 | Graph proportional relationships, interpreting its unit rate as the slope (𝑚) of the graph. Compare two different proportional relationships represented in different ways. | Grade 8 |
| Kansas | 8.EE.5 | Use similar triangles to explain why the slope (𝑚) is the same between any two distinct points on a non-vertical line in the coordinate plane and extend to include the use of the slope formula (𝑚 = (𝑦₂ - 𝑦₁)/(𝑥₂ - 𝑥₁) when given two coordinate points (𝑥₁, 𝑦₁) and (𝑥₂, 𝑦₂)). Generate the equation 𝑦 = 𝑚𝑥 for a line through the origin (proportional) and the equation 𝑦 = 𝑚𝑥 + 𝑏 for a line with slope 𝑚 intercepting the vertical axis at 𝑦-intercept 𝑏 (not proportional when 𝑏 ≠ 0). | Grade 8 |
| Kansas | 8.EE.7 | Fluently (efficiently, accurately, and flexibly) solve one-step, two-step, and multi-step linear equations and inequalities in one variable, including situations with the same variable appearing on both sides of the equal sign. | Grade 8 |
| Kansas | 8.F.1 | Explain that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output. (Function notation is not required in Grade 8.) | Grade 8 |
| Kansas | 8.F.2 | Compare properties of two linear functions represented in a variety of ways (algebraically, graphically, numerically in tables, or by verbal descriptions). | Grade 8 |
| Kansas | 8.F.3 | Interpret the equation 𝑦 = 𝑚𝑥 + 𝑏 as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. | Grade 8 |
| Kansas | 8.F.4 | Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (𝑥, 𝑦) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values. | Grade 8 |
| Kansas | 8.F.5 | Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally. | Grade 8 |
| Kansas | 8.G.1 | Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement: | Grade 8 |
| Kansas | 8.G.2 | Measure angles in whole-number degrees using a protractor. Draw angles of specified measure using a protractor and straight edge. | Grade 8 |
| Kansas | 8.G.3 | Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems, e.g., by using an equation with a symbol for the unknown angle measure. | Grade 8 |
| Kansas | 8.G.4 | Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and use them to solve simple equations for an unknown angle in a figure. | Grade 8 |
| Kansas | 8.G.5 | Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. | Grade 8 |
| Kansas | 8.G.6 | Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on drawing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle. | Grade 8 |
| Kansas | 8.G.8 | Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions. | Grade 8 |
| Kansas | 8.G.9 | Apply the Pythagorean Theorem to find the distance between two points in a coordinate system. | Grade 8 |
| Kansas | 8.G.10 | Use the formulas or informal reasoning to find the arc length, areas of sectors, surface areas and volumes of pyramids, cones, and spheres. | Grade 8 |
| Kansas | 8.G.12 | Solve real-world and mathematical problems involving arc length, area of two-dimensional shapes including sectors, volume and surface area of three-dimensional objects including pyramids, cones and spheres. | Grade 8 |
| Kansas | 8.SP.1 | Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association. | Grade 8 |
| Kansas | 8.SP.2 | Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line. | Grade 8 |
| Kansas | 8.NS.2 | Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g., 𝜋²). | Grade 8 |
| Kansas | N.RN.1 | Know and apply the properties of integer exponents to generate equivalent numerical and algebraic expressions. | High School |
| Kansas | A.APR.2 | Factor higher degree polynomials; identifying that some polynomials are prime. | High School |
| Kansas | A.CED.2 | Apply and extend previous understanding to create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. | High School |
| Kansas | A.CED.3 | Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context. | High School |
| Kansas | A.REI.2 | Apply and extend previous understanding to solve equations, inequalities, and compound inequalities in one variable, including literal equations and inequalities. | High School |
| Kansas | A.REI.6 | Analyze and solve pairs of simultaneous linear equations. | High School |
| Kansas | A.SSE.2 | Use the structure of an expression to identify ways to rewrite it. | High School |
| Kansas | A.SSE.3 | Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression. | High School |
| Kansas | F.BF.1 | Use functions to model real-world relationships. | High School |
| Kansas | F.IF.2 | Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. | High School |
| Kansas | F.IF.4 | For a function that models a relationship between two quantities, interpret key features of expressions, graphs and tables in terms of the quantities, and sketch graphs showing key features given a description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. | High School |
| Kansas | F.IF.7 | Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. | High School |
| Kansas | G.CO.3 | Given two congruent figures, describe a sequence of rigid motions that exhibits the congruence (isometry) between them using coordinates and the non-coordinate plane. | High School |
| Kansas | G.SRT.2 | Recognize transformations as functions that take points in the plane as inputs and give other points as outputs and describe the effect of dilations on two-dimensional figures. | High School |
| Kansas | G.SRT.3 | Given two similar figures, describe a sequence of transformations that exhibits the similarity between them using coordinates and the non-coordinate plane. | High School |
| Kansas | S.ID.5 | Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. | High School |
| Kentucky | K.CC.1 | Count | Kindergarten |
| Kentucky | K.CC.2 | Count forward beginning from a given number within the known sequence within 100 (instead of having to begin at 1). | Kindergarten |
| Kentucky | K.CC.3 | Represent numbers. | Kindergarten |
| Kentucky | K.CC.4 | Understand the relationship between numbers and quantities; connect counting to cardinality. | Kindergarten |
| Kentucky | K.CC.5 | Given a number from 1-20, count out that many objects. | Kindergarten |
| Kentucky | K.CC.6 | Identify whether the number of objects in one group is greater than, less than, or equal to the number of objects in another group. | Kindergarten |
| Kentucky | K.CC.7 | Compare two numbers between 1 and 10 presented as written numerals. | Kindergarten |
| Kentucky | K.G.1 | Name and describe shapes in the environment. | Kindergarten |
| Kentucky | K.G.2 | Correctly name shapes regardless of orientations or overall size. | Kindergarten |
| Kentucky | K.G.3 | Identify shapes as two-dimensional or three-dimensional. | Kindergarten |
| Kentucky | K.G.4 | Describe the similarities, differences and attributes of two and three dimensional shapes using different sizes and orientations. | Kindergarten |
| Kentucky | K.G.6 | Compose simple shapes to form larger shapes. | Kindergarten |
| Kentucky | K.MD.1 | Describe measurable attributes (length, height, weight, width, depth) of an object or a set of objects using appropriate vocabulary. | Kindergarten |
| Kentucky | K.MD.2 | Directly compare two objects with a measurable attribute in common, to see which object has “more of”/“less of” the attribute and describe the difference. | Kindergarten |
| Kentucky | K.MD.3 | Classify and sort objects or people by attributes. Limit objects or people in each category to be less than or equal to 10. | Kindergarten |
| Kentucky | K.MD.4 | Recognize and identify coins by name (penny, nickel, dime, quarter). | Kindergarten |
| Kentucky | K.NBT.1 | Compose and decompose numbers from 11 to 19 using quantities (numbers with units) of ten ones and some further ones. Understand that these numbers are composed of ten ones and one, two, three, four, five, six, seven, eight, or nine ones. | Kindergarten |
| Kentucky | K.OA.1 | Represent addition and subtraction with objects, fingers, mental images, drawings, sounds, acting out situations, verbal explanations, expressions, or equations. | Kindergarten |
| Kentucky | K.OA.2 | Solve addition and subtraction word problems and add and subtract within 10 by using objects or drawings to represent the problem. | Kindergarten |
| Kentucky | K.OA.3 | Decompose numbers less than or equal to 10. | Kindergarten |
| Kentucky | K.OA.4 | For any number from 1 to 9, find the number that makes 10 when added to the given number by using objects or drawings and record the answer with a drawing or equation. | Kindergarten |
| Kentucky | K.OA.5 | Fluently add and subtract within 5. | Kindergarten |
| Kentucky | 1.G.1 | Distinguish between defining attributes versus non-defining attributes; build and draw shapes to possess defining attributes. | Grade 1 |
| Kentucky | 1.G.2 | Compose shapes. | Grade 1 |
| Kentucky | 1.G.3 | Partition circles and rectangles into two and four equal shares, describe the shares using the words halves, fourths and quarters, and use the phrases half of, fourth of and quarter of. Describe the whole as two of or four of the shares. Understand for these examples that decomposing into more equal shares creates smaller shares. | Grade 1 |
| Kentucky | 1.MD.1 | Order three objects by length; compare the lengths of two objects indirectly by using a third object. | Grade 1 |
| Kentucky | 1.MD.2 | Express the length of an object as a whole number of same-size length units, by laying multiple copies of a shorter object (the length unit) end to end with no gaps or overlaps. | Grade 1 |
| Kentucky | 1.MD.3 | Assign values to time and money. | Grade 1 |
| Kentucky | 1.MD.4 | Investigate questions involving categorical data. | Grade 1 |
| Kentucky | 1.NBT.1 | Count and represent numbers. | Grade 1 |
| Kentucky | 1.NBT.2 | Understand the two-digits of a two-digit number represent amounts of tens and ones. | Grade 1 |
| Kentucky | 1.NBT.3 | Compare two two-digit numbers based on meanings of the tens and ones digits, recording the results of comparisons with the symbols >, =, and <. | Grade 1 |
| Kentucky | 1.NBT.4 | Add within 100 including adding a two-digit number and a one-digit number. Add a two-digit number and a multiple of 10. | Grade 1 |
| Kentucky | 1.NBT.5 | Given a two-digit number, mentally find 10 more or 10 less than the number, without having to count; explain the reasoning used. | Grade 1 |
| Kentucky | 1.NBT.6 | Subtract multiples of 10 in the range 10-90 from multiples of 10 in the range 10-90 (positive or zero differences). | Grade 1 |
| Kentucky | 1.OA.1 | Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart and comparing, with unknowns in all positions. | Grade 1 |
| Kentucky | 1.OA.3 | Apply properties of operations as strategies to add and subtract. | Grade 1 |
| Kentucky | 1.OA.4 | Understand subtraction as an unknown-addend problem. | Grade 1 |
| Kentucky | 1.OA.5 | Relate counting to addition and subtraction. | Grade 1 |
| Kentucky | 1.OA.6 | Add and subtract within 20. | Grade 1 |
| Kentucky | 1.OA.7 | Understand the meaning of the equal sign and determine if equations involving addition and subtraction are true or false. | Grade 1 |
| Kentucky | 1.OA.8 | Determine the unknown whole number in an addition or subtraction equation relating three whole numbers. | Grade 1 |
| Kentucky | 2.G.1 | Recognize and draw shapes having specified attributes, such as a given number of angles or sides. Identify triangles, quadrilaterals, pentagons, hexagons and cubes (identify number of faces). | Grade 2 |
| Kentucky | 2.G.2 | Partition a rectangle into rows and columns of same-size squares and count to find the total number of them. | Grade 2 |
| Kentucky | 2.G.3 | Partition circles and rectangles into two, three, or four equal shares; describe the shares using the words halves, thirds, half of, a third of, etc.; and describe the whole as two halves, three thirds, four fourths. Recognize that equal shares of identical wholes need not have the same shape. | Grade 2 |
| Kentucky | 2.MD.1 | Measure the length of an object by selecting and using appropriate tools such as rulers, yardsticks, meter sticks and measuring tapes. | Grade 2 |
| Kentucky | 2.MD.2 | Measure the length of an object twice, using length units of different lengths for the two measurements; describe how the two measurements relate to the size of the unit chosen. | Grade 2 |
| Kentucky | 2.MD.4 | Measure to determine how much longer one object is than another, expressing the length difference in terms of either a customary or metric standard length unit. | Grade 2 |
| Kentucky | 2.MD.5 | Use addition and subtraction within 100 to solve word problems involving lengths that are given in the same units by using drawings and equations with a symbol for the unknown number to represent the problem. | Grade 2 |
| Kentucky | 2.MD.7 | Tell and write time from analog and digital clocks to the nearest five minutes, using a.m. and p.m. | Grade 2 |
| Kentucky | 2.MD.8 | Solve word problems with adding and subtracting within 100, (not using dollars and cents simultaneously) using the ＄and ￠symbols appropriately (not including decimal notation). | Grade 2 |
| Kentucky | 2.MD.9 | Investigate questions involving measurements. | Grade 2 |
| Kentucky | 2.MD.10 | Create a pictograph and a bar graph (with single-unit scale) to represent a data set with up to four categories. Solve simple put together, take-apart and compare problems using information presented in a bar graph. | Grade 2 |
| Kentucky | 2.NBT.1 | Understand that the three digits of a three-digit number represent amounts of hundreds, tens and ones. | Grade 2 |
| Kentucky | 2.NBT.2 | Count forwards and backwards within 1000; skip-count by 5s, 10s and 100s. | Grade 2 |
| Kentucky | 2.NBT.3 | Read and write numbers to 1000 using base-ten numerals, number names and expanded form. | Grade 2 |
| Kentucky | 2.NBT.4 | Compare two three-digit numbers based on meanings of the hundreds, tens and ones digits, using >, =, and < symbols to record the results of comparisons. | Grade 2 |
| Kentucky | 2.NBT.5 | Fluently add and subtract within 100 using strategies based on place value, properties of operations and/or the relationship between addition and subtraction. | Grade 2 |
| Kentucky | 2.NBT.6 | Add up to four two-digit numbers using strategies based on place value and properties of operations. | Grade 2 |
| Kentucky | 2.NBT.7 | Add and subtract within 1000. | Grade 2 |
| Kentucky | 2.NBT.8 | Mentally add 10 or 100 to a given number 100–900 and mentally subtract 10 or 100 from a given number 100–900. | Grade 2 |
| Kentucky | 2.OA.1 | Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart and comparing, with unknowns in all positions, by using drawings and equations with a symbol for the unknown number to represent the problem. | Grade 2 |
| Kentucky | 2.OA.2 | Fluently add and subtract within 20 using mental strategies. | Grade 2 |
| Kentucky | 2.OA.3 | Determine whether a group of objects (up to 20) has an odd or even number of members; write an equation to express an even number as a sum of two equal addends. | Grade 2 |
| Kentucky | 2.OA.4 | Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends. | Grade 2 |
| Kentucky | 3.G.1 | Classify polygons by attributes. | Grade 3 |
| Kentucky | 3.G.2 | Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole. | Grade 3 |
| Kentucky | 3.MD.1 | Tell and write time to the nearest minute and measure elapsed time intervals in minutes. Solve word problems involving addition and subtraction of time intervals within and across the hour in minutes. | Grade 3 |
| Kentucky | 3.MD.2 | Measure and solve problems involving mass and liquid volume. | Grade 3 |
| Kentucky | 3.MD.3 | Investigate questions involving categorical data. | Grade 3 |
| Kentucky | 3.MD.4 | Investigate questions involving numerical data. | Grade 3 |
| Kentucky | 3.MD.5 | Recognize area as an attribute of plane figures and understand concepts of area measurement. | Grade 3 |
| Kentucky | 3.MD.6 | Measure areas by counting unit squares (square cm, square m, square in, square ft. and improvised units). | Grade 3 |
| Kentucky | 3.MD.7 | Relate area to the operations of multiplication and addition. | Grade 3 |
| Kentucky | 3.MD.8 | Solve real world and mathematical problems involving perimeters of polygons. | Grade 3 |
| Kentucky | 3.NBT.1 | Use place value understanding to round whole numbers to the nearest 10 or 100. | Grade 3 |
| Kentucky | 3.NBT.2 | Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations and/or the relationship between addition and subtraction. | Grade 3 |
| Kentucky | 3.NBT.3 | Multiply one-digit whole numbers by multiples of 10 in the range of 10–90 using strategies based on place value and properties of operations. | Grade 3 |
| Kentucky | 3.NF.1 | Understand a fraction 1/𝑏 as the quantity formed by 1 part when a whole is partitioned into 𝑏 equal parts; understand a fraction 𝑎/𝑏 as the quantity formed by a parts of size 1/𝑏. | Grade 3 |
| Kentucky | 3.NF.2 | Understand a fraction as a number on the number line; represent fractions on a number line. | Grade 3 |
| Kentucky | 3.NF.3 | Explain equivalence of fractions in special cases and compare fractions by reasoning about their size. | Grade 3 |
| Kentucky | 3.OA.1 | Interpret and demonstrate products of whole numbers. | Grade 3 |
| Kentucky | 3.OA.2 | Interpret and demonstrate whole-number quotients of whole numbers, where objects are partitioned into equal shares. | Grade 3 |
| Kentucky | 3.OA.3 | Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays and measurement quantities, by using drawings and equations with a symbol for the unknown number to represent the problem. | Grade 3 |
| Kentucky | 3.OA.4 | Determine the unknown whole number in a multiplication or division equation relating three whole numbers. | Grade 3 |
| Kentucky | 3.OA.5 | Apply properties of operations as strategies to multiply and divide. | Grade 3 |
| Kentucky | 3.OA.6 | Understand division as an unknown-factor problem. | Grade 3 |
| Kentucky | 3.OA.7 | Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division or properties of operations. | Grade 3 |
| Kentucky | 3.OA.8 | Use various strategies to solve two-step word problems using the four operations (involving only whole numbers with whole number answers). Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. | Grade 3 |
| Kentucky | 3.OA.9 | Identify arithmetic patterns (including patterns in the addition table or multiplication table) and explain them using properties of operations. | Grade 3 |
| Kentucky | 4.G.1 | Draw points, lines, line segments, rays, angles (right, acute, obtuse) and perpendicular and parallel lines. Identify these in two-dimensional figures. | Grade 4 |
| Kentucky | 4.G.2 | Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence of absence of angles of a specified size. Recognize right triangles as a category and identify right triangles. | Grade 4 |
| Kentucky | 4.G.3 | Identify lines of symmetry. | Grade 4 |
| Kentucky | 4.MD.1 | Know relative size of measurement units (mass, weight, liquid volume, length, time) within one system of units (metric system, U.S. standard system and time). | Grade 4 |
| Kentucky | 4.MD.2 | Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects and money. | Grade 4 |
| Kentucky | 4.MD.3 | Apply the area and perimeter formulas for rectangles in real world and mathematical problems. | Grade 4 |
| Kentucky | 4.MD.4 | Use dot plots to analyze data to a statistical question. | Grade 4 |
| Kentucky | 4.MD.5 | Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint and understand concepts of angle measurement. | Grade 4 |
| Kentucky | 4.MD.6 | Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure. | Grade 4 |
| Kentucky | 4.MD.7 | Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems. | Grade 4 |
| Kentucky | 4.NBT.1 | Recognize in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. | Grade 4 |
| Kentucky | 4.NBT.2 | Represent and compare multi-digit whole numbers. | Grade 4 |
| Kentucky | 4.NBT.3 | Use place value understanding to round multi-digit whole numbers to any place. | Grade 4 |
| Kentucky | 4.NBT.4 | Fluently add and subtract multi-digit whole numbers using an algorithm. | Grade 4 |
| Kentucky | 4.NBT.5.i | Multiply whole numbers. | Grade 4 |
| Kentucky | 4.NBT.5.ii | Multiply using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. | Grade 4 |
| Kentucky | 4.NBT.6.i | Divide up to four-digit dividends by one-digit divisors. Find whole number quotients and remainders. | Grade 4 |
| Kentucky | 4.NBT.6.ii | Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. | Grade 4 |
| Kentucky | 4.NF.1 | Understand and generate equivalent fractions. | Grade 4 |
| Kentucky | 4.NF.2 | Compare two fractions with different numerators and different denominators using the symbols . Recognize comparisons are valid only when the two fractions refer to the same whole. Justify the conclusions. | Grade 4 |
| Kentucky | 4.NF.3 | Understand a fraction 𝑎/𝑏 with 𝑎 > 1 as a sum of fractions 1/𝑏. | Grade 4 |
| Kentucky | 4.NF.4 | Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. | Grade 4 |
| Kentucky | 4.NF.5 | Convert and add fractions with denominators of 10 and 100. | Grade 4 |
| Kentucky | 4.NF.6 | Use decimal notation for fractions with denominators 10 or 100. | Grade 4 |
| Kentucky | 4.NF.7 | Compare two decimals to hundredths. | Grade 4 |
| Kentucky | 4.OA.1 | Interpret a multiplication equation as a comparison. Represent verbal statements of multiplicative comparisons as multiplication equations. | Grade 4 |
| Kentucky | 4.OA.2 | Multiply or divide to solve word problems involving multiplicative comparisons by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison. | Grade 4 |
| Kentucky | 4.OA.3 | Solve multistep problems. | Grade 4 |
| Kentucky | 4.OA.4 | Find factors and multiples of numbers in the range 1-100. | Grade 4 |
| Kentucky | 4.OA.5 | Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern not explicit in the rule itself. | Grade 4 |
| Kentucky | 5.G.1 | Use a pair perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis and the second number indicates how far to travel in the direction of the second. | Grade 5 |
| Kentucky | 5.G.2 | Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane and interpret coordinate values of points in the context of the situation. | Grade 5 |
| Kentucky | 5.G.3 | Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. | Grade 5 |
| Kentucky | 5.G.4 | Classify two-dimensional figures in a hierarchy based on properties. | Grade 5 |
| Kentucky | 5.MD.1 | Convert among different size measurement units (mass, weight, liquid volume, length, time) within one system of units (metric system, U.S. standard system and time). | Grade 5 |
| Kentucky | 5.MD.2 | Identify and gather data for statistical questions focused on both categorical and numerical data. Select an appropriate data display (bar graph, pictograph, dot plot). Make observations from the graph about the questions posed. | Grade 5 |
| Kentucky | 5.MD.3 | Recognize volume as an attribute of solid figures and understand concepts of volume measurement. | Grade 5 |
| Kentucky | 5.MD.4 | Measure volumes by counting unit cubic cm, cubic in, cubic ft. and improvised units. | Grade 5 |
| Kentucky | 5.MD.5 | Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume. | Grade 5 |
| Kentucky | 5.NBT.1 | Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. | Grade 5 |
| Kentucky | 5.NBT.2 | Multiply and divide by powers of 10. | Grade 5 |
| Kentucky | 5.NBT.3 | Read, write and compare decimals to thousandths. | Grade 5 |
| Kentucky | 5.NBT.4 | Use place value understanding to round decimals to any place. | Grade 5 |
| Kentucky | 5.NBT.5 | Fluently multiply multi-digit whole numbers (not to exceed four-digit by two-digit multiplication) using an algorithm. | Grade 5 |
| Kentucky | 5.NBT.6 | Divide up to four-digit dividends by two-digit divisors. | Grade 5 |
| Kentucky | 5.NBT.7 | Operations with decimals to hundredths. | Grade 5 |
| Kentucky | 5.NF.1 | Efficiently add and subtract fractions with unlike denominators (including mixed numbers) by… | Grade 5 |
| Kentucky | 5.NF.2 | Solve word problems involving addition and subtraction of fractions. | Grade 5 |
| Kentucky | 5.NF.3 | Interpret a fraction as division of the numerator by the denominator (𝑎/𝑏 = 𝑎 ÷ 𝑏). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers by using visual fraction models or equations to represent the problem. | Grade 5 |
| Kentucky | 5.NF.4 | Apply and extend previous understanding of multiplication to multiply a fraction or whole number by a fraction. | Grade 5 |
| Kentucky | 5.NF.5 | Interpret multiplication as scaling (resizing). | Grade 5 |
| Kentucky | 5.NF.6 | Solve real world problems involving multiplication of fractions and mixed numbers. | Grade 5 |
| Kentucky | 5.NF.7 | Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. | Grade 5 |
| Kentucky | 5.OA.1 | Use parentheses, brackets or braces in numerical expressions and evaluate expressions that include symbols. | Grade 5 |
| Kentucky | 5.OA.2 | Write simple expressions with numbers and interpret numerical expressions without evaluating them. | Grade 5 |
| Kentucky | 5.OA.3 | Generate numerical patterns for situations. | Grade 5 |
| Kentucky | 6.EE.1 | Write and evaluate numerical expressions involving whole-number exponents. | Grade 6 |
| Kentucky | 6.EE.2 | Write, read and evaluate expressions in which letters stand for numbers. | Grade 6 |
| Kentucky | 6.EE.3 | Apply the properties of operations to generate equivalent expressions. | Grade 6 |
| Kentucky | 6.EE.4 | Identify when two expressions are equivalent when the two expressions name the same number regardless of which value is substituted into them. | Grade 6 |
| Kentucky | 6.EE.5 | Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true. | Grade 6 |
| Kentucky | 6.EE.6 | Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or depending on the purpose at hand, any number in a specified set. | Grade 6 |
| Kentucky | 6.EE.7 | Solve real-world and mathematical problems by writing and solving equations of the form 𝑥 + 𝑝 = 𝑞 and 𝑝𝑥 = 𝑞 for cases in which 𝑝, 𝑞 and 𝑥 are all nonnegative rational numbers. | Grade 6 |
| Kentucky | 6.EE.8 | Write an inequality of the form 𝑥 > 𝑐, 𝑥 < 𝑐, 𝑥 ≥ 𝑐, or 𝑥 ≤ 𝑐 to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of these forms have infinitely many solutions; represent solutions of such inequalities on vertical and horizontal number lines. | Grade 6 |
| Kentucky | 6.EE.9 | Use variables to represent two quantities in a real-world problem that changes in relationship to one another; | Grade 6 |
| Kentucky | 6.G.1 | Find the area of right triangles, other triangles, special quadrilaterals and polygons by composing into rectangles or decomposing into triangles and quadrilaterals; apply these techniques in the context of solving real-world and mathematical problems. | Grade 6 |
| Kentucky | 6.G.2 | Find the volume of a right rectangular prism with rational number edge lengths. Apply the formulas 𝑉 = 𝑙𝑤ℎ and 𝑉 = 𝐵ℎ to find volumes of right rectangular prisms with rational number edge lengths in the context of solving real-world and mathematical problems. | Grade 6 |
| Kentucky | 6.G.3 | Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems. | Grade 6 |
| Kentucky | 6.G.4 | Classify three-dimensional figures including cubes, prisms, pyramids, cones and spheres. | Grade 6 |
| Kentucky | 6.RP.1 | Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. | Grade 6 |
| Kentucky | 6.RP.2 | Understand the concept of a unit rate 𝑎/𝑏 associated with a ratio 𝑎:𝑏 with 𝑏 ≠ 0 and use rate language in the context of a ratio relationship. | Grade 6 |
| Kentucky | 6.RP.3 | Use ratio and rate reasoning to solve real-world and mathematical problems. | Grade 6 |
| Kentucky | 6.SP.5 | Summarize numerical data sets in relation to their context, such as by: | Grade 6 |
| Kentucky | 6.NS.1 | Interpret and compute quotients of fractions and solve word problems involving division of fractions by fractions. | Grade 6 |
| Kentucky | 6.NS.2 | Fluently divide multi-digit numbers using an algorithm. | Grade 6 |
| Kentucky | 6.NS.3 | Fluently add, subtract, multiply and divide multi-digit decimals using an algorithm for each operation. | Grade 6 |
| Kentucky | 6.NS.5 | Understand that positive and negative numbers are used together to describe quantities having opposite directions or values; use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation. | Grade 6 |
| Kentucky | 6.NS.6 | Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes, using appropriate range and intervals, to represent points on the line and in the plane, that include negative numbers and coordinates. | Grade 6 |
| Kentucky | 6.NS.7 | Understand ordering and absolute value of rational numbers. | Grade 6 |
| Kentucky | 6.NS.8 | Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. | Grade 6 |
| Kentucky | 7.EE.1 | Apply properties of operations as strategies to add, subtract, factor and expand linear expressions with rational coefficients. | Grade 7 |
| Kentucky | 7.EE.2 | Understand that rewriting an expression in different forms in a problem context can clarify the problem and how the quantities in it are related. | Grade 7 |
| Kentucky | 7.EE.3 | Solve real-life and mathematical problems posed with positive and negative rational numbers in any form, using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. | Grade 7 |
| Kentucky | 7.EE.4 | Use variables to represent quantities in a real-world or mathematical problem and construct equations and inequalities to solve problems by reasoning about the quantities. | Grade 7 |
| Kentucky | 7.G.1 | Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale. | Grade 7 |
| Kentucky | 7.G.2 | Draw (freehand, with ruler and protractor and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle. | Grade 7 |
| Kentucky | 7.G.3 | Describe the two-dimensional figures that result from slicing three-dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids. | Grade 7 |
| Kentucky | 7.G.4 | Use formulas for area and circumference of circles and their relationships. | Grade 7 |
| Kentucky | 7.G.5 | Apply properties of supplementary, complementary, vertical and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure. | Grade 7 |
| Kentucky | 7.G.6 | Solve problems involving area of two-dimensional objects and surface area and volume of three-dimensional objects. | Grade 7 |
| Kentucky | 7.RP.1 | Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. | Grade 7 |
| Kentucky | 7.RP.2 | Recognize and represent proportional relationships between quantities. | Grade 7 |
| Kentucky | 7.RP.3 | Use percents to solve mathematical and real-world problems. | Grade 7 |
| Kentucky | 7.NS.1 | Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram. | Grade 7 |
| Kentucky | 7.NS.2 | Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers. | Grade 7 |
| Kentucky | 7.NS.3 | Solve real-world and mathematical problems involving the four operations with rational numbers. | Grade 7 |
| Kentucky | 8.EE.1 | Know and apply the properties of integer exponents to generate equivalent numerical expressions. | Grade 8 |
| Kentucky | 8.EE.2 | Use square root and cube root symbols to represent solutions to equations of the form x² = 𝑝 and x³ = 𝑝, where 𝑝 is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that perfect squares and perfect cubes are rational. | Grade 8 |
| Kentucky | 8.EE.3 | Use numbers expressed in the form of a single digit times an integer power of 10 (Scientific Notation) to estimate very large or very small quantities and express how many times larger or smaller one is than the other. | Grade 8 |
| Kentucky | 8.EE.4 | Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities. Interpret scientific notation that has been generated by technology. | Grade 8 |
| Kentucky | 8.EE.5 | Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. | Grade 8 |
| Kentucky | 8.EE.6 | Use similar triangles to explain why the slope, 𝑚, is the same between any two distinct points on a non-vertical line in the coordinate plane; know the equation 𝑦 = 𝑚𝑥 for a line through the origin and the equation 𝑦 = 𝑚𝑥 + 𝑏 for a line intercepting the vertical axis at 𝑏. | Grade 8 |
| Kentucky | 8.EE.7 | Solve linear equations in one variable. | Grade 8 |
| Kentucky | 8.EE.8 | Analyze and solve a system of two linear equations. | Grade 8 |
| Kentucky | 8.F.1 | Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output. | Grade 8 |
| Kentucky | 8.F.2 | Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). | Grade 8 |
| Kentucky | 8.F.3 | Understand properties of linear functions. | Grade 8 |
| Kentucky | 8.F.4 | Construct a function to model a linear relationship between two quantities. | Grade 8 |
| Kentucky | 8.F.5 | Use graphs to represent functions. | Grade 8 |
| Kentucky | 8.G.1 | Verify experimentally the properties of rotations, reflections and translations. | Grade 8 |
| Kentucky | 8.G.2 | Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections and translations. Given two congruent figures, describe a sequence that exhibits the congruence between them. | Grade 8 |
| Kentucky | 8.G.3 | Describe the effect of dilations, translations, rotations and reflections on two-dimensional figures using coordinates. | Grade 8 |
| Kentucky | 8.G.4 | Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations and dilations. Given two similar two-dimensional figures, describe a sequence that exhibits the similarity between them. | Grade 8 |
| Kentucky | 8.G.5 | Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal and the angle-angle criterion for similarity of triangles. | Grade 8 |
| Kentucky | 8.G.7 | Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions. | Grade 8 |
| Kentucky | 8.G.8 | Apply the Pythagorean Theorem to find the distance between two points in a coordinate system. | Grade 8 |
| Kentucky | 8.G.9 | Apply the formulas for the volumes and surface areas of cones, cylinders and spheres and use them to solve real-world and mathematical problems. | Grade 8 |
| Kentucky | 8.SP.1 | Construct and interpret scatter plots for bivariate numerical data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association and nonlinear association. | Grade 8 |
| Kentucky | 8.SP.2 | Know that lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a line and informally assess the model fit by judging the closeness of the data points to the line. | Grade 8 |
| Kentucky | 8.NS.2 | Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram and estimate the value of expressions. | Grade 8 |
| Kentucky | HS.A.14 | Create a system of equations or inequalities to represent constraints within a modeling context. Interpret the solution(s) to the corresponding system as viable or nonviable options within the context. | Algebra |
| Kentucky | HS.A.18 | Solve linear equations and inequalities in one variable, including literal equations with coefficients represented by letters. | Algebra |
| Knotion | K1.CYCA.B.4 | Relaciona la acción de aumentar una colección con agregar objetos. | Kindergarten |
| Knotion | K1.CYCA.C.6 | Identifican si el número de objetos de un grupo es mayor que, menor que, o igual que el número de objetos en otro grupo, por ejemplo, al usar estrategias para contar y para emparejar. | Kindergarten |
| Knotion | K1.MYD.A.1 | Utiliza objetos arbitrarios para establecer relaciones de comparación entre los atributos medibles. | Kindergarten |
| Knotion | K1.MYD.A.2 | Determina si un objeto es mayor o menor que otro. | Kindergarten |
| Knotion | K1.MYD.B.3 | Agrupa objetos de acuerdo con su forma. | Kindergarten |
| Knotion | K2.CYCA.C.6 | Elige el conjunto que tiene más o menos objetos después de haber observado un par o una tercia de colecciones. | Kindergarten |
| Knotion | K2.GE.A.1 | Observa objetos de su entorno y los compara con el cuadrado, el triángulo y el círculo. | Kindergarten |
| Knotion | K2.MYD.A.1 | Relaciona los instrumnetos de medición con el atributo del objeto. | Kindergarten |
| Knotion | K2.MYD.A.2 | Registra la información reunida por medio de un dibujo, una tabla, etcétera. | Kindergarten |
| Knotion | K2.MYD.B.3 | Ordena colecciones de diferente numerosidad: de mayor a menor. | Kindergarten |
| Knotion | K2.OYPA.A.1 | Relaciona la acción de aumentar una colección con agregar objetos. | Kindergarten |
| Knotion | K3.CYCA.A.1 | Identifica las regularidades de la sucesión numérica del 0 al 100. | Kindergarten |
| Knotion | K3.CYCA.A.2 | Cuentan hacia delante desde un número dado dentro de una secuencia conocida (en lugar de comenzar con el 1). | Kindergarten |
| Knotion | K3.CYCA.A.3 | Escribe y lee los números (1 a 20). | Kindergarten |
| Knotion | K3.CYCA.B.4 | Escribe y lee un listado de números que inician después del uno y lo completa, ya sea en la parte intermedia o lo continúa. | Kindergarten |
| Knotion | K3.CYCA.B.5 | Completa el elemento faltante de una secuencia de números o figuras incompleta. | Kindergarten |
| Knotion | K3.GE.A.1 | Distingue las similitudes y las diferencias de la forma de objetos de su entorno que pone en comparación. | Kindergarten |
| Knotion | K3.GE.A.2 | Nombran correctamente las figuras geométricas sin importar su orientación o su tamaño. | Kindergarten |
| Knotion | K3.GE.A.3 | Utiliza expresiones elementales para relacionar objetos de tres dimensiones con figuras de dos dimensiones. | Kindergarten |
| Knotion | K3.GE.B.4 | Utiliza el lenguaje formal para describir y comparar las características de objetos que tienen la forma del cuadrado, el triángulo y el círculo. | Kindergarten |
| Knotion | K3.GE.B.6 | Forma cuadrados y triángulos a partir de la combinación de cuadrados, rectángulos o triángulos de menor tamaño. | Kindergarten |
| Knotion | K3.MYD.A.1 | Relaciona los instrumnetos de medición con el atributo del objeto. | Kindergarten |
| Knotion | K3.MYD.A.2 | Hace dibujos para registrar los objetos de una colección en diversas situaciones. | Kindergarten |
| Knotion | K3.MYD.B.3 | Dado un número, selecciona objetos para formar una colección que tenga la misma, mayor o menor numerosidad. | Kindergarten |
| Knotion | K3.OYPA.A.1 | Relaciona las acciones de aumentar y disminuir con la suma y con la resta. | Kindergarten |
| Knotion | K3.OYPA.A.2 | Resuelven problemas verbales de sumal y resta, y suman y restan hasta 10, por ejemplo, utilizar objetos o dibujos para representar el problema. | Kindergarten |
| Knotion | K3.OYPA.A.3 | Utiliza material concreto, dibujos y/o números para descomponer números menores a veinte como la suma de una decena y las unidades faltantes. | Kindergarten |
| Knotion | K3.OYPA.A.4 | Para cualquier número entre el 1 al 9, encuentran el número que llega al 10 cuando se le suma al número determinado, por ejemplo, al utiizar objetos o dibujos, y representar la respuesta con un dibujo o una ecuación. | Kindergarten |
| Knotion | K3.OYPA.A.5 | Suman y restan con fluidez de y hasta el número 5. | Kindergarten |
| Knotion | K3.SND.A.1 | Componen y descomponen números del 11 al 19 en diez unidades y algunas más, por ejemplo, al utilizar objetos o dibujos, y representar cada composición o descomposición por medio de un dibujo o ecuación (por ejemplo, 18 = 10 + 8); comprenden que estos números están compuestos por diez unidades y una, dos, tres, cuatro, cinco, seis, siete, ocho o nueve unidades. | Kindergarten |
| Knotion | 1.GE.A.1 | Distinguen entre los atributos que definen las figuras geométricas (por ejemplo, los triángulos son cerrados con tres lados) y los atributos que no las definen (por ejemplo, color, orientación, o tamaño general); construyen y dibujan figuras geométricas que tienen atributos definidos. | Grade 1 |
| Knotion | 1.GE.A.2 | Componen figuras de dos dimensiones (rectángulos, cuadrados, trapezoides, triángulos, semicírculos y cuartos de círculos) o figuras geométricas de tres dimensiones (cubos, prismas rectos rectangulares, conos circulares rectos, y cilindros circulares rectos) para crear formas compuestas, y componer figuras nuevas de las compuestas. | Grade 1 |
| Knotion | 1.GE.A.3 | Parten círculos y rectángulos en dos y cuatro partes iguales , describen las partes utilizando las palabras mitades, cuartos, y cuartas partes, y usan las frases: la mitad de, cuarto de y una cuarta parte de. Describen un entero como un compuesto de dos o cuatro partes. Comprenden con estos ejemplos que la descomposición en varias partes iguales generan partes de menor tamaño. | Grade 1 |
| Knotion | 1.MYD.A.1 | Ordenan tres objetos según su longitud; comparan las longitudes de dos objetos indirectamente utilizando un tercer objeto. | Grade 1 |
| Knotion | 1.MYD.A.2 | Expresan la longitud de un objeto como un número entero de unidades de longitud, colocando copias de un objeto más corto (la unidad de longitud) de punta a punta; comprenden que la medida de la longitud de un objeto es la cantidad de unidades de una misma longitud que cubre al objeto sin espacios ni superposiciones. Se limita a contextos en los que el objeto que se está midiendo quede abarcado por un número entero de unidades de longitud sin espacios ni superposiciones. | Grade 1 |
| Knotion | 1.MYD.B.3 | Dicen y escriben la hora en medias horas utilizando relojes análogos y digitales. | Grade 1 |
| Knotion | 1.MYD.C.4 | Organizan, representan e interpretan datos que tienen hasta tres categorías; preguntan y responden a preguntas sobre la cantidad total de datos, cuántos hay en cada categoría, y si hay una cantidad mayor o menor entre las categorías. | Grade 1 |
| Knotion | 1.OYPA.A.1 | Utilizan la suma y la resta hasta el número 20 para resolver problemas verbales relacionados a situaciones en las cuales tienen que sumar, restar, unir, separar, y comparar, con valores desconocidos en todas las posiciones, por ejemplo, al representar el problema a través del uso de objetos, dibujos, y ecuaciones con un símbolo para el número desconocido. | Grade 1 |
| Knotion | 1.OYPA.B.3 | Aplican las propiedades de las operaciones como estrategias para sumar y restar. 3 Ejemplos: Si saben que 8 + 3 = 11, entonces, saben también que 3 + 8 = 11 (Propiedad conmutativa de la suma). Para sumar 2 + 6 + 4, los últimos dos números se pueden sumar para obtener el número 10, por lo tanto 2 + 6 + 4 = 2 + 10 = 12 (Propiedad asociativa de la suma). | Grade 1 |
| Knotion | 1.OYPA.B.4 | Comprenden la resta como un problema de un sumando desconocido. | Grade 1 |
| Knotion | 1.OYPA.C.5 | Relacionan el conteo con la suma y la resta (por ejemplo, al contar de 2 en 2 para sumar 2). | Grade 1 |
| Knotion | 1.OYPA.C.6 | Suman y restan hasta el número 20, demostrando fluidez al sumar y al restar hasta 10. Utilizan estrategias tales como el contar hacia adelante; el formar diez; el descomponer un número para obtener el diez ; el utilizar la relación entre la suma y la resta ; y el crear sumas equivalentes pero más sencillas o conocidas. | Grade 1 |
| Knotion | 1.OYPA.D.7 | Entienden el significado del signo igual, y determinan si las ecuaciones de suma y resta son verdaderas o falsas. Por ejemplo, ¿Cuáles de las siguientes ecuaciones son verdaderas y cuáles son falsas? 6 = 6, 7 = 8 -1, 5 + 2 = 2 + 5, 4 + 1 = 5 + 2. | Grade 1 |
| Knotion | 1.OYPA.D.8 | Determinan el número entero desconocido en una ecuación de suma o resta que relaciona tres números enteros. Por ejemplo, determinan el número desconocido que hace que la ecuación sea verdadera en cada una de las siguientes ecuaciones. | Grade 1 |
| Knotion | 1.SND.A.1 | Cuentan hasta 120, comenzando con cualquier número menor que 120. Dentro de este rango, leen y escriben numerales que representan una cantidad de objetos con un numeral escrito. | Grade 1 |
| Knotion | 1.SND.B.2 | Entienden que los dos dígitos de un número de dos dígitos representan cantidades de decenas y unidades. Entienden lo siguiente como casos especiales: 10 puede considerarse como un conjunto de 10 unidades llamado una decena. Los números entre 11 y 19 se componen por una decena y una, dos, tres, cuatro, cinco, seis, siete, ocho o nueve unidades. Los números 10, 20, 30, 40, 50, 60, 70, 80 y 90 se referieren a una, dos, tres, cuatro, cinco, seis, siete, ocho o nueve decenas (y 0 unidades). | Grade 1 |
| Knotion | 1.SND.B.3 | Comparan dos números de dos dígitos basándose en el significado de los dígitos en las unidades y decenas, anotando los resultados de las comparaciones con el uso de los símbolos >, =, y <. | Grade 1 |
| Knotion | 1.SND.C.4 | Suman hasta el 100, incluyendo el sumar un número de dos dígitos y un número de un dígito, así como el sumar un número de dos dígitos y un múltiplo de 10, utilizan modelos concretos o dibujos y estrategias basadas en el valor de posición, las propiedades de las operaciones, y/o la relación entre la suma y la resta; relacionan la estrategia con un método escrito, y explican el razonamiento aplicado. Entienden que al sumar números de dos dígitos, se suman decenas con decenas, unidades con unidades; y a veces es necesario el componer una decena. | Grade 1 |
| Knotion | 1.SND.C.5 | Dado un número de dos dígitos, hallan mentalmente 10 más o 10 menos que un número, sin la necesidad de contar; explican el razonamiento que utilizaron. | Grade 1 |
| Knotion | 1.SND.C.6 | Restan múltiplos de 10 en el rango de 10 a 90 a partir de múltiplos de 10 en el rango de 10 a 90 (con diferencias positivas o de cero), utilizando ejemplos concretos o dibujos, y estrategias basadas en el valor de posición, las propiedades de operaciones, y/o la relación entre la suma y la resta; relacionan la estrategia con un método escrito y explican el razonamiento utilizado. | Grade 1 |
| Knotion | 2.GE.A.1 | Reconocen y dibujan figuras que tengan atributos específicos, tales como un número dado de ángulos o un número dados de lados iguales. Identifican triángulos, cuadriláteros, pentágonos, hexágonos, y cubos. | Grade 2 |
| Knotion | 2.GE.A.2 | Dividen un rectángulo en hileras y columnas de cuadrados del mismo tamaño y cuentan para encontrar el número total de los mismos. | Grade 2 |
| Knotion | 2.GE.A.3 | Dividen círculos y rectángulos en dos, tres, o cuatro partes iguales, describen las partes usando las palabras medios, tercios, la mitad de, la tercera parte de, etc., y describen un entero como dos medios, tres tercios, cuatro cuartos. Reconocen que las partes iguales de enteros idénticos no necesariamente tienen que tener la misma forma. | Grade 2 |
| Knotion | 2.MYD.A.1 | Miden la longitud de un objeto seleccionando y usando herramientas apropiadas tales como reglas, yardas, reglas métricas, y cintas de medir. | Grade 2 |
| Knotion | 2.MYD.A.2 | Miden la longitud de un objeto dos veces, usando unidades de longitud de diferentes longitudes cada vez; describen como ambas medidas se relacionan al tamaño de la unidad escogida. | Grade 2 |
| Knotion | 2.MYD.A.4 | Miden para determinar cuanto más largo es un objeto que otro, y expresan la diferencia entre ambas longitudes usando una unidad de longitud estándar. | Grade 2 |
| Knotion | 2.MYD.B.5 | Usan la suma y la resta hasta 100 para resolver problemas verbales que envuelven longitudes dadas en unidades iguales, por ejemplo, al usar dibujos (como dibujos de reglas) y ecuaciones con un símbolo que represente el número desconocido en el problema. | Grade 2 |
| Knotion | 2.MYD.C.7 | Dicen y escriben la hora utilizando relojes análogos y digitales a los cinco minutos más cercanos, usando a.m. y p.m. | Grade 2 |
| Knotion | 2.MYD.C.8 | Resuelven problemas verbales relacionados a las billetes de dólar, monedas de veinticinco, de diez, de cinco y de un centavos, usando los símbolos $ y ¢ apropiadamente. Ejemplo; si tienes 2 monedas de diez centavos y 2 de centavo, ¿cuántos centavos tienes? | Grade 2 |
| Knotion | 2.MYD.D.10 | Dibijan una pictografía y una gráfica de barras (con escala unitaria) para representar un grupo de datos de hasta cuatro categorías. Resuelven problemas simples para unir, separar, y comparar usando la información representada en la gráfica de barras. | Grade 2 |
| Knotion | 2.MYD.D.9 | Generan datos de medición al medir las longitudes de varios objetos hasta la unidad entera más cercana, o al tomar las medidas del mismo objeto varias veces. Muestran las medidas por medio de un diagrama de puntos, en la cual la escala horizontal está marcada por unidades con números enteros. | Grade 2 |
| Knotion | 2.SND.A.1 | Comprenden que los tres dígitos de un número de tres dígitos representan cantidades de centenas, decenas y unidades; por ejemplo, 706 es igual a 7 centenas, 0 decenas y 6 unidades. Comprenden los siguientes casos especiales: 100 puede considerarse como un conjunto de diez decenas llamado centena. Los números 100, 200, 300, 400, 500, 600, 700, 800, 900 se refieren a una, dos, tres, cuatro, cinco, seis, siete, ocho o nueve centenas (y 0 decenas y 0 unidades). | Grade 2 |
| Knotion | 2.SND.A.2 | Cuentan hasta 1000; cuentan de 2 en 2, de 5 en 5, de 10 en 10, y de 100 en 100. | Grade 2 |
| Knotion | 2.SND.A.3 | Leen y escriben números hasta 1000 usando numerales en base diez, los nombres de los números, y en forma desarrollada. | Grade 2 |
| Knotion | 2.SND.A.4 | Comparan dos números de tres dígitos basándose en el significado de los dígitos de las centenas, decenas y las unidades usando los símbolos >, =, < para anotar los resultados de las comparaciones. | Grade 2 |
| Knotion | 2.OYPA.A.1 | Usan la suma y la resta hasta el número 100 para resolver problemas verbales de uno y dos pasos relacionados a situaciones en las cuales tienen que sumar, restar, unir, separar, y comparar, con valores desconocidos en todas las posiciones, por ejemplo, al representar el problema a través del uso de dibujos y ecuaciones con un símbolo para el número desconocido. | Grade 2 |
| Knotion | 2.OYPA.B.2 | Suman y restan con fluidez hasta el número 20 usando estrategias mentales. 2 Al final del segundo grado, saben de memoria todas las sumas de dos números de un solo dígito. | Grade 2 |
| Knotion | 2.OYPA.C.3 | Determinan si un grupo de objetos (hasta 20) tiene un número par o impar de miembros, por ejemplo, al emparejar objetos o al contar de dos en dos; escriben ecuaciones para expresar un número par como el resultado de una suma de dos sumandos iguales. | Grade 2 |
| Knotion | 2.OYPA.C.4 | Utilizan la suma para encontrar el número total de objetos colocados en forma rectangular con hasta 5 hileras y hasta 5 columnas; escriben una ecuación para expresar el total como la suma de sumandos iguales. | Grade 2 |
| Knotion | 2.SND.B.5 | Suman y restan hasta 100 con fluidez usando estrategias basadas en el valor de posicion, las propiedades de las operaciones, y/o la relación entre la suma y la resta. | Grade 2 |
| Knotion | 2.SND.B.6 | Suman hasta cuatro números de dos dígitos usando estrategias basadas en el valor decposiciona y las propiedades de las operaciones. | Grade 2 |
| Knotion | 2.SND.B.7 | Suman y restan hasta 1000, usando modelos concretos o dibujos y estrategias basadas en el valor de posición, las propiedades de las operaciones, y/o la relación entre la suma y la resta; relacionan la estrategia con un método escrito. Comprenden que al sumar o restar números de tres dígitos, se suman o restan centenas y centenas, decenas y decenas, unidades y unidades; y a veces es necesario componer y descomponer las decenas o las centenas. | Grade 2 |
| Knotion | 2.SND.B.8 | Suman mentalmente 10 ó 100 a un número dado del 100 a 900, y restan mentalmente 10 ó 100 de un número dado entre 100 a 900. | Grade 2 |
| Knotion | 3.FRA.A.1 | Comprenden una fracción 1/b como la cantidad formada por 1 parte cuando un entero se separa entre b partes iguales; comprenden una fracción a/b como la cantidad formada por partes a de tamaño 1/b. | Grade 3 |
| Knotion | 3.FRA.A.2 | Entienden una fracción como un número en una recta numérica; representan fracciones en un diagrama de recta numérica. a. Representan una fracción 1/b en una recta numérica al definir el intervalo del 0 al 1 como el entero y marcándolo en b partes iguales. Reconocen que cada parte tiene un tamaño 1/b y que el punto final de la parte basada en 0 sirve para localizar el número 1/b en la recta numérica. b. Representan una fracción a/b en una recta numérica al marcar la longitud a en el espacio 1/b a partir del 0. Reconocen que el intervalo resultante tiene un tamaño a/b y que su punto final localiza el número a /b sobre la recta numérica. | Grade 3 |
| Knotion | 3.FRA.A.3 | Explican la equivalencia de las fracciones en casos especiales, y comparan las fracciones al razonar sobre su tamaño. a. Reconocen a dos fracciones como equivalentes (iguales) si tienen el mismo tamaño, o el mismo punto en una recta numérica. b. Reconocen y generan fracciones equivalentes simples, por ejemplo, 1/2 = 2/4; 4/6 = 2/3. Explican porqué las fracciones son equivalentes, por ejemplo, al utilizar un modelo visual de fracciones. c. Expresan números enteros como fracciones, y reconocen fracciones que son equivalentes a números enteros. Ejemplos: Expresan 3 en la forma 3 = 3/1; reconocen que 6/1 = 6; localizan 4/4 y 1 en el mismo punto de una recta numérica. d. Comparan dos fracciones con el mismo numerador o el mismo denominador al razonar sobre su tamaño. Reconocen que las comparaciones son válidas solamente cuando las dos fracciones hacen referencia al mismo entero. Anotan los resultados de las comparaciones con los símbolos >, = o <, y justifican las conclusiones, por ejemplo, usando un modelo visual de fracciones. | Grade 3 |
| Knotion | 3.GE.A.1 | Comprenden que las figuras geométricas en diferentes categorías (por ejemplo, rombos, rectángulos y otros) pueden compartir atributos (por ejemplo, tener cuatro lados), y que los atributos compartidos pueden definir una categoría más amplia (por ejemplo, cuadriláteros). Reconocen los rombos, los rectángulos, y los cuadrados como ejemplos de cuadriláteros, y dibujan ejemplos de cuadriláteros que no pertenecen a ninguna de estas sub-categorías. | Grade 3 |
| Knotion | 3.GE.A.2 | Dividen figuras geométricas en partes con áreas iguales. Expresan el área de cada parte como una fracción unitaria del entero. Por ejemplo, al dividir una forma en 4 partes con áreas iguales, y describen el área de cada parte como 1/4 del área de la figura. | Grade 3 |
| Knotion | 3.MYD.A.1 | Dicen y escriben la hora al minuto más cercano y miden intervalos de tiempo en minutos. Resuelven problemas verbales de suma y resta sobre intervalos de tiempo en minutos, por ejemplo, al representar el problema en un diagrama de una recta numérica. | Grade 3 |
| Knotion | 3.MYD.A.2 | Miden y estiman volúmenes líquidos y las masas de los objetos utilizando las unidades estándares de gramos (g), kilogramos (kg), y litros (l). Suman, restan, multiplican, o dividen para resolver problemas verbales de un solo paso relacionados con masas o volúmenes dados en las mismas unidades, por ejemplo, al usar dibujos (un vaso de laboratorio graduado) para representar el problema. | Grade 3 |
| Knotion | 3.MYD.B.3 | Trazan una pictografía a escala y una gráfica de barra a escala para representar datos con varias categorías. Resuelven problemas de uno y dos pasos sobre cuántos más y cuántos menos utilizando la información presentada en gráficas de barra a escala. Por ejemplo, al dibujar una gráfica de barras en la cual cada cuadrado pudiera representar 5 mascotas. | Grade 3 |
| Knotion | 3.MYD.B.4 | Generan datos de medición al medir longitudes usando reglas marcadas con media pulgada y cuartos de pulgada. Muestran los datos trazando una línea, cuya escala horizontal queda marcada con las unidades apropiadas- números enteros, mitades, o cuartos. | Grade 3 |
| Knotion | 3.MYD.C.5 | Reconocen el área como un atributo de las figuras planas, y comprenden los conceptos de medición del área. a. Un cuadrado cuyos lados miden 1 unidad, se dice que tiene una unidad cuadrada de área y puede utilizarse para medir el área. b. Una figura plana que se puede cubrir sin espacios ni superposiciones por n unidades cuadradas se dice tener un área de n unidades cuadradas. | Grade 3 |
| Knotion | 3.MYD.C.6 | Miden áreas al contar unidades cuadradas (centímetros cuadrados, metros cuadrados, pulgadas cuadradas, pies cuadrados y unidades improvisadas). | Grade 3 |
| Knotion | 3.MYD.C.7 | Relacionan el área con las operaciones de multiplicación y suma. | Grade 3 |
| Knotion | 3.MYD.D.8 | Resuelven problemas de matemáticas y del mundo real relacionados con los perímetros de polígonos, incluyendo el encontrar el perímetro dadas las longitudes laterales, el encontrar la longitud desconocida de uno de los lados, y muestran rectángulos con el mismo perímetro y diferentes áreas o con la misma área y diferentes perímetros. | Grade 3 |
| Knotion | 3.OYPA.A.1 | Interpretan productos de números enteros, por ejemplo, interpretan 5 x 7 como la cantidad total de objetos en 5 grupos de 7 objetos cada uno. Por ejemplo, al describir un contexto en el que una cantidad total de objetos pueda expresarse como 5 x 7. | Grade 3 |
| Knotion | 3.OYPA.A.2 | Interpretan los cocientes de números enteros, por ejemplo, al interpretar 56 · 8 como la cantidad de objetos en cada parte cuando se reparten 56 objetos entre 8 partes iguales, o como una cantidad de partes cuando se reparten 56 objetos en grupos iguales de 8 objetos cada uno. Por ejemplo, al describir un contexto en el cual una cantidad de partes o una cantidad de grupos se puede expresar como 56 · 8. | Grade 3 |
| Knotion | 3.OYPA.A.3 | Utilizan operaciones de multiplicación y división hasta el número 100 para resolver problemas verbales en situaciones relacionados con grupos iguales, matrices, y cantidades de medición, por ejemplo, al usar dibujos y ecuaciones con un símbolo para el número desconocido al representar el problema. | Grade 3 |
| Knotion | 3.OYPA.A.4 | Determinan el número entero desconocido en una ecuación de multiplicación o división relacionada con tres números enteros. Por ejemplo, al determinar el número desconocido que hace que la ecuación sea verdadera en cada una de las siguientes ecuaciones: 8 × ? = 48, 5 = ? - 3, 6 × 6 = ? | Grade 3 |
| Knotion | 3.OYPA.B.5 | Aplican propiedades de operaciones como estrategias para multiplicar y dividir. Ejemplos: Si se sabe que 6 x 4 = 24, entonces también se sabe que 4 x 6 = 24 (Propiedad conmutativa de la multiplicación). Se puede hallar 3 x 5 x 2 con 3 x 5 = 15, y luego 15 x 2 = 30, o con 5 x 2 = 10, y luego 3 x 10 = 30 (Propiedad asociativa de la multiplicación). Al saber que 8 x 5 = 40 y que 8 x 2 = 16, se puede hallar que 8 x 7 es como 8 x (5 + 2) = (8 x 5) + (8 x 2) = 40 + 16 = 56 (Propiedad distributiva). | Grade 3 |
| Knotion | 3.OYPA.B.6 | Entender la división como un problema de factor desconocido. Por ejemplo, el hallar 32 · 8 al determinar el número que al multiplicarse por 8 da 32. | Grade 3 |
| Knotion | 3.OYPA.C.7 | Multiplican y dividen hasta el número 100 con facilidad, a través del uso de estrategias como la relación entre la multiplicación y la división (por ejemplo, al saber que 8 x 5 = 40, se sabe que 40 · 5 = 8), o las propiedades de las operaciones. Al final del Tercer grado, saben de memoria todos los productos de dos números de un sólo dígito. | Grade 3 |
| Knotion | 3.OYPA.D.8 | Resuelven problemas verbales de dos pasos utilizando las cuatro operaciones. Representan estos problemas utilizando ecuaciones con una letra que representa | Grade 3 |
| Knotion | 3.SND.A.1 | Utilizan el entendimiento del valor posicional para redondear los números enteros hasta la decena (10) o centena (100) más próxima. | Grade 3 |
| Knotion | 3.SND.A.2 | Suman y restan con facilidad hasta el número 1000 usando estrategias y algoritmos basados en el valor posicional, las propiedades de las operaciones, y/o la relación entre la suma y la resta. | Grade 3 |
| Knotion | 3.SND.A.3 | Multiplican números enteros de un sólo dígito por múltiplos de 10 en el rango del 10 a 90 (por ejemplo, 9 x 80, 5 x 60) usando estrategias basadas en el valor posicional y en las propiedades de las operaciones. | Grade 3 |
| Knotion | 4.FRA.A.1 | Explican por qué la fracción a/b es equivalente a la fracción (n × a)/(n × b) al utilizar modelos visuales de fracciones, poniendo atención a como el número y el tamaño de las partes difiere aún cuando ambas fracciones son del mismo tamaño. Utilizan este principio para reconocer y generar fracciones equivalentes. | Grade 4 |
| Knotion | 4.FRA.A.2 | Comparan dos fracciones con numeradores distintos y denominadores distintos, por ejemplo, al crear denominadores o numeradores comunes, o al comparar una fracción de referencia como 1/2. Reconocen que las comparaciones son válidas solamente cuando las dos fracciones se refieren al mismo entero. Anotan los resultados de las comparaciones con los símbolos >, = ó <, y justifican las conclusiones, por ejemplo, utilizando un modelo visual de fracciones. | Grade 4 |
| Knotion | 4.FRA.B.3 | Entienden la fracción a/b cuando a > 1 como una suma de fracciones 1/b. a. Entienden la suma y la resta de fracciones como la unión y la separación de partes que se refieren a un mismo entero. b. Descomponen de varias maneras una fracción en una suma de fracciones con el mismo denominador, anotando cada descomposición con una ecuación. Justifican las descomposiciones, por ejemplo, utilizando un modelo visual de fracciones. Ejemplos: 3/8 = 1/8 + 1/8 + 1/8 ; 3/8 = 1/8 + 2/8; 21/8 = 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8. c. Suman y restan números mixtos con el mismo denominador, por ejemplo, al reemplazar cada número mixto por una fracción equivalente, y/o al utilizar las propiedades de las operaciones y la relación entre la suma y la resta. d. Resuelven problemas verbales sobre sumas y restas de fracciones relacionados a un mismo entero y con el mismo denominador, por ejemplo, utilizando modelos visuales de fracciones y ecuaciones para representar el problema. | Grade 4 |
| Knotion | 4.FRA.B.4 | Aplican y amplían los conocimientos previos sobrela multiplicación para multiplicar una fracción por un número entero. a. Entienden que una fracción a/b es un múltiplo de 1/b. Por ejemplo, utilizan un modelo visual de fracciones para representar 5/4 como el producto 5 × (1/4), anotando la conclusión mediante la ecuación 5/4 = 5 × (1/4). b.Entienden que un múltiplo de a/b es un múltiplo de 1/b, y utilizan este entendimiento para multiplicar una fracción por un número entero. Por ejemplo, utilizan un modelo visual de fracciones para expresar 3 × (2/5) como 6 × (1/5), reconociendo el producto como 6/5. (En general, n × (a/b) = (n × a)/b). c. Resuelven problemas verbales relacionados a la multiplicación de una fracción por un número entero, por ejemplo, utilizan modelos visuales de fracciones y ecuaciones para representar el problema. Por ejemplo, si cada persona en una fiesta come 3/8 de una libra de carne, y hay 5 personas en la fiesta, ¿cuántas libras de carne se necesitaran? ¿Entre qué números enteros está tu respuesta? | Grade 4 |
| Knotion | 4.FRA.C.5 | Expresan una fracción con denominador 10 como una fracción equivalente con denominador 1000, y utilizan esta técnica para sumar dos fracciones condenominadores respectivos de 10 y 1000. Por ejemplo, expresan 3/10 como 30/100 y suman 3/10 + 4/100 = 34/100. | Grade 4 |
| Knotion | 4.FRA.C.6 | Utilizan la notación decimal para las fracciones con denominadores de 10 ó 100. Por ejemplo, al escribir 0.62 como 62/100; al describir una longitud como 0.62 metros; al localizar 0.62 en una recta numérica. | Grade 4 |
| Knotion | 4.FRA.C.7 | Comparan dos decimales hasta las centésimas al razonar sobre su tamaño. Reconocen que las comparaciones son válidas solamente cuando ambos decimales se refieren al mismo entero. Anotan los resultados de las comparaciones con los símbolos >, = ó <, y justifican las conclusiones, por ejemplo, utilizando una recta numérica u otro modelo visual. (CA) | Grade 4 |
| Knotion | 4.GE.A.1 | Dibujan puntos, rectas, segmentos de rectas, semirrectas, ángulos (rectos, agudos, obtusos), y rectas perpendiculares y paralelas. Identifican estos elementos en las figuras bidimensionales. | Grade 4 |
| Knotion | 4.GE.A.2 | Clasifican las figuras bidimensionales basándoseen la presencia o ausencia de rectas paralelas o perpendiculares, o en la presencia o ausencia deángulos de un tamaño especificado. Reconocen que los triángulos rectos forman una categoría en sí, e identifican triángulos rectos. | Grade 4 |
| Knotion | 4.GE.A.3 | Reconocen que en una figura bidimensional, el eje de simetría es una recta que corta la figura de tal manera que la figura se puede doblar a lo largo de la recta en partes exactamente iguales. Identifican figuras con simetría axial y dibujan ejes de simetría. | Grade 4 |
| Knotion | 4.MYD.A.1 | Reconocen los tamaños relativos de las unidadesde medición dentro de un sistema de unidades, incluyendo km, m, cm; kg, g; lb, oz.; L, mL; h, min, s. Dentro de un mismo sistema de medición, expresan las medidas en una unidad más grande en términos de una unidad más pequeña. Anotan las medidas equivalentes en una tabla de dos columnas. Por ejemplo, saben que 1 pie es 12 veces más largo que 1 pulgada. Expresan la longitud de una culebra de 4 pies como 48 pulgadas. Generan una tabla de conversión para pies y pulgadas con una lista de pares de números (1, 12), (2, 24), (3, 36), ... | Grade 4 |
| Knotion | 4.MYD.A.2 | Utilizan las cuatro operaciones para resolver problemas verbales sobre distancias, intervalos de tiempo, volúmenes líquidos, masas de objetos y dinero, incluyendo problemas con fracciones simples o decimales, y problemas que requieren expresar las medidas dadas en una unidad más grande en términos de una unidad más pequeña. Representan cantidades medidas utilizando diagramas tales como rectas numéricas con escalas de medición. | Grade 4 |
| Knotion | 4.MYD.A.3 | Aplican fórmulas de área y perímetro de rectángulos para resolver problemas matemáticos y del mundo real. Por ejemplo, hallan el ancho de una habitación rectangular dadas el área y la longitud del piso, usando la fórmula del área como una ecuación de multiplicación con un factor desconocido. | Grade 4 |
| Knotion | 4.MYD.B.4 | Hacen un diagrama de puntos para representar un conjunto de datos de medidas en fracciones de una unidad (1/2, 1/4, 1/8). Resuelven problemas sobre sumas y restas de fracciones utilizando la información presentada en los diagramas de puntos. Por ejemplo, al utilizar un diagrama de puntos, hallan e interpretan la diferencia de longitud entre los ejemplares más largos y más cortos en una colección de insectos. | Grade 4 |
| Knotion | 4.MYD.C.5 | Reconocen que los ángulos son elementos geométricos formados cuando dos semirrectas comparten un extremo común, y entienden los conceptos de la medición de ángulos. a. Un ángulo se mide con respecto a un círculo, con su centro en el extremo común de las semirrectas, tomando en cuenta la fracción del arco circular entre los puntos donde ambas semirrectas intersecan el círculo. Un ángulo que pasa por 1/360 de un círculo se llama ángulo de un gradoy se puede utilizar para medir ángulos. b. Un ángulo que pasa por n ángulos de un grado tiene una medida angular de n grados. | Grade 4 |
| Knotion | 4.MYD.C.6 | Miden ángulos en grados de números enteros utilizando un transportador. Dibujan ángulos con medidas dadas. | Grade 4 |
| Knotion | 4.MYD.C.7 | Reconocen la medida de un ángulo como una suma. Cuando un ángulo se descompone en partes que no se superponen, la medida del ángulo entero es la suma de las medidas de los ángulos de las partes. Resuelven problemas de suma y resta para encontrar ángulos desconocidos en problemas del mundo real y en problemas matemáticos, por ejemplo, al usar una ecuación con un símbolo para la medida desconocida del ángulo. | Grade 4 |
| Knotion | 4.OYPA.A.1 | Interpretan una ecuación de multiplicación como una comparación, por ejemplo, 35 = 5x7 como un enunciado de que 35 es 5 veces 7, y 7 veces 5. Representan enunciados verbales de comparaciones multiplicativas como ecuaciones de multiplicación. | Grade 4 |
| Knotion | 4.OYPA.A.2 | Multiplican o dividen para resolver problemas verbales que incluyen comparaciones multiplicativas, por ejemplo, para representar el problema usando dibujos y ecuaciones con un símbolo para el número desconocido, distinguen una comparación multiplicativa de una comparación de suma. | Grade 4 |
| Knotion | 4.OYPA.A.3 | Resuelven problemas verbales de pasos múltiples con números enteros, cuya respuestas son números enteros, usando las cuatro operaciones, incluyendo problemas en los que los residuos deben ser interpretados. Representan estos problemas usando ecuaciones con una letra que representa la cantidad desconocida. Evalúan si las respuestas son razonables usando cálculos mentales y estrategias de estimación incluyendo el redondeo. | Grade 4 |
| Knotion | 4.OYPA.B.4 | Hallan todos los pares de factores de números enteros dentro del rango 1-100. Reconocen que un número entero es un múltiplo de cada uno de sus factores. Determinan si cierto número entero dentro del rango 1-100 es un múltiplo de cierto número de un solo dígito. Determinan si un número entero dentro del rango 1-100 es primo o compuesto. | Grade 4 |
| Knotion | 4.OYPA.C.5 | Generan un patrón de números o figuras que sigue una regla dada. Identifican las características aparentes del patrón que no eran explícitas en la regla misma. Por ejemplo, dada la regla ñadir 3 y con el número 1 para comenzar, generan términos en la secuencia resultante y observan que los términos parecen alternarse entre números impares y pares. Explican informalmente porqué los números continuarán alternándose de esta manera. | Grade 4 |
| Knotion | 4.SND.A.1 | Reconocen que en un número entero de dígitos múltiples, un dígito en determinado lugar representa diez veces lo que representa en el lugar a su derecha. Por ejemplo, reconocen que 700 · 70 = 10 al aplicar conceptos de valor de posición y de división. | Grade 4 |
| Knotion | 4.SND.A.2 | Leen y escriben números enteros con dígitos múltiples usando numerales en base diez, los nombres de los números, y sus formas desarrolladas. Comparan dos números de dígitos múltiples basándose en el valor de los dígitos en cada lugar, utilizando los símbolos >, = y < para anotar los resultados de las comparaciones. | Grade 4 |
| Knotion | 4.SND.A.3 | Utilizan la comprensión del valor de posición para redondear números enteros con dígitos múltiples a cualquier lugar. | Grade 4 |
| Knotion | 4.SND.B.4 | Suman y restan con fluidez los números enteros con dígitos múltiples utilizando el algoritmo convencional. | Grade 4 |
| Knotion | 4.SND.B.5 | Multiplican un número entero de hasta cuatro dígitos por un número entero de un dígito, y multiplican dos números de dos dígitos, utilizando estrategias basadas en el valor de posición y las propiedades de operaciones. Ilustran y explican el cálculo utilizando ecuaciones, matrices rectangulares, y/o modelos de área. | Grade 4 |
| Knotion | 4.SND.B.6 | Hallan cocientes y residuos de números enteros, a partir de divisiones con dividendos de hasta cuatrodígitos y divisores de un dígito, utilizando estrategias basadas en el valor de posición, las propiedades de las operaciones y/o la relación entre la multiplicación y la división. Ilustran y explican el cálculo utilizando ecuaciones, matrices rectangulares, y/o modelos de área. | Grade 4 |
| Knotion | 5.FRA.A.1 | Suman y restan fracciones con denominadores distintos (incluyendo números mixtos) reemplazando las fracciones dadas por fracciones equivalentes de tal forma que produzcan una suma equivalente o una resta con denominadores comunes. Por ejemplo, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (En general, a/b + c/d = (ad + bc) / bd). | Grade 5 |
| Knotion | 5.FRA.A.2 | Resuelven problemas verbales de suma y resta de fracciones que se refieran a un entero, incluyendo casos de denominadores distintos, por ejemplo, al emplear modelos visuales de fracciones o ecuaciones para representar el problema. Utilizan las fracciones de referencia y el sentido numérico para hacer cálculos mentales y evaluar la lógica de las respuestas. Por ejemplo, reconocen como incorrecto el resultado 2/5 + 1/2 = 3/7, observando que 3/7 < 1/2. | Grade 5 |
| Knotion | 5.FRA.B.3 | Interpretan una fracción como la división del numerador por el denominador (a/b = a·b). Resuelven problemas verbales relacionados a la división de números enteros que resulten en fracciones o números mixtos por ejemplo, emplean modelos visuales de fracciones o ecuaciones para representar el problema. Por ejemplo, al interpretar 3/4 como el resultado de la división de 3 entre 4, notando que 3/4 multiplicados por 4 es igual a 3, y que cuando se comparten igualmente 3 enteros entre 4 personas, cada persona termina con una parte de ¾ de tamaño. Si 9 personas quieren compartir, por igual y en base al peso, un saco de arroz de 50 libras, ¿cuántas libras de arroz debe recibir cada persona? ¿Entre qué números enteros se encuentra la respuesta? | Grade 5 |
| Knotion | 5.FRA.B.4 | Aplican y extienden conocimientos previos sobre la multiplicación para multiplicar una fracción o un número entero por una fracción. a. Interpretan el producto (a/b) × q como tantas partes a de la repartición de q en partes iguales de b; de manera equivalente, como el resultado de la secuencia de operaciones a × q · b. Por ejemplo, al emplear un modelo visual de fracciones para representar (2/3) × 4 = 8/3, y crear un contexto para esta ecuación. Hacen lo mismo con (2/3) × (4/5) = 8/15. (En general, (a /b) × (c /d) = ac/bd). b. Hallan el área de un rectángulo cuyos lados se miden en unidades fraccionarias, cubriéndolo con unidades cuadradas de la unidad fraccionaria correspondiente a sus lados, y demuestran que el área sería la misma que se hallaría si se multiplicaran las longitudes de los lados. Multiplican los números fraccionarios de las longitudes de los lados para hallar el área de rectángulos, y representar los productos de las fracciones como áreas rectangulares. | Grade 5 |
| Knotion | 5.FRA.B.5 | Interpretan la multiplicación como el poner a escala (cambiar el tamaño de) al: a. Comparan el tamaño de un producto al tamaño de un factor en base al tamaño del otro factor, sin efectuar la multiplicación indicada. b. Explican por qué al multiplicar un determinado número por una fracción mayor que 1 se obtiene un producto mayor que el número dado (reconocen la multiplicación de números enteros mayores que 1 como un caso común); explican por qué la multiplicación de determinado número por una fracción menor que 1 resulta en un producto menor que el número dado; y relacionan el principio de las fracciones equivalentes a/b = (n x a) / (n x b) con el fin de multiplicar a/ b por 1. | Grade 5 |
| Knotion | 5.FRA.B.6 | Resuelven problemas del mundo real relacionados a la multiplicación de fracciones y números mixtos, por ejemplo, al usar modelos visuales de fracciones o ecuaciones para representar el problema. | Grade 5 |
| Knotion | 5.FRA.B.7 | Aplican y extienden conocimientos previos sobre la división para dividir fracciones unitarias entre números enteros y números enteros entre fracciones unitarias. a. Interpretan la división de una fracción unitaria entre un número entero distinto al cero, y calculan sus cocientes. Por ejemplo, crean el contexto de un cuento para (1/3) · 4, y utilizan un modelo visual de fracciones para expresar el cociente. Utilizan la relación entre la multiplicación y la división para explicar que (1/3) · 4 = 1/12 porque (1/12) × 4 = 1/3. b. Interpretan la división de un número entero entre una fracción unitaria y calculan sus cocientes. Por ejemplo, crean en el contexto de un cuento 4 · (1/5), y utilizan un modelo visual de fracciones para expresar el cociente. Utilizan la relación entre la multiplicación y la división para explicar que 4 · (1/5) =20 porque 20 ×(1/5)= 4. c. Resuelven problemas del mundo real relacionados a la división de fracciones unitarias entre números enteros distintos al cero y la división de números enteros entre fracciones unitarias, por ejemplo, utilizan modelos visuales de fracciones y ecuaciones para representar el problema. Por ejemplo, ¿cuánto chocolate tendrá cada persona si 3 personas comparten ½ libra de chocolate en partes iguales?¿Cuántas porciones de 1/3 de taza hay en 2 tazas de pasas? | Grade 5 |
| Knotion | 5.GE.A.1 | Utilizan un par de rectas numéricas perpendiculares, llamadas ejes, para definir un sistema de coordenadas, situando la intersección de las rectas (el origen) para que coincida con el 0 de cada recta y con un punto determinado en el plano que se pueda ubicar usando un par de números ordenados, llamados coordenadas. Entienden que el primer número indica la distancia que se recorre desde el origen en dirección sobre un eje, y el segundo número indica la distancia que se recorre sobre el segundo eje, siguiendo la convención de que los nombre de los dos ejes y los de las coordenadas correspondan (por ejemplo, el eje x con la coordenada x, el eje y con la coordenada y). | Grade 5 |
| Knotion | 5.GE.A.2 | Representan problemas matemáticos y del mundo real al representar gráficamente puntos en el primer cuadrante del plano de coordenadas e interpretan los valores de los puntos de las coordenadas según el contexto. | Grade 5 |
| Knotion | 5.GE.B.3 | Entienden que los atributos que pertenecen a una categoría de figuras bidimensionales también pertenecen a todas las subcategorías de dicha categoría. Por ejemplo, todos los rectángulos tienen cuatro ángulos rectos y los cuadrados son rectángulos; por lo tanto, todos los cuadrados tienen cuatro ángulos rectos. | Grade 5 |
| Knotion | 5.GE.B.4 | Clasifican las figuras bidimensionales dentro de una jerarquía, según sus propiedades. | Grade 5 |
| Knotion | 5.MYD.A.1 | Convierten unidades de medición estándar de diferentes tamaños dentro de un sistema de medición dado (por ejemplo, convierten 5 cm en 0.05 m), y utilizan estas conversiones en la solución de problemas de varios pasos y del mundo real. | Grade 5 |
| Knotion | 5.MYD.B.2 | Hacen un diagrama de puntos para mostrar un conjunto de medidas en unidades fraccionarias (1/2, 1/4, 1/8). Efectúan operaciones con fracciones apropiadas a este grado, para resolver problemas relacionados con la información presentada en los diagramas de puntos. Por ejemplo, dadas diferentes medidas de líquido en vasos idénticos de laboratorio, hallan la cantidad de líquido que cada vaso contiene si la cantidad total en todos los vasos fuera redistribuida igualmente. | Grade 5 |
| Knotion | 5.MYD.C.3 | Reconocen el volumen como un atributo de las figuras sólidas y entienden los conceptos de la medición del volumen. a. Se dice que un cubo con lados de 1 unidad, llamado unidad cúbica, tiene una unidad cúbica de volumen, y ésta se puede utilizar para medir el volumen. b. Se dice que una figura sólida que se puede rellenar con la unidad cúbica n sin dejar espacios o superposiciones tiene un volumen de n unidades cúbicas. | Grade 5 |
| Knotion | 5.MYD.C.4 | Miden volúmenes contando unidades cúbicas, utilizando centímetros cúbicos, pulgadas cúbicas, pies cúbicos, y otras unidades improvisadas. | Grade 5 |
| Knotion | 5.MYD.C.5 | Relacionan el volumen con las operaciones de multiplicación y suma para resolver problemas matemáticos y del mundo real relativos al volumen. | Grade 5 |
| Knotion | 5.OYPA.A.1 | Incorpora símbolos de agrupación como paréntesis, corchetes y llaves, para separar operaciones dentro de una expresión y denotar jerarquía de resolución. | Grade 5 |
| Knotion | 5.OYPA.A.2 | Escriben expresiones simples que contengan cálculos numéricos, e interpretan expresiones numéricas sin evaluarlas. Por ejemplo, expresan el cálculo suma 8 más 7, luego multiplica por 2 como 2 x (8 + 7). Reconocen que 3 x (18,932 + 921) es tres veces mayor que 18,932 + 921, sin tener que calcular la suma o producto indicado. | Grade 5 |
| Knotion | 5.OYPA.B.3 | Generan dos patrones numéricos utilizando dos reglas dadas. Identifican la relación aparente entre términos correspondientes. Forman pares ordenados que consisten de los términos correspondientes de ambos patrones, y marcan los pares ordenados en un plano de coordenadas. Por ejemplo, dada la regla Sumar 3 y el número inicial 0, y dada la regla Sumar 6 y el número inicial 0, generan los términos en cada secuencia y observan que cada término de una secuencia, es el doble que el término correspondiente en la otra secuencia. Explican informalmente por qué esto es así. | Grade 5 |
| Knotion | 5.SND.A.1 | Reconocen que en un número de varios dígitos, cualquier dígito en determinado lugar representa 10 veces lo que representa el mismo dígito en el lugar a su derecha y 1/10 de lo que representa en el lugar a su izquierda. | Grade 5 |
| Knotion | 5.SND.A.2 | Explican los patrones en la cantidad de ceros que tiene un producto cuando se multiplica un número por una potencia de 10, y explican los patrones en la posición del punto decimal cuando hay que multiplicar o dividir un decimal por una potencia de 10. Utilizan número enteros como exponentes para denotar la potencia de 10. | Grade 5 |
| Knotion | 5.SND.A.3 | Leen, escriben, y comparan decimales hasta las milésimas. | Grade 5 |
| Knotion | 5.SND.A.4 | Utilizan el entendimiento del valor de posición para redondear decimales a cualquier lugar. | Grade 5 |
| Knotion | 5.SND.B.5 | Multiplican números enteros de varios dígitos con fluidez, utilizando el algoritmo convencional. | Grade 5 |
| Knotion | 5.SND.B.6 | Encuentran números enteros como cocientes de números enteros con dividendos de hasta cuatro dígitos y divisores de dos dígitos, utilizando estrategias basadas en el valor de posición, las propiedades de las operaciones, y/o la relación entre la multiplicación y la división. Ilustran y explican el cálculo utilizando ecuaciones, matrices rectangulares y modelos de área. | Grade 5 |
| Knotion | 6.EXEC.A.1 | Escriben y evalúan expresiones numéricas relacionadas a los exponentes de números enteros. | Grade 6 |
| Knotion | 6.EXEC.A.2 | Escriben, leen y evalúan expresiones en las cuales las letras representan números. | Grade 6 |
| Knotion | 6.EXEC.A.3 | Aplican las propiedades de las operaciones para generar expresiones equivalentes. Por ejemplo, al aplicar la propiedad distributiva a la expresión 3(2 + x) para obtener la expresión equivalente 6 + 3x; al aplicar la propiedad distributiva a la expresión 24 + 18y para obtener la expresión equivalente 6(4x + 3y); al aplicar las propiedades de las operaciones a y + y + y para obtener la expresión equivalente 3y. | Grade 6 |
| Knotion | 6.EXEC.A.4 | . Identifican cuándo es que dos expresiones son equivalentes (por ejemplo: cuándo ambas expresiones simbolizan el mismo número sin importar el valor que se sustituya en ellas). Por ejemplo, la expresión y + y + y es equivalente a la expresión 3y porque ambas simbolizan el mismo número sin importar el número que represente y. | Grade 6 |
| Knotion | 6.EXEC.B.5 | Entienden el resolver una ecuación o una desigualdad como un proceso en el cual se contesta una pregunta: ¿qué valores de un conjunto especificado, si es que los hay, hacen que la ecuación o la desigualdad sea verdadera? Utilizan la sustitución para determinar si un número dado en un conjunto especificado hace que una ecuación o desigualdad sea verdadera. | Grade 6 |
| Knotion | 6.EXEC.B.6 | Utilizan variables para representar números y escribir expresiones al resolver problemas matemáticos o del mundo real; entienden que una variable puede representar un número desconocido, o, según el propósito, cualquier número en un conjunto especificado. | Grade 6 |
| Knotion | 6.EXEC.B.7 | Resuelven problemas matemáticos o del mundo real al escribir y resolver ecuaciones de la forma x + p = q además px = q en casos en los que p, q además de x son todos números racionales no negativos. | Grade 6 |
| Knotion | 6.EXEC.B.8 | Escriben una desigualdad de la forma x > c ó x c ó x < c tienen un número infinito de soluciones; representan las soluciones de dichas desigualdades sobre una recta numérica. | Grade 6 |
| Knotion | 6.EXEC.C.9 | Usan variables para representar dos cantidades que cambian en relación una con la otra, en un problema del mundo real; escriben una ecuación para expresar una cantidad, considerada como la variable dependiente, en términos de la otra cantidad, considerada como la variable independiente. Analizan la relación entre variables dependientes e independientes utilizando gráficas y tablas, y relacionan éstas a la ecuación. Por ejemplo, en un problema que tenga que ver con movimiento a velocidad constante, hacen una lista y una gráfica de pares ordenados de distancias y tiempos, y escriben la ecuación d = 65t para representar la relación entre la distancia y el tiempo. | Grade 6 |
| Knotion | 6.GE.A.3 | Dibujan polígonos en un plano de coordenadas dadas las coordenadas para los vértices; utilizan coordenadas para hallar la longitud de un lado que conecta dos puntos cuya primera o segunda coordenada es la misma. Aplican estas técnicas al contexto de la resolución de problemas matemáticos y del mundo real. | Grade 6 |
| Knotion | 6.GE.A.4 | Reconoce la relación entre un cuerpo geométrico y su desarrollo plano, y hallan el área total de estas figuras. Aplican estas técnicas al contexto de la resolución de problemas matemáticos y del mundo real. | Grade 6 |
| Knotion | 6.PRO.B.5 | Resumen conjuntos de datos numéricos en relación a su contexto, mediante: a. El reporte del número de observaciones. b. La descripción de la naturaleza del atributo bajo investigación, incluyendo la manera en que se midió y las unidades de medida que se utilizaron. c. Las medidas cuantitativas de tendencia central (mediana y/o media) y la variabilidad (rango entre cuartiles y/o desviación media absoluta), así como la descripción de cualquier patrón general y las desviaciones notables en ese patrón general, con referencia al contexto en el que se juntaron los datos. d. La relación entre la elección de las medidas de centro y la variabilidad a la forma de la distribución de los datos y el contexto en el que los datos se reunieron. | Grade 6 |
| Knotion | 6.RAZ.A.1 | Relaciona la noción de razón con proporción. | Grade 6 |
| Knotion | 6.RAZ.A.2 | Entienden el concepto de una tasa por unidad a/b asociada con una razón a:b para b ? 0, y utilizan el lenguaje de las tasas en el contexto de una relación de razones. Por ejemplo, Esta receta tiene una razón de 3 tazas de harina por 4 tazas de azúcar, asi que hay 3/4 de taza de harina por cada taza de azúcar. Pagamos $75 por 15 hamburguesas, lo cual es una tasa de $5 por hamburguesa. | Grade 6 |
| Knotion | 6.RAZ.A.3 | Utilizan el razonamiento sobre las razones y tasas para resolver problemas matemáticos y del mundo real, por ejemplo, al razonar sobre tablas de razones equivalentes, diagramas de cintas, diagramas de rectas numéricas dobles, o ecuaciones. | Grade 6 |
| Knotion | 6.SN.A.1 | Interpretan y calculan cocientes de fracciones, y resuelven problemas verbales relacionados a la división de fracciones entre fracciones. | Grade 6 |
| Knotion | 6.SN.B.2 | Dividen con facilidad números de múltiples dígito utilizando el algoritmo convencional. | Grade 6 |
| Knotion | 6.SN.B.3 | Suman, restan, multiplican y dividen decimales demúltiples dígitos utilizando el algoritmo convencional para cada operación, con facilidad. | Grade 6 |
| Knotion | 6.SN.C.5 | Entienden que los números positivos y negativos se usan juntos para describir cantidades que tienen valores o sentidos opuestos (por ejemplo, la temperatura sobre/bajo cero, la elevación sobre/bajo el nivel del mar, los créditos/débitos, la carga eléctrica positiva/negativa); utilizan números positivos y negativos para representar cantidades en contextos del mundo real, explicando el significado del 0 en cada situación. | Grade 6 |
| Knotion | 6.SN.C.6 | Entienden un número racional como un punto en una recta numérica. Extienden el conocimiento adquirido en los grados anteriores sobre las rectas numéricas y los ejes de coordenadas para representar puntos de números negativos en la recta y en el plano de coordenadas. | Grade 6 |
| Knotion | 6.SN.C.7 | Interpretan los enunciados de desigualdad como enunciados sobre la posición relativa de dos números en una recta numérica. Por ejemplo, al interpretar ?3 > ?7 como un enunciado de que ?3 está situado a la derecha de ?7 en una recta numérica orientada de izquierda a derecha. | Grade 6 |
| Knotion | 6.SN.C.8 | Resuelven problemas matemáticos y del mundo real al marcar puntos en los cuatro cuadrantes de un plano de coordenadas. Incluyen el uso de coordenadas y el valor absoluto para hallar las distancias entre puntos que tienen la misma primera o segunda coordenada. | Grade 6 |
| Knotion | 7.EXEC.A.1 | Aplican las propiedades de operaciones como estrategias para sumar, restar, factorizar y expander expresiones lineales con coeficientes racionales. | Grade 7 |
| Knotion | 7.EXEC.A.2 | Comprenden que el volver a escribir una expresión en diferentes formas en el contexto de un problema, puede aclarar algo sobre un problema y la forma en las que las cantidades se relacionan. Por ejemplo, a + a + 0.05a = 1.05a, significa que un aumento del 5% es lo mismo que multiplicar por 1.05. | Grade 7 |
| Knotion | 7.EXEC.A.3 | Resuelven problemas matemáticos de varios pasos relacionados con el mundo real, en los que se exponen números racionales positivos y negativos de cualquier tipo (números enteros, fracciones y decimales), al utilizar herramientas estratégicamente. Aplican las propiedades de operaciones con el fin de calcular números en cualquier forma; convierten números en cualquiera de sus formas según sea lo apropiado; y evaluan la racionalidad de las respuestas utilizando cálculos mentales y estrategias de estimación. Por ejemplo, si una mujer que gana $25 / hora obtiene un aumento del 10%, ganará 1/10 de su salario adicional por hora, o $2.50, lo que significa un salario nuevo de $27.50. Si se desea colocar un toallero de 93/4 pulgadas de largo en el centro de una puerta que tiene un ancho de 271/2 pulgadas, se deberá colocar la barra como a 9 pulgadas de distancia de cada borde; este estimado se puede usar para revisar el cálculo exacto. | Grade 7 |
| Knotion | 7.EXEC.A.4 | Utilizan variables para representar cantidades en problemas matemáticos o del mundo real, y para construir ecuaciones y ecuaciones de desigualdad simples para resolver problemas al razonar acerca de las cantidades. | Grade 7 |
| Knotion | 7.GE.A.1 | Resuelven problemas relacionados con dibujos aescala de figuras geométricas, incluyendo longitudes y áreas reales calculadas a partir de un dibujo a escala y reproducen un dibujo a escala en una escala diferente. | Grade 7 |
| Knotion | 7.GE.A.2 | Dibujan (a pulso, con regla y un transportador, y con recursos tecnológicos) figuras geométricas con ciertas condiciones dadas. Se concentran en la construcción de triángulos a partir de tres medidas de ángulos o lados, notan cuando las condiciones determinan un sólo triángulo, más de un triángulo o que no hay un triángulo. | Grade 7 |
| Knotion | 7.GE.A.3 | Describen las figuras bidimensionales que resultan al rebanar figuras tridimensionales en secciones planas de prismas rectangulares rectos y pirámides rectangulares rectas | Grade 7 |
| Knotion | 7.GE.B.4 | Saben las fórmulas para el área y circunferencia de un círculo y las utilizan para la solución de problemas; proveen una derivación informal de la relación entre la circunferencia y el área de un círculo. | Grade 7 |
| Knotion | 7.GE.B.5 | Utilizan las propiedades de ángulos suplementarios, complementarios, verticales y adyacentes en problemas de pasos múltiples para escribir y resolver ecuaciones simples para un ángulo desconocido en una figura. | Grade 7 |
| Knotion | 7.RAZ.A.1 | Calculan razones unitarias relacionadas con proporciones de fracciones, incluyendo relaciones de longitud, áreas y otras cantidades medidas en unidades similares o diferentes. Por ejemplo, si una persona camina 1/2 milla en 1/4 de hora, calculan la tasa de unidad como la fracción completa de 1/2 · 1/4 millas por hora, que equivale a 2 millas por hora. | Grade 7 |
| Knotion | 7.RAZ.A.2 | Reconocen y representan relaciones de proporcionalidad entre cantidades. | Grade 7 |
| Knotion | 7.RAZ.A.3 | Utilizan relaciones de proporcionalidad para solucionar problemas de pasos multiple, sobre razones y porcentaje. Ejemplos: interés simple, impuestos, márgenes de ganancias o rebajas, propinas y comisiones, honorarios, aumentos y disminuciones en los porcentajes, porcentaje de errores. | Grade 7 |
| Knotion | 7.SN.A.1 | Describen situaciones en las que se combinen cantidades opuestas para obtener 0. Por ejemplo, un átomo de hidrógeno tiene una carga 0 debido a que sus dos elementos tienen tiene cargas opuestas. | Grade 7 |
| Knotion | 7.SN.A.2 | Comprenden que la multiplicación se extiende desde fracciones hasta números racionales al requerir que las operaciones continúen satisfaciendo las propiedades de las operaciones, particularmente la propiedad distributiva, dando resultado a productos tales como (-1) (-1) = 1, y las reglas para multiplicar números con sus signos correspondientes. Interpretan los productos de números racionales al describir contextos del mundo real. | Grade 7 |
| Knotion | 7.SN.A.3 | Resuelven problemas matemáticos y del mundo real relacionados con las cuatro operaciones con números racionales. | Grade 7 |
| Knotion | 8.EXEC.A.1 | Conocen y aplican las propiedades de los exponentes enteros para generar expresiones numéricas equivalentes. | Grade 8 |
| Knotion | 8.EXEC.A.2 | Usan los símbolos de la raíz cuadrada y la raíz cúbica para representar soluciones a ecuaciones del tipo x2 = p y x3 = p, donde p es un número racional positivo. Evaluan las raíces cuadradas de cuadrados perfectos pequeños y las raíces cúbicas de cubos perfectos pequeños. Saben que ?2 es irracional. | Grade 8 |
| Knotion | 8.EXEC.A.3 | Usan números expresados mediante un único dígito multiplicado por una potencia de 10 de un entero para estimar cantidades muy grandes o muy pequeñas, y para expresar cuantas veces mayor es una cantidad con respecto a otra. Por ejemplo, al estimar la población de los Estados Unidos como 3 × 108 y la población del mundo como 7 × 109 , y determinar que la población del mundo es más de 20 veces más grande. | Grade 8 |
| Knotion | 8.EXEC.A.4 | Realizan operaciones con números expresados en notación científica, incluyendo problemas donde se utilicen ambas la notación decimal y científica. Usan notación científica y escogen unidades de tamaño apropiado para medir cantidades muy grandes o muy pequeñas (por ejemplo, usan milímetros por año para la expansión del lecho marino). Interpretan la notación científica que ha sido generada por medio de tecnología. | Grade 8 |
| Knotion | 8.EXEC.B.5 | Grafican relaciones proporcionales, interpretando la tasa unitaria como la pendiente de la gráfica. Comparan dos relaciones proporcionales diferentes representadas de manera diferente. Por ejemplo, comparan una gráfica de tiempo-distancia con una ecuación de tiempo y distancia para determinar cuál de los dos objetos en movimiento tiene una velocidad mayor. | Grade 8 |
| Knotion | 8.EXEC.B.6 | Usan triángulos similares para explicar porqué la pendiente m es igual entre dos puntos definidos sobre una línea no vertical en el plano de coordenadas; derivan la ecuación y = mx para una línea a través del origen y la ecuación y = mx + b para una línea que interseca el eje vertical en b. | Grade 8 |
| Knotion | 8.EXEC.C.7 | Dan ejemplos de ecuaciones lineales de una variable con una solución, muchas soluciones infinitas, o sin solución. Demuestran cuál de estas posibilidades es el caso al transformar sucesivamente la ecuación dada en formas más simples, hasta que resulte una ecuación equivalente del tipo x = a, a = a, o a = b (donde a y b son números diferentes). | Grade 8 |
| Knotion | 8.EXEC.C.8 | Comprenden que las soluciones para un sistema de dos ecuaciones lineales con dos variables corresponden a puntos de intersección de sus gráficas, porque los puntos de intersección satisfacen ambas ecuaciones simultáneamente. | Grade 8 |
| Knotion | 8.FUN.A.1 | Comprenden que una función es una regla que asigna exactamente una salida a cada entrada. La gráfica de una función es el conjunto de pares ordenados que consiste de una entrada y la salida correspondiente. | Grade 8 |
| Knotion | 8.FUN.A.2 | Comparan propiedades de dos funciones, cada una de las cuales está representada de manera diferente (algebraicamente, gráficamente, numéricamente en tablas, o por descripciones verbales). Por ejemplo, dada una función lineal representada por una tabla de valores y una función lineal representada por una expresión algebraica, determinan cual función tiene la mayor tasa de cambio. | Grade 8 |
| Knotion | 8.FUN.A.3 | Interpretan la ecuación y = mx + b como la definición de una función lineal, cuya gráfica es una línea recta; dan ejemplos de funciones que no son lineales. Por ejemplo, la función A = s2 produce el área de un cuadrado como una función de su longitud lateral no es lineal porque su gráfica contiene los puntos (1,1), (2,4) y (3,9), que no están sobre una línea recta | Grade 8 |
| Knotion | 8.FUN.B.4 | Construyen una función para representar una relación lineal entre dos cantidades. Determinan la tasa de cambio y el valor inicial de la función a partir de una descripción de una relación o a partir de dos valores (x, y), incluyendo leerlas en una tabla o en una gráfica. Interpretan la tasa de cambio y el valor inicial de una función lineal en términos de la situación que modela, y en términos de su gráfica o de una tabla de valores. | Grade 8 |
| Knotion | 8.FUN.B.5 | Describen de manera cualitativa la relación funcional entre dos cantidades al analizar una gráfica (por ejemplo, donde la función crece o decrece, es lineal o no lineal). Esbozan una gráfica que exhibe las características cualitativas de una función que ha sido descrita verbalmente. | Grade 8 |
| Knotion | 8.GE.A.2 | Entienden que una figura bidimensional es congruente con otra si se puede obtener la segunda a partir de la primera por una secuencia de rotaciones, reflexiones, y traslaciones; dadas dos figuras congruentes, describen una secuencia que exhibe la congruencia entre ellas. | Grade 8 |
| Knotion | 8.GE.A.3 | Describen el efecto de dilataciones, traslaciones, rotaciones, y reflexiones sobre figuras bidimensionales usando coordenadas. | Grade 8 |
| Knotion | 8.GE.A.4 | Entienden que una figura bidimensional es similar a otra si se puede obtener la segunda a partir de la primera por una secuencia de rotaciones, reflexiones, traslaciones, y dilataciones; dadas dos figuras bidimensionales similares, describen una secuencia que exhibe la semejanza entre ellas. | Grade 8 |
| Knotion | 8.GE.A.5 | Usan argumentos informales para establecer hechos sobre la suma de ángulos y el ángulo exterior de triángulos, sobre los ángulos creados cuando una transversal corta líneas paralelas, y el criterio ángulo-ángulo de la semejanza de triángulos. Por ejemplo, arreglan tres copias del mismo triángulo de manera que la suma de los tres ángulos parezca formar una línea, y dan un argumento en términos de transversales que explique porqué ocurre esto. | Grade 8 |
| Knotion | 8.GE.B.7 | Aplican el Teorema de Pitágoras para determinar las longitudes laterales desconocidas en triángulos rectos en problemas del mundo real y matemáticos en dos y tres dimensiones. | Grade 8 |
| Knotion | 8.GE.B.8 | Aplican el Teorema de Pitágoras para encontrar la distancia entre dos puntos en un sistema de coordenadas. | Grade 8 |
| Knotion | 8.GE.C.9 | Conocen las fórmulas de volumen para conos, cilindros, y esferas y las utilizan para resolver problemas matemáticos y del mundo real. | Grade 8 |
| Knotion | 8.PRO.A.1 | Construyen e interpretan diagramas de dispersión para datos bivariados entrada de medición para investigar patrones de asociación entre dos cantidades. Describen patrones como agrupaciones, valores atípicos, asociación positiva o negativa, asociación lineal, y asociación no lineal. | Grade 8 |
| Knotion | 8.PRO.A.2 | Saben que líneas rectas se utilizan ampliamente para modelar relaciones entre dos variables cuantitativas. Para diagramas de dispersión que sugieren una asociación lineal, ajustan informalmente una línea recta, y evalúan informalmente el ajuste del modelo juzgando la cercanía de los puntos de datos a la línea. | Grade 8 |
| Knotion | 8.SN.A.2 | Usan aproximaciones racionales de números irracionales para comparar el tamaño de números irracionales, ubicarlos aproximadamente sobre un diagrama numérico lineal, y estimar el valor de expresiones (por ejemplo, ?2). Por ejemplo, al truncar la expansión decimal de ?2 , demuestran que ?2 está entre 1 y 2, luego entre 1.4 y 1.5, y explican como continuar para obtener mejores aproximaciones. | Grade 8 |
| Knotion | A-APR.B.3 | Identifica los ceros de los polinomios cuando haya factorizaciones apropiadas y utiliza los ceros para construir un bosquejo gráfico de la función que define el polinomio. | Álgebra |
| Knotion | A-CED.A.2 | Crea ecuaciones en dos variables o más para representar relaciones entre cantidades; representa ecuaciones de forma gráfica en los ejes con etiquetas de referencia y escalas. | Álgebra |
| Knotion | A-SSE.A.2 | Utiliza la estructura de una expresión para identificar formas de volver a escribirla. | Álgebra |
| Knotion | A-SSE.B.3 | Elige y produce una forma equivalente de la expresión para revelar y explicar propiedades de la cantidad que representa. | Álgebra |
| Knotion | F-IF.A.2 | Utiliza la notación, evalúa las funciones de las variables independientes en sus dominios e interpreta las expresiones que usen la notación en términos del contexto. | Álgebra |
| Knotion | F-IF.B.4 | Para una función que modela una relación entre dos cantidades, interpreta las características fundamentales de las gráficas y las tablas en términos de las cantidades, y realiza bocetos de gráficas que muestren las características fundamentales tras recibir una descripción verbal de la relación. Entre las características fundamentales están: intersecciones; intervalos en los que la función es creciente, decreciente, positiva o negativa; máximos y mínimos relativos; simetrías; comportamiento en los extremos; y periodicidad. | Álgebra |
| Knotion | F-BF.A.1 | Escribe una función que describa la relación entre dos cantidades. | Álgebra |
| Knotion | F-IF.C.7 | Realiza gráficas de funciones expresadas de manera simbólica y muestra características fundamentales de la gráfica, a mano en casos sencillos y usando la tecnología para casos más complicados. | Álgebra |
| Knotion | S-ID.B.6 | Representa los datos en dos variables cuantitativas en un gráfico de dispersión y describe cómo se relacionan las variables. | Álgebra |
| Louisiana | K.CC.A.1 | Count to 100 by ones and by tens. | Kindergarten |
| Louisiana | K.CC.A.2 | Count forward beginning from a given number within the known sequence (instead of having to begin at 1). | Kindergarten |
| Louisiana | K.CC.A.3 | Write numbers from 0 to 20. Represent a number of objects with a written numeral 0–20 (with 0 representing a count of no objects). | Kindergarten |
| Louisiana | K.CC.B.4 | Understand the relationship between numbers and quantities; connect counting to cardinality. | Kindergarten |
| Louisiana | K.CC.B.5 | Count to answer “How many?” questions. | Kindergarten |
| Louisiana | K.CC.C.6 | Identify whether the number of objects in one group is greater than, less than, or equal to the number of objects in another group, e.g., by using matching and counting strategies. | Kindergarten |
| Louisiana | K.CC.C.7 | Compare two numbers between 1 and 10 presented as written numerals. | Kindergarten |
| Louisiana | K.G.A.1 | Describe objects in the environment using names of shapes, and describe the relative positions of these objects using terms such as above, below, beside, in front of, behind, and next to. | Kindergarten |
| Louisiana | K.G.A.2 | Correctly name shapes regardless of their orientations or overall size. | Kindergarten |
| Louisiana | K.G.A.3 | Identify shapes as two-dimensional (lying in a plane, “flat”) or three-dimensional (“solid”). | Kindergarten |
| Louisiana | K.G.B.4 | Analyze and compare two- and three-dimensional shapes, in different sizes and orientations, using informal language to describe their similarities, differences, parts (e.g., number of sides and vertices/“corners”) and other attributes (e.g., having sides of equal length). | Kindergarten |
| Louisiana | K.G.B.6 | Compose simple shapes to form larger shapes. | Kindergarten |
| Louisiana | K.MD.A.1 | Describe measurable attributes of objects, such as length or weight. Describe several measurable attributes of a single object. | Kindergarten |
| Louisiana | K.MD.A.2 | Directly compare two objects with a measurable attribute in common, to see which object has “more of”/“less of” the attribute, and describe the difference. | Kindergarten |
| Louisiana | K.MD.B.3 | Classify objects into given categories based on their attributes; count the numbers of objects in each category and sort the categories by count. | Kindergarten |
| Louisiana | K.MD.C.4 | Recognize pennies, nickels, dimes, and quarters by name and value (e.g., This is a nickel and it is worth 5 cents.) | Kindergarten |
| Louisiana | K.OA.A.1 | Represent addition and subtraction with objects, fingers, mental images, drawings, sounds (e.g., claps), acting out situations, verbal explanations, expressions, or equations. | Kindergarten |
| Louisiana | K.OA.A.2 | Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem. | Kindergarten |
| Louisiana | K.OA.A.3 | Decompose numbers less than or equal to 10 into pairs in more than one way, e.g., by using objects or drawings, and record each decomposition by a drawing or equation (e.g., 5 = 2 + 3 and 5 = 4 + 1). | Kindergarten |
| Louisiana | K.OA.A.4 | For any number from 1 to 9, find the number that makes 10 when added to the given number, e.g., by using objects or drawings, and record the answer with a drawing or equation. | Kindergarten |
| Louisiana | K.OA.A.5 | Fluently add and subtract within 5. | Kindergarten |
| Louisiana | 1.G.A.1 | Distinguish between defining attributes (e.g., triangles are closed and three-sided) versus non-defining attributes (e.g., color, orientation, overall size); build and draw shapes that possess defining attributes. | Grade 1 |
| Louisiana | 1.G.A.2 | Compose two-dimensional shapes (rectangles, squares, trapezoids, triangles, half-circles, and quarter-circles) and three-dimensional shapes (cubes, right rectangular prisms, right circular cones, and right circular cylinders) to create a composite shape, and compose new shapes from the composite shape. | Grade 1 |
| Louisiana | 1.G.A.3 | Partition circles and rectangles into two and four equal shares, describe the shares using the words halves, fourths, and quarters, and use the phrases half of, fourth of, and quarter of. Describe the whole as two of, or four of the shares. Understand for these examples that decomposing into more equal shares creates smaller shares. | Grade 1 |
| Louisiana | 1.MD.A.1 | Order three objects by length; compare the lengths of two objects indirectly by using a third object. | Grade 1 |
| Louisiana | 1.MD.A.2 | Express the length of an object as a whole number of length units, by laying multiple copies of a shorter object (the length unit) end to end; understand that the length measurement of an object is the number of same-size length units that span it with no gaps or overlaps. | Grade 1 |
| Louisiana | 1.MD.B.3 | Tell and write time in hours and half-hours using analog and digital clocks. | Grade 1 |
| Louisiana | 1.MD.C.4 | Organize, represent, and interpret data with up to three categories; ask and answer questions about the total number of data points, how many in each category, and how many more or less are in one category than in another. | Grade 1 |
| Louisiana | 1.MD.D.5 | Determine the value of a collection of coins up to 50 cents. (Pennies, nickels, dimes, and quarters in isolation; not to include a combination of different coins.) | Grade 1 |
| Louisiana | 1.NBT.A.1 | Count to 120, starting at any number less than 120. In this range, read and write numerals and represent a number of objects with a written numeral. | Grade 1 |
| Louisiana | 1.NBT.B.2 | Understand that the two digits of a two-digit number represent amounts of tens and ones. | Grade 1 |
| Louisiana | 1.NBT.B.3 | Compare two two-digit numbers based on meanings of the tens and ones digits, recording the results of comparisons with the symbols >, =, and <. | Grade 1 |
| Louisiana | 1.NBT.C.4 | Add within 100, including adding a two-digit number and a one-digit number, and adding a two-digit number and a multiple of 10. | Grade 1 |
| Louisiana | 1.NBT.C.5 | Given a two-digit number, mentally find 10 more or 10 less than the number, without having to count; explain the reasoning used. | Grade 1 |
| Louisiana | 1.NBT.C.6 | Subtract multiples of 10 in the range 10–90 from multiples of 10 in the range 10–90 (positive or zero differences), using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. | Grade 1 |
| Louisiana | 1.OA.A.1 | Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions (e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem). | Grade 1 |
| Louisiana | 1.OA.B.3 | Apply properties of operations to add and subtract. | Grade 1 |
| Louisiana | 1.OA.B.4 | Understand subtraction as an unknown-addend problem. For example, subtract 10 – 8 by finding the number that makes 10 when added to 8. | Grade 1 |
| Louisiana | 1.OA.C.5 | Relate counting to addition and subtraction (e.g., by counting on 2 to add 2). | Grade 1 |
| Louisiana | 1.OA.C.6 | Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use mental strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to a ten (e.g., 13 – 4 = 13 – 3 – 1 = 10 – 1 = 9); using the relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 – 8 = 4); and creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13). | Grade 1 |
| Louisiana | 1.OA.D.7 | Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false. | Grade 1 |
| Louisiana | 1.OA.D.8 | Determine the unknown whole number in an addition or subtraction equation relating three whole numbers. | Grade 1 |
| Louisiana | 2.G.A.1 | Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces. Identify triangles, quadrilaterals, pentagons, hexagons, and cubes. | Grade 2 |
| Louisiana | 2.G.A.2 | Partition a rectangle into rows and columns of same-size squares and count to find the total number of them. | Grade 2 |
| Louisiana | 2.G.A.3 | Partition circles and rectangles into two, three, or four equal shares, describe the shares using the words halves, thirds, half of, a third of, etc., and describe the whole as two halves, three thirds, four fourths. Recognize that equal shares of identical wholes need not have the same shape. | Grade 2 |
| Louisiana | 2.MD.A.1 | Measure the length of an object by selecting and using appropriate tools such as rulers, yardsticks, meter sticks, and measuring tapes. | Grade 2 |
| Louisiana | 2.MD.A.2 | Measure the length of an object twice, using length units of different lengths for the two measurements; describe how the two measurements relate to the size of the unit chosen. | Grade 2 |
| Louisiana | 2.MD.A.4 | Measure to determine how much longer one object is than another, expressing the length difference in terms of a standard length unit. | Grade 2 |
| Louisiana | 2.MD.B.5 | Use addition and subtraction within 100 to solve word problems involving lengths that are given in the same units, e.g., by using drawings (such as drawings of rulers) and equations with a symbol for the unknown number to represent the problem. | Grade 2 |
| Louisiana | 2.MD.C.7 | Tell and write time from analog and digital clocks to the nearest five minutes, using a.m. and p.m. | Grade 2 |
| Louisiana | 2.MD.C.8 | Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies, using $ and ¢ symbols appropriately. | Grade 2 |
| Louisiana | 2.MD.D.9 | Generate measurement data by measuring lengths of several objects to the nearest whole unit, or by making repeated measurements of the same object. Show the measurements by making a line plot, where the horizontal scale is marked off in whole-number units. | Grade 2 |
| Louisiana | 2.MD.D.10 | Draw a picture graph and a bar graph (with single-unit scale) to represent a data set with up to four categories. Solve simple put-together, take-apart, and compare problems using information presented in a bar graph. | Grade 2 |
| Louisiana | 2.NBT.A.1 | Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones. | Grade 2 |
| Louisiana | 2.NBT.A.2 | Count within 1000; skip-count by 5s, 10s, and 100s. | Grade 2 |
| Louisiana | 2.NBT.A.3 | Read and write numbers to 1000 using base-ten numerals, number names, and expanded form. | Grade 2 |
| Louisiana | 2.NBT.A.4 | Compare two three-digit numbers based on meanings of the hundreds, tens, and ones digits, using >, =, and < symbols to record the results of comparisons. | Grade 2 |
| Louisiana | 2.NBT.B.5 | Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction. | Grade 2 |
| Louisiana | 2.NBT.B.6 | Add up to four two-digit numbers using strategies based on place value and properties of operations. | Grade 2 |
| Louisiana | 2.NBT.B.7 | Add and subtract within 1000 using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; justify the reasoning used with a written explanation. Understand that in adding or subtracting three-digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds. | Grade 2 |
| Louisiana | 2.NBT.B.8 | Mentally add 10 or 100 to a given number 100–900, and mentally subtract 10 or 100 from a given number 100–900. | Grade 2 |
| Louisiana | 2.OA.A.1 | Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem. | Grade 2 |
| Louisiana | 2.OA.B.2 | Fluently add and subtract within 20 using mental strategies. By the end of Grade 2, know from memory all sums of two one-digit numbers. | Grade 2 |
| Louisiana | 2.OA.C.3 | Determine whether a group of objects (up to 20) has an odd or even number of members, e.g., by pairing objects or counting them by 2s; write an equation to express an even number as a sum of two equal addends. | Grade 2 |
| Louisiana | 2.OA.C.4 | Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends. | Grade 2 |
| Louisiana | 3.G.A.1 | Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories. | Grade 3 |
| Louisiana | 3.G.A.2 | Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole. | Grade 3 |
| Louisiana | 3.MD.A.1 | Understand time to the nearest minute. | Grade 3 |
| Louisiana | 3.MD.A.2 | Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l). Add, subtract, multiply, or divide to solve one-step word problems involving masses or volumes that are given in the same units, e.g., by using drawings (such as a beaker with a measurement scale) to represent the problem. | Grade 3 |
| Louisiana | 3.MD.B.3 | Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and two-step “how many more” and “how many less” problems using information presented in scaled bar graphs. | Grade 3 |
| Louisiana | 3.MD.B.4 | Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Show the data by making a line plot, where the horizontal scale is marked off in appropriate units—whole numbers, halves, or quarters. | Grade 3 |
| Louisiana | 3.MD.C.5 | Recognize area as an attribute of plane figures and understand concepts of area measurement. | Grade 3 |
| Louisiana | 3.MD.C.6 | Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units). | Grade 3 |
| Louisiana | 3.MD.C.7 | Relate area to the operations of multiplication and addition. | Grade 3 |
| Louisiana | 3.MD.D.8 | Solve real-world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters. | Grade 3 |
| Louisiana | 3.NF.A.1 | Understand a fraction 1/b, with denominators 2, 3, 4, 6, and 8, as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b. | Grade 3 |
| Louisiana | 3.NF.A.2 | Understand a fraction with denominators 2, 3, 4, 6, and 8 as a number on a number line diagram. | Grade 3 |
| Louisiana | 3.NF.A.3 | Explain equivalence of fractions with denominators 2, 3, 4, 6, and 8 in special cases, and compare fractions by reasoning about their size. | Grade 3 |
| Louisiana | 3.NBT.A.1 | Use place value understanding to round whole numbers to the nearest 10 or 100. | Grade 3 |
| Louisiana | 3.NBT.A.2 | Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction. | Grade 3 |
| Louisiana | 3.NBT.A.3 | Multiply one-digit whole numbers by multiples of 10 in the range 10–90 (e.g., 9 × 80, 5 × 60) using strategies based on place value and properties of operations. | Grade 3 |
| Louisiana | 3.OA.A.1 | Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each. | Grade 3 |
| Louisiana | 3.OA.A.2 | Interpret whole-number quotients of whole numbers, e.g., interpret 56 ÷ 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each. | Grade 3 |
| Louisiana | 3.OA.A.3 | Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem. | Grade 3 |
| Louisiana | 3.OA.A.4 | Determine the unknown whole number in a multiplication or division equation relating three whole numbers. | Grade 3 |
| Louisiana | 3.OA.B.5 | Apply properties of operations as strategies to multiply and divide. | Grade 3 |
| Louisiana | 3.OA.B.6 | Understand division as an unknown-factor problem. | Grade 3 |
| Louisiana | 3.OA.C.7 | Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 × 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers. | Grade 3 |
| Louisiana | 3.OA.D.8 | Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. | Grade 3 |
| Louisiana | 3.OA.D.9 | Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations. | Grade 3 |
| Louisiana | 4.G.A.1 | Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures. | Grade 4 |
| Louisiana | 4.G.A.2 | Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles. | Grade 4 |
| Louisiana | 4.G.A.3 | Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify line-symmetric figures and draw lines of symmetry. | Grade 4 |
| Louisiana | 4.MD.A.1 | Know relative sizes of measurement units within one system of units including ft, in; km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table. (Conversions are limited to one-step conversions.) | Grade 4 |
| Louisiana | 4.MD.A.2 | Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving whole numbers and/or simple fractions (addition and subtraction of fractions with like denominators and multiplying a fraction times a fraction or a whole number), and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. | Grade 4 |
| Louisiana | 4.MD.A.3 | Apply the area and perimeter formulas for rectangles in real-world and mathematical problems. | Grade 4 |
| Louisiana | 4.MD.B.4 | Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots. | Grade 4 |
| Louisiana | 4.MD.C.5 | Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement. | Grade 4 |
| Louisiana | 4.MD.C.6 | Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure. | Grade 4 |
| Louisiana | 4.MD.C.7 | Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real-world and mathematical problems, e.g., by using an equation with a letter for the unknown angle measure. | Grade 4 |
| Louisiana | 4.MD.D.8 | Recognize area as additive. Find areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas of the non-overlapping parts, applying this technique to solve real-world problems. | Grade 4 |
| Louisiana | 4.NBT.A.1 | Recognize that in a multi-digit whole number less than or equal to 1,000,000, a digit in one place represents ten times what it represents in the place to its right. | Grade 4 |
| Louisiana | 4.NBT.A.2 | Read and write multi-digit whole numbers less than or equal to 1,000,000 using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. | Grade 4 |
| Louisiana | 4.NBT.A.3 | Use place value understanding to round multi-digit whole numbers, less than or equal to 1,000,000, to any place. | Grade 4 |
| Louisiana | 4.NBT.B.4 | Fluently add and subtract multi-digit whole numbers with sums less than or equal to 1,000,000, using the standard algorithm. | Grade 4 |
| Louisiana | 4.NBT.B.5 | Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. | Grade 4 |
| Louisiana | 4.NBT.B.6 | Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. | Grade 4 |
| Louisiana | 4.NF.A.1 | Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. (Denominators are limited to 2, 3, 4, 5, 6, 8, 10, 12, and 100.) | Grade 4 |
| Louisiana | 4.NF.A.2 | Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model. (Denominators are limited to 2, 3, 4, 5, 6, 8, 10, 12, and 100.) | Grade 4 |
| Louisiana | 4.NF.B.3 | Understand a fraction a/b with a > 1 as a sum of fractions 1/b. (Denominators are limited to 2, 3, 4, 5, 6, 8, 10, 12, and 100.) | Grade 4 |
| Louisiana | 4.NF.B.4 | Multiply a fraction by a whole number. (Denominators are limited to 2, 3, 4, 5, 6, 8, 10, 12, and 100.) | Grade 4 |
| Louisiana | 4.NF.C.5 | Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100. | Grade 4 |
| Louisiana | 4.NF.C.6 | Use decimal notation for fractions with denominators 10 or 100. | Grade 4 |
| Louisiana | 4.NF.C.7 | Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual model. | Grade 4 |
| Louisiana | 4.OA.A.1 | Interpret a multiplication equation as a comparison and represent verbal statements of multiplicative comparisons as multiplication equations, e.g., interpret 35 = 5 x 7 as a statement that 35 is 5 times as many as 7, and 7 times as many as 5. | Grade 4 |
| Louisiana | 4.OA.A.2 | Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and/or equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison. | Grade 4 |
| Louisiana | 4.OA.A.3 | Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. | Grade 4 |
| Louisiana | 4.OA.B.4 | Using whole numbers in the range 1–100. | Grade 4 |
| Louisiana | 4.OA.C.5 | Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. | Grade 4 |
| Louisiana | 5.G.A.1 | Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number in the ordered pair indicates how far to travel from the origin in the direction of one axis, and the second number in the ordered pair indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate). | Grade 5 |
| Louisiana | 5.G.A.2 | Represent real-world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. | Grade 5 |
| Louisiana | 5.G.B.3 | Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. | Grade 5 |
| Louisiana | 5.G.B.4 | Classify quadrilaterals in a hierarchy based on properties. (Students will define a trapezoid as a quadrilateral with at least one pair of parallel sides.) | Grade 5 |
| Louisiana | 5.MD.A.1 | Convert among different-sized standard measurement units within a given measurement system, and use these conversions in solving multi-step, real-world problems (e.g., convert 5 cm to 0.05 m; 9 ft to 108 in). | Grade 5 |
| Louisiana | 5.MD.B.2 | Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. | Grade 5 |
| Louisiana | 5.MD.C.3 | Recognize volume as an attribute of solid figures and understand concepts of volume measurement. | Grade 5 |
| Louisiana | 5.MD.C.4 | Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. | Grade 5 |
| Louisiana | 5.MD.C.5 | Relate volume to the operations of multiplication and addition and solve real-world and mathematical problems involving volume. | Grade 5 |
| Louisiana | 5.NBT.A.1 | Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. | Grade 5 |
| Louisiana | 5.NBT.A.2 | Explain and apply patterns in the number of zeros of the product when multiplying a number by powers of 10. Explain and apply patterns in the values of the digits in the product or the quotient, when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. | Grade 5 |
| Louisiana | 5.NBT.A.3 | Read, write, and compare decimals to thousandths. | Grade 5 |
| Louisiana | 5.NBT.A.4 | Use place value understanding to round decimals to any place. | Grade 5 |
| Louisiana | 5.NBT.B.5 | Fluently multiply multi-digit whole numbers using the standard algorithm. | Grade 5 |
| Louisiana | 5.NBT.B.6 | Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, subtracting multiples of the divisor, and/or the relationship between multiplication and division. Illustrate and/or explain the calculation by using equations, rectangular arrays, area models, or other strategies based on place value. | Grade 5 |
| Louisiana | 5.NBT.B.7 | Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; justify the reasoning used with a written explanation. | Grade 5 |
| Louisiana | 5.NF.A.1 | Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. | Grade 5 |
| Louisiana | 5.NF.A.2 | Solve word problems involving addition and subtraction of fractions. | Grade 5 |
| Louisiana | 5.NF.B.3 | Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. | Grade 5 |
| Louisiana | 5.NF.B.4 | Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. | Grade 5 |
| Louisiana | 5.NF.B.5 | Interpret multiplication as scaling (resizing). | Grade 5 |
| Louisiana | 5.NF.B.6 | Solve real-world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. | Grade 5 |
| Louisiana | 5.NF.B.7 | Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. | Grade 5 |
| Louisiana | 5.OA.A.1 | Use parentheses or brackets in numerical expressions, and evaluate expressions with these symbols. | Grade 5 |
| Louisiana | 5.OA.A.2 | Write simple expressions that record calculations with whole numbers, fractions, and decimals, and interpret numerical expressions without evaluating them. | Grade 5 |
| Louisiana | 5.OA.B.3 | Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. | Grade 5 |
| Louisiana | 6.EE.A.1 | Write and evaluate numerical expressions involving whole-number exponents. | Grade 6 |
| Louisiana | 6.EE.A.2 | Write, read, and evaluate expressions in which letters stand for numbers. | Grade 6 |
| Louisiana | 6.EE.A.3 | Apply the properties of operations to generate equivalent expressions. | Grade 6 |
| Louisiana | 6.EE.A.4 | Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). | Grade 6 |
| Louisiana | 6.EE.B.5 | Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true. | Grade 6 |
| Louisiana | 6.EE.B.6 | Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set. | Grade 6 |
| Louisiana | 6.EE.B.7 | Solve real-world and mathematical problems by writing and solving equations and inequalities of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers. Inequalities will include , ≤, and ≥. | Grade 6 |
| Louisiana | 6.EE.B.8 | Write an inequality of the form x > c or x c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams. | Grade 6 |
| Louisiana | 6.EE.C.9 | Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. | Grade 6 |
| Louisiana | 6.G.A.1 | Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems. | Grade 6 |
| Louisiana | 6.G.A.2 | Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas V = lwh and V = Bh to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems. | Grade 6 |
| Louisiana | 6.G.A.3 | Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems. | Grade 6 |
| Louisiana | 6.G.A.4 | Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems. | Grade 6 |
| Louisiana | 6.RP.A.1 | Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. | Grade 6 |
| Louisiana | 6.RP.A.2 | Understand the concept of a unit rate a/b associated with a ratio a:b with b ≠ 0, and use rate language in the context of a ratio relationship. | Grade 6 |
| Louisiana | 6.RP.A.3 | Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. | Grade 6 |
| Louisiana | 6.SP.B.5 | Summarize numerical data sets in relation to their context, such as by: | Grade 6 |
| Louisiana | 6.NS.A.1 | Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. | Grade 6 |
| Louisiana | 6.NS.B.2 | Fluently divide multi-digit numbers using the standard algorithm. | Grade 6 |
| Louisiana | 6.NS.B.3 | Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation. | Grade 6 |
| Louisiana | 6.NS.C.5 | Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation. | Grade 6 |
| Louisiana | 6.NS.C.6 | Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates. | Grade 6 |
| Louisiana | 6.NS.C.7 | Understand ordering and absolute value of rational numbers. | Grade 6 |
| Louisiana | 6.NS.C.8 | Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. | Grade 6 |
| Louisiana | 7.EE.A.1 | Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients to include multiple grouping symbols (e.g., parentheses, brackets, and braces). | Grade 7 |
| Louisiana | 7.EE.A.2 | Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. | Grade 7 |
| Louisiana | 7.EE.B.3 | Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. | Grade 7 |
| Louisiana | 7.EE.B.4 | Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. | Grade 7 |
| Louisiana | 7.G.A.1 | Solve problems involving scale drawings of geometric figures, such as computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale. | Grade 7 |
| Louisiana | 7.G.A.2 | Draw (freehand, with ruler and protractor, or with technology) geometric shapes with given conditions. (Focus is on triangles from three measures of angles or sides, noticing when the conditions determine one and only one triangle, more than one triangle, or no triangle.) | Grade 7 |
| Louisiana | 7.G.A.3 | Describe the two-dimensional figures that result from slicing three-dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids. | Grade 7 |
| Louisiana | 7.G.B.4 | Know the formulas for the area and circumference of a circle and solve problems; give an informal derivation of the relationship between the circumference and area of a circle. | Grade 7 |
| Louisiana | 7.G.B.5 | Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and use them to solve simple equations for an unknown angle in a figure. | Grade 7 |
| Louisiana | 7.G.B.6 | Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. (Pyramids limited to surface area only.) | Grade 7 |
| Louisiana | 7.RP.A.1 | Compute unit rates associated with ratios of fractions, including ratios of lengths, areas, and other quantities measured in like or different units. | Grade 7 |
| Louisiana | 7.RP.A.2 | Recognize and represent proportional relationships between quantities. | Grade 7 |
| Louisiana | 7.RP.A.3 | Use proportional relationships to solve multi-step ratio and percent problems of simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, and percent error. | Grade 7 |
| Louisiana | 7.NS.A.1 | Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram. | Grade 7 |
| Louisiana | 7.NS.A.2 | Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers. | Grade 7 |
| Louisiana | 7.NS.A.3 | Solve real-world and mathematical problems involving the four operations with rational numbers. | Grade 7 |
| Louisiana | 8.EE.A.1 | Know and apply the properties of integer exponents to generate equivalent numerical expressions. | Grade 8 |
| Louisiana | 8.EE.A.2 | Use square root and cube root symbols to represent solutions to equations of the form x² = p and x³ = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that √2 is irrational. | Grade 8 |
| Louisiana | 8.EE.A.3 | Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other. | Grade 8 |
| Louisiana | 8.EE.A.4 | Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology. | Grade 8 |
| Louisiana | 8.EE.B.5 | Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. | Grade 8 |
| Louisiana | 8.EE.B.6 | Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b. | Grade 8 |
| Louisiana | 8.EE.C.7 | Solve linear equations in one variable. | Grade 8 |
| Louisiana | 8.EE.C.8 | Analyze and solve pairs of simultaneous linear equations. | Grade 8 |
| Louisiana | 8.F.A.1 | Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output. (Function notation is not required in this grade level.) | Grade 8 |
| Louisiana | 8.F.A.2 | Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). | Grade 8 |
| Louisiana | 8.F.A.3 | Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; categorize functions as linear or nonlinear when given equations, graphs, or tables. | Grade 8 |
| Louisiana | 8.F.B.4 | Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values. | Grade 8 |
| Louisiana | 8.F.B.5 | Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally. | Grade 8 |
| Louisiana | 8.G.A.1 | Verify experimentally the properties of rotations, reflections, and translations. | Grade 8 |
| Louisiana | 8.G.A.2 | Explain that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them. (Rotations are only about the origin and reflections are only over the y-axis and x-axis in Grade 8.) | Grade 8 |
| Louisiana | 8.G.A.3 | Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates. (Rotations are only about the origin, dilations only use the origin as the center of dilation, and reflections are only over the y-axis and x-axis in Grade 8.) | Grade 8 |
| Louisiana | 8.G.A.4 | Explain that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two-dimensional figures, describe a sequence that exhibits the similarity between them. (Rotations are only about the origin, dilations only use the origin as the center of dilation, and reflections are only over the y-axis and x-axis in Grade 8.) | Grade 8 |
| Louisiana | 8.G.A.5 | Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. | Grade 8 |
| Louisiana | 8.G.B.7 | Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions. | Grade 8 |
| Louisiana | 8.G.B.8 | Apply the Pythagorean Theorem to find the distance between two points in a coordinate system. | Grade 8 |
| Louisiana | 8.G.C.9 | Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems. | Grade 8 |
| Louisiana | 8.SP.A.1 | Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association. | Grade 8 |
| Louisiana | 8.SP.A.2 | Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line. | Grade 8 |
| Louisiana | 8.NS.A.2 | Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g., π²). | Grade 8 |
| Louisiana | A1: A-SSE.A.2 | Use the structure of an expression to identify ways to rewrite it. | High School |
| Louisiana | A1: A-SSE.B.3 | Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression. | High School |
| Louisiana | A1: A-APR.B.3 | Identify zeros of quadratic functions, and use the zeros to sketch a graph of the function defined by the polynomial. | High School |
| Louisiana | A1: A-CED.A.2 | Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. | High School |
| Louisiana | A1: A-CED.A.3 | Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. | High School |
| Louisiana | A1: A-REI.B.3 | Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. | High School |
| Louisiana | A1: F-IF.A.2 | Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. | High School |
| Louisiana | A1: F-IF.B.4 | For linear, piecewise linear (to include absolute value), quadratic, and exponential functions that model a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; and end behavior. | High School |
| Louisiana | A1: F-IF.C.7 | Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. | High School |
| Louisiana | A1: F-BF.A.1 | Write a linear, quadratic, or exponential function that describes a relationship between two quantities. | High School |
| Louisiana | A1: S-ID.B.6 | Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. | High School |
| Louisiana | A1: S-ID.C.8 | Compute (using technology) and interpret the correlation coefficient of a linear fit. | High School |
| Maine | K.CC.A.1 | Count to 100 by ones and by tens. | Kindergarten |
| Maine | K.CC.A.2 | Count forward beginning from a given number within the known sequence (instead of having to begin at 1). | Kindergarten |
| Maine | K.CC.A.3 | Write numbers from 0 to 20. Represent a number of objects with a written numeral 0-20 (with 0 representing a count of no objects). | Kindergarten |
| Maine | K.CC.B.4 | Understand the relationship between numbers and quantities; connect counting to cardinality. | Kindergarten |
| Maine | K.CC.B.5 | Count to answer “how many?” questions about as many as 20 things arranged in a line, a rectangular array, or a circle, or as many as 10 things in a scattered configuration; given a number from 1-20, count out that many objects. | Kindergarten |
| Maine | K.CC.C.6 | Identify whether the number of objects in one group is greater than, less than, or equal to the number of objects in another group, e.g., by using matching and counting strategies. | Kindergarten |
| Maine | K.CC.C.7 | Compare two numbers between 1 and 10 presented as written numerals. | Kindergarten |
| Maine | K.G.A.1 | Describe objects in the environment using names of shapes, and describe the relative positions of these objects using terms such as above, below, beside, in front of, behind, and next to. | Kindergarten |
| Maine | K.G.A.2 | Correctly name shapes regardless of their orientations or overall size. | Kindergarten |
| Maine | K.G.A.3 | Identify shapes as two-dimensional (lying in a plane, “flat”) or three-dimensional (“solid”). | Kindergarten |
| Maine | K.G.B.4 | Analyze and compare two- and three-dimensional shapes, in different sizes and orientations, using informal language to describe their similarities, differences, parts (e.g., number of sides and vertices/“corners”) and other attributes (e.g., having sides of equal length). | Kindergarten |
| Maine | K.G.B.6 | Compose simple shapes to form larger shapes. | Kindergarten |
| Maine | K.MD.A.1 | Describe measurable attributes of objects, such as length or weight. Describe several measurable attributes of a single object. | Kindergarten |
| Maine | K.MD.A.2 | Directly compare two objects with a measurable attribute in common, to see which object has “more of”/“less of” the attribute, and describe the difference. | Kindergarten |
| Maine | K.MD.B.3 | Classify objects into given categories; count the numbers of objects in each category and sort the categories by count. | Kindergarten |
| Maine | K.NBT.A.1 | Compose and decompose numbers from 11 to 19 into ten ones and some further ones, e.g., by using objects or drawings, and record each composition or decomposition by a drawing or equation (e.g., 18 = 10 + 8); understand that these numbers are composed of ten ones and one, two, three, four, five, six, seven, eight, or nine ones. | Kindergarten |
| Maine | K.OA.A.1 | Represent addition and subtraction with objects, fingers, mental images, drawings, sounds (e.g., claps), acting out situations, verbal explanations, expressions, or equations. | Kindergarten |
| Maine | K.OA.A.2 | Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem. | Kindergarten |
| Maine | K.OA.A.3 | Decompose numbers less than or equal to 10 into pairs in more than one way, e.g., by using objects or drawings, and record each decomposition by a drawing or equation (e.g., 5 = 2 + 3 and 5 = 4 + 1). | Kindergarten |
| Maine | K.OA.A.4 | For any number from 1 to 9, find the number that makes 10 when added to the given number, e.g., by using objects or drawings, and record the answer with a drawing or equation. | Kindergarten |
| Maine | K.OA.A.5 | Fluently add and subtract within 5. | Kindergarten |
| Maine | 1.G.A.1 | Distinguish between defining attributes (e.g., triangles are closed and three-sided) versus non-defining attributes (e.g., color, orientation, overall size); build and draw shapes to possess defining attributes. | Grade 1 |
| Maine | 1.G.A.2 | Compose two-dimensional shapes (rectangles, squares, trapezoids, triangles, half-circles, and quarter-circles) or three-dimensional shapes (cubes, right rectangular prisms, right circular cones, and right circular cylinders) to create a composite shape, and compose new shapes from the composite shape. | Grade 1 |
| Maine | 1.G.A.3 | Partition circles and rectangles into two and four equal shares, describe the shares using the words halves, fourths, and quarters, and use the phrases half of, fourth of, and quarter of. Describe the whole as two of, or four of the shares. Understand for these examples that decomposing into more equal shares creates smaller shares. | Grade 1 |
| Maine | 1.MD.A.1 | Order three objects by length; compare the lengths of two objects indirectly by using a third object. | Grade 1 |
| Maine | 1.MD.A.2 | Express the length of an object as a whole number of length units, by laying multiple copies of a shorter object (the length unit) end to end; understand that the length measurement of an object is the number of same-size length units that span it with no gaps or overlaps. | Grade 1 |
| Maine | 1.MD.B.3 | Tell and write time in hours and half-hours using analog and digital clocks. | Grade 1 |
| Maine | 1.MD.C.4 | Organize, represent, and interpret data with up to three categories; ask and answer questions about the total number of data points, how many in each category, and how many more or less are in one category than in another. | Grade 1 |
| Maine | 1.NBT.A.1 | Count to 120, starting at any number less than 120. In this range, read and write numerals and represent a number of objects with a written numeral. | Grade 1 |
| Maine | 1.NBT.B.2 | Understand that the two digits of a two-digit number represent amounts of tens and ones. | Grade 1 |
| Maine | 1.NBT.B.3 | Compare two two-digit numbers based on meanings of the tens and ones digits, recording the results of comparisons with the symbols >, =, and <. | Grade 1 |
| Maine | 1.NBT.C.4 | Add within 100, including adding a two-digit number and a one-digit number, and adding a two-digit number and a multiple of 10, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Understand that in adding two-digit numbers, one adds tens and tens, ones and ones; and sometimes it is necessary to compose a ten. | Grade 1 |
| Maine | 1.NBT.C.5 | Given a two-digit number, mentally find 10 more or 10 less than the number, without having to count; explain the reasoning used. | Grade 1 |
| Maine | 1.NBT.C.6 | Subtract multiples of 10 in the range 10-90 from multiples of 10 in the range 10-90 (positive or zero differences), using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. | Grade 1 |
| Maine | 1.OA.A.1 | Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem. | Grade 1 |
| Maine | 1.OA.B.3 | Apply properties of operations as strategies to add and subtract. | Grade 1 |
| Maine | 1.OA.B.4 | Understand subtraction as an unknown-addend problem. | Grade 1 |
| Maine | 1.OA.C.5 | Relate counting to addition and subtraction (e.g., by counting on 2 to add 2). | Grade 1 |
| Maine | 1.OA.C.6 | Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to a ten (e.g., 13 - 4 = 13 - 3 - 1 = 10 - 1 = 9); using the relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 - 8 = 4); and creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13). | Grade 1 |
| Maine | 1.OA.D.7 | Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false. | Grade 1 |
| Maine | 1.OA.D.8 | Determine the unknown whole number in an addition or subtraction equation relating three whole numbers. | Grade 1 |
| Maine | 2.G.A.1 | Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces. Identify triangles, quadrilaterals, pentagons, hexagons, and cubes. | Grade 2 |
| Maine | 2.G.A.2 | Partition a rectangle into rows and columns of same-size squares and count to find the total number of them. | Grade 2 |
| Maine | 2.G.A.3 | Partition circles and rectangles into two, three, or four equal shares, describe the shares using the words halves, thirds, half of, a third of, etc., and describe the whole as two halves, three thirds, four fourths. Recognize that equal shares of identical wholes need not have the same shape. | Grade 2 |
| Maine | 2.MD.A.1 | Measure the length of an object by selecting and using appropriate tools such as rulers, yardsticks, meter sticks, and measuring tapes. | Grade 2 |
| Maine | 2.MD.A.2 | Measure the length of an object twice, using length units of different lengths for the two measurements; describe how the two measurements relate to the size of the unit chosen. | Grade 2 |
| Maine | 2.MD.A.4 | Measure to determine how much longer one object is than another, expressing the length difference in terms of a standard length unit. | Grade 2 |
| Maine | 2.MD.B.5 | Use addition and subtraction within 100 to solve word problems involving lengths that are given in the same units, e.g., by using drawings (such as drawings of rulers) and equations with a symbol for the unknown number to represent the problem. | Grade 2 |
| Maine | 2.MD.C.7 | Tell and write time from analog and digital clocks to the nearest five minutes, using a.m. and p.m. | Grade 2 |
| Maine | 2.MD.C.8 | Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies, using $ and ¢ symbols appropriately. | Grade 2 |
| Maine | 2.MD.D.9 | Generate measurement data by measuring lengths of several objects to the nearest whole unit, or by making repeated measurements of the same object. Show the measurements by making a line plot, where the horizontal scale is marked off in whole-number units. | Grade 2 |
| Maine | 2.MD.D.10 | Draw a picture graph and a bar graph (with single-unit scale) to represent a data set with up to four categories. Solve simple put-together, take-apart, and compare problems using information presented in a bar graph. | Grade 2 |
| Maine | 2.NBT.A.1 | Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones. | Grade 2 |
| Maine | 2.NBT.A.2 | Count within 1000; skip-count by 5s, 10s, and 100s. | Grade 2 |
| Maine | 2.NBT.A.3 | Read and write numbers to 1000 using base-ten numerals, number names, and expanded form. | Grade 2 |
| Maine | 2.NBT.A.4 | Compare two three-digit numbers based on meanings of the hundreds, tens, and ones digits, using >, =, and < symbols to record the results of comparisons. | Grade 2 |
| Maine | 2.NBT.B.5 | Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction. | Grade 2 |
| Maine | 2.NBT.B.6 | Add up to four two-digit numbers using strategies based on place value and properties of operations. | Grade 2 |
| Maine | 2.NBT.B.7 | Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method. Understand that in adding or subtracting three-digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds. | Grade 2 |
| Maine | 2.NBT.B.8 | Mentally add 10 or 100 to a given number 100–900, and mentally subtract 10 or 100 from a given number 100–900. | Grade 2 |
| Maine | 2.OA.A.1 | Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem. | Grade 2 |
| Maine | 2.OA.B.2 | Fluently add and subtract within 20 using mental strategies. By end of Grade 2, know from memory all sums of two one-digit numbers. | Grade 2 |
| Maine | 2.OA.C.3 | Determine whether a group of objects (up to 20) has an odd or even number of members, e.g., by pairing objects or counting them by 2s; write an equation to express an even number as a sum of two equal addends. | Grade 2 |
| Maine | 2.OA.C.4 | Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends. | Grade 2 |
| Maine | 3.G.A.1 | Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories. | Grade 3 |
| Maine | 3.G.A.2 | Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole. | Grade 3 |
| Maine | 3.MD.A.1 | Tell and write time to the nearest minute and measure time intervals in minutes. Solve word problems involving addition and subtraction of time intervals in minutes, e.g., by representing the problem on a number line diagram. | Grade 3 |
| Maine | 3.MD.A.2 | Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l). Add, subtract, multiply, or divide to solve one-step word problems involving masses or volumes that are given in the same units, e.g., by using drawings (such as a beaker with a measurement scale) to represent the problem. | Grade 3 |
| Maine | 3.MD.B.3 | Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and two-step “how many more” and “how many less” problems using information presented in scaled bar graphs. | Grade 3 |
| Maine | 3.MD.B.4 | Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Show the data by making a line plot, where the horizontal scale is marked off in appropriate units-whole numbers, halves, or quarters. | Grade 3 |
| Maine | 3.MD.C.5 | Recognize area as an attribute of plane figures and understand concepts of area measurement. | Grade 3 |
| Maine | 3.MD.C.6 | Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units). | Grade 3 |
| Maine | 3.MD.C.7 | Relate area to the operations of multiplication and addition. | Grade 3 |
| Maine | 3.MD.D.8 | Solve real world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters. | Grade 3 |
| Maine | 3.NBT.A.1 | Use place value understanding to round whole numbers to the nearest 10 or 100. | Grade 3 |
| Maine | 3.NBT.A.2 | Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction. | Grade 3 |
| Maine | 3.NBT.A.3 | Multiply one-digit whole numbers by multiples of 10 in the range 10–90 (e.g., 9 × 80, 5 × 60) using strategies based on place value and properties of operations. | Grade 3 |
| Maine | 3.NF.A.1 | Understand a fraction 1/𝘣 as the quantity formed by 1 part when a whole is partitioned into 𝘣 equal parts; understand a fraction 𝘢/𝑏 as the quantity formed by 𝘢 parts of size 1/𝘣. | Grade 3 |
| Maine | 3.NF.A.2 | Understand a fraction as a number on the number line; represent fractions on a number line diagram. | Grade 3 |
| Maine | 3.NF.A.3 | Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size. | Grade 3 |
| Maine | 3.OA.A.1 | Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each. | Grade 3 |
| Maine | 3.OA.A.2 | Interpret whole-number quotients of whole numbers, e.g., interpret 56 ÷ 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each. | Grade 3 |
| Maine | 3.OA.A.3 | Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem. | Grade 3 |
| Maine | 3.OA.A.4 | Determine the unknown whole number in a multiplication or division equation relating three whole numbers. | Grade 3 |
| Maine | 3.OA.B.5 | Apply properties of operations as strategies to multiply and divide. | Grade 3 |
| Maine | 3.OA.B.6 | Understand division as an unknown-factor problem. | Grade 3 |
| Maine | 3.OA.C.7 | Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 × 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers. | Grade 3 |
| Maine | 3.OA.D.8 | Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. | Grade 3 |
| Maine | 3.OA.D.9 | Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations. | Grade 3 |
| Maine | 4.G.A.1 | Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures. | Grade 4 |
| Maine | 4.G.A.2 | Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles. | Grade 4 |
| Maine | 4.G.A.3 | Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify line-symmetric figures and draw lines of symmetry. | Grade 4 |
| Maine | 4.MD.A.1 | Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table. | Grade 4 |
| Maine | 4.MD.A.2 | Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. | Grade 4 |
| Maine | 4.MD.A.3 | Apply the area and perimeter formulas for rectangles in real world and mathematical problems. | Grade 4 |
| Maine | 4.MD.B.4 | Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots. | Grade 4 |
| Maine | 4.MD.C.5 | Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement. | Grade 4 |
| Maine | 4.MD.C.6 | Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure. | Grade 4 |
| Maine | 4.MD.C.7 | Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems, e.g., by using an equation with a symbol for the unknown angle measure. | Grade 4 |
| Maine | 4.NBT.A.1 | Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. | Grade 4 |
| Maine | 4.NBT.A.2 | Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. | Grade 4 |
| Maine | 4.NBT.A.3 | Use place value understanding to round multi-digit whole numbers to any place. | Grade 4 |
| Maine | 4.NBT.B.4 | Fluently add and subtract multi-digit whole numbers using the standard algorithm. | Grade 4 |
| Maine | 4.NBT.B.5 | Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. | Grade 4 |
| Maine | 4.NBT.B.6 | Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. | Grade 4 |
| Maine | 4.NF.A.1 | Explain why a fraction 𝘢/𝘣 is equivalent to a fraction (𝘯 × 𝘢)/(𝘯 × 𝘣) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. | Grade 4 |
| Maine | 4.NF.A.2 | Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model. | Grade 4 |
| Maine | 4.NF.B.3 | Understand a fraction 𝘢/𝘣 with 𝘢 > 1 as a sum of fractions 1/𝘣. | Grade 4 |
| Maine | 4.NF.B.4 | Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. | Grade 4 |
| Maine | 4.NF.C.5 | Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100. | Grade 4 |
| Maine | 4.NF.C.6 | Use decimal notation for fractions with denominators 10 or 100. | Grade 4 |
| Maine | 4.NF.C.7 | Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual model. | Grade 4 |
| Maine | 4.OA.A.1 | Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 × 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations. | Grade 4 |
| Maine | 4.OA.A.2 | Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison. | Grade 4 |
| Maine | 4.OA.A.3 | Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. | Grade 4 |
| Maine | 4.OA.B.4 | Find all factor pairs for a whole number in the range 1-100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1-100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1-100 is prime or composite. | Grade 4 |
| Maine | 4.OA.C.5 | Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. | Grade 4 |
| Maine | 5.G.A.1 | Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., 𝘹-axis and 𝘹-coordinate, 𝘺-axis and 𝘺-coordinate). | Grade 5 |
| Maine | 5.G.A.2 | Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. | Grade 5 |
| Maine | 5.G.B.3 | Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. | Grade 5 |
| Maine | 5.G.B.4 | Classify two-dimensional figures in a hierarchy based on properties. | Grade 5 |
| Maine | 5.MD.A.1 | Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. | Grade 5 |
| Maine | 5.MD.B.2 | Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. | Grade 5 |
| Maine | 5.MD.C.3 | Recognize volume as an attribute of solid figures and understand concepts of volume measurement. | Grade 5 |
| Maine | 5.MD.C.4 | Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. | Grade 5 |
| Maine | 5.MD.C.5 | Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume. | Grade 5 |
| Maine | 5.NBT.A.1 | Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. | Grade 5 |
| Maine | 5.NBT.A.2 | Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. | Grade 5 |
| Maine | 5.NBT.A.3 | Read, write, and compare decimals to thousandths. | Grade 5 |
| Maine | 5.NBT.A.4 | Use place value understanding to round decimals to any place. | Grade 5 |
| Maine | 5.NBT.B.5 | Fluently multiply multi-digit whole numbers using the standard algorithm. | Grade 5 |
| Maine | 5.NBT.B.6 | Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. | Grade 5 |
| Maine | 5.NBT.B.7 | Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. | Grade 5 |
| Maine | 5.NF.A.1 | Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. | Grade 5 |
| Maine | 5.NF.A.2 | Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. | Grade 5 |
| Maine | 5.NF.B.3 | Interpret a fraction as division of the numerator by the denominator (𝘢/𝘣 = 𝘢 ÷ 𝘣). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. | Grade 5 |
| Maine | 5.NF.B.4 | Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. | Grade 5 |
| Maine | 5.NF.B.5 | Interpret multiplication as scaling (resizing). | Grade 5 |
| Maine | 5.NF.B.6 | Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. | Grade 5 |
| Maine | 5.NF.B.7 | Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. | Grade 5 |
| Maine | 5.OA.A.1 | Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. | Grade 5 |
| Maine | 5.OA.A.2 | Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. | Grade 5 |
| Maine | 5.OA.B.3 | Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. | Grade 5 |
| Maine | 6.EE.A.1 | Write and evaluate numerical expressions involving whole-number exponents. | Grade 6 |
| Maine | 6.EE.A.2 | Write, read, and evaluate expressions in which letters stand for numbers. | Grade 6 |
| Maine | 6.EE.A.3 | Apply the properties of operations to generate equivalent expressions. | Grade 6 |
| Maine | 6.EE.A.4 | Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). | Grade 6 |
| Maine | 6.EE.B.5 | Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true. | Grade 6 |
| Maine | 6.EE.B.6 | Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set. | Grade 6 |
| Maine | 6.EE.B.7 | Solve real-world and mathematical problems by writing and solving equations of the form 𝘹 + 𝘱 = 𝘲 and 𝘱𝘹 = 𝘲 for cases in which 𝘱, 𝘲 and 𝘹 are all nonnegative rational numbers. | Grade 6 |
| Maine | 6.EE.B.8 | Write an inequality of the form 𝘹 > 𝘤 or 𝘹 𝘤 or 𝘹 < 𝘤 have infinitely many solutions; represent solutions of such inequalities on number line diagrams. | Grade 6 |
| Maine | 6.EE.C.9 | Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. | Grade 6 |
| Maine | 6.G.A.1 | Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems. | Grade 6 |
| Maine | 6.G.A.2 | Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas 𝘝 = 𝘭 𝘸 𝘩 and 𝘝 = 𝘣 𝘩 to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems. | Grade 6 |
| Maine | 6.G.A.3 | Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems. | Grade 6 |
| Maine | 6.G.A.4 | Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems. | Grade 6 |
| Maine | 6.RP.A.1 | Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. | Grade 6 |
| Maine | 6.RP.A.2 | Understand the concept of a unit rate 𝘢/𝘣 associated with a ratio 𝘢:𝘣 with 𝘣 ≠ 0, and use rate language in the context of a ratio relationship. | Grade 6 |
| Maine | 6.RP.A.3 | Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. | Grade 6 |
| Maine | 6.SP.B.5 | Summarize numerical data sets in relation to their context, such as by: | Grade 6 |
| Maine | 6.NS.A.1 | Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. | Grade 6 |
| Maine | 6.NS.B.2 | Fluently divide multi-digit numbers using the standard algorithm. | Grade 6 |
| Maine | 6.NS.B.3 | Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation. | Grade 6 |
| Maine | 6.NS.C.5 | Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation. | Grade 6 |
| Maine | 6.NS.C.6 | Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates. | Grade 6 |
| Maine | 6.NS.C.7 | Understand ordering and absolute value of rational numbers. | Grade 6 |
| Maine | 6.NS.C.8 | Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. | Grade 6 |
| Maine | 7.EE.A.1 | Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients. | Grade 7 |
| Maine | 7.EE.A.2 | Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. | Grade 7 |
| Maine | 7.EE.B.3 | Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. | Grade 7 |
| Maine | 7.EE.B.4 | Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. | Grade 7 |
| Maine | 7.G.A.1 | Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale. | Grade 7 |
| Maine | 7.G.A.2 | Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle. | Grade 7 |
| Maine | 7.G.A.3 | Describe the two-dimensional figures that result from slicing three-dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids. | Grade 7 |
| Maine | 7.G.B.4 | Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle. | Grade 7 |
| Maine | 7.G.B.5 | Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure. | Grade 7 |
| Maine | 7.G.B.6 | Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. | Grade 7 |
| Maine | 7.RP.A.1 | Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. | Grade 7 |
| Maine | 7.RP.A.2 | Recognize and represent proportional relationships between quantities. | Grade 7 |
| Maine | 7.RP.A.3 | Use proportional relationships to solve multistep ratio and percent problems. | Grade 7 |
| Maine | 7.NS.A.1 | Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram. | Grade 7 |
| Maine | 7.NS.A.2 | Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers. | Grade 7 |
| Maine | 7.NS.A.3 | Solve real-world and mathematical problems involving the four operations with rational numbers. | Grade 7 |
| Maine | 8.EE.A.1 | Know and apply the properties of integer exponents to generate equivalent numerical expressions. | Grade 8 |
| Maine | 8.EE.A.2 | Use square root and cube root symbols to represent solutions to equations of the form 𝘹² = 𝘱 and 𝘹³ = 𝘱, where 𝘱 is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that √2 is irrational. | Grade 8 |
| Maine | 8.EE.A.3 | Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other. | Grade 8 |
| Maine | 8.EE.A.4 | Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology. | Grade 8 |
| Maine | 8.EE.B.5 | Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. | Grade 8 |
| Maine | 8.EE.B.6 | Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation 𝘺 = 𝘮𝘹 for a line through the origin and the equation 𝘺 = 𝘮𝘹 + 𝘣 for a line intercepting the vertical axis at 𝘣. | Grade 8 |
| Maine | 8.EE.C.7 | Solve linear equations in one variable. | Grade 8 |
| Maine | 8.EE.C.8 | Analyze and solve pairs of simultaneous linear equations. | Grade 8 |
| Maine | 8.F.A.1 | Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output. | Grade 8 |
| Maine | 8.F.A.2 | Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). | Grade 8 |
| Maine | 8.F.A.3 | Interpret the equation 𝘺 = 𝘮𝘹 + 𝘣 as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. | Grade 8 |
| Maine | 8.F.B.4 | Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (𝘹, 𝘺) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values. | Grade 8 |
| Maine | 8.F.B.5 | Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally. | Grade 8 |
| Maine | 8.G.A.1 | Verify experimentally the properties of rotations, reflections, and translations. | Grade 8 |
| Maine | 8.G.A.2 | Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them. | Grade 8 |
| Maine | 8.G.A.3 | Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates. | Grade 8 |
| Maine | 8.G.A.4 | Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two-dimensional figures, describe a sequence that exhibits the similarity between them. | Grade 8 |
| Maine | 8.G.A.5 | Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. | Grade 8 |
| Maine | 8.G.B.7 | Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions. | Grade 8 |
| Maine | 8.G.B.8 | Apply the Pythagorean Theorem to find the distance between two points in a coordinate system. | Grade 8 |
| Maine | 8.G.C.9 | Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems. | Grade 8 |
| Maine | 8.SP.A.1 | Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association. | Grade 8 |
| Maine | 8.SP.A.2 | Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line. | Grade 8 |
| Maine | 8.NS.A.2 | Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g., π²). | Grade 8 |
| Maine | A-APR.B.3 | Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial. | High School |
| Maine | A-CED.A.2 | Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. | High School |
| Maine | A-CED.A.3 | Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context. | High School |
| Maine | A-REI.B.3 | Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. | High School |
| Maine | A-SSE.A.2 | Use the structure of an expression to identify ways to rewrite it. | High School |
| Maine | A-SSE.B.3 | Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression. | High School |
| Maine | F-BF.A.1 | Write a function that describes a relationship between two quantities. | High School |
| Maine | F-IF.A.2 | Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. | High School |
| Maine | F-IF.B.4 | For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. | High School |
| Maine | F-IF.C.7 | Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. | High School |
| Maine | S-ID.B.6 | Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. | High School |
| Manitoba | K.N.1 | Say the number sequence by 1s, starting anywhere from 1 to 30 and from 10 to 1. | Kindergarten |
| Manitoba | K.N.2 | Subitize and name familiar arrangements of 1 to 6 dots (or objects). | Kindergarten |
| Manitoba | K.N.3 | Relate a numeral, 1 to 10, to its respective quantity. | Kindergarten |
| Manitoba | K.N.4 | Represent and describe numbers 2 to 10 in two parts, concretely and pictorially. | Kindergarten |
| Manitoba | K.N.5.1 | Demonstrate an understanding of counting to 10 by indicating that the last number said identifies how many. | Kindergarten |
| Manitoba | K.N.5.2 | Demonstrate an understanding of counting to 10 by showing that any set has only one count. | Kindergarten |
| Manitoba | K.N.6.1 | Compare quantities, 1 to 10, using one-to-one correspondence. | Kindergarten |
| Manitoba | K.N.6.2 | Compare quantities, 1 to 10, by ordering numbers representing different quantities. | Kindergarten |
| Manitoba | 1.N.1.1 | Say the number sequence by 1s forward and backward between any two given numbers (0 to 100). | Grade 1 |
| Manitoba | 1.N.1.3 | Say the number sequence by 5s and 10s to 100, forward starting at 0. | Grade 1 |
| Manitoba | 1.N.2 | Subitize and name familiar arrangements of 1 to 10 dots (or objects). | Grade 1 |
| Manitoba | 1.N.3.1 | Demonstrate an understanding of counting by using the counting-on strategy. | Grade 1 |
| Manitoba | 1.N.4 | Represent and describe numbers to 20, concretely, pictorially, and symbolically. | Grade 1 |
| Manitoba | 1.N.5 | Compare and order sets containing up to 20 elements to solve problems using referents and one-to-one correspondence. | Grade 1 |
| Manitoba | 1.N.7 | Demonstrate, concretely and pictorially, how a number, up to 30, can be represented by a variety of equal groups with and without singles. | Grade 1 |
| Manitoba | 1.N.9.1 | Demonstrate an understanding of addition of numbers with answers to 20 and their corresponding subtraction facts, concretely, pictorially, and symbolically, by using familiar and mathematical language to describe additive and subtractive actions from their experience. | Grade 1 |
| Manitoba | 1.N.9.2 | Demonstrate an understanding of addition of numbers with answers to 20 and their corresponding subtraction facts, concretely, pictorially, and symbolically, by creating and solving problems in context that involve addition and subtraction. | Grade 1 |
| Manitoba | 1.N.9.3 | Demonstrate an understanding of addition of numbers with answers to 20 and their corresponding subtraction facts, concretely, pictorially, and symbolically, by modelling addition and subtraction using a variety of concrete and visual representations, and recording the process symbolically. | Grade 1 |
| Manitoba | 1.N.10 | Describe and use mental mathematics strategies including counting on, counting back, using one more, one less, making 10, starting from known doubles, using addition to subtract to determine the basic addition and related subtraction facts to 18. | Grade 1 |
| Manitoba | 1.PR.3 | Describe equality as a balance and inequality as an imbalance, concretely and pictorially (0 to 20). | Grade 1 |
| Manitoba | 1.PR.4 | Record equalities using the equal symbol (0 to 20). | Grade 1 |
| Manitoba | 1.SS.2 | Sort 3-D objects and 2-D shapes using one attribute, and explain the sorting rule. | Grade 1 |
| Manitoba | 2.N.1.1 | Say the number sequence from 0 to 100 by 2s, 5s, and 10s, forward and backward, using starting points that are multiples of 2, 5, and 10 respectively. | Grade 2 |
| Manitoba | 2.N.1.2 | Say the number sequence from 0 to 100 by 10s using starting points from 1 to 9. | Grade 2 |
| Manitoba | 2.N.1.3 | Say the number sequence from 0 to 100 by 2s starting from 1. | Grade 2 |
| Manitoba | 2.N.4 | Represent and describe numbers to 100, concretely, pictorially, and symbolically. | Grade 2 |
| Manitoba | 2.N.5 | Compare and order numbers up to 100. | Grade 2 |
| Manitoba | 2.N.6 | Estimate quantities to 100 using referents. | Grade 2 |
| Manitoba | 2.N.7 | Illustrate, concretely and pictorially, the meaning of place value for numbers to 100. | Grade 2 |
| Manitoba | 2.N.9.1 | Demonstrate an understanding of addition (limited to 1- and 2-digit numerals) with answers to 100 and the corresponding subtraction by using personal strategies for adding and subtracting with and without the support of manipulatives. | Grade 2 |
| Manitoba | 2.N.9.2 | Demonstrate an understanding of addition (limited to 1- and 2-digit numerals) with answers to 100 and the corresponding subtraction by creating and solving problems that involve addition and subtraction. | Grade 2 |
| Manitoba | 2.N.9.3 | Demonstrate an understanding of addition (limited to 1- and 2-digit numerals) with answers to 100 and the corresponding subtraction by explaining that the order in which numbers are added does not affect the sum. | Grade 2 |
| Manitoba | 2.N.9.4 | Demonstrate an understanding of addition (limited to 1- and 2-digit numerals) with answers to 100 and the corresponding subtraction by explaining that the order in which numbers are subtracted may affect the difference. | Grade 2 |
| Manitoba | 2.N.10 | Apply mental mathematics strategies, including using doubles, using one more, one less, using two more, two less, building on a known double, using addition for subtraction to develop recall of basic addition facts to 18 and related subtractions facts. | Grade 2 |
| Manitoba | 2.PR.3 | Demonstrate and explain the meaning of equality and inequality by using manipulatives and diagrams (0 to 100). | Grade 2 |
| Manitoba | 2.PR.4 | Record equalities and inequalities symbolically using the equal symbol or the not-equal symbol. | Grade 2 |
| Manitoba | 2.SS.6 | Sort 2-D shapes and 3-D objects using two attributes, and explain the sorting rule. | Grade 2 |
| Manitoba | 2.SS.7 | Describe, compare, and construct 3-D objects, including cubes, spheres, cones, cylinders, prisms and pyramids. | Grade 2 |
| Manitoba | 2.SS.8 | Describe, compare, and construct 2-D shapes, including triangles, squares, rectangles and circles. | Grade 2 |
| Manitoba | 2.SS.9 | Identify 2-D shapes as parts of 3-D objects in the environment. | Grade 2 |
| Manitoba | 2.SP.2 | Construct and interpret concrete graphs and pictographs to solve problems. | Grade 2 |
| Manitoba | 3.N.1.1 | Say the number sequence between any two given numbers forward and backward from 0 to 1000 by 10s or 100s, using any starting point. | Grade 3 |
| Manitoba | 3.N.1.2 | Say the number sequence between any two given numbers forward and backward from 0 to 1000 by 5s, using starting points that are multiples of 5. | Grade 3 |
| Manitoba | 3.N.1.3 | Say the number sequence between any two given numbers forward and backward from 0 to 1000 by 25s, using starting points that are multiples of 25. | Grade 3 |
| Manitoba | 3.N.2 | Represent and describe numbers to 1000, concretely, pictorially, and symbolically. | Grade 3 |
| Manitoba | 3.N.3 | Compare and order numbers to 1000. | Grade 3 |
| Manitoba | 3.N.4 | Estimate quantities less than 1000 using referents. | Grade 3 |
| Manitoba | 3.N.5 | Illustrate, concretely and pictorially, the meaning of place value for numerals to 1000. | Grade 3 |
| Manitoba | 3.N.6.1 | Describe and apply mental mathematics strategies for adding two 2-digit numerals, such as adding from left to right. | Grade 3 |
| Manitoba | 3.N.6.2 | Describe and apply mental mathematics strategies for adding two 2-digit numerals, such as taking one addend to the nearest multiple of ten and then compensating. | Grade 3 |
| Manitoba | 3.N.6.3 | Describe and apply mental mathematics strategies for adding two 2-digit numerals, such as using doubles. | Grade 3 |
| Manitoba | 3.N.7.1 | Describe and apply mental mathematics strategies for subtracting two 2-digit numerals, such as taking the subtrahend to the nearest multiple of ten and then compensating. | Grade 3 |
| Manitoba | 3.N.7.2 | Describe and apply mental mathematics strategies for subtracting two 2-digit numerals, such as thinking of addition. | Grade 3 |
| Manitoba | 3.N.7.3 | Describe and apply mental mathematics strategies for subtracting two 2-digit numerals, such as using doubles. | Grade 3 |
| Manitoba | 3.N.8 | Apply estimation strategies to predict sums and differences of two 2-digit numerals in a problem-solving context. | Grade 3 |
| Manitoba | 3.N.9.1 | Demonstrate an understanding of addition and subtraction of numbers with answers to 1000 (limited to 1-, 2-, and 3-digit numerals) by using personal strategies for adding and subtracting with and without the support of manipulatives. | Grade 3 |
| Manitoba | 3.N.10 | Apply mental math strategies to determine addition facts and related subtraction facts to 18 (9 + 9). | Grade 3 |
| Manitoba | 3.N.11.1 | Demonstrate an understanding of multiplication to 5 × 5 by representing and explaining multiplication using equal grouping and arrays. | Grade 3 |
| Manitoba | 3.N.11.2 | Demonstrate an understanding of multiplication to 5 × 5 by creating and solving problems in context that involve multiplication. | Grade 3 |
| Manitoba | 3.N.11.3 | Demonstrate an understanding of multiplication to 5 × 5 by modelling multiplication using concrete and visual representations, and recording the process symbolically. | Grade 3 |
| Manitoba | 3.N.11.4 | Demonstrate an understanding of multiplication to 5 × 5 by relating multiplication to repeated addition. | Grade 3 |
| Manitoba | 3.N.11.5 | Demonstrate an understanding of multiplication to 5 × 5 by relating multiplication to division. | Grade 3 |
| Manitoba | 3.N.12.1 | Demonstrate an understanding of division by representing and explaining division using equal sharing and equal grouping limited to division related to multiplication facts up to 5 × 5. | Grade 3 |
| Manitoba | 3.N.12.2 | Demonstrate an understanding of division by creating and solving problems in context that involve equal sharing and equal grouping limited to division related to multiplication facts up to 5 × 5. | Grade 3 |
| Manitoba | 3.N.12.3 | Demonstrate an understanding of division by modelling equal sharing and equal grouping using concrete and visual representations, and recording the process symbolically limited to division related to multiplication facts up to 5 × 5. | Grade 3 |
| Manitoba | 3.N.12.4 | Demonstrate an understanding of division by relating division to repeated subtraction limited to division related to multiplication facts up to 5 × 5. | Grade 3 |
| Manitoba | 3.N.12.5 | Demonstrate an understanding of division by relating division to multiplication limited to division related to multiplication facts up to 5 × 5. | Grade 3 |
| Manitoba | 3.N.13.1 | Demonstrate an understanding of fractions by explaining that a fraction represents a portion of a whole divided into equal parts. | Grade 3 |
| Manitoba | 3.N.13.2 | Demonstrate an understanding of fractions by describing situations in which fractions are used. | Grade 3 |
| Manitoba | 3.N.13.3 | Demonstrate an understanding of fractions by comparing fractions of the same whole with like denominators. | Grade 3 |
| Manitoba | 3.PR.3 | Solve one-step addition and subtraction equations involving symbols representing an unknown number. | Grade 3 |
| Manitoba | 3.SS.1 | Relate the passage of time to common activities using non-standard and standard units (minutes, hours, days, weeks, months, years). | Grade 3 |
| Manitoba | 3.SS.2 | Relate the number of seconds to a minute, the number of minutes to an hour, and the number of days to a month in a problem-solving context. | Grade 3 |
| Manitoba | 3.SS.3.2 | Demonstrate an understanding of measuring length (cm, m) by modelling and describing the relationship between the units cm and m. | Grade 3 |
| Manitoba | 3.SS.3.4 | Demonstrate an understanding of measuring length (cm, m) by measuring and recording length, width, and height. | Grade 3 |
| Manitoba | 3.SS.4.2 | Demonstrate an understanding of measuring mass (g, kg) by modelling and describing the relationship between the units g and kg. | Grade 3 |
| Manitoba | 3.SS.7 | Sort regular and irregular polygons, including triangles, quadrilaterals, pentagons, hexagons, and octagons according to the number of sides. | Grade 3 |
| Manitoba | 3.SP.1 | Collect first-hand data and organize it using tally marks, line plots, charts, and lists to answer questions. | Grade 3 |
| Manitoba | 3.SP.2 | Construct, label, and interpret bar graphs to solve problems. | Grade 3 |
| Manitoba | 4.N.2 | Compare and order numbers to 10,000. | Grade 4 |
| Manitoba | 4.N.3.1 | Demonstrate an understanding of addition of numbers with answers to 10,000 and their corresponding subtractions (limited to 3- and 4-digit numbers), concretely, pictorially, and symbolically, by using personal strategies. | Grade 4 |
| Manitoba | 4.N.3.2 | Demonstrate an understanding of addition of numbers with answers to 10,000 and their corresponding subtractions (limited to 3- and 4-digit numbers), concretely, pictorially, and symbolically, by using the standard algorithms. | Grade 4 |
| Manitoba | 4.N.3.3 | Demonstrate an understanding of addition of numbers with answers to 10,000 and their corresponding subtractions (limited to 3- and 4-digit numbers), concretely, pictorially, and symbolically, by estimating sums and differences. | Grade 4 |
| Manitoba | 4.N.3.4 | Demonstrate an understanding of addition of numbers with answers to 10,000 and their corresponding subtractions (limited to 3- and 4-digit numbers), concretely, pictorially, and symbolically, by solving problems. | Grade 4 |
| Manitoba | 4.N.5.1 | Describe and apply mental mathematics strategies, such as skip-counting from a known fact to develop an understanding of basic multiplication facts to 9 × 9 and related division facts. | Grade 4 |
| Manitoba | 4.N.5.5 | Describe and apply mental mathematics strategies, such as using repeated doubling to develop an understanding of basic multiplication facts to 9 × 9 and related division facts. | Grade 4 |
| Manitoba | 4.N.6.1 | Demonstrate an understanding of multiplication (2- or 3-digit numerals by 1-digit numerals) to solve problems by using personal strategies for multiplication with and without concrete materials. | Grade 4 |
| Manitoba | 4.N.6.2 | Demonstrate an understanding of multiplication (2- or 3-digit numerals by 1-digit numerals) to solve problems by using arrays to represent multiplication. | Grade 4 |
| Manitoba | 4.N.6.3 | Demonstrate an understanding of multiplication (2- or 3-digit numerals by 1-digit numerals) to solve problems by connecting concrete representations to symbolic representations. | Grade 4 |
| Manitoba | 4.N.6.4 | Demonstrate an understanding of multiplication (2- or 3-digit numerals by 1-digit numerals) to solve problems by estimating products. | Grade 4 |
| Manitoba | 4.N.7.1 | Demonstrate an understanding of division (1-digit divisor and up to 2-digit dividend) to solve problems by using personal strategies for dividing with and without concrete materials. | Grade 4 |
| Manitoba | 4.N.7.2 | Demonstrate an understanding of division (1-digit divisor and up to 2-digit dividend) to solve problems by estimating quotients. | Grade 4 |
| Manitoba | 4.N.7.3 | Demonstrate an understanding of division (1-digit divisor and up to 2-digit dividend) to solve problems by relating division to multiplication. | Grade 4 |
| Manitoba | 4.N.8.1 | Demonstrate an understanding of fractions less than or equal to one by using concrete and pictorial representations to name and record fractions for parts of a whole or a set. | Grade 4 |
| Manitoba | 4.N.8.2 | Demonstrate an understanding of fractions less than or equal to one by using concrete and pictorial representations to compare and order fractions. | Grade 4 |
| Manitoba | 4.N.8.3 | Demonstrate an understanding of fractions less than or equal to one by using concrete and pictorial representations to model and explain that for different wholes, two identical fractions may not represent the same quantity. | Grade 4 |
| Manitoba | 4.N.8.4 | Demonstrate an understanding of fractions less than or equal to one by using concrete and pictorial representations to provide examples of where fractions are used. | Grade 4 |
| Manitoba | 4.N.9 | Describe and represent decimals (tenths and hundredths), concretely, pictorially, and symbolically. | Grade 4 |
| Manitoba | 4.N.10 | Relate decimals to fractions (to hundredths). | Grade 4 |
| Manitoba | 4.N.11.1 | Demonstrate an understanding of addition and subtraction of decimals (limited to hundredths) by using compatible numbers. | Grade 4 |
| Manitoba | 4.N.11.2 | Demonstrate an understanding of addition and subtraction of decimals (limited to hundredths) by estimating sums and differences. | Grade 4 |
| Manitoba | 4.N.11.3 | Demonstrate an understanding of addition and subtraction of decimals (limited to hundredths) by using mental math strategies to solve problems. | Grade 4 |
| Manitoba | 4.PR.1 | Identify and describe patterns found in tables and charts, including a multiplication chart. | Grade 4 |
| Manitoba | 4.PR.2 | Reproduce a pattern shown in a table or chart using concrete materials. | Grade 4 |
| Manitoba | 4.PR.3 | Represent and describe patterns and relationships using charts and tables to solve problems. | Grade 4 |
| Manitoba | 4.PR.4 | Identify and explain mathematical relationships using charts and diagrams to solve problems. | Grade 4 |
| Manitoba | 4.PR.5 | Express a problem as an equation in which a symbol is used to represent an unknown number. | Grade 4 |
| Manitoba | 4.PR.6 | Solve one-step equations involving a symbol to represent an unknown number. | Grade 4 |
| Manitoba | 4.SS.1 | Read and record time using digital and analog clocks, including 24-hour clocks. | Grade 4 |
| Manitoba | 4.SS.3.1 | Demonstrate an understanding of area of regular and irregular 2-D shapes by recognizing that area is measured in square units. | Grade 4 |
| Manitoba | 4.SS.3.4 | Demonstrate an understanding of area of regular and irregular 2-D shapes by determining and recording area (cm2 or m2). | Grade 4 |
| Manitoba | 4.SS.6.1 | Demonstrate an understanding of line symmetry by identifying symmetrical 2-D shapes. | Grade 4 |
| Manitoba | 4.SS.6.2 | Demonstrate an understanding of line symmetry by creating symmetrical 2-D shapes. | Grade 4 |
| Manitoba | 4.SS.6.3 | Demonstrate an understanding of line symmetry by drawing one or more lines of symmetry in a 2-D shape. | Grade 4 |
| Manitoba | 4.SP.2 | Construct and interpret pictographs and bar graphs involving many-to-one correspondence to draw conclusions. | Grade 4 |
| Manitoba | 5.N.2 | Apply estimation strategies, including front-end rounding, compensation, compatible numbers, and in problem-solving contexts. | Grade 5 |
| Manitoba | 5.N.3 | Apply mental math strategies to determine multiplication and related division facts to 81 (9 × 9). | Grade 5 |
| Manitoba | 5.N.4.1 | Apply mental mathematics strategies for multiplication, such as annexing then adding zeros. | Grade 5 |
| Manitoba | 5.N.4.2 | Apply mental mathematics strategies for multiplication, such as halving and doubling. | Grade 5 |
| Manitoba | 5.N.4.3 | Apply mental mathematics strategies for multiplication, such as using the distributive property. | Grade 5 |
| Manitoba | 5.N.5.1 | Demonstrate an understanding of multiplication (1- and 2-digit multipliers and up to 4-digit multiplicands), concretely, pictorially, and symbolically, by using personal strategies to solve problems. | Grade 5 |
| Manitoba | 5.N.5.2 | Demonstrate an understanding of multiplication (1- and 2-digit multipliers and up to 4-digit multiplicands), concretely, pictorially, and symbolically, by using the standard algorithm to solve problems. | Grade 5 |
| Manitoba | 5.N.5.3 | Demonstrate an understanding of multiplication (1- and 2-digit multipliers and up to 4-digit multiplicands), concretely, pictorially, and symbolically, by estimating products to solve problems. | Grade 5 |
| Manitoba | 5.N.6.1 | Demonstrate an understanding of division (1- and 2-digit divisors and up to 4-digit dividends), concretely, pictorially, and symbolically, and interpret remainders by using personal strategies to solve problems. | Grade 5 |
| Manitoba | 5.N.6.2 | Demonstrate an understanding of division (1- and 2-digit divisors and up to 4-digit dividends), concretely, pictorially, and symbolically, and interpret remainders by using the standard algorithm to solve problems. | Grade 5 |
| Manitoba | 5.N.6.3 | Demonstrate an understanding of division (1- and 2-digit divisors and up to 4-digit dividends), concretely, pictorially, and symbolically, and interpret remainders by estimating quotients to solve problems. | Grade 5 |
| Manitoba | 5.N.7.1 | Demonstrate an understanding of fractions by using concrete and pictorial representations to create sets of equivalent fractions. | Grade 5 |
| Manitoba | 5.N.7.2 | Demonstrate an understanding of fractions by using concrete and pictorial representations to compare fractions with like and unlike denominators. | Grade 5 |
| Manitoba | 5.N.8 | Describe and represent decimals (tenths, hundredths, thousandths) concretely, pictorially, and symbolically. | Grade 5 |
| Manitoba | 5.N.9 | Relate decimals to fractions (tenths, hundredths, thousandths). | Grade 5 |
| Manitoba | 5.N.10 | Compare and order decimals (tenths, hundredths, thousandths) by using benchmarks, place value, and equivalent decimals. | Grade 5 |
| Manitoba | 5.N.11 | Demonstrate an understanding of addition and subtraction of decimals (to thousandths), concretely, pictorially, and symbolically, by using personal strategies, using the standard algorithms, using estimation, and solving problems. | Grade 5 |
| Manitoba | 5.PR.2 | Solve problems involving single-variable (expressed as symbols or letters), one-step equations with whole-number coefficients, and whole-number solutions. | Grade 5 |
| Manitoba | 5.SS.5 | Describe and provide examples of edges and faces of 3-D objects, and sides of 2-D shapes, that are parallel, intersecting, perpendicular, vertical, and horizontal. | Grade 5 |
| Manitoba | 5.SS.6 | Identify and sort quadrilaterals, including rectangles, squares, trapezoids, parallelograms, and rhombuses according to their attributes. | Grade 5 |
| Manitoba | 5.SS.7 | Perform a single transformation (translation, rotation, or reflection) of a 2-D shape, and draw and describe the image. | Grade 5 |
| Manitoba | 5.SS.8 | Identify a single transformation (translation, rotation, or reflection) of 2-D shapes. | Grade 5 |
| Manitoba | 6.N.3.1 | Demonstrate an understanding of factors and multiples by determining multiples and factors of numbers less than 100. | Grade 6 |
| Manitoba | 6.N.3.2 | Demonstrate an understanding of factors and multiples by identifying prime and composite numbers. | Grade 6 |
| Manitoba | 6.N.3.3 | Demonstrate an understanding of factors and multiples by solving problems involving factors or multiples. | Grade 6 |
| Manitoba | 6.N.5 | Demonstrate an understanding of ratio, concretely, pictorially, and symbolically. | Grade 6 |
| Manitoba | 6.N.6 | Demonstrate an understanding of percent (limited to whole numbers), concretely, pictorially, and symbolically. | Grade 6 |
| Manitoba | 6.N.7 | Demonstrate an understanding of integers, concretely, pictorially, and symbolically. | Grade 6 |
| Manitoba | 6.N.8.1 | Demonstrate an understanding of multiplication and division of decimals (involving 1-digit whole-number multipliers, 1-digit natural number divisors, and multipliers and divisors that are multiples of 10), concretely, pictorially, and symbolically, by using personal strategies. | Grade 6 |
| Manitoba | 6.N.8.2 | Demonstrate an understanding of multiplication and division of decimals (involving 1-digit whole-number multipliers, 1-digit natural number divisors, and multipliers and divisors that are multiples of 10), concretely, pictorially, and symbolically, by using the standard algorithms. | Grade 6 |
| Manitoba | 6.N.8.3 | Demonstrate an understanding of multiplication and division of decimals (involving 1-digit whole-number multipliers, 1-digit natural number divisors, and multipliers and divisors that are multiples of 10), concretely, pictorially, and symbolically, by using estimation. | Grade 6 |
| Manitoba | 6.N.8.4 | Demonstrate an understanding of multiplication and division of decimals (involving 1-digit whole-number multipliers, 1-digit natural number divisors, and multipliers and divisors that are multiples of 10), concretely, pictorially, and symbolically, by solving problems. | Grade 6 |
| Manitoba | 6.N.9 | Explain and apply the order of operations, excluding exponents (limited to whole numbers). | Grade 6 |
| Manitoba | 6.PR.1 | Demonstrate an understanding of the relationships within tables of values to solve problems. | Grade 6 |
| Manitoba | 6.PR.2 | Represent and describe patterns and relationships using graphs and tables. | Grade 6 |
| Manitoba | 6.PR.4 | Demonstrate and explain the meaning of preservation of equality, concretely, pictorially, and symbolically. | Grade 6 |
| Manitoba | 6.SS.1.1 | Demonstrate an understanding of angles by identifying examples of angles in the environment. | Grade 6 |
| Manitoba | 6.SS.1.2 | Demonstrate an understanding of angles by classifying angles according to their measure. | Grade 6 |
| Manitoba | 6.SS.1.3 | Demonstrate an understanding of angles by estimating the measure of angles using 45°, 90°, and 180° as reference angles. | Grade 6 |
| Manitoba | 6.SS.1.4 | Demonstrate an understanding of angles by determining angle measures in degrees. | Grade 6 |
| Manitoba | 6.SS.1.5 | Demonstrate an understanding of angles by drawing and labelling angles when the measure is specified. | Grade 6 |
| Manitoba | 6.SS.2 | Demonstrate that the sum of interior angles is 180° in a triangle and 360° in a quadrilateral. | Grade 6 |
| Manitoba | 6.SS.4 | Construct and compare triangles, including scalene, isosceles, equilateral, right, obtuse, and acute in different orientations. | Grade 6 |
| Manitoba | 6.SS.5 | Describe and compare the sides and angles of regular and irregular polygons. | Grade 6 |
| Manitoba | 6.SS.6 | Perform a combination of transformations (translations, rotations, or reflections) on a single 2-D shape, and draw and describe the image. | Grade 6 |
| Manitoba | 6.SS.7 | Perform a combination of successive transformations of 2-D shapes to create a design, and identify and describe the transformations. | Grade 6 |
| Manitoba | 6.SS.8 | Identify and plot points in the first quadrant of a Cartesian plane using whole-number ordered pairs. | Grade 6 |
| Manitoba | 6.SS.9 | Perform and describe single transformations of a 2-D shape in the first quadrant of a Cartesian plane (limited to whole-number vertices). | Grade 6 |
| Manitoba | 6.SP.3 | Graph collected data and analyze the graph to solve problems. | Grade 6 |
| Manitoba | 7.N.2 | Demonstrate an understanding of the addition, subtraction, multiplication, and division of decimals to solve problems (for more than 1-digit divisors or 2-digit multipliers, technology could be used). | Grade 7 |
| Manitoba | 7.N.3 | Solve problems involving percents from 1% to 100%. | Grade 7 |
| Manitoba | 7.N.5 | Demonstrate an understanding of adding and subtracting positive fractions and mixed numbers, with like and unlike denominators, concretely, pictorially, and symbolically (limited to positive sums and differences). | Grade 7 |
| Manitoba | 7.N.6 | Demonstrate an understanding of addition and subtraction of integers, concretely, pictorially, and symbolically. | Grade 7 |
| Manitoba | 7.N.7 | Compare and order fractions, decimals (to thousandths), and integers by using benchmarks, place value and equivalent fractions and/or decimals. | Grade 7 |
| Manitoba | 7.PR.2 | Construct a table of values from a relation, graph the table of values, and analyze the graph to draw conclusions and solve problems. | Grade 7 |
| Manitoba | 7.PR.3 | Demonstrate an understanding of preservation of equality by modelling preservation of equality, concretely, pictorially, and symbolically and applying preservation of equality to solve equations. | Grade 7 |
| Manitoba | 7.PR.5 | Evaluate an expression given the value of the variable(s). | Grade 7 |
| Manitoba | 7.PR.6 | Model and solve problems that can be represented by one-step linear equations of the form x + a = b, concretely, pictorially, and symbolically, where a and b are integers. | Grade 7 |
| Manitoba | 7.PR.7 | Model and solve problems that can be represented by linear equations of the form: ax + b = c, ax = b, concretely, pictorially, and symbolically, where a, b, and c, are whole numbers. | Grade 7 |
| Manitoba | 7.SS.4 | Identify and plot points in the four quadrants of a Cartesian plane using ordered pairs. | Grade 7 |
| Manitoba | 8.N.1 | Demonstrate an understanding of perfect squares and square roots, concretely, pictorially, and symbolically (limited to whole numbers). | Grade 8 |
| Manitoba | 8.N.3 | Demonstrate an understanding of percents greater than or equal to 0%. | Grade 8 |
| Manitoba | 8.N.4 | Demonstrate an understanding of ratio and rate. | Grade 8 |
| Manitoba | 8.N.5 | Solve problems that involve rates, ratios, and proportional reasoning. | Grade 8 |
| Manitoba | 8.N.6 | Demonstrate an understanding of multiplying and dividing positive fractions and mixed numbers, concretely, pictorially, and symbolically. | Grade 8 |
| Manitoba | 8.N.7 | Demonstrate an understanding of multiplication and division of integers, concretely, pictorially, and symbolically. | Grade 8 |
| Manitoba | 8.N.8 | Solve problems involving positive rational numbers. | Grade 8 |
| Manitoba | 8.PR.1 | Graph and analyze two-variable linear relations. | Grade 8 |
| Manitoba | 8.PR.2 | Model and solve problems using linear equations concretely, pictorially, and symbolically, where a, b, and c, are integers | Grade 8 |
| Manitoba | 8.SS.1 | Develop and apply the Pythagorean theorem to solve problems. | Grade 8 |
| Manitoba | 10I.A.3 | Demonstrate an understanding of powers with integral and rational exponents. | Algebra |
| Manitoba | 9.PR.2 | Graph linear relations, analyze the graph, and interpolate or extrapolate to solve problems. | Algebra |
| Manitoba | 9.PR.4 | Explain and illustrate strategies to solve single variable linear inequalities with rational coefficients within a problem-solving context. | Algebra |
| Manitoba | 9.PR.5 | Demonstrate an understanding of polynomials (limited to polynomials of degree less than or equal to 2). | Algebra |
| Manitoba | 9.PR.6 | Model, record, and explain the operations of addition and subtraction of polynomial expressions, concretely, pictorially, and symbolically (limited to polynomials of degree less than or equal to 2). | Algebra |
| Manitoba | 10I.R.2 | Demonstrate an understanding of relations and functions. | Algebra |
| Manitoba | 10I.R.4.4 | Describe and represent linear relations, using graphs. | Algebra |
| Manitoba | 10I.R.8 | Represent a linear function, using function notation. | Algebra |
| Manitoba | 10I.R.7.5 | Determine the equation of a linear relation, given a scatterplot. | Algebra |
| Manitoba | 11P.R.4.5 | Analyze quadratic functions of the form y = ax^2 + bx + c to identify characteristics of the corresponding graph, including x- and y-intercepts. | Algebra |
| Manitoba | 9.SS.4 | Draw and interpret scale diagrams of 2-D shapes. | Algebra |
| Maryland | K.CC.A.1 | Count to 100 by ones and by tens. | Kindergarten |
| Maryland | K.CC.A.2 | Count forward beginning from a given number within the known sequence (instead of having to begin at 1). | Kindergarten |
| Maryland | K.CC.A.3 | Write numbers from 0 to 20. Represent a number of objects with a written numeral 0-20 (with 0 representing a count of no objects). | Kindergarten |
| Maryland | K.CC.B.4 | Understand the relationship between numbers and quantities; connect counting to cardinality. | Kindergarten |
| Maryland | K.CC.B.5 | Count to answer “how many?” questions about as many as 20 things arranged in a line, a rectangular array, or a circle, or as many as 10 things in a scattered configuration; given a number from 1-20, count out that many objects. | Kindergarten |
| Maryland | K.CC.C.6 | Identify whether the number of objects in one group is greater than, less than, or equal to the number of objects in another group, e.g., by using matching and counting strategies (Include groups with up to ten objects). | Kindergarten |
| Maryland | K.CC.C.7 | Compare two numbers between 1 and 10 presented as written numerals. | Kindergarten |
| Maryland | K.G.A.1 | Describe objects in the environment using names of shapes, and describe the relative positions of these objects using terms such as above, below, beside, in front of, behind, and next to. | Kindergarten |
| Maryland | K.G.A.2 | Correctly name shapes regardless of their orientations or overall size. | Kindergarten |
| Maryland | K.G.A.3 | Identify shapes as two-dimensional (lying in a plane, “flat”) or three-dimensional (“solid”). | Kindergarten |
| Maryland | K.G.B.4 | Analyze and compare two- and three-dimensional shapes, in different sizes and orientations, using informal language to describe their similarities, differences, parts (e.g., number of sides and vertices/”corners”) and other attributes (e.g., having sides of equal length). | Kindergarten |
| Maryland | K.G.B.6 | Compose simple shapes to form larger shapes. | Kindergarten |
| Maryland | K.MD.A.1 | Describe measurable attributes of objects, such as length or weight. Describe several measurable attributes of a single object. | Kindergarten |
| Maryland | K.MD.A.2 | Directly compare two objects with a measurable attribute in common, to see which object has “more of”/”less of” the attribute, and describe the difference. | Kindergarten |
| Maryland | K.MD.B.3 | Classify objects into given categories; count the number of objects in each category and sort the categories by count (Limit category counts to be less than or equal to 10.). | Kindergarten |
| Maryland | K.NBT.A.1 | Compose and decompose numbers from 11 to 19 into ten ones and some further ones, e.g., by using objects or drawings, and record each composition or decomposition by a drawing or equation (such as 18 = 10 + 8); understand that these numbers are composed of ten ones and one, two, three, four, five, six, seven, eight, or nine ones. | Kindergarten |
| Maryland | K.OA.A.1 | Represent addition and subtraction with objects, fingers, mental images, drawings, sounds (e.g., claps), acting out situations, or verbal explanations, expressions, or equations. | Kindergarten |
| Maryland | K.OA.A.2 | Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem. | Kindergarten |
| Maryland | K.OA.A.3 | Decompose numbers less than or equal to 10 into pairs in more than one way, e.g., by using objects or drawing, and record each decomposition by a drawing or equation (e.g., 5 = 2 + 3 and 5 = 4 + 1). | Kindergarten |
| Maryland | K.OA.A.4 | For any number from 1 to 9, find the number that makes 10 when added to the given number, e.g., by using objects or drawings and record the answer with a drawing or equation. | Kindergarten |
| Maryland | K.OA.A.5 | Fluently add and subtract within 5. | Kindergarten |
| Maryland | 1.G.A.1 | Distinguish between defining attributes (e.g., triangles are closed and three-sided) versus non-defining attributes (e.g., color, orientation, overall size); build and draw shapes to possess defining attributes. | Grade 1 |
| Maryland | 1.G.A.2 | Compose two-dimensional shapes (rectangles, squares, trapezoids, triangles, half-circles, and quarter-circles) or three-dimensional shapes (cubes, right rectangular prisms, right circular cones, and right circular cylinders) to create a composite shape, and compose new shapes from the composite shape. | Grade 1 |
| Maryland | 1.G.A.3 | Partition circles and rectangles into two and four equal shares, describe the shares using the words halves, fourths, and quarters, and use the phrases half of, fourth of, and quarter of. Describe the whole as two of, or four of the shares. Understand for these examples that decomposing into more equal shares creates smaller shares. | Grade 1 |
| Maryland | 1.MD.A.1 | Order three objects by length; compare the lengths of two objects indirectly by using a third object. | Grade 1 |
| Maryland | 1.MD.A.2 | Express the length of an object as a whole number of length units, by laying multiple copies of a shorter object (the length unit) end to end; understand that the length measurement of an object is the number of same-size length units that span it with no gaps or overlaps. | Grade 1 |
| Maryland | 1.MD.B.3 | Tell and write time in hours and half-hours using analog and digital clocks. | Grade 1 |
| Maryland | 1.MD.C.4 | Organize, represent, and interpret data with up to three categories; ask and answer questions about the total number of data points, how many in each category, and how many more or less are in one category than in another. | Grade 1 |
| Maryland | 1.NBT.A.1 | Count to 120 starting at any number less than 120. In this range, read and write numerals and represent a number of objects with a written numeral. | Grade 1 |
| Maryland | 1.NBT.B.2 | Understand that the two digits of a two-digit number represent amounts of tens and ones. | Grade 1 |
| Maryland | 1.NBT.B.3 | Compare two two-digit numbers based on meanings of the tens and ones digits, recording the results of comparisons with the symbols >,=, and <. | Grade 1 |
| Maryland | 1.NBT.C.4 | Add within 100, including adding a two-digit number and a one-digit number, and adding a two-digit number and a multiple of 10, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Understand that in adding two-digit numbers, one adds tens and tens, ones and ones, and sometimes it is necessary to compose a ten. | Grade 1 |
| Maryland | 1.NBT.C.5 | Given a two-digit number, mentally find 10 more or 10 less than the number, without having to count; explain the reasoning used. | Grade 1 |
| Maryland | 1.NBT.C.6 | Subtract multiples of 10 in the range of 10-90 from multiples of 10 in the range of 10-90 (positive or zero differences), using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. | Grade 1 |
| Maryland | 1.OA.A.1 | Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem. | Grade 1 |
| Maryland | 1.OA.B.3 | Apply properties of operations as strategies to add and subtract. (Students need not use formal terms for these properties.) | Grade 1 |
| Maryland | 1.OA.B.4 | Understand subtraction as an unknown-addend problem. | Grade 1 |
| Maryland | 1.OA.C.5 | Relate counting to addition and subtraction (e.g., by counting on 2 to add 2). | Grade 1 |
| Maryland | 1.OA.C.6 | Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on, making ten (e.g., 8 + 6 = 8 + 2 + 4, which leads to 10 + 4 = 14); decomposing a number leading to a ten (13 – 4 = 13 – 3 – 1, which leads to 10 – 1 = 9); using the relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 – 8 = 4); and creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1, which equals 13). | Grade 1 |
| Maryland | 1.OA.D.7 | Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false. | Grade 1 |
| Maryland | 1.OA.D.8 | Determine the unknown whole number in an addition or subtraction equation relating three whole numbers. | Grade 1 |
| Maryland | 2.G.A.1 | Recognize and draw shapes having specific attributes, such as a given number of angles or a given number of equal faces. Identify triangles, quadrilaterals, pentagons, hexagons, and cubes. | Grade 2 |
| Maryland | 2.G.A.2 | Partition a rectangle into rows and columns of same-size squares and count to find the total number of them. | Grade 2 |
| Maryland | 2.G.A.3 | Partition circles and rectangles into two, three, or four equal shares, describe the shares using the words halves, thirds, half of, a third of, etc., and describe the whole as two halves, three thirds, four fourths. Recognize that equal shares of identical wholes need not have the same shape. | Grade 2 |
| Maryland | 2.MD.A.1 | Measure the length of an object by selecting and using appropriate tools such as rulers, yardsticks, meter sticks, and measuring tapes. | Grade 2 |
| Maryland | 2.MD.A.2 | Measure the length of an object twice, using length units of different lengths for the two measurements; describe how the two measurements relate to the size of the unit chosen. | Grade 2 |
| Maryland | 2.MD.A.4 | Measure to determine how much longer one object is than another, expressing the length difference in terms of a standard length unit. | Grade 2 |
| Maryland | 2.MD.B.5 | Use addition and subtraction within 100 to solve word problems involving lengths that are given in the same units, e.g., by using drawings (such as drawings of rulers) and equations with a symbol for the unknown number to represent the problem. | Grade 2 |
| Maryland | 2.MD.C.7 | Tell and write time from analog and digital clocks to the nearest five minutes, using a.m. and p.m. | Grade 2 |
| Maryland | 2.MD.C.8 | Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies, using $ and ¢ symbols appropriately. | Grade 2 |
| Maryland | 2.MD.D.9 | Generate measurement data by measuring lengths of several objects to the nearest whole unit, or by making repeated measurements of the same object. Show the measurements by making a line plot, where the horizontal scale is marked off in whole-number units. | Grade 2 |
| Maryland | 2.MD.D.10 | Draw a picture graph and a bar graph (with single-unit scale) to represent a data set with up to four categories. Solve simple put-together, take-apart, and compare problems using information presented in a bar graph. | Grade 2 |
| Maryland | 2.NBT.A.1 | Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones. | Grade 2 |
| Maryland | 2.NBT.A.2 | Count within 1000; skip-count by 5s, 10s, and 100s. | Grade 2 |
| Maryland | 2.NBT.A.3 | Read and write numbers to 1000 using base-ten numerals, number names, and expanded form. | Grade 2 |
| Maryland | 2.NBT.A.4 | Compare two three-digit numbers based on meanings of the hundreds, tens, and ones digits, using >, =, and < symbols to record the results of comparisons. | Grade 2 |
| Maryland | 2.NBT.B.5 | Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction. | Grade 2 |
| Maryland | 2.NBT.B.6 | Add up to four two-digit numbers using strategies based on place value, properties of operations. | Grade 2 |
| Maryland | 2.NBT.B.7 | Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method. Understand that in adding or subtracting three- digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds. | Grade 2 |
| Maryland | 2.NBT.B.8 | Use place value understanding and properties of operations to add and subtract. Mentally add 10 or 100 to a given number 100-900, and mentally subtract 10 or 100 from a given number 100-900. | Grade 2 |
| Maryland | 2.OA.A.1 | Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using drawings, and equations with a symbol for the unknown number to represent the problem. | Grade 2 |
| Maryland | 2.OA.B.2 | Fluently add and subtract within 20 using mental strategies. By end of Grade 2, know from memory all sums of two one-digit numbers. | Grade 2 |
| Maryland | 2.OA.C.3 | Determine whether a group of objects up to 20 has an odd or even number of members, e.g., by pairing objects or counting them by 2s; write an equation to express an even number as a sum of two equal addends. | Grade 2 |
| Maryland | 2.OA.C.4 | Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends. | Grade 2 |
| Maryland | 3.G.A.1 | Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories. | Grade 3 |
| Maryland | 3.G.A.2 | Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole. | Grade 3 |
| Maryland | 3.MD.A.1 | Tell and write time to the nearest minute and measure time intervals in minutes. Solve word problems involving addition and subtraction of time intervals in minutes, e.g., by representing the problem on a number line diagram. | Grade 3 |
| Maryland | 3.MD.A.2 | Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l). Add, subtract, multiply, or divide to solve one-step word problems involving masses or volumes that are given in the same units, e.g., by using drawings (such as a beaker with a measurement scale) to represent the problem. | Grade 3 |
| Maryland | 3.MD.B.3 | Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and two-step “how many more” and “how may less” problems using information presented in scaled bar graphs. | Grade 3 |
| Maryland | 3.MD.B.4 | Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Show the data by making a line plot where the horizontal scale is marked off in appropriate units–whole numbers, halves, or quarters. | Grade 3 |
| Maryland | 3.MD.C.5 | Recognize area as an attribute of plane figures and understand concept of area measurement. | Grade 3 |
| Maryland | 3.MD.C.6 | Measure areas by counting unit squares (square cm, square m, square in., square ft., and improvised units). | Grade 3 |
| Maryland | 3.MD.C.7 | Relate area to the operations of multiplication and addition. | Grade 3 |
| Maryland | 3.MD.D.8 | Solve real world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters. | Grade 3 |
| Maryland | 3.NBT.A.1 | Use place value understanding to round whole numbers to the nearest 10 or 100. | Grade 3 |
| Maryland | 3.NBT.A.2 | Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction. | Grade 3 |
| Maryland | 3.NBT.A.3 | Multiply one-digit whole numbers by multiples of 10 in the range of 10-90 (e.g., 9 x 80, 5 x 60) using strategies based on place value and properties of operations. | Grade 3 |
| Maryland | 3.NF.A.1 | Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b. | Grade 3 |
| Maryland | 3.NF.A.2 | Understand a fraction as a number on the number line; represent fractions on a number line diagram. | Grade 3 |
| Maryland | 3.NF.A.3 | Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size. | Grade 3 |
| Maryland | 3.OA.A.1 | Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each. | Grade 3 |
| Maryland | 3.OA.A.2 | Interpret whole-number quotients of whole numbers, e.g., interpret 56 ÷ 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each. | Grade 3 |
| Maryland | 3.OA.A.3 | Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem. | Grade 3 |
| Maryland | 3.OA.A.4 | Determine the unknown whole number in a multiplication or division equation relating three whole numbers. | Grade 3 |
| Maryland | 3.OA.B.5 | Apply properties of operations as strategies to multiply and divide. | Grade 3 |
| Maryland | 3.OA.B.6 | Understand division as an unknown-factor problem. | Grade 3 |
| Maryland | 3.OA.C.7 | Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 × 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers. | Grade 3 |
| Maryland | 3.OA.D.8 | Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. | Grade 3 |
| Maryland | 3.OA.D.9 | Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations. | Grade 3 |
| Maryland | 4.G.A.1 | Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures. | Grade 4 |
| Maryland | 4.G.A.2 | Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles. | Grade 4 |
| Maryland | 4.G.A.3 | Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify line-symmetric figures and draw lines of symmetry. | Grade 4 |
| Maryland | 4.MD.A.1 | Know relative sizes of measurement units within one system of units including km, m, cm, kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table. | Grade 4 |
| Maryland | 4.MD.A.2 | Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. | Grade 4 |
| Maryland | 4.MD.A.3 | Apply the area and perimeter formulas for rectangles in real world and mathematical problems. | Grade 4 |
| Maryland | 4.MD.B.4 | Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots. | Grade 4 |
| Maryland | 4.MD.C.5 | Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement. | Grade 4 |
| Maryland | 4.MD.C.6 | Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure. | Grade 4 |
| Maryland | 4.MD.C.7 | Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems, e.g., by using an equation with a symbol for the unknown angle measure. | Grade 4 |
| Maryland | 4.NBT.A.1 | Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. | Grade 4 |
| Maryland | 4.NBT.A.2 | Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. | Grade 4 |
| Maryland | 4.NBT.A.3 | Use place value understanding to round multi-digit whole numbers to any place. | Grade 4 |
| Maryland | 4.NBT.B.4 | Fluently add and subtract multi-digit whole numbers using the standard algorithm. | Grade 4 |
| Maryland | 4.NBT.B.5 | Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. | Grade 4 |
| Maryland | 4.NBT.B.6 | Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. | Grade 4 |
| Maryland | 4.NF.A.1 | Explain why a fraction a/b is equivalent to a fraction (n x a)/(n x b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. | Grade 4 |
| Maryland | 4.NF.A.2 | Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as ½. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, <, and justify the conclusions, e.g., by using a visual fraction model. | Grade 4 |
| Maryland | 4.NF.B.3 | Understand a fraction a/b with a > 1 as a sum of fractions 1/b. | Grade 4 |
| Maryland | 4.NF.B.4 | Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. | Grade 4 |
| Maryland | 4.NF.C.5 | Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100. | Grade 4 |
| Maryland | 4.NF.C.6 | Use decimal notation for fractions with denominators 10 and 100. | Grade 4 |
| Maryland | 4.NF.C.7 | Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, =, <, and justify the conclusions, e.g., by using a visual model. | Grade 4 |
| Maryland | 4.OA.A.1 | Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 × 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations. | Grade 4 |
| Maryland | 4.OA.A.2 | Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison. | Grade 4 |
| Maryland | 4.OA.A.3 | Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. | Grade 4 |
| Maryland | 4.OA.B.4 | Find all factor pairs for a whole number in the range 1-100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1-100 is a multiple of a given one-digit number. Determine whether a given whole number in the range of 1-100 is prime or composite. | Grade 4 |
| Maryland | 4.OA.C.5 | Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. | Grade 4 |
| Maryland | 5.G.A.1 | Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate). | Grade 5 |
| Maryland | 5.G.A.2 | Represent real world mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. | Grade 5 |
| Maryland | 5.G.B.3 | Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. | Grade 5 |
| Maryland | 5.G.B.4 | Classify two-dimensional figures in a hierarchy based on properties. | Grade 5 |
| Maryland | 5.MD.A.1 | Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step real world problems. | Grade 5 |
| Maryland | 5.MD.B.2 | Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations for this grade to solve problems involving information presented in line plots. | Grade 5 |
| Maryland | 5.MD.C.3 | Recognize volume as an attribute of solid figures and understand concepts of volume measurement. | Grade 5 |
| Maryland | 5.MD.C.4 | Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. | Grade 5 |
| Maryland | 5.MD.C.5 | Relate volume to the operations of multiplication and addition, and solve real world and mathematical problems involving volume. | Grade 5 |
| Maryland | 5.NBT.A.1 | Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. | Grade 5 |
| Maryland | 5.NBT.A.2 | Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole number exponents to denote powers of 10. | Grade 5 |
| Maryland | 5.NBT.A.3 | Read, write, and compare decimals to thousandths. (builds on grade 4 work to hundredths) | Grade 5 |
| Maryland | 5.NBT.A.4 | Use place value understanding to round decimals to any place. | Grade 5 |
| Maryland | 5.NBT.B.5 | Fluently multiply multi-digit whole numbers using the standard algorithm. | Grade 5 |
| Maryland | 5.NBT.B.6 | Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. | Grade 5 |
| Maryland | 5.NBT.B.7 | Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. | Grade 5 |
| Maryland | 5.NF.A.1 | Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. | Grade 5 |
| Maryland | 5.NF.A.2 | Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. | Grade 5 |
| Maryland | 5.NF.B.3 | Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. | Grade 5 |
| Maryland | 5.NF.B.4 | Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. | Grade 5 |
| Maryland | 5.NF.B.5 | Interpret multiplication as scaling (resizing). | Grade 5 |
| Maryland | 5.NF.B.6 | Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. | Grade 5 |
| Maryland | 5.NF.B.7 | Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. | Grade 5 |
| Maryland | 5.OA.A.1 | Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. | Grade 5 |
| Maryland | 5.OA.A.2 | Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. | Grade 5 |
| Maryland | 5.OA.B.3 | Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. | Grade 5 |
| Maryland | 6.EE.1 | Write and evaluate numerical expressions involving whole-number exponents. | Grade 6 |
| Maryland | 6.EE.2 | Write, read, and evaluate expressions in which letters stand for numbers. | Grade 6 |
| Maryland | 6.EE.3 | Apply the properties of operations to generate equivalent expressions. | Grade 6 |
| Maryland | 6.EE.4 | Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). | Grade 6 |
| Maryland | 6.EE.5 | Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true. | Grade 6 |
| Maryland | 6.EE.6 | Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set. | Grade 6 |
| Maryland | 6.EE.7 | Solve real-world and mathematical problems by writing and solving equations of the form 𝘹 + 𝘱 = 𝘲 and 𝘱𝘹 = 𝘲 for cases in which 𝘱, 𝘲 and 𝘹 are all nonnegative rational numbers. | Grade 6 |
| Maryland | 6.EE.8 | Write an inequality of the form 𝘹 > 𝘤 or 𝘹 𝘤 or 𝘹 < 𝘤 have infinitely many solutions; represent solutions of such inequalities on number line diagrams. | Grade 6 |
| Maryland | 6.EE.9 | Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. | Grade 6 |
| Maryland | 6.G.1 | Find area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems. | Grade 6 |
| Maryland | 6.G.2 | Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas 𝘝 = 𝘭 𝘸 𝘩 and 𝘝 = 𝘣 𝘩 to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems. | Grade 6 |
| Maryland | 6.G.3 | Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems. | Grade 6 |
| Maryland | 6.G.4 | Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems. | Grade 6 |
| Maryland | 6.RP.1 | Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. | Grade 6 |
| Maryland | 6.RP.2 | Understand the concept of a unit rate 𝘢/𝘣 associated with a ratio 𝘢:𝘣 with 𝘣 ≠ 0, and use rate language in the context of a ratio relationship. | Grade 6 |
| Maryland | 6.RP.3 | Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. | Grade 6 |
| Maryland | 6.SP.5 | Summarize numerical data sets in relation to their context, such as by: | Grade 6 |
| Maryland | 6.NS.1 | Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. | Grade 6 |
| Maryland | 6.NS.2 | Fluently divide multi-digit numbers using the standard algorithm. | Grade 6 |
| Maryland | 6.NS.3 | Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation. | Grade 6 |
| Maryland | 6.NS.5 | Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation. | Grade 6 |
| Maryland | 6.NS.6 | Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates. | Grade 6 |
| Maryland | 6.NS.7 | Understand ordering and absolute value of rational numbers. | Grade 6 |
| Maryland | 6.NS.8 | Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. | Grade 6 |
| Maryland | 7.EE.1 | Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients. | Grade 7 |
| Maryland | 7.EE.2 | Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. | Grade 7 |
| Maryland | 7.EE.3 | Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically; apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. | Grade 7 |
| Maryland | 7.EE.4 | Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. | Grade 7 |
| Maryland | 7.G.1 | Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale. | Grade 7 |
| Maryland | 7.G.2 | Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle. | Grade 7 |
| Maryland | 7.G.3 | Describe the two-dimensional figures that result from slicing three-dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids. | Grade 7 |
| Maryland | 7.G.4 | Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle. | Grade 7 |
| Maryland | 7.G.5 | Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure. | Grade 7 |
| Maryland | 7.G.6 | Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. | Grade 7 |
| Maryland | 7.RP.1 | Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. | Grade 7 |
| Maryland | 7.RP.2 | Recognize and represent proportional relationships between quantities. | Grade 7 |
| Maryland | 7.RP.3 | Use proportional relationships to solve multistep ratio and percent problems. | Grade 7 |
| Maryland | 7.NS.1 | Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers, and represent addition and subtraction on a horizontal or vertical number line diagram. | Grade 7 |
| Maryland | 7.NS.2 | Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers. | Grade 7 |
| Maryland | 7.NS.3 | Solve real-world and mathematical problems involving the four operations with rational numbers. | Grade 7 |
| Maryland | 8.EE.1 | Know and apply the properties of integer exponents to generate equivalent numerical expressions. | Grade 8 |
| Maryland | 8.EE.2 | Use square root and cube root symbols to represent solutions to equations of the form 𝘹² = 𝘱 and 𝘹³ = 𝘱, where 𝘱 is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that √2 is irrational. | Grade 8 |
| Maryland | 8.EE.3 | Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other. | Grade 8 |
| Maryland | 8.EE.4 | Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology. | Grade 8 |
| Maryland | 8.EE.5 | Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. | Grade 8 |
| Maryland | 8.EE.6 | Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation 𝘺 = 𝘮𝘹 for a line through the origin and the equation 𝘺 = 𝘮𝘹 + 𝘣 for a line intercepting the vertical axis at 𝘣. | Grade 8 |
| Maryland | 8.EE.7 | Solve linear equations in one variable. | Grade 8 |
| Maryland | 8.EE.8 | Analyze and solve pairs of simultaneous linear equations. | Grade 8 |
| Maryland | 8.F.1 | Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output. | Grade 8 |
| Maryland | 8.F.2 | Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). | Grade 8 |
| Maryland | 8.F.3 | Interpret the equation 𝘺 = 𝘮𝘹 + 𝘣 as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. | Grade 8 |
| Maryland | 8.F.4 | Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (𝘹, 𝘺) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values. | Grade 8 |
| Maryland | 8.F.5 | Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally. | Grade 8 |
| Maryland | 8.G.1 | Verify experimentally the properties of rotations, reflections, and translations. | Grade 8 |
| Maryland | 8.G.2 | Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them. | Grade 8 |
| Maryland | 8.G.3 | Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates. | Grade 8 |
| Maryland | 8.G.4 | Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two-dimensional figures, describe a sequence that exhibits the similarity between them. | Grade 8 |
| Maryland | 8.G.5 | Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. | Grade 8 |
| Maryland | 8.G.7 | Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions. | Grade 8 |
| Maryland | 8.G.8 | Apply the Pythagorean Theorem to find the distance between two points in a coordinate system. | Grade 8 |
| Maryland | 8.G.9 | Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems. | Grade 8 |
| Maryland | 8.SP.1 | Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association. | Grade 8 |
| Maryland | 8.SP.2 | Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line. | Grade 8 |
| Maryland | 8.NS.2 | Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g., π²). | Grade 8 |
| Massachusetts | K.CC.A.1 | Count to 100 by ones and by tens. | Kindergarten |
| Massachusetts | K.CC.A.2 | Count forward beginning from a given number within the known sequence (instead of having to begin at one). | Kindergarten |
| Massachusetts | K.CC.A.3 | Write numbers from 0 to 20. Represent a number of objects with a written numeral 0–20 (with 0 representing a count of no objects). | Kindergarten |
| Massachusetts | K.CC.B.4 | Understand the relationship between numbers and quantities; connect counting to cardinality. | Kindergarten |
| Massachusetts | K.CC.B.5 | Count to answer “how many?” questions about as many as 20 things arranged in a line, a rectangular array, or a circle, or as many as 10 things in a scattered configuration; given a number from 1–20, count out that many objects. | Kindergarten |
| Massachusetts | K.CC.C.6 | Identify whether the number of objects in one group is greater than, less than, or equal to the number of objects in another group for groups with up to 10 objects, e.g., by using matching and counting strategies. | Kindergarten |
| Massachusetts | K.CC.C.7 | Compare two numbers between 1 and 10 presented as written numerals. | Kindergarten |
| Massachusetts | K.G.A.1 | Describe objects in the environment using names of shapes, and describe the relative positions of these objects using terms such as above, below, beside, in front of, behind, and next to. | Kindergarten |
| Massachusetts | K.G.A.2 | Correctly name shapes regardless of their orientation or overall size. | Kindergarten |
| Massachusetts | K.G.A.3 | Identify shapes as two-dimensional (lying in a plane, “flat”) or three-dimensional (“solid”). | Kindergarten |
| Massachusetts | K.G.B.4 | Analyze and compare two- and three-dimensional shapes, in different sizes and orientations, using informal language to describe their similarities, differences, parts (e.g., number of sides and vertices/“corners”) and other attributes (e.g., having sides of equal length). | Kindergarten |
| Massachusetts | K.G.B.6 | Compose simple shapes to form larger shapes. | Kindergarten |
| Massachusetts | K.MD.A.1 | Describe measurable attributes of objects, such as length or weight. Describe several measurable attributes of a single object. | Kindergarten |
| Massachusetts | K.MD.A.2 | Directly compare two objects with a measurable attribute in common, to see which object has “more of”/“less of” the attribute, and describe the difference. | Kindergarten |
| Massachusetts | K.MD.B.3 | Classify objects into given categories; count the numbers of objects in each category (up to and including 10) and sort the categories by count. | Kindergarten |
| Massachusetts | K.NBT.A.1 | Compose and decompose numbers from 11 to 19 into ten ones and some further ones, e.g., by using objects or drawings, and record each composition or decomposition by a drawing or equation (e.g., 18 = 10 + 8); understand that these numbers are composed of ten ones and one, two, three, four, five, six, seven, eight, or nine ones. | Kindergarten |
| Massachusetts | K.OA.A.1 | Represent addition and subtraction with objects, fingers, mental images, drawings, sounds (e.g., claps), acting out situations, verbal explanations, expressions, or equations. | Kindergarten |
| Massachusetts | K.OA.A.2 | Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem. | Kindergarten |
| Massachusetts | K.OA.A.3 | Decompose numbers less than or equal to 10 into pairs in more than one way, e.g., by using objects or drawings, and record each decomposition by a drawing or equation (e.g., 5 = 2 + 3 and 5 = 4 + 1). | Kindergarten |
| Massachusetts | K.OA.A.4 | For any number from 1 to 9, find the number that makes 10 when added to the given number, e.g., by using objects or drawings, and record the answer with a drawing or equation. | Kindergarten |
| Massachusetts | K.OA.A.5 | Fluently add and subtract within 5, including zero. | Kindergarten |
| Massachusetts | 1.G.A.1 | Distinguish between defining attributes (e.g., triangles are closed and three-sided) versus non-defining attributes (e.g., color, orientation, overall size); build and draw shapes that possess defining attributes. | Grade 1 |
| Massachusetts | 1.G.A.2 | Compose two-dimensional shapes (rectangles, squares, trapezoids, triangles, half-circles, and quarter-circles) or three-dimensional shapes (cubes, right rectangular prisms, right circular cones, and right circular cylinders) to create a composite shape, and compose new shapes from the composite shape. | Grade 1 |
| Massachusetts | 1.G.A.3 | Partition circles and rectangles into two and four equal shares, describe the shares using the words halves, fourths, and quarters, and use the phrases half of, fourth of, and quarter of. Describe the whole as two of, or four of the shares. Understand for these examples that decomposing into more equal shares creates smaller shares. | Grade 1 |
| Massachusetts | 1.MD.A.1 | Order three objects by length; compare the lengths of two objects indirectly by using a third object. | Grade 1 |
| Massachusetts | 1.MD.A.2 | Express the length of an object as a whole number of length units, by laying multiple copies of a shorter object (the length unit) end to end; understand that the length measurement of an object is the number of same-size length units that span it with no gaps or overlaps. | Grade 1 |
| Massachusetts | 1.MD.B.3 | Tell and write time in hours and half-hours using analog and digital clocks. | Grade 1 |
| Massachusetts | 1.MD.C.4 | Organize, represent, and interpret data with up to three categories; ask and answer questions about the total number of data points, how many in each category, and how many more or less are in one category than in another. | Grade 1 |
| Massachusetts | 1.MD.D.5 | Identify the values of all U.S. coins and know their comparative values (e.g., a dime is of greater value than a nickel). Find equivalent values (e.g., a nickel is equivalent to five pennies). Use appropriate notation (e.g., 69¢). Use the values of coins in the solutions of problems (up to 100¢). | Grade 1 |
| Massachusetts | 1.NBT.A.1 | Count to 120, starting at any number less than 120. In this range, read and write numerals and represent a number of objects with a written numeral. | Grade 1 |
| Massachusetts | 1.NBT.B.2 | Understand that the two digits of a two-digit number represent amounts of tens and ones. | Grade 1 |
| Massachusetts | 1.NBT.B.3 | Compare two two-digit numbers based on meanings of the tens and ones digits, recording the results of comparisons with the symbols >, =, and <. | Grade 1 |
| Massachusetts | 1.NBT.C.4 | Add within 100, including adding a two-digit number and a one-digit number, and adding a two-digit number and a multiple of 10, using concrete models or drawings, and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Understand that in adding two-digit numbers, one adds tens and tens, ones and ones; and sometimes it is necessary to compose a ten. | Grade 1 |
| Massachusetts | 1.NBT.C.5 | Given a two-digit number, mentally find 10 more or 10 less than the number, without having to count; explain the reasoning used. Identify arithmetic patterns of 10 more and 10 less than using strategies based on place value. | Grade 1 |
| Massachusetts | 1.NBT.C.6 | Subtract multiples of 10 in the range 10–90 from multiples of 10 in the range 10–90 (positive or zero differences), using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. | Grade 1 |
| Massachusetts | 1.OA.A.1 | Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using objects, drawings, and equations (number sentences) with a symbol for the unknown number to represent the problem. | Grade 1 |
| Massachusetts | 1.OA.B.3 | Apply properties of operations to add. | Grade 1 |
| Massachusetts | 1.OA.B.4 | Understand subtraction as an unknown-addend problem. | Grade 1 |
| Massachusetts | 1.OA.C.5 | Relate counting to addition and subtraction (e.g., by counting on 2 to add 2). | Grade 1 |
| Massachusetts | 1.OA.C.6 | Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use mental strategies such as counting on; making 10 (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to a 10 (e.g., 13 – 4 = 13 – 3 – 1 = 10 – 1 = 9); using the relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 – 8 = 4); and creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13). | Grade 1 |
| Massachusetts | 1.OA.D.7 | Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false. | Grade 1 |
| Massachusetts | 1.OA.D.8 | Determine the unknown whole number in an addition or subtraction equation relating three whole numbers. | Grade 1 |
| Massachusetts | 2.G.A.1 | Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces. Identify triangles, squares, rectangles, rhombuses, trapezoids, pentagons, hexagons, and cubes. | Grade 2 |
| Massachusetts | 2.G.A.2 | Partition a rectangle into rows and columns of same-size squares and count to find the total number of them. | Grade 2 |
| Massachusetts | 2.G.A.3 | Partition circles and rectangles into two, three, or four equal shares, describe the shares using the words halves, thirds, half of, a third of, etc., and describe the whole as two halves, three thirds, four fourths. Recognize that equal shares of identical wholes need not have the same shape. | Grade 2 |
| Massachusetts | 2.MD.A.1 | Measure the length of an object by selecting and using appropriate tools such as rulers, yardsticks, meter sticks, and measuring tapes. | Grade 2 |
| Massachusetts | 2.MD.A.2 | Measure the length of an object twice, using length units of different lengths for the two measurements; describe how the two measurements relate to the size of the unit chosen. | Grade 2 |
| Massachusetts | 2.MD.A.4 | Measure to determine how much longer one object is than another, expressing the length difference in terms of a standard length unit. | Grade 2 |
| Massachusetts | 2.MD.B.5 | Use addition and subtraction within 100 to solve word problems involving lengths that are given in the same units, e.g., by using drawings (such as drawings of rulers) and equations with a symbol for the unknown number to represent the problem. | Grade 2 |
| Massachusetts | 2.MD.C.7 | Tell and write time from analog and digital clocks to the nearest five minutes, using a.m. and p.m. | Grade 2 |
| Massachusetts | 2.MD.C.8 | Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies (up to $10), using $ and ¢ symbols appropriately and whole dollar amounts. | Grade 2 |
| Massachusetts | 2.MD.D.9 | Generate measurement data by measuring lengths of several objects to the nearest whole unit, or by making repeated measurements of the same object. Organize and record the data on a line plot (dot plot) where the horizontal scale is marked off in whole-number units. | Grade 2 |
| Massachusetts | 2.MD.D.10 | Draw a picture graph and a bar graph (with single-unit scale) to represent a data set with up to four categories. Solve simple put-together, take-apart, and compare problems, using information presented in a bar graph. | Grade 2 |
| Massachusetts | 2.NBT.A.1 | Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones. | Grade 2 |
| Massachusetts | 2.NBT.A.2 | Count within 1,000; skip-count by 5s, 10s, and 100s. Identify patterns in skip counting starting at any number. | Grade 2 |
| Massachusetts | 2.NBT.A.3 | Read and write numbers to 1,000 using base-ten numerals, number names, and expanded form. | Grade 2 |
| Massachusetts | 2.NBT.A.4 | Compare two three-digit numbers based on meanings of the hundreds, tens, and ones digits, using >, =, and < symbols to record the results of comparisons. | Grade 2 |
| Massachusetts | 2.NBT.B.5 | Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction. | Grade 2 |
| Massachusetts | 2.NBT.B.6 | Add up to four two-digit numbers using strategies based on place value and properties of operations. | Grade 2 |
| Massachusetts | 2.NBT.B.7 | Add and subtract within 1,000, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method. Understand that in adding or subtracting three-digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds. | Grade 2 |
| Massachusetts | 2.NBT.B.8 | Mentally add 10 or 100 to a given number 100–900, and mentally subtract 10 or 100 from a given number 100–900. | Grade 2 |
| Massachusetts | 2.OA.A.1 | Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem. | Grade 2 |
| Massachusetts | 2.OA.B.2 | Fluently add and subtract within 20 using mental strategies. By end of grade 2, know from memory all sums of two single-digit numbers and related differences. | Grade 2 |
| Massachusetts | 2.OA.C.3 | Determine whether a group of objects (up to 20) has an odd or even number of members, e.g., by pairing objects or counting them by 2s; write an equation to express an even number as a sum of two equal addends. | Grade 2 |
| Massachusetts | 2.OA.C.4 | Use addition to find the total number of objects arranged in rectangular arrays with up to five rows and up to five columns; write an equation to express the total as a sum of equal addends. | Grade 2 |
| Massachusetts | 3.G.A.1 | Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals). Compare and classify shapes by their sides and angles (right angle/non-right angle). Recognize rhombuses, rectangles, squares, and trapezoids as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories. | Grade 3 |
| Massachusetts | 3.G.A.2 | Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole. | Grade 3 |
| Massachusetts | 3.MD.A.1 | Tell and write time to the nearest minute and measure time intervals in minutes. Solve word problems involving addition and subtraction of time intervals in minutes, e.g., by representing the problem on a number line diagram. | Grade 3 |
| Massachusetts | 3.MD.A.2 | Measure and estimate liquid volumes and masses of objects using standard metric units of grams (g), kilograms (kg), and liters (l). Add, subtract, multiply, or divide to solve one-step word problems involving masses or volumes that are given in the same metric units, e.g., by using drawings (such as a beaker with a measurement scale) to represent the problem. | Grade 3 |
| Massachusetts | 3.MD.B.3 | Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and two-step “how many more” and “how many less” problems using information presented in scaled bar graphs. | Grade 3 |
| Massachusetts | 3.MD.B.4 | Generate measurement data by measuring lengths of objects using rulers marked with halves and fourths of an inch. Record and show the data by making a line plot (dot plot), where the horizontal scale is marked off in appropriate units—whole numbers, halves, or fourths. | Grade 3 |
| Massachusetts | 3.MD.C.5 | Recognize area as an attribute of plane figures and understand concepts of area measurement. | Grade 3 |
| Massachusetts | 3.MD.C.6 | Measure areas by counting unit squares (square cm, square m, square in., square ft., and non-standard units). | Grade 3 |
| Massachusetts | 3.MD.C.7 | Relate area to the operations of multiplication and addition. | Grade 3 |
| Massachusetts | 3.MD.D.8 | Solve real-world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters. | Grade 3 |
| Massachusetts | 3.NBT.A.1 | Use place value understanding to round whole numbers to the nearest 10 or 100. | Grade 3 |
| Massachusetts | 3.NBT.A.2 | Fluently add and subtract within 1,000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction. | Grade 3 |
| Massachusetts | 3.NBT.A.3 | Multiply one-digit whole numbers by multiples of 10 in the range 10–90 (e.g., 9 × 80, 5 × 60) using strategies based on place value and properties of operations. | Grade 3 |
| Massachusetts | 3.NF.A.1 | Understand a fraction 1/𝘣 as the quantity formed by 1 part when a whole (a single unit) is partitioned into 𝘣 equal parts; understand a fraction 𝘢/𝘣 as the quantity formed by 𝘢 parts of size 1/𝘣. | Grade 3 |
| Massachusetts | 3.NF.A.2 | Understand a fraction as a number on the number line; represent fractions on a number line diagram. | Grade 3 |
| Massachusetts | 3.NF.A.3 | Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size. | Grade 3 |
| Massachusetts | 3.OA.A.1 | Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in five groups of seven objects each. | Grade 3 |
| Massachusetts | 3.OA.A.2 | Interpret whole-number quotients of whole numbers, e.g., interpret 56 ÷ 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each. | Grade 3 |
| Massachusetts | 3.OA.A.3 | Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem. | Grade 3 |
| Massachusetts | 3.OA.A.4 | Determine the unknown whole number in a multiplication or division equation relating three whole numbers. | Grade 3 |
| Massachusetts | 3.OA.B.5 | Apply properties of operations to multiply. | Grade 3 |
| Massachusetts | 3.OA.B.6 | Understand division as an unknown-factor problem. | Grade 3 |
| Massachusetts | 3.OA.C.7 | Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 × 5 = 40, one knows 40 × 5 = 8) or properties of operations. By the end of grade 3, know from memory all products of two single-digit numbers and related division facts. | Grade 3 |
| Massachusetts | 3.OA.D.8 | Solve two-step word problems using the four operations for problems posed with whole numbers and having whole number answers. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies, including rounding. | Grade 3 |
| Massachusetts | 3.OA.D.9 | Identify arithmetic patterns (including patterns in the addition table or multiplication table) and explain them using properties of operations. | Grade 3 |
| Massachusetts | 4.G.A.1 | Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures. | Grade 4 |
| Massachusetts | 4.G.A.2 | Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles. | Grade 4 |
| Massachusetts | 4.G.A.3 | Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify line-symmetric figures and draw lines of symmetry. | Grade 4 |
| Massachusetts | 4.MD.A.1 | Know relative sizes of measurement units within one system of units, including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table. | Grade 4 |
| Massachusetts | 4.MD.A.2 | Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. | Grade 4 |
| Massachusetts | 4.MD.A.3 | Apply the area and perimeter formulas for rectangles in real-world and mathematical problems. | Grade 4 |
| Massachusetts | 4.MD.B.4 | Make a line plot (dot plot) representation to display a data set of measurements in fractions of a unit (½, ¼, ⅛). Solve problems involving addition and subtraction of fractions by using information presented in line plots (dot plots). | Grade 4 |
| Massachusetts | 4.MD.C.5 | Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement. | Grade 4 |
| Massachusetts | 4.MD.C.6 | Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure. | Grade 4 |
| Massachusetts | 4.MD.C.7 | Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real-world and mathematical problems, e.g., by using an equation with a symbol for the unknown angle measure. | Grade 4 |
| Massachusetts | 4.NBT.A.1 | Recognize that in a multi-digit whole number, a digit in any place represents 10 times as much as it represents in the place to its right. | Grade 4 |
| Massachusetts | 4.NBT.A.2 | Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. | Grade 4 |
| Massachusetts | 4.NBT.A.3 | Use place value understanding to round multi-digit whole numbers to any place. | Grade 4 |
| Massachusetts | 4.NBT.B.4 | Fluently add and subtract multi-digit whole numbers using the standard algorithm. | Grade 4 |
| Massachusetts | 4.NBT.B.5 | Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. | Grade 4 |
| Massachusetts | 4.NBT.B.6 | Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. | Grade 4 |
| Massachusetts | 4.NF.A.1 | Explain why a fraction 𝘢/𝘣 is equivalent to a fraction (𝘯 × 𝘢)/(𝘯 × 𝘣) by using visual fraction models, with attention to how the numbers and sizes of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions, including fractions greater than 1. | Grade 4 |
| Massachusetts | 4.NF.A.2 | Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model. | Grade 4 |
| Massachusetts | 4.NF.B.3 | Understand a fraction 𝘢/𝘣 with 𝘢 > 1 as a sum of fractions 1/𝘣. | Grade 4 |
| Massachusetts | 4.NF.B.4 | Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. | Grade 4 |
| Massachusetts | 4.NF.C.5 | Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100. | Grade 4 |
| Massachusetts | 4.NF.C.6 | Use decimal notation to represent fractions with denominators 10 or 100. | Grade 4 |
| Massachusetts | 4.NF.C.7 | Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual model. | Grade 4 |
| Massachusetts | 4.OA.A.1 | Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 × 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations. | Grade 4 |
| Massachusetts | 4.OA.A.2 | Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison. | Grade 4 |
| Massachusetts | 4.OA.A.3 | Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. | Grade 4 |
| Massachusetts | 4.OA.B.4 | Find all factor pairs for a whole number in the range 1–100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1–100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1–100 is prime or composite. | Grade 4 |
| Massachusetts | 4.OA.C.5 | Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. | Grade 4 |
| Massachusetts | 5.G.A.1 | Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the zero on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., 𝑥-axis and 𝑥-coordinate, 𝑦-axis and 𝑦-coordinate). | Grade 5 |
| Massachusetts | 5.G.A.2 | Represent real-world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. | Grade 5 |
| Massachusetts | 5.G.B.3 | Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. | Grade 5 |
| Massachusetts | 5.G.B.4 | Classify two-dimensional figures in a hierarchy based on properties. | Grade 5 |
| Massachusetts | 5.MD.A.1 | Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real-world problems. | Grade 5 |
| Massachusetts | 5.MD.B.2 | Make a line plot (dot plot) to display a data set of measurements in fractions of a unit. Use operations on fractions for this grade to solve problems involving information presented in line plot (dot plot). | Grade 5 |
| Massachusetts | 5.MD.C.3 | Recognize volume as an attribute of solid figures and understand concepts of volume measurement. | Grade 5 |
| Massachusetts | 5.MD.C.4 | Measure volumes by counting unit cubes, using cubic cm, cubic in., cubic ft., and non-standard units. | Grade 5 |
| Massachusetts | 5.MD.C.5 | Relate volume to the operations of multiplication and addition and solve real-world and mathematical problems involving volume. | Grade 5 |
| Massachusetts | 5.NBT.A.1 | Recognize that in a multi-digit number, including decimals, a digit in any place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. | Grade 5 |
| Massachusetts | 5.NBT.A.2 | Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. | Grade 5 |
| Massachusetts | 5.NBT.A.3 | Read, write, and compare decimals to thousandths. | Grade 5 |
| Massachusetts | 5.NBT.A.4 | Use place value understanding to round decimals to any place. | Grade 5 |
| Massachusetts | 5.NBT.B.5 | Fluently multiply multi-digit whole numbers. (Include two-digit × four-digit numbers and, three-digit × three-digit numbers) using the standard algorithm. | Grade 5 |
| Massachusetts | 5.NBT.B.6 | Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. | Grade 5 |
| Massachusetts | 5.NBT.B.7 | Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction and between multiplication and division; relate the strategy to a written method and explain the reasoning used. | Grade 5 |
| Massachusetts | 5.NF.A.1 | Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. | Grade 5 |
| Massachusetts | 5.NF.A.2 | Solve word problems involving addition and subtraction of fractions referring to the same whole (the whole can be a set of objects), including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. | Grade 5 |
| Massachusetts | 5.NF.B.3 | Interpret a fraction as division of the numerator by the denominator (𝘢/𝘣 = 𝘢 ÷ 𝘣). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. | Grade 5 |
| Massachusetts | 5.NF.B.4 | Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. | Grade 5 |
| Massachusetts | 5.NF.B.5 | Interpret multiplication as scaling (resizing). | Grade 5 |
| Massachusetts | 5.NF.B.6 | Solve real-world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. | Grade 5 |
| Massachusetts | 5.NF.B.7 | Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. | Grade 5 |
| Massachusetts | 5.OA.A.1 | Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols, e.g., (6 × 30) + (6 × ½). | Grade 5 |
| Massachusetts | 5.OA.A.2 | Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. | Grade 5 |
| Massachusetts | 5.OA.B.3 | Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. | Grade 5 |
| Massachusetts | 6.EE.A.1 | Write and evaluate numerical expressions involving whole-number exponents. | Grade 6 |
| Massachusetts | 6.EE.A.2 | Write, read, and evaluate expressions in which letters stand for numbers. | Grade 6 |
| Massachusetts | 6.EE.A.3 | Apply the properties of operations to generate equivalent expressions. | Grade 6 |
| Massachusetts | 6.EE.A.4 | Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). | Grade 6 |
| Massachusetts | 6.EE.B.5 | Understand solving an equation or inequality as a process of answering a question: Which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true. | Grade 6 |
| Massachusetts | 6.EE.B.6 | Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set. | Grade 6 |
| Massachusetts | 6.EE.B.7 | Solve real-world and mathematical problems by writing and solving equations of the form 𝘹 + 𝘱 = 𝘲 and 𝘱𝘹 = 𝘲 for cases in which 𝘱, 𝘲 and 𝘹 are all nonnegative rational numbers. | Grade 6 |
| Massachusetts | 6.EE.B.8 | Write an inequality of the form 𝘹 > 𝘤 or 𝘹 𝘤 or 𝘹 < 𝘤 have infinitely many solutions; represent solutions of such inequalities on number line diagrams. | Grade 6 |
| Massachusetts | 6.EE.C.9 | Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. | Grade 6 |
| Massachusetts | 6.G.A.1 | Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems. | Grade 6 |
| Massachusetts | 6.G.A.2 | Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas 𝘝 = 𝘭𝘸𝘩 and 𝘝 = 𝘉𝘩 to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems. | Grade 6 |
| Massachusetts | 6.G.A.3 | Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems. | Grade 6 |
| Massachusetts | 6.G.A.4 | Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface areas of these figures. Apply these techniques in the context of solving real-world and mathematical problems. | Grade 6 |
| Massachusetts | 6.RP.A.1 | Understand the concept of a ratio including the distinctions between part:part and part:whole and the value of a ratio; part/part and part/whole. Use ratio language to describe a ratio relationship between two quantities. | Grade 6 |
| Massachusetts | 6.RP.A.2 | Understand the concept of a unit rate 𝘢/𝘣 associated with a ratio 𝘢:𝘣 with 𝘣 ≠ 0, and use rate language in the context of a ratio relationship, including the use of units. | Grade 6 |
| Massachusetts | 6.RP.A.3 | Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. | Grade 6 |
| Massachusetts | 6.SP.B.5 | Summarize numerical data sets in relation to their context, such as by: | Grade 6 |
| Massachusetts | 6.NS.A.1 | Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. | Grade 6 |
| Massachusetts | 6.NS.B.2 | Fluently divide multi-digit numbers using the standard algorithm. | Grade 6 |
| Massachusetts | 6.NS.B.3 | Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation. | Grade 6 |
| Massachusetts | 6.NS.C.5 | Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, and positive/negative electric charge). Use positive and negative numbers (whole numbers, fractions, and decimals) to represent quantities in real-world contexts, explaining the meaning of zero in each situation. | Grade 6 |
| Massachusetts | 6.NS.C.6 | Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates. | Grade 6 |
| Massachusetts | 6.NS.C.7 | Understand ordering and absolute value of rational numbers. | Grade 6 |
| Massachusetts | 6.NS.C.8 | Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. | Grade 6 |
| Massachusetts | 7.EE.A.1 | Apply properties of operations to add, subtract, factor, and expand linear expressions with rational coefficients. | Grade 7 |
| Massachusetts | 7.EE.A.2 | Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. | Grade 7 |
| Massachusetts | 7.EE.B.3 | Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. | Grade 7 |
| Massachusetts | 7.EE.B.4 | Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. | Grade 7 |
| Massachusetts | 7.G.A.1 | Solve problems involving scale drawings of geometric figures, such as computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale. | Grade 7 |
| Massachusetts | 7.G.A.2 | Draw (freehand, with ruler and protractor, and with technology) two-dimensional geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle. | Grade 7 |
| Massachusetts | 7.G.A.3 | Describe the shape of the two-dimensional face of the figure that results from slicing three-dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids. | Grade 7 |
| Massachusetts | 7.G.B.4 | Circles and measurement: | Grade 7 |
| Massachusetts | 7.G.B.5 | Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write simple equations and use them to solve for an unknown angle in a figure. | Grade 7 |
| Massachusetts | 7.G.B.6 | Solve real-world and mathematical problems involving area, volume, and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. | Grade 7 |
| Massachusetts | 7.RP.A.1 | Compute unit rates associated with ratios of fractions, including ratios of lengths, areas, and other quantities measured in like or different units. | Grade 7 |
| Massachusetts | 7.RP.A.2 | Recognize and represent proportional relationships between quantities. | Grade 7 |
| Massachusetts | 7.RP.A.3 | Use proportional relationships to solve multi-step ratio, rate, and percent problems. | Grade 7 |
| Massachusetts | 7.NS.A.1 | Apply and extend previous understandings of addition and subtraction to add and subtract integers and other rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram. | Grade 7 |
| Massachusetts | 7.NS.A.2 | Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide integers and other rational numbers. | Grade 7 |
| Massachusetts | 7.NS.A.3 | Solve real-world and mathematical problems involving the four operations with integers and other rational numbers. | Grade 7 |
| Massachusetts | 8.EE.A.1 | Know and apply the properties of integer exponents to generate equivalent numerical expressions. | Grade 8 |
| Massachusetts | 8.EE.A.2 | Use square root and cube root symbols to represent solutions to equations of the form 𝘹² = 𝘱 and 𝘹³ = 𝘱, where 𝘱 is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that √2 is irrational. | Grade 8 |
| Massachusetts | 8.EE.A.3 | Use numbers expressed in the form of a single digit multiplied by an integer power of 10 to estimate very large or very small quantities, and express how many times as much one is than the other. | Grade 8 |
| Massachusetts | 8.EE.A.4 | Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology. | Grade 8 |
| Massachusetts | 8.EE.B.5 | Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. | Grade 8 |
| Massachusetts | 8.EE.B.6 | Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane. Derive the equation 𝘺 = 𝘮𝘹 for a line through the origin and the equation 𝘺 = 𝘮𝘹 + 𝘣 for a line intercepting the vertical axis at 𝘣. | Grade 8 |
| Massachusetts | 8.EE.C.7 | Solve linear equations in one variable. | Grade 8 |
| Massachusetts | 8.EE.C.8 | Analyze and solve pairs of simultaneous linear equations. | Grade 8 |
| Massachusetts | 8.F.A.1 | Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output. | Grade 8 |
| Massachusetts | 8.F.A.2 | Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). | Grade 8 |
| Massachusetts | 8.F.A.3 | Interpret the equation 𝘺 = 𝘮𝘹 + 𝘣 as defining a linear function whose graph is a straight line; give examples of functions that are not linear. | Grade 8 |
| Massachusetts | 8.F.B.4 | Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (𝘹, 𝘺) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values. | Grade 8 |
| Massachusetts | 8.F.B.5 | Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally. | Grade 8 |
| Massachusetts | 8.G.A.1 | Verify experimentally the properties of rotations, reflections, and translations. | Grade 8 |
| Massachusetts | 8.G.A.2 | Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations. Given two congruent figures, describe a sequence that exhibits the congruence between them. | Grade 8 |
| Massachusetts | 8.G.A.3 | Describe the effects of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates. | Grade 8 |
| Massachusetts | 8.G.A.4 | Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations. Given two similar two-dimensional figures, describe a sequence that exhibits the similarity between them. | Grade 8 |
| Massachusetts | 8.G.A.5 | Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. | Grade 8 |
| Massachusetts | 8.G.B.7 | Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions. | Grade 8 |
| Massachusetts | 8.G.B.8 | Apply the Pythagorean Theorem to find the distance between two points in a coordinate system. | Grade 8 |
| Massachusetts | 8.G.C.9 | Know the formulas for the volumes of cones, cylinders, and spheres, and use them to solve real-world and mathematical problems. | Grade 8 |
| Massachusetts | 8.SP.A.1 | Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association. | Grade 8 |
| Massachusetts | 8.SP.A.2 | Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line and informally assess the model fit by judging the closeness of the data points to the line. | Grade 8 |
| Massachusetts | 8.NS.A.2 | Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g., π²). | Grade 8 |
| Massachusetts | A-APR.B.3 | Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial. | High School |
| Massachusetts | A-CED.A.2 | Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. | High School |
| Massachusetts | A-CED.A.3 | Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context. | High School |
| Massachusetts | A-REI.B.3 | Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. | High School |
| Massachusetts | A-SSE.A.2 | Use the structure of an expression to identify ways to rewrite it. | High School |
| Massachusetts | A-SSE.B.3 | Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression. | High School |
| Massachusetts | F-BF.A.1 | Write a function (linear, quadratic, exponential, simple rational, radical, logarithmic, and trigonometric) that describes a relationship between two quantities. | High School |
| Massachusetts | F-IF.A.2 | Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. | High School |
| Massachusetts | F-IF.B.4 | For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. | High School |
| Massachusetts | F-IF.C.7 | Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. | High School |
| Massachusetts | S-ID.B.6 | Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. | High School |
| Michigan | K.CC.A.1 | Count to 100 by ones and by tens. | Kindergarten |
| Michigan | K.CC.A.2 | Count forward beginning from a given number within the known sequence (instead of having to begin at 1). | Kindergarten |
| Michigan | K.CC.A.3 | Write numbers from 0 to 20. Represent a number of objects with a written numeral 0-20 (with 0 representing a count of no objects). | Kindergarten |
| Michigan | K.CC.B.4 | Understand the relationship between numbers and quantities; connect counting to cardinality. | Kindergarten |
| Michigan | K.CC.B.5 | Count to answer “how many?” questions about as many as 20 things arranged in a line, a rectangular array, or a circle, or as many as 10 things in a scattered configuration; given a number from 1-20, count out that many objects. | Kindergarten |
| Michigan | K.CC.C.6 | Identify whether the number of objects in one group is greater than, less than, or equal to the number of objects in another group, e.g., by using matching and counting strategies. | Kindergarten |
| Michigan | K.CC.C.7 | Compare two numbers between 1 and 10 presented as written numerals. | Kindergarten |
| Michigan | K.G.A.1 | Describe objects in the environment using names of shapes, and describe the relative positions of these objects using terms such as above, below, beside, in front of, behind, and next to. | Kindergarten |
| Michigan | K.G.A.2 | Correctly name shapes regardless of their orientations or overall size. | Kindergarten |
| Michigan | K.G.A.3 | Identify shapes as two-dimensional (lying in a plane, “flat”) or three-dimensional (“solid”). | Kindergarten |
| Michigan | K.G.B.4 | Analyze and compare two- and three-dimensional shapes, in different sizes and orientations, using informal language to describe their similarities, differences, parts (e.g., number of sides and vertices/“corners”) and other attributes (e.g., having sides of equal length). | Kindergarten |
| Michigan | K.G.B.6 | Compose simple shapes to form larger shapes. | Kindergarten |
| Michigan | K.MD.A.1 | Describe measurable attributes of objects, such as length or weight. Describe several measurable attributes of a single object. | Kindergarten |
| Michigan | K.MD.A.2 | Directly compare two objects with a measurable attribute in common, to see which object has “more of”/“less of” the attribute, and describe the difference. | Kindergarten |
| Michigan | K.MD.B.3 | Classify objects into given categories; count the numbers of objects in each category and sort the categories by count. | Kindergarten |
| Michigan | K.NBT.A.1 | Compose and decompose numbers from 11 to 19 into ten ones and some further ones, e.g., by using objects or drawings, and record each composition or decomposition by a drawing or equation (e.g., 18 = 10 + 8); understand that these numbers are composed of ten ones and one, two, three, four, five, six, seven, eight, or nine ones. | Kindergarten |
| Michigan | K.OA.A.1 | Represent addition and subtraction with objects, fingers, mental images, drawings, sounds (e.g., claps), acting out situations, verbal explanations, expressions, or equations. | Kindergarten |
| Michigan | K.OA.A.2 | Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem. | Kindergarten |
| Michigan | K.OA.A.3 | Decompose numbers less than or equal to 10 into pairs in more than one way, e.g., by using objects or drawings, and record each decomposition by a drawing or equation (e.g., 5 = 2 + 3 and 5 = 4 + 1). | Kindergarten |
| Michigan | K.OA.A.4 | For any number from 1 to 9, find the number that makes 10 when added to the given number, e.g., by using objects or drawings, and record the answer with a drawing or equation. | Kindergarten |
| Michigan | K.OA.A.5 | Fluently add and subtract within 5. | Kindergarten |
| Michigan | 1.G.A.1 | Distinguish between defining attributes (e.g., triangles are closed and three-sided) versus non-defining attributes (e.g., color, orientation, overall size); build and draw shapes to possess defining attributes. | Grade 1 |
| Michigan | 1.G.A.2 | Compose two-dimensional shapes (rectangles, squares, trapezoids, triangles, half-circles, and quarter-circles) or three-dimensional shapes (cubes, right rectangular prisms, right circular cones, and right circular cylinders) to create a composite shape, and compose new shapes from the composite shape. | Grade 1 |
| Michigan | 1.G.A.3 | Partition circles and rectangles into two and four equal shares, describe the shares using the words halves, fourths, and quarters, and use the phrases half of, fourth of, and quarter of. Describe the whole as two of, or four of the shares. Understand for these examples that decomposing into more equal shares creates smaller shares. | Grade 1 |
| Michigan | 1.MD.A.1 | Order three objects by length; compare the lengths of two objects indirectly by using a third object. | Grade 1 |
| Michigan | 1.MD.A.2 | Express the length of an object as a whole number of length units, by laying multiple copies of a shorter object (the length unit) end to end; understand that the length measurement of an object is the number of same-size length units that span it with no gaps or overlaps. | Grade 1 |
| Michigan | 1.MD.B.3 | Tell and write time in hours and half-hours using analog and digital clocks. | Grade 1 |
| Michigan | 1.MD.C.4 | Organize, represent, and interpret data with up to three categories; ask and answer questions about the total number of data points, how many in each category, and how many more or less are in one category than in another. | Grade 1 |
| Michigan | 1.NBT.A.1 | Count to 120, starting at any number less than 120. In this range, read and write numerals and represent a number of objects with a written numeral. | Grade 1 |
| Michigan | 1.NBT.B.2 | Understand that the two digits of a two-digit number represent amounts of tens and ones. | Grade 1 |
| Michigan | 1.NBT.B.3 | Compare two two-digit numbers based on meanings of the tens and ones digits, recording the results of comparisons with the symbols >, =, and <. | Grade 1 |
| Michigan | 1.NBT.C.4 | Add within 100, including adding a two-digit number and a one-digit number, and adding a two-digit number and a multiple of 10, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Understand that in adding two-digit numbers, one adds tens and tens, ones and ones; and sometimes it is necessary to compose a ten. | Grade 1 |
| Michigan | 1.NBT.C.5 | Given a two-digit number, mentally find 10 more or 10 less than the number, without having to count; explain the reasoning used. | Grade 1 |
| Michigan | 1.NBT.C.6 | Subtract multiples of 10 in the range 10-90 from multiples of 10 in the range 10-90 (positive or zero differences), using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. | Grade 1 |
| Michigan | 1.OA.A.1 | Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem. | Grade 1 |
| Michigan | 1.OA.B.3 | Apply properties of operations as strategies to add and subtract. | Grade 1 |
| Michigan | 1.OA.B.4 | Understand subtraction as an unknown-addend problem. | Grade 1 |
| Michigan | 1.OA.C.5 | Relate counting to addition and subtraction (e.g., by counting on 2 to add 2). | Grade 1 |
| Michigan | 1.OA.C.6 | Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to a ten (e.g., 13 - 4 = 13 - 3 - 1 = 10 - 1 = 9); using the relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 - 8 = 4); and creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13). | Grade 1 |
| Michigan | 1.OA.D.7 | Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false. | Grade 1 |
| Michigan | 1.OA.D.8 | Determine the unknown whole number in an addition or subtraction equation relating three whole numbers. | Grade 1 |
| Michigan | 2.G.A.1 | Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces. Identify triangles, quadrilaterals, pentagons, hexagons, and cubes. | Grade 2 |
| Michigan | 2.G.A.2 | Partition a rectangle into rows and columns of same-size squares and count to find the total number of them. | Grade 2 |
| Michigan | 2.G.A.3 | Partition circles and rectangles into two, three, or four equal shares, describe the shares using the words halves, thirds, half of, a third of, etc., and describe the whole as two halves, three thirds, four fourths. Recognize that equal shares of identical wholes need not have the same shape. | Grade 2 |
| Michigan | 2.MD.A.1 | Measure the length of an object by selecting and using appropriate tools such as rulers, yardsticks, meter sticks, and measuring tapes. | Grade 2 |
| Michigan | 2.MD.A.2 | Measure the length of an object twice, using length units of different lengths for the two measurements; describe how the two measurements relate to the size of the unit chosen. | Grade 2 |
| Michigan | 2.MD.A.4 | Measure to determine how much longer one object is than another, expressing the length difference in terms of a standard length unit. | Grade 2 |
| Michigan | 2.MD.B.5 | Use addition and subtraction within 100 to solve word problems involving lengths that are given in the same units, e.g., by using drawings (such as drawings of rulers) and equations with a symbol for the unknown number to represent the problem. | Grade 2 |
| Michigan | 2.MD.C.7 | Tell and write time from analog and digital clocks to the nearest five minutes, using a.m. and p.m. | Grade 2 |
| Michigan | 2.MD.C.8 | Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies, using $ and ¢ symbols appropriately. | Grade 2 |
| Michigan | 2.MD.D.9 | Generate measurement data by measuring lengths of several objects to the nearest whole unit, or by making repeated measurements of the same object. Show the measurements by making a line plot, where the horizontal scale is marked off in whole-number units. | Grade 2 |
| Michigan | 2.MD.D.10 | Draw a picture graph and a bar graph (with single-unit scale) to represent a data set with up to four categories. Solve simple put-together, take-apart, and compare problems using information presented in a bar graph. | Grade 2 |
| Michigan | 2.NBT.A.1 | Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones. | Grade 2 |
| Michigan | 2.NBT.A.2 | Count within 1000; skip-count by 5s, 10s, and 100s. | Grade 2 |
| Michigan | 2.NBT.A.3 | Read and write numbers to 1000 using base-ten numerals, number names, and expanded form. | Grade 2 |
| Michigan | 2.NBT.A.4 | Compare two three-digit numbers based on meanings of the hundreds, tens, and ones digits, using >, =, and < symbols to record the results of comparisons. | Grade 2 |
| Michigan | 2.NBT.B.5 | Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction. | Grade 2 |
| Michigan | 2.NBT.B.6 | Add up to four two-digit numbers using strategies based on place value and properties of operations. | Grade 2 |
| Michigan | 2.NBT.B.7 | Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method. Understand that in adding or subtracting three-digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds. | Grade 2 |
| Michigan | 2.NBT.B.8 | Mentally add 10 or 100 to a given number 100–900, and mentally subtract 10 or 100 from a given number 100–900. | Grade 2 |
| Michigan | 2.OA.A.1 | Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem. | Grade 2 |
| Michigan | 2.OA.B.2 | Fluently add and subtract within 20 using mental strategies. By end of Grade 2, know from memory all sums of two one-digit numbers. | Grade 2 |
| Michigan | 2.OA.C.3 | Determine whether a group of objects (up to 20) has an odd or even number of members, e.g., by pairing objects or counting them by 2s; write an equation to express an even number as a sum of two equal addends. | Grade 2 |
| Michigan | 2.OA.C.4 | Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends. | Grade 2 |
| Michigan | 3.G.A.1 | Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories. | Grade 3 |
| Michigan | 3.G.A.2 | Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole. | Grade 3 |
| Michigan | 3.MD.A.1 | Tell and write time to the nearest minute and measure time intervals in minutes. Solve word problems involving addition and subtraction of time intervals in minutes, e.g., by representing the problem on a number line diagram. | Grade 3 |
| Michigan | 3.MD.A.2 | Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l). Add, subtract, multiply, or divide to solve one-step word problems involving masses or volumes that are given in the same units, e.g., by using drawings (such as a beaker with a measurement scale) to represent the problem. | Grade 3 |
| Michigan | 3.MD.B.3 | Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and two-step “how many more” and “how many less” problems using information presented in scaled bar graphs. | Grade 3 |
| Michigan | 3.MD.B.4 | Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Show the data by making a line plot, where the horizontal scale is marked off in appropriate units-whole numbers, halves, or quarters. | Grade 3 |
| Michigan | 3.MD.C.5 | Recognize area as an attribute of plane figures and understand concepts of area measurement. | Grade 3 |
| Michigan | 3.MD.C.6 | Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units). | Grade 3 |
| Michigan | 3.MD.C.7 | Relate area to the operations of multiplication and addition. | Grade 3 |
| Michigan | 3.MD.D.8 | Solve real world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters. | Grade 3 |
| Michigan | 3.NBT.A.1 | Use place value understanding to round whole numbers to the nearest 10 or 100. | Grade 3 |
| Michigan | 3.NBT.A.2 | Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction. | Grade 3 |
| Michigan | 3.NBT.A.3 | Multiply one-digit whole numbers by multiples of 10 in the range 10–90 (e.g., 9 × 80, 5 × 60) using strategies based on place value and properties of operations. | Grade 3 |
| Michigan | 3.NF.A.1 | Understand a fraction 1/𝘣 as the quantity formed by 1 part when a whole is partitioned into 𝘣 equal parts; understand a fraction 𝘢/𝑏 as the quantity formed by 𝘢 parts of size 1/𝘣. | Grade 3 |
| Michigan | 3.NF.A.2 | Understand a fraction as a number on the number line; represent fractions on a number line diagram. | Grade 3 |
| Michigan | 3.NF.A.3 | Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size. | Grade 3 |
| Michigan | 3.OA.A.1 | Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each. | Grade 3 |
| Michigan | 3.OA.A.2 | Interpret whole-number quotients of whole numbers, e.g., interpret 56 ÷ 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each. | Grade 3 |
| Michigan | 3.OA.A.3 | Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem. | Grade 3 |
| Michigan | 3.OA.A.4 | Determine the unknown whole number in a multiplication or division equation relating three whole numbers. | Grade 3 |
| Michigan | 3.OA.B.5 | Apply properties of operations as strategies to multiply and divide. | Grade 3 |
| Michigan | 3.OA.B.6 | Understand division as an unknown-factor problem. | Grade 3 |
| Michigan | 3.OA.C.7 | Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 × 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers. | Grade 3 |
| Michigan | 3.OA.D.8 | Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. | Grade 3 |
| Michigan | 3.OA.D.9 | Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations. | Grade 3 |
| Michigan | 4.G.A.1 | Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures. | Grade 4 |
| Michigan | 4.G.A.2 | Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles. | Grade 4 |
| Michigan | 4.G.A.3 | Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify line-symmetric figures and draw lines of symmetry. | Grade 4 |
| Michigan | 4.MD.A.1 | Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table. | Grade 4 |
| Michigan | 4.MD.A.2 | Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. | Grade 4 |
| Michigan | 4.MD.A.3 | Apply the area and perimeter formulas for rectangles in real world and mathematical problems. | Grade 4 |
| Michigan | 4.MD.B.4 | Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots. | Grade 4 |
| Michigan | 4.MD.C.5 | Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement. | Grade 4 |
| Michigan | 4.MD.C.6 | Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure. | Grade 4 |
| Michigan | 4.MD.C.7 | Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems, e.g., by using an equation with a symbol for the unknown angle measure. | Grade 4 |
| Michigan | 4.NBT.A.1 | Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. | Grade 4 |
| Michigan | 4.NBT.A.2 | Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. | Grade 4 |
| Michigan | 4.NBT.A.3 | Use place value understanding to round multi-digit whole numbers to any place. | Grade 4 |
| Michigan | 4.NBT.B.4 | Fluently add and subtract multi-digit whole numbers using the standard algorithm. | Grade 4 |
| Michigan | 4.NBT.B.5 | Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. | Grade 4 |
| Michigan | 4.NBT.B.6 | Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. | Grade 4 |
| Michigan | 4.NF.A.1 | Explain why a fraction 𝘢/𝘣 is equivalent to a fraction (𝘯 × 𝘢)/(𝘯 × 𝘣) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. | Grade 4 |
| Michigan | 4.NF.A.2 | Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model. | Grade 4 |
| Michigan | 4.NF.B.3 | Understand a fraction 𝘢/𝘣 with 𝘢 > 1 as a sum of fractions 1/𝘣. | Grade 4 |
| Michigan | 4.NF.B.4 | Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. | Grade 4 |
| Michigan | 4.NF.C.5 | Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100. | Grade 4 |
| Michigan | 4.NF.C.6 | Use decimal notation for fractions with denominators 10 or 100. | Grade 4 |
| Michigan | 4.NF.C.7 | Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual model. | Grade 4 |
| Michigan | 4.OA.A.1 | Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 × 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations. | Grade 4 |
| Michigan | 4.OA.A.2 | Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison. | Grade 4 |
| Michigan | 4.OA.A.3 | Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. | Grade 4 |
| Michigan | 4.OA.B.4 | Find all factor pairs for a whole number in the range 1-100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1-100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1-100 is prime or composite. | Grade 4 |
| Michigan | 4.OA.C.5 | Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. | Grade 4 |
| Michigan | 5.G.A.1 | Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., 𝘹-axis and 𝘹-coordinate, 𝘺-axis and 𝘺-coordinate). | Grade 5 |
| Michigan | 5.G.A.2 | Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. | Grade 5 |
| Michigan | 5.G.B.3 | Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. | Grade 5 |
| Michigan | 5.G.B.4 | Classify two-dimensional figures in a hierarchy based on properties. | Grade 5 |
| Michigan | 5.MD.A.1 | Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. | Grade 5 |
| Michigan | 5.MD.B.2 | Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. | Grade 5 |
| Michigan | 5.MD.C.3 | Recognize volume as an attribute of solid figures and understand concepts of volume measurement. | Grade 5 |
| Michigan | 5.MD.C.4 | Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. | Grade 5 |
| Michigan | 5.MD.C.5 | Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume. | Grade 5 |
| Michigan | 5.NBT.A.1 | Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. | Grade 5 |
| Michigan | 5.NBT.A.2 | Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. | Grade 5 |
| Michigan | 5.NBT.A.3 | Read, write, and compare decimals to thousandths. | Grade 5 |
| Michigan | 5.NBT.A.4 | Use place value understanding to round decimals to any place. | Grade 5 |
| Michigan | 5.NBT.B.5 | Fluently multiply multi-digit whole numbers using the standard algorithm. | Grade 5 |
| Michigan | 5.NBT.B.6 | Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. | Grade 5 |
| Michigan | 5.NBT.B.7 | Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. | Grade 5 |
| Michigan | 5.NF.A.1 | Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. | Grade 5 |
| Michigan | 5.NF.A.2 | Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. | Grade 5 |
| Michigan | 5.NF.B.3 | Interpret a fraction as division of the numerator by the denominator (𝘢/𝘣 = 𝘢 ÷ 𝘣). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. | Grade 5 |
| Michigan | 5.NF.B.4 | Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. | Grade 5 |
| Michigan | 5.NF.B.5 | Interpret multiplication as scaling (resizing). | Grade 5 |
| Michigan | 5.NF.B.6 | Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. | Grade 5 |
| Michigan | 5.NF.B.7 | Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. | Grade 5 |
| Michigan | 5.OA.A.1 | Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. | Grade 5 |
| Michigan | 5.OA.A.2 | Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. | Grade 5 |
| Michigan | 5.OA.B.3 | Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. | Grade 5 |
| Michigan | 6.EE.A.1 | Write and evaluate numerical expressions involving whole-number exponents. | Grade 6 |
| Michigan | 6.EE.A.2 | Write, read, and evaluate expressions in which letters stand for numbers. | Grade 6 |
| Michigan | 6.EE.A.3 | Apply the properties of operations to generate equivalent expressions. | Grade 6 |
| Michigan | 6.EE.A.4 | Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). | Grade 6 |
| Michigan | 6.EE.B.5 | Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true. | Grade 6 |
| Michigan | 6.EE.B.6 | Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set. | Grade 6 |
| Michigan | 6.EE.B.7 | Solve real-world and mathematical problems by writing and solving equations of the form 𝘹 + 𝘱 = 𝘲 and 𝘱𝘹 = 𝘲 for cases in which 𝘱, 𝘲 and 𝘹 are all nonnegative rational numbers. | Grade 6 |
| Michigan | 6.EE.B.8 | Write an inequality of the form 𝘹 > 𝘤 or 𝘹 𝘤 or 𝘹 < 𝘤 have infinitely many solutions; represent solutions of such inequalities on number line diagrams. | Grade 6 |
| Michigan | 6.EE.C.9 | Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. | Grade 6 |
| Michigan | 6.G.A.1 | Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems. | Grade 6 |
| Michigan | 6.G.A.2 | Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas 𝘝 = 𝘭 𝘸 𝘩 and 𝘝 = 𝘣 𝘩 to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems. | Grade 6 |
| Michigan | 6.G.A.3 | Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems. | Grade 6 |
| Michigan | 6.G.A.4 | Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems. | Grade 6 |
| Michigan | 6.RP.A.1 | Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. | Grade 6 |
| Michigan | 6.RP.A.2 | Understand the concept of a unit rate 𝘢/𝘣 associated with a ratio 𝘢:𝘣 with 𝘣 ≠ 0, and use rate language in the context of a ratio relationship. | Grade 6 |
| Michigan | 6.RP.A.3 | Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. | Grade 6 |
| Michigan | 6.SP.B.5 | Summarize numerical data sets in relation to their context, such as by: | Grade 6 |
| Michigan | 6.NS.A.1 | Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. | Grade 6 |
| Michigan | 6.NS.B.2 | Fluently divide multi-digit numbers using the standard algorithm. | Grade 6 |
| Michigan | 6.NS.B.3 | Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation. | Grade 6 |
| Michigan | 6.NS.C.5 | Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation. | Grade 6 |
| Michigan | 6.NS.C.6 | Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates. | Grade 6 |
| Michigan | 6.NS.C.7 | Understand ordering and absolute value of rational numbers. | Grade 6 |
| Michigan | 6.NS.C.8 | Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. | Grade 6 |
| Michigan | 7.EE.A.1 | Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients. | Grade 7 |
| Michigan | 7.EE.A.2 | Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. | Grade 7 |
| Michigan | 7.EE.B.3 | Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. | Grade 7 |
| Michigan | 7.EE.B.4 | Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. | Grade 7 |
| Michigan | 7.G.A.1 | Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale. | Grade 7 |
| Michigan | 7.G.A.2 | Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle. | Grade 7 |
| Michigan | 7.G.A.3 | Describe the two-dimensional figures that result from slicing three-dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids. | Grade 7 |
| Michigan | 7.G.B.4 | Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle. | Grade 7 |
| Michigan | 7.G.B.5 | Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure. | Grade 7 |
| Michigan | 7.G.B.6 | Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. | Grade 7 |
| Michigan | 7.RP.A.1 | Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. | Grade 7 |
| Michigan | 7.RP.A.2 | Recognize and represent proportional relationships between quantities. | Grade 7 |
| Michigan | 7.RP.A.3 | Use proportional relationships to solve multistep ratio and percent problems. | Grade 7 |
| Michigan | 7.NS.A.1 | Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram. | Grade 7 |
| Michigan | 7.NS.A.2 | Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers. | Grade 7 |
| Michigan | 7.NS.A.3 | Solve real-world and mathematical problems involving the four operations with rational numbers. | Grade 7 |
| Michigan | 8.EE.A.1 | Know and apply the properties of integer exponents to generate equivalent numerical expressions. | Grade 8 |
| Michigan | 8.EE.A.2 | Use square root and cube root symbols to represent solutions to equations of the form 𝘹² = 𝘱 and 𝘹³ = 𝘱, where 𝘱 is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that √2 is irrational. | Grade 8 |
| Michigan | 8.EE.A.3 | Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other. | Grade 8 |
| Michigan | 8.EE.A.4 | Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology. | Grade 8 |
| Michigan | 8.EE.B.5 | Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. | Grade 8 |
| Michigan | 8.EE.B.6 | Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation 𝘺 = 𝘮𝘹 for a line through the origin and the equation 𝘺 = 𝘮𝘹 + 𝘣 for a line intercepting the vertical axis at 𝘣. | Grade 8 |
| Michigan | 8.EE.C.7 | Solve linear equations in one variable. | Grade 8 |
| Michigan | 8.EE.C.8 | Analyze and solve pairs of simultaneous linear equations. | Grade 8 |
| Michigan | 8.F.A.1 | Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output. | Grade 8 |
| Michigan | 8.F.A.2 | Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). | Grade 8 |
| Michigan | 8.F.A.3 | Interpret the equation 𝘺 = 𝘮𝘹 + 𝘣 as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. | Grade 8 |
| Michigan | 8.F.B.4 | Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (𝘹, 𝘺) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values. | Grade 8 |
| Michigan | 8.F.B.5 | Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally. | Grade 8 |
| Michigan | 8.G.A.1 | Verify experimentally the properties of rotations, reflections, and translations. | Grade 8 |
| Michigan | 8.G.A.2 | Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them. | Grade 8 |
| Michigan | 8.G.A.3 | Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates. | Grade 8 |
| Michigan | 8.G.A.4 | Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two-dimensional figures, describe a sequence that exhibits the similarity between them. | Grade 8 |
| Michigan | 8.G.A.5 | Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. | Grade 8 |
| Michigan | 8.G.B.7 | Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions. | Grade 8 |
| Michigan | 8.G.B.8 | Apply the Pythagorean Theorem to find the distance between two points in a coordinate system. | Grade 8 |
| Michigan | 8.G.C.9 | Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems. | Grade 8 |
| Michigan | 8.SP.A.1 | Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association. | Grade 8 |
| Michigan | 8.SP.A.2 | Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line. | Grade 8 |
| Michigan | 8.NS.A.2 | Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g., π²). | Grade 8 |
| Michigan | A-APR.B.3 | Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial. | High School |
| Michigan | A-CED.A.2 | Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. | High School |
| Michigan | A-CED.A.3 | Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context. | High School |
| Michigan | A-REI.B.3 | Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. | High School |
| Michigan | A-SSE.A.2 | Use the structure of an expression to identify ways to rewrite it. | High School |
| Michigan | A-SSE.B.3 | Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression. | High School |
| Michigan | F-BF.A.1 | Write a function that describes a relationship between two quantities. | High School |
| Michigan | F-IF.A.2 | Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. | High School |
| Michigan | F-IF.B.4 | For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. | High School |
| Michigan | F-IF.C.7 | Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. | High School |
| Michigan | S-ID.B.6 | Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. | High School |
| Minnesota | K.1.1.1 | Recognize that a number can be used to represent how many objects are in a set or to represent the position of an object in a sequence. | Kindergarten |
| Minnesota | K.1.1.2 | Read, write, and represent whole numbers from 0 to at least 31. Representations may include numerals, pictures, real objects and picture graphs, spoken words, and manipulatives such as connecting cubes. | Kindergarten |
| Minnesota | K.1.1.3 | Count, with and without objects, forward and backward to at least 20. | Kindergarten |
| Minnesota | K.1.1.4 | Find a number that is 1 more or 1 less than a given number. | Kindergarten |
| Minnesota | K.1.1.5 | Compare and order whole numbers, with and without objects, from 0 to 20. | Kindergarten |
| Minnesota | K.1.2.1 | Use objects and draw pictures to find the sums and differences of numbers between 0 and 10. | Kindergarten |
| Minnesota | K.1.2.2 | Compose and decompose numbers up to 10 with objects and pictures. | Kindergarten |
| Minnesota | K.3.1.1 | Recognize basic two- and three-dimensional shapes such as squares, circles, triangles, rectangles, trapezoids, hexagons, cubes, cones, cylinders and spheres. | Kindergarten |
| Minnesota | K.3.1.2 | Sort objects using characteristics such as shape, size, color and thickness. | Kindergarten |
| Minnesota | K.3.1.3 | Use basic shapes and spatial reasoning to model objects in the real-world. | Kindergarten |
| Minnesota | K.3.2.1 | Use words to compare objects according to length, size, weight and position. | Kindergarten |
| Minnesota | K.3.2.2 | Order 2 or 3 objects using measurable attributes, such as length and weight. | Kindergarten |
| Minnesota | 1.1.1.1 | Use place value to describe whole numbers between 10 and 100 in terms of tens and ones. | Grade 1 |
| Minnesota | 1.1.1.2 | Read, write and represent whole numbers up to 120. Representations may include numerals, addition and subtraction, pictures, tally marks, number lines and manipulatives, such as bundles of sticks and base 10 blocks. | Grade 1 |
| Minnesota | 1.1.1.3 | Count, with and without objects, forward and backward from any given number up to 120. | Grade 1 |
| Minnesota | 1.1.1.4 | Find a number that is 10 more or 10 less than a given number. | Grade 1 |
| Minnesota | 1.1.1.5 | Compare and order whole numbers up to 100. | Grade 1 |
| Minnesota | 1.1.1.7 | Use counting and comparison skills to create and analyze bar graphs and tally charts. | Grade 1 |
| Minnesota | 1.1.2.1 | Use words, pictures, objects, length-based models (connecting cubes), numerals and number lines to model and solve addition and subtraction problems in part-part-total, adding to, taking away from and comparing situations. | Grade 1 |
| Minnesota | 1.1.2.2 | Compose and decompose numbers up to 12 with an emphasis on making ten. | Grade 1 |
| Minnesota | 1.1.2.3 | Recognize the relationship between counting and addition and subtraction. Skip count by 2s, 5s, and 10s. | Grade 1 |
| Minnesota | 1.2.2.1 | Represent real-world situations involving addition and subtraction basic facts, using objects and number sentences. | Grade 1 |
| Minnesota | 1.2.2.2 | Determine if equations involving addition and subtraction are true. | Grade 1 |
| Minnesota | 1.2.2.3 | Use number sense and models of addition and subtraction, such as objects and number lines, to identify the missing number in an equation such as: 2 + 4 = ⧠; 3 + ⧠ = 7; 5 = ⧠ – 3. | Grade 1 |
| Minnesota | 1.2.2.4 | Use addition or subtraction basic facts to represent a given problem situation using a number sentence. | Grade 1 |
| Minnesota | 1.3.1.1 | Describe characteristics of two- and three-dimensional objects, such as triangles, squares, rectangles, circles, rectangular prisms, cylinders, cones and spheres. | Grade 1 |
| Minnesota | 1.3.1.2 | Compose (combine) and decompose (take apart) two- and three-dimensional figures such as triangles, squares, rectangles, circles, rectangular prisms and cylinders. | Grade 1 |
| Minnesota | 1.3.2.1 | Measure the length of an object in terms of multiple copies of another object. | Grade 1 |
| Minnesota | 1.3.2.2 | Tell time to the hour and half-hour. | Grade 1 |
| Minnesota | 1.3.2.3 | Identify pennies, nickels and dimes and find the value of a group of these coins, up to one dollar. | Grade 1 |
| Minnesota | 2.1.1.1 | Read, write and represent whole numbers up to 1000. Representations may include numerals, addition, subtraction, multiplication, words, pictures, tally marks, number lines and manipulatives, such as bundles of sticks and base 10 blocks. | Grade 2 |
| Minnesota | 2.1.1.2 | Use place value to describe whole numbers between 10 and 1000 in terms of hundreds, tens and ones. Know that 100 is 10 tens, and 1000 is 10 hundreds. | Grade 2 |
| Minnesota | 2.1.1.3 | Find 10 more or 10 less than a given three-digit number. Find 100 more or 100 less than a given three-digit number. | Grade 2 |
| Minnesota | 2.1.1.5 | Compare and order whole numbers up to 1000. | Grade 2 |
| Minnesota | 2.1.2.1 | Use strategies to generate addition and subtraction facts including making tens, fact families, doubles plus or minus one, counting on, counting back, and the commutative and associative properties. Use the relationship between addition and subtraction to generate basic facts. | Grade 2 |
| Minnesota | 2.1.2.2 | Demonstrate fluency with basic addition facts and related subtraction facts. | Grade 2 |
| Minnesota | 2.1.2.4 | Use mental strategies and algorithms based on knowledge of place value to add and subtract two-digit numbers. Strategies may include decomposition, expanded notation, and partial sums and differences. | Grade 2 |
| Minnesota | 2.1.2.5 | Solve real-world and mathematical addition and subtraction problems involving whole numbers with up to 2 digits. | Grade 2 |
| Minnesota | 2.1.2.6 | Use addition and subtraction to create and obtain information from tables, bar graphs and tally charts. | Grade 2 |
| Minnesota | 2.2.1.1 | Identify, create and describe simple number patterns involving repeated addition or subtraction, skip counting and arrays of objects such as counters or tiles. Use patterns to solve problems in various contexts. | Grade 2 |
| Minnesota | 2.2.2.1 | Understand how to interpret number sentences involving addition, subtraction and unknowns represented by letters. Use objects and number lines and create real-world situations to represent number sentences. | Grade 2 |
| Minnesota | 2.2.2.2 | Use number sentences involving addition, subtraction, and unknowns to represent given problem situations. Use number sense and properties of addition and subtraction to find values for the unknowns that make the number sentences true. | Grade 2 |
| Minnesota | 2.3.1.2 | Identify and name basic two- and three-dimensional shapes, such as squares, circles, triangles, rectangles, trapezoids, hexagons, cubes, rectangular prisms, cones, cylinders and spheres. | Grade 2 |
| Minnesota | 2.3.2.1 | Understand the relationship between the size of the unit of measurement and the number of units needed to measure the length of an object. | Grade 2 |
| Minnesota | 2.3.2.2 | Demonstrate an understanding of the relationship between length and the numbers on a ruler by using a ruler to measure lengths to the nearest centimeter or inch. | Grade 2 |
| Minnesota | 2.3.3.2 | Identify pennies, nickels, dimes and quarters. Find the value of a group of coins and determine combinations of coins that equal a given amount. | Grade 2 |
| Minnesota | 3.1.1.1 | Read, write and represent whole numbers up to 100,000. Representations may include numerals, expressions with operations, words, pictures, number lines, and manipulatives such as bundles of sticks and base 10 blocks. | Grade 3 |
| Minnesota | 3.1.1.2 | Use place value to describe whole numbers between 1000 and 100,000 in terms of ten thousands, thousands, hundreds, tens and ones. | Grade 3 |
| Minnesota | 3.1.1.4 | Round numbers to the nearest 10,000, 1000, 100 and 10. Round up and round down to estimate sums and differences. | Grade 3 |
| Minnesota | 3.1.1.5 | Compare and order whole numbers up to 100,000. | Grade 3 |
| Minnesota | 3.1.2.1 | Add and subtract multi-digit numbers, using efficient and generalizable procedures based on knowledge of place value, including standard algorithms. | Grade 3 |
| Minnesota | 3.1.2.2 | Use addition and subtraction to solve real-world and mathematical problems involving whole numbers. Use various strategies, including the relationship between addition and subtraction, the use of technology, and the context of the problem to assess the reasonableness of results. | Grade 3 |
| Minnesota | 3.1.2.3 | Represent multiplication facts by using a variety of approaches, such as repeated addition, equal-sized groups, arrays, area models, equal jumps on a number line and skip counting. Represent division facts by using a variety of approaches, such as repeated subtraction, equal sharing and forming equal groups. Recognize the relationship between multiplication and division. | Grade 3 |
| Minnesota | 3.1.2.4 | Solve real-world and mathematical problems involving multiplication and division, including both "how many in each group" and "how many groups" division problems. | Grade 3 |
| Minnesota | 3.1.2.5 | Use strategies and algorithms based on knowledge of place value, equality and properties of addition and multiplication to multiply a two- or three-digit number by a one-digit number. Strategies may include mental strategies, partial products, the standard algorithm, and the commutative, associative, and distributive properties. | Grade 3 |
| Minnesota | 3.1.3.1 | Read and write fractions with words and symbols. Recognize that fractions can be used to represent parts of a whole, parts of a set, points on a number line, or distances on a number line. | Grade 3 |
| Minnesota | 3.1.3.2 | Understand that the size of a fractional part is relative to the size of the whole. | Grade 3 |
| Minnesota | 3.1.3.3 | Order and compare unit fractions and fractions with like denominators by using models and an understanding of the concept of numerator and denominator. | Grade 3 |
| Minnesota | 3.2.1.1 | Create, describe, and apply single-operation input-output rules involving addition, subtraction and multiplication to solve problems in various contexts. | Grade 3 |
| Minnesota | 3.2.2.1 | Understand how to interpret number sentences involving multiplication and division basic facts and unknowns. Create real-world situations to represent number sentences. | Grade 3 |
| Minnesota | 3.2.2.2 | Use multiplication and division basic facts to represent a given problem situation using a number sentence. Use number sense and multiplication and division basic facts to find values for the unknowns that make the number sentences true. | Grade 3 |
| Minnesota | 3.3.1.1 | Identify parallel and perpendicular lines in various contexts, and use them to describe and create geometric shapes, such as right triangles, rectangles, parallelograms and trapezoids. | Grade 3 |
| Minnesota | 3.3.1.2 | Sketch polygons with a given number of sides or vertices (corners), such as pentagons, hexagons and octagons. | Grade 3 |
| Minnesota | 3.3.2.1 | Use half units when measuring distances. | Grade 3 |
| Minnesota | 3.3.2.2 | Find the perimeter of a polygon by adding the lengths of the sides. | Grade 3 |
| Minnesota | 3.3.3.1 | Tell time to the minute, using digital and analog clocks. Determine elapsed time to the minute. | Grade 3 |
| Minnesota | 3.3.3.2 | Know relationships among units of time. | Grade 3 |
| Minnesota | 3.4.1.1 | Collect, display and interpret data using frequency tables, bar graphs, picture graphs and number line plots having a variety of scales. Use appropriate titles, labels and units. | Grade 3 |
| Minnesota | 4.1.1.1 | Demonstrate fluency with multiplication and division facts. | Grade 4 |
| Minnesota | 4.1.1.2 | Use an understanding of place value to multiply a number by 10, 100 and 1000. | Grade 4 |
| Minnesota | 4.1.1.3 | Multiply multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. | Grade 4 |
| Minnesota | 4.1.1.4 | Estimate products and quotients of multi-digit whole numbers by using rounding, benchmarks and place value to assess the reasonableness of results. | Grade 4 |
| Minnesota | 4.1.1.5 | Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of technology, and the context of the problem to assess the reasonableness of results. | Grade 4 |
| Minnesota | 4.1.1.6 | Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide multi-digit whole numbers by one- or two-digit numbers. Strategies may include mental strategies, partial quotients, the commutative, associative, and distributive properties and repeated subtraction. | Grade 4 |
| Minnesota | 4.1.2.1 | Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. | Grade 4 |
| Minnesota | 4.1.2.2 | Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. | Grade 4 |
| Minnesota | 4.1.2.3 | Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. | Grade 4 |
| Minnesota | 4.1.2.4 | Read and write decimals with words and symbols; use place value to describe decimals in terms of thousands, hundreds, tens, ones, tenths, hundredths and thousandths. | Grade 4 |
| Minnesota | 4.1.2.5 | Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks. | Grade 4 |
| Minnesota | 4.1.2.6 | Read and write tenths and hundredths in decimal and fraction notations using words and symbols; know the fraction and decimal equivalents for halves and fourths. | Grade 4 |
| Minnesota | 4.1.2.7 | Round decimals to the nearest tenth. | Grade 4 |
| Minnesota | 4.2.1.1 | Create and use input-output rules involving addition, subtraction, multiplication and division to solve problems in various contexts. Record the inputs and outputs in a chart or table. | Grade 4 |
| Minnesota | 4.2.2.1 | Understand how to interpret number sentences involving multiplication, division and unknowns. Use real-world situations involving multiplication or division to represent number sentences. | Grade 4 |
| Minnesota | 4.2.2.2 | Use multiplication, division and unknowns to represent a given problem situation using a number sentence. Use number sense, properties of multiplication, and the relationship between multiplication and division to find values for the unknowns that make the number sentences true. | Grade 4 |
| Minnesota | 4.3.1.1 | Describe, classify and sketch triangles, including equilateral, right, obtuse and acute triangles. Recognize triangles in various contexts. | Grade 4 |
| Minnesota | 4.3.1.2 | Describe, classify and draw quadrilaterals, including squares, rectangles, trapezoids, rhombuses, parallelograms and kites. Recognize quadrilaterals in various contexts. | Grade 4 |
| Minnesota | 4.3.2.1 | Measure angles in geometric figures and real-world objects with a protractor or angle ruler. | Grade 4 |
| Minnesota | 4.3.2.2 | Compare angles according to size. Classify angles as acute, right and obtuse. | Grade 4 |
| Minnesota | 4.3.2.3 | Understand that the area of a two-dimensional figure can be found by counting the total number of same size square units that cover a shape without gaps or overlaps. Justify why length and width are multiplied to find the area of a rectangle by breaking the rectangle into one unit by one unit squares and viewing these as grouped into rows and columns. | Grade 4 |
| Minnesota | 4.3.2.4 | Find the areas of geometric figures and real-world objects that can be divided into rectangular shapes. Use square units to label area measurements. | Grade 4 |
| Minnesota | 4.3.3.2 | Apply reflections to figures by reflecting over verticl or horizontal lines and relate reflections to lines of symmetry. | Grade 4 |
| Minnesota | 4.4.1.1 | Use tables, bar graphs, timelines and Venn diagrams to display data sets. The data may include fractions or decimals. Understand that spreadsheet tables and graphs can be used to display data. | Grade 4 |
| Minnesota | 5.1.1.1 | Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal. | Grade 5 |
| Minnesota | 5.1.1.4 | Solve real-world and mathematical problems requiring addition, subtraction, multiplication and division of multi-digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results. | Grade 5 |
| Minnesota | 5.1.2.1 | Read and write decimals using place value to describe decimals in terms of groups from millionths to millions. | Grade 5 |
| Minnesota | 5.1.2.3 | Order fractions and decimals, including mixed numbers and improper fractions, and locate on a number line. | Grade 5 |
| Minnesota | 5.1.2.4 | Recognize and generate equivalent decimals, fractions, mixed numbers and improper fractions in various contexts. | Grade 5 |
| Minnesota | 5.1.2.5 | Round numbers to the nearest 0.1, 0.01 and 0.001. | Grade 5 |
| Minnesota | 5.1.3.1 | Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. | Grade 5 |
| Minnesota | 5.1.3.2 | Model addition and subtraction of fractions and decimals using a variety of representations. | Grade 5 |
| Minnesota | 5.1.3.3 | Estimate sums and differences of decimals and fractions to assess the reasonableness of results. | Grade 5 |
| Minnesota | 5.1.3.4 | Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. | Grade 5 |
| Minnesota | 5.2.1.1 | Create and use rules, tables, spreadsheets and graphs to describe patterns of change and solve problems. | Grade 5 |
| Minnesota | 5.2.1.2 | Use a rule or table to represent ordered pairs of positive integers and graph these ordered pairs on a coordinate system. | Grade 5 |
| Minnesota | 5.2.2.1 | Apply the commutative, associative and distributive properties and order of operations to generate equivalent numerical expressions and to solve problems involving whole numbers. | Grade 5 |
| Minnesota | 5.2.3.2 | Represent real-world situations using equations and inequalities involving variables. Create real-world situations corresponding to equations and inequalities. | Grade 5 |
| Minnesota | 5.2.3.3 | Evaluate expressions and solve equations involving variables when values for the variables are given. | Grade 5 |
| Minnesota | 5.3.1.1 | Describe and classify three-dimensional figures including cubes, prisms and pyramids by the number of edges, faces or vertices as well as the types of faces. | Grade 5 |
| Minnesota | 5.3.1.2 | Recognize and draw a net for a three-dimensional figure. | Grade 5 |
| Minnesota | 5.3.2.1 | Develop and use formulas to determine the area of triangles, parallelograms and figures that can be decomposed into triangles. | Grade 5 |
| Minnesota | 5.3.2.2 | Use various tools and strategies to measure the volume and surface area of objects that are shaped like rectangular prisms. | Grade 5 |
| Minnesota | 5.3.2.3 | Understand that the volume of a three-dimensional figure can be found by counting the total number of same-size cubic units that fill a shape without gaps or overlaps. Use cubic units to label volume measurements. | Grade 5 |
| Minnesota | 5.3.2.4 | Develop and use the formulas 𝑉 = 𝑙𝑤𝘩 and 𝑉 = 𝐵𝘩 to determine the volume of rectangular prisms. Justify why base area 𝐵 and height 𝘩 are multiplied to find the volume of a rectangular prism by breaking the prism into layers of unit cubes. | Grade 5 |
| Minnesota | 5.4.1.1 | Know and use the definitions of the mean, median and range of a set of data. Know how to use a spreadsheet to find the mean, median and range of a data set. Understand that the mean is a "leveling out" of data. | Grade 5 |
| Minnesota | 5.4.1.2 | Create and analyze double-bar graphs and line graphs by applying understanding of whole numbers, fractions and decimals. Know how to create spreadsheet tables and graphs to display data. | Grade 5 |
| Minnesota | 6.1.1.1 | Locate positive rational numbers on a number line and plot pairs of positive rational numbers on a coordinate grid. | Grade 6 |
| Minnesota | 6.1.1.2 | Compare positive rational numbers represented in various forms. Use the symbols . | Grade 6 |
| Minnesota | 6.1.1.3 | Understand that percent represents parts out of 100 and ratios to 100. | Grade 6 |
| Minnesota | 6.1.1.4 | Determine equivalences among fractions, decimals and percents; select among these representations to solve problems. | Grade 6 |
| Minnesota | 6.1.1.6 | Determine greatest common factors and least common multiples. Use common factors and common multiples to calculate with fractions and find equivalent fractions. | Grade 6 |
| Minnesota | 6.1.1.7 | Convert between equivalent representations of positive rational numbers. | Grade 6 |
| Minnesota | 6.1.2.1 | Identify and use ratios to compare quantities; understand that comparing quantities using ratios is not the same as comparing quantities using subtraction. | Grade 6 |
| Minnesota | 6.1.2.2 | Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations. | Grade 6 |
| Minnesota | 6.1.2.3 | Determine the rate for ratios of quantities with different units. | Grade 6 |
| Minnesota | 6.1.2.4 | Use reasoning about multiplication and division to solve ratio and rate problems. | Grade 6 |
| Minnesota | 6.1.3.1 | Multiply and divide decimals and fractions, using efficient and generalizable procedures, including standard algorithms. | Grade 6 |
| Minnesota | 6.1.3.2 | Use the meanings of fractions, multiplication, division and the inverse relationship between multiplication and division to make sense of procedures for multiplying and dividing fractions. | Grade 6 |
| Minnesota | 6.1.3.3 | Calculate the percent of a number and determine what percent one number is of another number to solve problems in various contexts. | Grade 6 |
| Minnesota | 6.1.3.4 | Solve real-world and mathematical problems requiring arithmetic with decimals, fractions and mixed numbers. | Grade 6 |
| Minnesota | 6.1.3.5 | Estimate solutions to problems with whole numbers, fractions and decimals and use the estimates to assess the reasonableness of results in the context of the problem. | Grade 6 |
| Minnesota | 6.2.1.1 | Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. | Grade 6 |
| Minnesota | 6.2.1.2 | Represent the relationship between two varying quantities with function rules, graphs and tables; translate between any two of these representations. | Grade 6 |
| Minnesota | 6.2.2.1 | Apply the associative, commutative and distributive properties and order of operations to generate equivalent expressions and to solve problems involving positive rational numbers. | Grade 6 |
| Minnesota | 6.2.3.1 | Represent real-world or mathematical situations using equations and inequalities involving variables and positive rational numbers. | Grade 6 |
| Minnesota | 6.2.3.2 | Solve equations involving positive rational numbers using number sense, properties of arithmetic and the idea of maintaining equality on both sides of the equation. Interpret a solution in the original context and assess the reasonableness of results. | Grade 6 |
| Minnesota | 6.3.1.1 | Calculate the surface area and volume of prisms and use appropriate units, such as cm^2 and cm^3. Justify the formulas used. Justification may involve decomposition, nets or other models. | Grade 6 |
| Minnesota | 6.3.1.2 | Calculate the area of quadrilaterals. Quadrilaterals include squares, rectangles, rhombuses, parallelograms, trapezoids and kites. When formulas are used, be able to explain why they are valid. | Grade 6 |
| Minnesota | 6.3.2.1 | Solve problems using the relationships between the angles formed by intersecting lines. | Grade 6 |
| Minnesota | 6.3.2.2 | Determine missing angle measures in a triangle using the fact that the sum of the interior angles of a triangle is 180°. Use models of triangles to illustrate this fact. | Grade 6 |
| Minnesota | 6.3.3.1 | Solve problems in various contexts involving conversion of weights, capacities, geometric measurements and times within measurement systems using appropriate units. | Grade 6 |
| Minnesota | 6.3.3.2 | Estimate weights, capacities and geometric measurements using benchmarks in measurement systems with appropriate units. | Grade 6 |
| Minnesota | 6.4.1.2 | Determine the probability of an event using the ratio between the size of the event and the size of the sample space; represent probabilities as percents, fractions and decimals between 0 and 1 inclusive. Understand that probabilities measure likelihood. | Grade 6 |
| Minnesota | 6.4.1.4 | Calculate experimental probabilities from experiments; represent them as percents, fractions and decimals between 0 and 1 inclusive. Use experimental probabilities to make predictions when actual probabilities are unknown. | Grade 6 |
| Minnesota | 7.1.1.1 | Know that every rational number can be written as the ratio of two integers or as a terminating or repeating decimal. Recognize that π is not rational, but that it can be approximated by rational numbers such as 22/7 and 3.14. | Grade 7 |
| Minnesota | 7.1.1.3 | Locate positive and negative rational numbers on the number line, understand the concept of opposites, and plot pairs of positive and negative rational numbers on a coordinate grid. | Grade 7 |
| Minnesota | 7.1.1.4 | Compare positive and negative rational numbers expressed in various forms using the symbols , =, ≤, ≥. | Grade 7 |
| Minnesota | 7.1.1.5 | Recognize and generate equivalent representations of positive and negative rational numbers, including equivalent fractions. | Grade 7 |
| Minnesota | 7.1.2.1 | Add, subtract, multiply and divide positive and negative rational numbers that are integers, fractions and terminating decimals; use efficient and generalizable procedures, including standard algorithms; raise positive rational numbers to whole-number exponents. | Grade 7 |
| Minnesota | 7.1.2.2 | Use real-world contexts and the inverse relationship between addition and subtraction to explain why the procedures of arithmetic with negative rational numbers make sense. | Grade 7 |
| Minnesota | 7.1.2.4 | Solve problems in various contexts involving calculations with positive and negative rational numbers and positive integer exponents, including computing simple and compound interest. | Grade 7 |
| Minnesota | 7.1.2.5 | Use proportional reasoning to solve problems involving ratios in various contexts. | Grade 7 |
| Minnesota | 7.1.2.6 | Demonstrate an understanding of the relationship between the absolute value of a rational number and distance on a number line. Use the symbol for absolute value. | Grade 7 |
| Minnesota | 7.2.1.1 | Understand that a relationship between two variables, 𝑥 and 𝑦, is proportional if it can be expressed in the form 𝑦/𝑥 = 𝑘 or 𝑦 = 𝑘𝑥. Distinguish proportional relationships from other relationships, including inversely proportional relationships (𝑥𝑦=𝑘 or 𝑦= 𝑘/𝑥). | Grade 7 |
| Minnesota | 7.2.1.2 | Understand that the graph of a proportional relationship is a line through the origin whose slope is the unit rate (constant of proportionality). Know how to use graphing technology to examine what happens to a line when the unit rate is changed. | Grade 7 |
| Minnesota | 7.2.2.1 | Represent proportional relationships with tables, verbal descriptions, symbols, equations and graphs; translate from one representation to another. Determine the unit rate (constant of proportionality or slope) given any of these representations. | Grade 7 |
| Minnesota | 7.2.2.2 | Solve multi-step problems involving proportional relationships in numerous contexts. | Grade 7 |
| Minnesota | 7.2.2.4 | Represent real-world or mathematical situations using equations and inequalities involving variables and positive and negative rational numbers. | Grade 7 |
| Minnesota | 7.2.3.1 | Use properties of algebra to generate equivalent numerical and algebraic expressions containing rational numbers, grouping symbols and whole number exponents. Properties of algebra include associative, commutative and distributive laws. | Grade 7 |
| Minnesota | 7.2.3.2 | Evaluate algebraic expressions containing rational numbers and whole number exponents at specified values of their variables. | Grade 7 |
| Minnesota | 7.2.3.3 | Apply understanding of order of operations and grouping symbols when using calculators and other technologies. | Grade 7 |
| Minnesota | 7.2.4.1 | Represent relationships in various contexts with equations involving variables and positive and negative rational numbers. Use the properties of equality to solve for the value of a variable. Interpret the solution in the original context. | Grade 7 |
| Minnesota | 7.2.4.2 | Solve equations resulting from proportional relationships in various contexts. | Grade 7 |
| Minnesota | 7.3.1.1 | Demonstrate an understanding of the proportional relationship between the diameter and circumference of a circle and that the unit rate (constant of proportionality) is ?. Calculate the circumference and area of circles and sectors of circles to solve problems in various contexts. | Grade 7 |
| Minnesota | 7.3.1.2 | Calculate the volume and surface area of cylinders and justify the formulas used. | Grade 7 |
| Minnesota | 7.3.2.1 | Describe the properties of similarity, compare geometric figures for similarity, and determine scale factors. | Grade 7 |
| Minnesota | 7.3.2.3 | Use proportions and ratios to solve problems involving scale drawings and conversions of measurement units. | Grade 7 |
| Minnesota | 7.3.2.4 | Graph and describe translations and reflections of figures on a coordinate grid and determine the coordinates of the vertices of the figure after the transformation. | Grade 7 |
| Minnesota | 7.4.1.1 | Design simple experiments and collect data. Determine mean, median and range for quantitative data and from data represented in a display. Use these quantities to draw conclusions about the data, compare different data sets, and make predictions. | Grade 7 |
| Minnesota | 7.4.1.2 | Describe the impact that inserting or deleting a data point has on the mean and the median of a data set. Know how to create data displays using a spreadsheet to examine this impact. | Grade 7 |
| Minnesota | 7.4.2.1 | Use reasoning with proportions to display and interpret data in circle graphs (pie charts) and histograms. Choose the appropriate data display and know how to create the display using a spreadsheet or other graphing technology. | Grade 7 |
| Minnesota | 8.1.1.2 | Compare real numbers; locate real numbers on a number line. Identify the square root of a positive integer as an integer, or if it is not an integer, locate it as a real number between two consecutive positive integers. | Grade 8 |
| Minnesota | 8.1.1.3 | Determine rational approximations for solutions to problems involving real numbers. | Grade 8 |
| Minnesota | 8.1.1.4 | Know and apply the properties of positive and negative integer exponents to generate equivalent numerical expressions. | Grade 8 |
| Minnesota | 8.1.1.5 | Express approximations of very large and very small numbers using scientific notation; understand how calculators display numbers in scientific notation. Multiply and divide numbers expressed in scientific notation, express the answer in scientific notation, using the correct number of significant digits when physical measurements are involved. | Grade 8 |
| Minnesota | 8.2.1.1 | Understand that a function is a relationship between an independent variable and a dependent variable in which the value of the independent variable determines the value of the dependent variable. Use functional notation, such as 𝑓(𝑥), to represent such relationships. | Grade 8 |
| Minnesota | 8.2.1.2 | Use linear functions to represent relationships in which changing the input variable by some amount leads to a change in the output variable that is a constant times that amount. | Grade 8 |
| Minnesota | 8.2.1.3 | Understand that a function is linear if it can be expressed in the form 𝑓(𝑥) = 𝑚𝑥+𝑏 or if its graph is a straight line. | Grade 8 |
| Minnesota | 8.2.2.1 | Represent linear functions with tables, verbal descriptions, symbols, equations and graphs; translate from one representation to another. | Grade 8 |
| Minnesota | 8.2.2.2 | Identify graphical properties of linear functions including slopes and intercepts. Know that the slope equals the rate of change, and that the 𝑦-intercept is zero when the function represents a proportional relationship. | Grade 8 |
| Minnesota | 8.2.2.3 | Identify how coefficient changes in the equation 𝑓(𝑥)=𝑚𝑥+𝑏 affect the graphs of linear functions. Know how to use graphing technology to examine these effects. | Grade 8 |
| Minnesota | 8.2.3.1 | Evaluate algebraic expressions, including expressions containing radicals and absolute values, at specified values of their variables. | Grade 8 |
| Minnesota | 8.2.4.1 | Use linear equations to represent situations involving a constant rate of change, including proportional and non-proportional relationships. | Grade 8 |
| Minnesota | 8.2.4.2 | Solve multi-step equations in one variable. Solve for one variable in a multi-variable equation in terms of the other variables. Justify the steps by identifying the properties of equalities used. | Grade 8 |
| Minnesota | 8.2.4.3 | Express linear equations in slope-intercept, point-slope and standard forms, and convert between these forms. Given sufficient information, find an equation of a line. | Grade 8 |
| Minnesota | 8.2.4.4 | Use linear inequalities to represent relationships in various contexts. | Grade 8 |
| Minnesota | 8.2.4.5 | Solve linear inequalities using properties of inequalities. Graph the solutions on a number line. | Grade 8 |
| Minnesota | 8.2.4.7 | Represent relationships in various contexts using systems of linear equations. Solve systems of linear equations in two variables symbolically, graphically and numerically. | Grade 8 |
| Minnesota | 8.2.4.9 | Use the relationship between square roots and squares of a number to solve problems. | Grade 8 |
| Minnesota | 8.3.1.1 | Use the Pythagorean Theorem to solve problems involving right triangles. | Grade 8 |
| Minnesota | 8.3.1.2 | Determine the distance between two points on a horizontal or vertical line in a coordinate system. Use the Pythagorean Theorem to find the distance between any two points in a coordinate system. | Grade 8 |
| Minnesota | 8.3.2.2 | Analyze polygons on a coordinate system by determining the slopes of their sides. | Grade 8 |
| Minnesota | 8.4.1.1 | Collect, display and interpret data using scatterplots. Use the shape of the scatterplot to informally estimate a line of best fit and determine an equation for the line. Use appropriate titles, labels and units. Know how to use graphing technology to display scatterplots and corresponding lines of best fit. | Grade 8 |
| Minnesota | 8.4.1.2 | Use a line of best fit to make statements about approximate rate of change and to make predictions about values not in the original data set. | Grade 8 |
| Minnesota | 8.4.1.3 | Assess the reasonableness of predictions using scatterplots by interpreting them in the original context. | Grade 8 |
| Minnesota | 9.2.1.1 | Understand the definition of a function. Use functional notation and evaluate a function at a given point in its domain. | Algebra |
| Minnesota | 9.2.1.2 | Distinguish between functions and other relations defined symbolically, graphically or in tabular form. | Algebra |
| Minnesota | 9.2.1.3 | Find the domain of a function defined symbolically, graphically or in a real-world context. | Algebra |
| Minnesota | 9.2.1.4 | Obtain information and draw conclusions from graphs of functions and other relations. | Algebra |
| Minnesota | 9.2.1.5 | Identify the vertex, line of symmetry and intercepts of the parabola corresponding to a quadratic function, using symbolic and graphical methods, when the function is expressed in the form 𝑓(𝑥) = 𝑎𝑥 ² + 𝑏𝑥 + 𝑐, in the form 𝑓(𝑥) = 𝑎(𝑥 – ℎ)² + 𝑘 , or in factored form. | Algebra |
| Minnesota | 9.2.1.6 | Identify intercepts, zeros, maxima, minima and intervals of increase and decrease from the graph of a function. | Algebra |
| Minnesota | 9.2.1.8 | Make qualitative statements about the rate of change of a function, based on its graph or table of values. | Algebra |
| Minnesota | 9.2.1.9 | Determine how translations affect the symbolic and graphical forms of a function. Know how to use graphing technology to examine translations. | Algebra |
| Minnesota | 9.2.2.1 | Represent and solve problems in various contexts using linear and quadratic functions. | Algebra |
| Minnesota | 9.2.2.2 | Represent and solve problems in various contexts using exponential functions, such as investment growth, depreciation and population growth. | Algebra |
| Minnesota | 9.2.2.3 | Sketch graphs of linear, quadratic and exponential functions, and translate between graphs, tables and symbolic representations. Know how to use graphing technology to graph these functions. | Algebra |
| Minnesota | 9.2.2.6 | Sketch the graphs of common non-linear functions such as 𝑓(𝑥)= √𝑥, 𝑓(𝑥) = |𝑥|, 𝑓(𝑥)= 1/𝑥, 𝑓(𝑥) = 𝑥³, and translations of these functions, such as 𝑓(𝑥) = √(𝑥-2) + 4. Know how to use graphing technology to graph these functions. | Algebra |
| Minnesota | 9.2.3.3 | Factor common monomial factors from polynomials, factor quadratic polynomials, and factor the difference of two squares. | Algebra |
| Minnesota | 9.2.3.4 | Add, subtract, multiply, divide and simplify algebraic fractions. | Algebra |
| Minnesota | 9.2.3.6 | Apply the properties of positive and negative rational exponents to generate equivalent algebraic expressions, including those involving 𝑛th roots. | Algebra |
| Minnesota | 9.2.3.7 | Justify steps in generating equivalent expressions by identifying the properties used. Use substitution to check the equality of expressions for some particular values of the variables; recognize that checking with substitution does not guarantee equality of expressions for all values of the variables. | Algebra |
| Minnesota | 9.2.4.1 | Represent relationships in various contexts using quadratic equations and inequalities. Solve quadratic equations and inequalities by appropriate methods including factoring, completing the square, graphing and the quadratic formula. Find non-real complex roots when they exist. Recognize that a particular solution may not be applicable in the original context. Know how to use calculators, graphing utilities or other technology to solve quadratic equations and inequalities. | Algebra |
| Minnesota | 9.2.4.4 | Represent relationships in various contexts using systems of linear inequalities; solve them graphically. Indicate which parts of the boundary are included in and excluded from the solution set using solid and dotted lines. | Algebra |
| Minnesota | 9.2.4.7 | Solve equations that contain radical expressions. Recognize that extraneous solutions may arise when using symbolic methods. | Algebra |
| Minnesota | 9.3.1.1 | Determine the surface area and volume of pyramids, cones and spheres. Use measuring devices or formulas as appropriate. | Algebra |
| Minnesota | 9.3.1.2 | Compose and decompose two- and three-dimensional figures; use decomposition to determine the perimeter, area, surface area and volume of various figures. | Algebra |
| Minnesota | 9.3.1.3 | Understand that quantities associated with physical measurements must be assigned units; apply such units correctly in expressions, equations and problem solutions that involve measurements; and convert between measurement systems. | Algebra |
| Minnesota | 9.3.1.4 | Understand and apply the fact that the effect of a scale factor 𝑘 on length, area and volume is to multiply each by 𝑘, 𝑘² and 𝑘³, respectively. | Algebra |
| Minnesota | 9.3.2.4 | Construct logical arguments and write proofs of theorems and other results in geometry, including proofs by contradiction. Express proofs in a form that clearly justifies the reasoning, such as two-column proofs, paragraph proofs, flow charts or illustrations. | Algebra |
| Minnesota | 9.3.3.1 | Know and apply properties of parallel and perpendicular lines, including properties of angles formed by a transversal, to solve problems and logically justify results. | Algebra |
| Minnesota | 9.3.3.2 | Know and apply properties of angles, including corresponding, exterior, interior, vertical, complementary and supplementary angles, to solve problems and logically justify results. | Algebra |
| Minnesota | 9.3.3.3 | Know and apply properties of equilateral, isosceles and scalene triangles to solve problems and logically justify results. | Algebra |
| Minnesota | 9.3.3.4 | Apply the Pythagorean Theorem and its converse to solve problems and logically justify results. | Algebra |
| Minnesota | 9.3.3.6 | Know and apply properties of congruent and similar figures to solve problems and logically justify results. | Algebra |
| Minnesota | 9.3.4.4 | Use coordinate geometry to represent and analyze line segments and polygons, including determining lengths, midpoints and slopes of line segments. | Algebra |
| Minnesota | 9.3.4.6 | Use numeric, graphic and symbolic representations of transformations in two dimensions, such as reflections, translations, scale changes and rotations about the origin by multiples of 90 degrees, to solve problems involving figures on a coordinate grid. | Algebra |
| Minnesota | 9.4.1.1 | Describe a data set using data displays, including box-and-whisker plots; describe and compare data sets using summary statistics, including measures of center, location and spread. Measures of center and location include mean, median, quartile and percentile. Measures of spread include standard deviation, range and inter-quartile range. Know how to use calculators, spreadsheets or other technology to display data and calculate summary statistics. | Algebra |
| Minnesota | 9.4.1.3 | Use scatterplots to analyze patterns and describe relationships between two variables. Using technology, determine regression lines (line of best fit) and correlation coefficients; use regression lines to make predictions and correlation coefficients to assess the reliability of those predictions. | Algebra |
| Mississippi | K.CC.1 | Count to 100 by ones and by tens. | Kindergarten |
| Mississippi | K.CC.2 | Count forward beginning from a given number within the known sequence (instead of having to begin at 1). | Kindergarten |
| Mississippi | K.CC.3 | Write numbers from 0 to 20. Represent a number of objects with a written numeral 0– 20 (with 0 representing a count of no objects). | Kindergarten |
| Mississippi | K.CC.4 | Understand the relationship between numbers and quantities; connect counting to cardinality. | Kindergarten |
| Mississippi | K.CC.5 | Count to answer “how many?” questions about as many as 20 things arranged in a line, a rectangular array, or a circle, or as many as 10 things in a scattered configuration; given a number from 1–20, count out that many objects. | Kindergarten |
| Mississippi | K.CC.6 | Identify whether the number of objects in one group is greater than, less than, or equal to the number of objects in another group, e.g., by using matching and counting strategies. | Kindergarten |
| Mississippi | K.CC.7 | Compare two numbers between 1 and 20 presented as written numerals. | Kindergarten |
| Mississippi | K.G.1 | Describe objects in the environment using names of shapes, and describe the relative positions of these objects using terms such as above, below, beside, in front of, behind, and next to. | Kindergarten |
| Mississippi | K.G.2 | Correctly name shapes regardless of their orientations or overall size. | Kindergarten |
| Mississippi | K.G.3 | Identify shapes as two-dimensional (lying in a plane, “flat”) or three-dimensional (“solid”). | Kindergarten |
| Mississippi | K.G.4 | Analyze and compare two- and three-dimensional shapes, in different sizes and orientations, using informal language to describe their similarities, differences, parts (e.g., number of sides and vertices/“corners”) and other attributes (e.g., having sides of equal length). | Kindergarten |
| Mississippi | K.G.6 | Compose simple shapes to form larger shapes. | Kindergarten |
| Mississippi | K.MD.1 | Describe measurable attributes of objects, such as length or weight. Describe several measurable attributes of a single object. | Kindergarten |
| Mississippi | K.MD.2 | Directly compare two objects with a measurable attribute in common, to see which object has “more of”/“less of” the attribute, and describe the difference. | Kindergarten |
| Mississippi | K.MD.3 | Classify objects into given categories; count the numbers of objects in each category and sort the categories by count. | Kindergarten |
| Mississippi | K.NBT.1 | Compose and decompose numbers from 11 to 19 into ten ones and some further ones to understand that these numbers are composed of ten ones and one, two, three, four, five, six, seven, eight, or nine ones, e.g., by using objects or drawings, and record each composition or decomposition by a drawing or equation (e.g., 18 = 10 + 8). | Kindergarten |
| Mississippi | K.OA.1 | Represent addition and subtraction, in which all parts and whole of the problem are within 10, with objects, fingers, mental images, drawings, sounds (e.g., claps), acting out situations, verbal explanations, expressions, or equations. | Kindergarten |
| Mississippi | K.OA.2 | Solve addition and subtraction word problems within 10 involving situations of adding to, taking from, putting together and taking apart with unknowns in all positions by using objects or drawings to represent the problem. | Kindergarten |
| Mississippi | K.OA.3 | Decompose numbers less than or equal to 10 into pairs in more than one way, e.g., by using objects or drawings, and record each decomposition by a drawing or equation (e.g., 5 = 2 + 3 and 5 = 4 + 1). | Kindergarten |
| Mississippi | K.OA.4 | For any number from 1 to 9, find the number that makes 10 when added to the given number, e.g., by using objects or drawings, and record the answer with a drawing or equation. | Kindergarten |
| Mississippi | K.OA.5 | Fluently add and subtract within 5. | Kindergarten |
| Mississippi | 1.G.1 | Distinguish between defining attributes (e.g., triangles are closed and three-sided) versus non-defining attributes (e.g., color, orientation, overall size); build and draw shapes to possess defining attributes. | Grade 1 |
| Mississippi | 1.G.2 | Compose two-dimensional shapes (rectangles, squares, trapezoids, triangles, half-circles, and quarter-circles) or three-dimensional shapes (cubes, right rectangular prisms, right circular cones, and right circular cylinders) to create a composite shape, and compose new shapes from the composite shape. | Grade 1 |
| Mississippi | 1.G.3 | Partition circles and rectangles into two and four equal shares, describe the shares using the words halves, fourths, and quarters, and use the phrases half of, fourth of, and quarter of. Describe the whole as two of, or four of the shares. Understand for these examples that decomposing into more equal shares creates smaller shares. | Grade 1 |
| Mississippi | 1.MD.1 | Order three objects by length; compare the lengths of two objects indirectly by using a third object. | Grade 1 |
| Mississippi | 1.MD.2 | Express the length of an object as a whole number of length units, by laying multiple copies of a shorter object (the length unit) end to end; understand that the length measurement of an object is the number of same-size length units that span it with no gaps or overlaps. | Grade 1 |
| Mississippi | 1.MD.3a | Tell and write time in hours and half-hours using analog and digital clocks. | Grade 1 |
| Mississippi | 1.MD.4 | Organize, represent, and interpret data with up to three categories; ask and answer questions about the total number of data points, how many in each category, and how many more or less are in one category than in another. | Grade 1 |
| Mississippi | 1.MD.5a | Identify the value of all U.S. coins (penny, nickel, dime, quarter, half-dollar, and dollar coins). Use appropriate cent and dollar notation (e.g., 25¢, $1). | Grade 1 |
| Mississippi | 1.MD.5b | Know the comparative values of all U.S. coins (e.g., a dime is of greater value than a nickel). | Grade 1 |
| Mississippi | 1.MD.5c | Count like U.S. coins up to the equivalent of a dollar. | Grade 1 |
| Mississippi | 1.MD.5d | Find the equivalent value for all greater value U.S. coins using like value smaller coins (e.g., 5 pennies equal 1 nickel; 10 pennies equal dime, but not 1 nickel and 5 pennies equal 1 dime). | Grade 1 |
| Mississippi | 1.NBT.1 | Count to 120, starting at any number less than 120. In this range, read and write numerals and represent a number of objects with a written numeral. | Grade 1 |
| Mississippi | 1.NBT.2 | Understand that the two digits of a two-digit number represent amounts of tens and ones. | Grade 1 |
| Mississippi | 1.NBT.3 | Compare two two-digit numbers based on meanings of the tens and ones digits, recording the results of comparisons with the symbols >, =, and <. | Grade 1 |
| Mississippi | 1.NBT.4 | Add within 100, including adding a two-digit number and a one-digit number, and adding a two-digit number and a multiple of 10, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Understand that in adding two-digit numbers, one adds tens and tens, ones and ones; and sometimes it is necessary to compose a ten. | Grade 1 |
| Mississippi | 1.NBT.5 | Given a two-digit number, mentally find 10 more or 10 less than the number, without having to count; explain the reasoning used. | Grade 1 |
| Mississippi | 1.NBT.6 | Subtract multiples of 10 in the range 10–90 from multiples of 10 in the range 10–90 (positive or zero differences), using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. | Grade 1 |
| Mississippi | 1.OA.1 | Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem. | Grade 1 |
| Mississippi | 1.OA.3 | Apply properties of operations as strategies to add and subtract. | Grade 1 |
| Mississippi | 1.OA.4 | Understand subtraction as an unknown-addend problem. | Grade 1 |
| Mississippi | 1.OA.5 | Relate counting to addition and subtraction (e.g., by counting on 2 to add 2). | Grade 1 |
| Mississippi | 1.OA.6 | Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to a ten (e.g., 13 – 4 = 13 – 3 – 1 = 10 – 1 = 9); using the relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 – 8 = 4); and creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13). | Grade 1 |
| Mississippi | 1.OA.7 | Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false. | Grade 1 |
| Mississippi | 1.OA.8 | Determine the unknown whole number in an addition or subtraction equation relating three whole numbers. | Grade 1 |
| Mississippi | 2.G.1 | Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces. Identify triangles, quadrilaterals, pentagons, hexagons, and cubes. | Grade 2 |
| Mississippi | 2.G.2 | Partition a rectangle into rows and columns of same-size squares and count to find the total number of them. | Grade 2 |
| Mississippi | 2.G.3 | Partition circles and rectangles into two, three, or four equal shares, describe the shares using the words halves, thirds, half of, a third of, etc., and describe the whole as two halves, three thirds, four fourths. Recognize that equal shares of identical wholes need not have the same shape. | Grade 2 |
| Mississippi | 2.MD.1 | Measure the length of an object by selecting and using appropriate tools such as rulers, yardsticks, meter sticks, and measuring tapes. | Grade 2 |
| Mississippi | 2.MD.2 | Measure the length of an object twice, using length units of different lengths for the two measurements; describe how the two measurements relate to the size of the unit chosen. | Grade 2 |
| Mississippi | 2.MD.4 | Measure to determine how much longer one object is than another, expressing the length difference in terms of a standard length unit. | Grade 2 |
| Mississippi | 2.MD.5 | Use addition and subtraction within 100 to solve word problems involving lengths that are given in the same units, e.g., by using drawings (such as drawings of rulers) and equations with a symbol for the unknown number to represent the problem. | Grade 2 |
| Mississippi | 2.MD.7 | Tell and write time from analog and digital clocks to the nearest five minutes, using a.m. and p.m. | Grade 2 |
| Mississippi | 2.MD.8a | Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies, using $ and ¢ symbols appropriately. | Grade 2 |
| Mississippi | 2.MD.9 | Generate measurement data by measuring lengths of several objects to the nearest whole unit, or by making repeated measurements of the same object. Show the measurements by making a line plot, where the horizontal scale is marked off in whole-number units. | Grade 2 |
| Mississippi | 2.MD.10 | Draw a picture graph and a bar graph (with single-unit scale) to represent a data set with up to four categories. Solve simple put-together, take-apart, and compare problems using information presented in a bar graph. | Grade 2 |
| Mississippi | 2.NBT.1 | Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones. | Grade 2 |
| Mississippi | 2.NBT.2 | Count within 1000; skip-count by 5s starting at any number ending in 5 or 0. Skip-count by 10s and 100s starting at any number. | Grade 2 |
| Mississippi | 2.NBT.3 | Read and write numbers to 1000 using base-ten numerals, number names, and expanded form. | Grade 2 |
| Mississippi | 2.NBT.4 | Compare two three-digit numbers based on meanings of the hundreds, tens, and ones digits, using >, =, and < symbols to record the results of comparisons. | Grade 2 |
| Mississippi | 2.NBT.5 | Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction. | Grade 2 |
| Mississippi | 2.NBT.6 | Add up to four two-digit numbers using strategies based on place value and properties of operations. | Grade 2 |
| Mississippi | 2.NBT.7 | Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method. Understand that in adding or subtracting three-digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds. | Grade 2 |
| Mississippi | 2.NBT.8 | Mentally add 10 or 100 to a given number 100–900, and mentally subtract 10 or 100 from a given number 100–900. | Grade 2 |
| Mississippi | 2.OA.1 | Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem. | Grade 2 |
| Mississippi | 2.OA.2 | Fluently add and subtract within 20 using mental strategies. By end of Grade 2, know from memory all sums of two one-digit numbers. | Grade 2 |
| Mississippi | 2.OA.3 | Determine whether a group of objects (up to 20) has an odd or even number of members, e.g., by pairing objects or counting them by 2s; write an equation to express an even number as a sum of two equal addends. | Grade 2 |
| Mississippi | 2.OA.4 | Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends. | Grade 2 |
| Mississippi | 3.G.1 | Understand that shapes in different categories (e.g., rhombuses, rectangles, circles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories. | Grade 3 |
| Mississippi | 3.G.2 | Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole. | Grade 3 |
| Mississippi | 3.MD.1 | Tell and write time to the nearest minute and measure time intervals in minutes. Solve word problems involving addition and subtraction of time intervals in minutes, e.g., by representing the problem on a number line diagram. | Grade 3 |
| Mississippi | 3.MD.2 | Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l). Add, subtract, multiply, or divide to solve one-step word problems involving masses or volumes that are given in the same units, e.g., by using drawings (such as a beaker with a measurement scale) to represent the problem. | Grade 3 |
| Mississippi | 3.MD.3 | Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and two-step “how many more” and “how many less” problems using information presented in scaled bar graphs. | Grade 3 |
| Mississippi | 3.MD.4 | Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Show the data by making a line plot, where the horizontal scale is marked off in appropriate units—whole numbers, halves, or quarters. | Grade 3 |
| Mississippi | 3.MD.5 | Recognize area as an attribute of plane figures and understand concepts of area measurement. | Grade 3 |
| Mississippi | 3.MD.6 | Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units). | Grade 3 |
| Mississippi | 3.MD.7 | Relate area to the operations of multiplication and addition. | Grade 3 |
| Mississippi | 3.MD.8 | Solve real world and mathematical problems involving perimeters of polygons, including: finding the perimeter given the side lengths, finding an unknown side length, and exhibiting (including, but not limited to: modeling, drawing, designing, and creating) rectangles with the same perimeter and different areas or with the same area and different perimeters. | Grade 3 |
| Mississippi | 3.NBT.1 | Use place value understanding to round whole numbers to the nearest 10 or 100. | Grade 3 |
| Mississippi | 3.NBT.2 | Fluently add and subtract (including subtracting across zeros) within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction. Include problems with whole dollar amounts. | Grade 3 |
| Mississippi | 3.NBT.3 | Multiply one-digit whole numbers by multiples of 10 in the range 10–90 (e.g., 9 × 80, 5 × 60) using strategies based on place value and properties of operations. | Grade 3 |
| Mississippi | 3.NF.1 | Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b. | Grade 3 |
| Mississippi | 3.NF.2 | Understand a fraction as a number on the number line; represent fractions on a number line diagram. | Grade 3 |
| Mississippi | 3.NF.3 | Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size. | Grade 3 |
| Mississippi | 3.OA.1 | Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each. | Grade 3 |
| Mississippi | 3.OA.2 | Interpret whole-number quotients of whole numbers, e.g., interpret 56 ÷ 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each. | Grade 3 |
| Mississippi | 3.OA.3 | Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem. | Grade 3 |
| Mississippi | 3.OA.4 | Determine the unknown whole number in a multiplication or division equation relating three whole numbers, with factors 0-10. | Grade 3 |
| Mississippi | 3.OA.5 | Apply properties of operations as strategies to multiply and divide. | Grade 3 |
| Mississippi | 3.OA.6 | Understand division as an unknown-factor problem, where a remainder does not exist. | Grade 3 |
| Mississippi | 3.OA.7 | Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 × 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. Know from memory all products of two one-digit numbers; and fully understand the concept when a remainder does not exist under division. | Grade 3 |
| Mississippi | 3.OA.8 | Solve two-step (two operational steps) word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Include problems with whole dollar amounts. | Grade 3 |
| Mississippi | 3.OA.9 | Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations. | Grade 3 |
| Mississippi | 4.G.1 | Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures. | Grade 4 |
| Mississippi | 4.G.2 | Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles. | Grade 4 |
| Mississippi | 4.G.3 | Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify line-symmetric figures and draw lines of symmetry. | Grade 4 |
| Mississippi | 4.MD.1 | Know relative sizes of measurement units within one system of units including km, m, cm, mm; kg, g, mg; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table. | Grade 4 |
| Mississippi | 4.MD.2 | Use the four operations to solve word problems involving intervals of time, money, distances, liquid volumes and masses of objects including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. | Grade 4 |
| Mississippi | 4.MD.3 | Apply the area and perimeter formulas for rectangles in real world and mathematical problems. | Grade 4 |
| Mississippi | 4.MD.4 | Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots. | Grade 4 |
| Mississippi | 4.MD.5 | Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement. | Grade 4 |
| Mississippi | 4.MD.6 | Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure. | Grade 4 |
| Mississippi | 4.MD.7 | Recognize angle measure as additive. When an angle is decomposed into nonoverlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems, e.g., by using an equation with a symbol for the unknown angle measure. | Grade 4 |
| Mississippi | 4.NBT.1 | Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. | Grade 4 |
| Mississippi | 4.NBT.2 | Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. | Grade 4 |
| Mississippi | 4.NBT.3 | Use place value understanding to round multi-digit whole numbers to any place. | Grade 4 |
| Mississippi | 4.NBT.4 | Fluently add and subtract (including subtracting across zeros) multi-digit whole numbers using the standard algorithm. | Grade 4 |
| Mississippi | 4.NBT.5 | Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. | Grade 4 |
| Mississippi | 4.NBT.6 | Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. | Grade 4 |
| Mississippi | 4.NF.1 | Recognizing that the value of “n” cannot be 0, explain why a fraction a/b is equivalent to a fraction (n × a)/ (n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. | Grade 4 |
| Mississippi | 4.NF.2 | Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model. | Grade 4 |
| Mississippi | 4.NF.3 | Understand a fraction a/b with a > 1 as a sum of fractions 1/b. | Grade 4 |
| Mississippi | 4.NF.4 | Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. | Grade 4 |
| Mississippi | 4.NF.5 | Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100. | Grade 4 |
| Mississippi | 4.NF.6 | Use decimal notation for fractions with denominators 10 or 100. | Grade 4 |
| Mississippi | 4.NF.7 | Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual model. | Grade 4 |
| Mississippi | 4.OA.1 | Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 × 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations. | Grade 4 |
| Mississippi | 4.OA.2 | Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison. | Grade 4 |
| Mississippi | 4.OA.3 | Solve multistep (two or more operational steps) word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. | Grade 4 |
| Mississippi | 4.OA.4 | Find all factor pairs for a whole number in the range 1–100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1–100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1–100 is prime or composite. | Grade 4 |
| Mississippi | 4.OA.5 | Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. | Grade 4 |
| Mississippi | 5.G.1 | Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate). | Grade 5 |
| Mississippi | 5.G.2 | Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. | Grade 5 |
| Mississippi | 5.G.3 | Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. | Grade 5 |
| Mississippi | 5.G.4 | Classify two-dimensional figures in a hierarchy based on properties. | Grade 5 |
| Mississippi | 5.MD.1 | Convert among different-sized standard measurement units within a given measurement system (customary and metric) (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. | Grade 5 |
| Mississippi | 5.MD.2 | Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. | Grade 5 |
| Mississippi | 5.MD.3 | Recognize volume as an attribute of solid figures and understand concepts of volume measurement. | Grade 5 |
| Mississippi | 5.MD.4 | Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. | Grade 5 |
| Mississippi | 5.MD.5 | Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume. | Grade 5 |
| Mississippi | 5.NBT.1 | Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left (e.g., “In the number 3.33, the underlined digit represents 3/10, which is 10 times the amount represented by the digit to its right (3/100) and is 1/10 the amount represented by the digit to its left (3)). | Grade 5 |
| Mississippi | 5.NBT.2 | Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. | Grade 5 |
| Mississippi | 5.NBT.3 | Read, write, and compare decimals to thousandths. | Grade 5 |
| Mississippi | 5.NBT.4 | Use place value understanding to round decimals to any place. | Grade 5 |
| Mississippi | 5.NBT.5 | Fluently multiply multi-digit whole numbers using the standard algorithm. | Grade 5 |
| Mississippi | 5.NBT.6 | Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. | Grade 5 |
| Mississippi | 5.NBT.7 | Add, subtract, multiply, and divide decimals to hundredths, using concrete models (to include, but not limited to: base ten blocks, decimal tiles, etc.) or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. | Grade 5 |
| Mississippi | 5.NF.1 | Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. | Grade 5 |
| Mississippi | 5.NF.2 | Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. | Grade 5 |
| Mississippi | 5.NF.3 | Interpret a fraction as division of the numerator by the denominator (a/b = a y b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. | Grade 5 |
| Mississippi | 5.NF.4 | Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. | Grade 5 |
| Mississippi | 5.NF.5 | Interpret multiplication as scaling (resizing). | Grade 5 |
| Mississippi | 5.NF.6 | Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. | Grade 5 |
| Mississippi | 5.NF.7 | Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. | Grade 5 |
| Mississippi | 5.OA.1 | Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. | Grade 5 |
| Mississippi | 5.OA.2 | Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. | Grade 5 |
| Mississippi | 5.OA.3 | Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. | Grade 5 |
| Mississippi | 6.EE.1 | Write and evaluate numerical expressions involving whole-number exponents. | Grade 6 |
| Mississippi | 6.EE.2 | Write, read, and evaluate expressions in which letters stand for numbers. | Grade 6 |
| Mississippi | 6.EE.3 | Apply the properties of operations to generate equivalent expressions. | Grade 6 |
| Mississippi | 6.EE.4 | Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). | Grade 6 |
| Mississippi | 6.EE.5 | Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true. | Grade 6 |
| Mississippi | 6.EE.6 | Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set. | Grade 6 |
| Mississippi | 6.EE.7 | Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers. | Grade 6 |
| Mississippi | 6.EE.8 | Write an inequality of the form x > c or x c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams. | Grade 6 |
| Mississippi | 6.EE.9 | Use variables to represent two quantities in a real-world problem that change in relationship to one another. Write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. | Grade 6 |
| Mississippi | 6.G.1 | Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems. | Grade 6 |
| Mississippi | 6.G.2 | Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas V = lwh and V = bh to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems. | Grade 6 |
| Mississippi | 6.G.3 | Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems. | Grade 6 |
| Mississippi | 6.G.4 | Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems. | Grade 6 |
| Mississippi | 6.RP.1 | Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. | Grade 6 |
| Mississippi | 6.RP.2 | Understand the concept of a unit rate a/b associated with a ratio a:b with b ≠ 0, and use rate language in the context of a ratio relationship. | Grade 6 |
| Mississippi | 6.RP.3 | Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. | Grade 6 |
| Mississippi | 6.SP.5 | Summarize numerical data sets in relation to their context, such as by: | Grade 6 |
| Mississippi | 6.NS.1 | Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. | Grade 6 |
| Mississippi | 6.NS.2 | Fluently divide multi-digit numbers using the standard algorithm. | Grade 6 |
| Mississippi | 6.NS.3 | Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation. | Grade 6 |
| Mississippi | 6.NS.5 | Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation. | Grade 6 |
| Mississippi | 6.NS.6 | Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates. | Grade 6 |
| Mississippi | 6.NS.7 | Understand ordering and absolute value of rational numbers. | Grade 6 |
| Mississippi | 6.NS.8 | Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. | Grade 6 |
| Mississippi | 7.EE.1 | Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients. | Grade 7 |
| Mississippi | 7.EE.2 | Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. | Grade 7 |
| Mississippi | 7.EE.3 | Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. | Grade 7 |
| Mississippi | 7.EE.4 | Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. | Grade 7 |
| Mississippi | 7.G.1 | Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale. | Grade 7 |
| Mississippi | 7.G.2 | Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle. | Grade 7 |
| Mississippi | 7.G.3 | Describe the two-dimensional figures that result from slicing three-dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids. | Grade 7 |
| Mississippi | 7.G.4 | Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle. | Grade 7 |
| Mississippi | 7.G.5 | Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure. | Grade 7 |
| Mississippi | 7.G.6 | Solve real-world and mathematical problems involving area, volume and surface area of two-and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. | Grade 7 |
| Mississippi | 7.RP.1 | Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. | Grade 7 |
| Mississippi | 7.RP.2 | Recognize and represent proportional relationships between quantities. | Grade 7 |
| Mississippi | 7.RP.3 | Use proportional relationships to solve multistep ratio and percent problems. | Grade 7 |
| Mississippi | 7.NS.1 | Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram. | Grade 7 |
| Mississippi | 7.NS.2 | Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers. | Grade 7 |
| Mississippi | 7.NS.3 | Solve real-world and mathematical problems involving the four operations with rational numbers. | Grade 7 |
| Mississippi | 8.EE.1 | Know and apply the properties of integer exponents to generate equivalent numerical expressions. | Grade 8 |
| Mississippi | 8.EE.2 | Use square root and cube root symbols to represent solutions to equations of the form x² = p and x³ = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that √2 is irrational. | Grade 8 |
| Mississippi | 8.EE.3 | Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other. | Grade 8 |
| Mississippi | 8.EE.4 | Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology. | Grade 8 |
| Mississippi | 8.EE.5 | Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. | Grade 8 |
| Mississippi | 8.EE.6 | Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b. | Grade 8 |
| Mississippi | 8.EE.7 | Solve linear equations in one variable. | Grade 8 |
| Mississippi | 8.EE.8 | Analyze and solve pairs of simultaneous linear equations. | Grade 8 |
| Mississippi | 8.F.1 | Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output. | Grade 8 |
| Mississippi | 8.F.2 | Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). | Grade 8 |
| Mississippi | 8.F.3 | Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. | Grade 8 |
| Mississippi | 8.F.4 | Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values. | Grade 8 |
| Mississippi | 8.F.5 | Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally. | Grade 8 |
| Mississippi | 8.G.1 | Verify experimentally the properties of rotations, reflections, and translations. | Grade 8 |
| Mississippi | 8.G.2 | Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them. | Grade 8 |
| Mississippi | 8.G.3 | Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates. | Grade 8 |
| Mississippi | 8.G.4 | Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two-dimensional figures, describe a sequence that exhibits the similarity between them. | Grade 8 |
| Mississippi | 8.G.5 | Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. | Grade 8 |
| Mississippi | 8.G.7 | Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions. | Grade 8 |
| Mississippi | 8.G.8 | Apply the Pythagorean Theorem to find the distance between two points in a coordinate system. | Grade 8 |
| Mississippi | 8.G.9 | Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems. | Grade 8 |
| Mississippi | 8.SP.1 | Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association. | Grade 8 |
| Mississippi | 8.SP.2 | Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line. | Grade 8 |
| Mississippi | 8.NS.2 | Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g., π²). | Grade 8 |
| Missouri | K.DS.A.1 | Classify objects into given categories; count the number of objects in each category. | Kindergarten |
| Missouri | K.DS.A.2 | Compare category counts using appropriate language. | Kindergarten |
| Missouri | K.GM.A.1 | Describe several measureable attributes of objects. | Kindergarten |
| Missouri | K.GM.A.2 | Compare the measurable attributes of two objects. | Kindergarten |
| Missouri | K.GM.B.5 | Identify pennies, nickels, dimes and quarters. | Kindergarten |
| Missouri | K.GM.C.6 | Identify shapes and describe objects in the environment using names of shapes, recognizing the name stays the same regardless of orientation or size. | Kindergarten |
| Missouri | K.GM.C.7 | Describe the relative positions of objects in space. | Kindergarten |
| Missouri | K.GM.C.8 | Identify and describe the attribute of shapes, and use the attributes to sort a collection of shapes. | Kindergarten |
| Missouri | K.GM.C.10 | Compose simple shapes to form larger shapes using manipulatives. | Kindergarten |
| Missouri | K.NS.A.1 | Count to 100 by ones and tens. | Kindergarten |
| Missouri | K.NS.A.2 | Count forward beginning from a given number between 1 and 20. | Kindergarten |
| Missouri | K.NS.A.4 | Read and write numerals and represent a number of objects from 0 to 20. | Kindergarten |
| Missouri | K.NS.B.5 | Say the number names when counting objects, in the standard order, pairing each object with one and only one number name and each number name with one and only one object. | Kindergarten |
| Missouri | K.NS.B.6 | Demonstrate that the last number name said tells the number of objects counted and the number of objects is the same regardless of their arrangement or the order in which they were counted. | Kindergarten |
| Missouri | K.NS.B.7 | Demonstrate that each successive number name refers to a quantity that is one larger than the previous number. | Kindergarten |
| Missouri | K.NS.B.9 | Demonstrate that a number can be used to represent how many are in a set. | Kindergarten |
| Missouri | K.NS.C.10 | Compare two or more sets of objects and identify which set is equal to, more than or less than the other. | Kindergarten |
| Missouri | K.NS.C.11 | Compare two numerals, between 1 and 10, and determine which is more than or less than the other. | Kindergarten |
| Missouri | K.NBT.A.1 | Compose and decompose numbers from 11 to 19 into sets of tens with additional ones. | Kindergarten |
| Missouri | K.RA.A.1 | Represent addition and subtraction within 10. | Kindergarten |
| Missouri | K.RA.A.2 | Demonstrate fluency for addition and subtraction within 5. | Kindergarten |
| Missouri | K.RA.A.3 | Decompose numbers less than or equal to 10 in more than one way. | Kindergarten |
| Missouri | K.RA.A.4 | Make 10 for any number from 1 to 9. | Kindergarten |
| Missouri | 1.DS.A.1 | Collect, organize and represent data with up to three categories. | Grade 1 |
| Missouri | 1.DS.A.2 | Draw conclusions from object graphs, picture graphs, T-charts and tallies. | Grade 1 |
| Missouri | 1.GM.A.1 | Distinguish between defining attributes versus non-defining attributes; build and draw shapes that possess defining attributes. | Grade 1 |
| Missouri | 1.GM.A.2 | Compose and decompose two- and three-dimensional shapes to build an understanding of part-whole relationships and the properties of the original and composite shapes. | Grade 1 |
| Missouri | 1.GM.A.4 | Partition circles and rectangles into two or four equal shares, and describe the shares and the wholes verbally. | Grade 1 |
| Missouri | 1.GM.B.5 | Order three or more objects by length. | Grade 1 |
| Missouri | 1.GM.B.6 | Compare the lengths of two objects indirectly by using a third object. | Grade 1 |
| Missouri | 1.GM.B.7 | Demonstrate the ability to measure length or distance using objects. | Grade 1 |
| Missouri | 1.GM.C.8 | Tell and write time in hours and half-hours using analog and digital clocks. | Grade 1 |
| Missouri | 1.GM.C.9 | Know the value of a penny, nickel, dime and quarter. | Grade 1 |
| Missouri | 1.NS.A.1 | Count to 120, starting at any number less than 120. | Grade 1 |
| Missouri | 1.NS.A.2 | Read and write numerals and represent a number of objects with a written numeral. | Grade 1 |
| Missouri | 1.NBT.A.1 | Understand that 10 can be thought of as a bundle of 10 ones called a ten. | Grade 1 |
| Missouri | 1.NBT.A.2 | Understand two-digit numbers are composed of ten (s) and ones (s). | Grade 1 |
| Missouri | 1.NBT.A.3 | Compare two two-digit numbers using the symbols >, = or <. | Grade 1 |
| Missouri | 1.NBT.B.5 | Add within 100. | Grade 1 |
| Missouri | 1.NBT.B.6 | Calculate 10 more or 10 less than a given number mentally without having to count. | Grade 1 |
| Missouri | 1.NBT.B.7 | Add or subtract a multiple of 10 from another two-digit number, and justify the solution. | Grade 1 |
| Missouri | 1.RA.A.1 | Use addition and subtraction within 20 to solve problems. | Grade 1 |
| Missouri | 1.RA.A.3 | Develop the meaning of the equal sign and determine if equations involving addition and subtraction are true or false. | Grade 1 |
| Missouri | 1.RA.A.4 | Determine the unknown whole number in an addition or subtraction equation relating three whole numbers. | Grade 1 |
| Missouri | 1.RA.B.5 | Use properties as strategies to add and subtract. | Grade 1 |
| Missouri | 1.RA.B.6 | Demonstrate that subtraction can be solved as an unknown-addend problem. | Grade 1 |
| Missouri | 1.RA.C.7 | Add and subtract within 20. | Grade 1 |
| Missouri | 1.RA.C.8 | Demonstrate fluency with addition and subtraction within 10. | Grade 1 |
| Missouri | 2.DS.A.1 | Create a line plot to represent a set of numeric data, given a horizontal scale marked in whole numbers. | Grade 2 |
| Missouri | 2.DS.A.2 | Generate measurement data to the nearest whole unit, and display the data in a line plot. | Grade 2 |
| Missouri | 2.DS.A.3 | Draw a picture graph or a bar graph to represent a data set with up to four categories. | Grade 2 |
| Missouri | 2.DS.A.4 | Solve problems using information presented in line plots, picture graphs and bar graphs. | Grade 2 |
| Missouri | 2.DS.A.5 | Draw conclusions from line plots, picture graphs and bar graphs. | Grade 2 |
| Missouri | 2.GM.A.1 | Recognize and draw shapes having specified attributes, such as a given number of angles or sides. | Grade 2 |
| Missouri | 2.GM.A.2 | Partition a rectangle into rows and columns of same-size squares and count to find the total number of squares. | Grade 2 |
| Missouri | 2.GM.A.3 | Partition circles and rectangles into two, three or four equal shares, and describe the shares and the whole. | Grade 2 |
| Missouri | 2.GM.B.4 | Measure the length of an object by selecting and using appropriate tools. | Grade 2 |
| Missouri | 2.GM.B.5 | Analyze the results of measuring the same object with different units. | Grade 2 |
| Missouri | 2.GM.B.7 | Measure to determine how much longer one object is than another. | Grade 2 |
| Missouri | 2.GM.C.8 | Use addition and subtraction within 100 to solve problems involving lengths that are given in the same units. | Grade 2 |
| Missouri | 2.GM.D.10 | Tell and write time from analog and digital clocks to the nearest five minutes, using a.m. and p.m. | Grade 2 |
| Missouri | 2.GM.D.12 | Find the value of combinations of dollar bills, quarters, dimes, nickels and pennies, using $ appropriately. | Grade 2 |
| Missouri | 2.GM.D.13 | Find combinations of coins that equal a given amount. | Grade 2 |
| Missouri | 2.NBT.A.1 | Understand three-digit numbers are composed of hundreds, tens and ones. | Grade 2 |
| Missouri | 2.NBT.A.2 | Understand that 100 can be thought of as 10 tens called a hundred. | Grade 2 |
| Missouri | 2.NBT.A.3 | Count within 1000 by 1s, 10s and 100s starting with any number. | Grade 2 |
| Missouri | 2.NBT.A.4 | Read and write numbers to 1000 using number names, base-ten numerals and expanded form. | Grade 2 |
| Missouri | 2.NBT.A.5 | Compare two three-digit numbers using the symbols >, = or <. | Grade 2 |
| Missouri | 2.NBT.B.6 | Demonstrate fluency with addition and subtraction within 100. | Grade 2 |
| Missouri | 2.NBT.B.7 | Add up to four two-digit numbers. | Grade 2 |
| Missouri | 2.NBT.B.8 | Add or subtract within 1000, and justify the solution. | Grade 2 |
| Missouri | 2.NBT.B.9 | Use the relationship between addition and subtraction to solve problems. | Grade 2 |
| Missouri | 2.NBT.B.10 | Add or subtract mentally 10 or 100 to or from a given number within 1000. | Grade 2 |
| Missouri | 2.NBT.C.11 | Write and solve problems involving addition and subtraction within 100. | Grade 2 |
| Missouri | 2.RA.A.1 | Demonstrate fluency with addition and subtraction within 20. | Grade 2 |
| Missouri | 2.RA.B.2 | Determine if a set of objects has an odd or even number of members. | Grade 2 |
| Missouri | 2.RA.B.3 | Find the total number of objects arranged in a rectangular array with up to 5 rows and 5 columns, and write an equation to represent the total as a sum of equal addends. | Grade 2 |
| Missouri | 3.DS.A.1 | Create frequency tables, scaled picture graphs and bar graphs to represent a data set with several categories. | Grade 3 |
| Missouri | 3.DS.A.2 | Solve one- and two-step problems using information presented in bar and/or picture graphs. | Grade 3 |
| Missouri | 3.DS.A.3 | Create a line plot to represent data. | Grade 3 |
| Missouri | 3.DS.A.4 | Use data shown in a line plot to answer questions. | Grade 3 |
| Missouri | 3.GM.A.1 | Understand that shapes in different categories may share attributes and that the shared attributes can define a larger category. | Grade 3 |
| Missouri | 3.GM.A.2 | Distinguish rhombuses and rectangles as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to these subcategories. | Grade 3 |
| Missouri | 3.GM.A.3 | Partition shapes into parts with equal areas, and express the area of each part as a unit fraction of the whole. | Grade 3 |
| Missouri | 3.GM.B.4 | Tell and write time to the nearest minute. | Grade 3 |
| Missouri | 3.GM.B.5 | Estimate time intervals in minutes. | Grade 3 |
| Missouri | 3.GM.B.6 | Solve problems involving addition and subtraction of minutes. | Grade 3 |
| Missouri | 3.GM.B.7 | Measure or estimate length, liquid volume and weight of objects. | Grade 3 |
| Missouri | 3.GM.B.8 | Use the four operations to solve problems involving lengths, liquid volumes or weights given in the same units. | Grade 3 |
| Missouri | 3.GM.C.9 | Calculate area by using unit squares to cover a plane figure with no gaps or overlaps. | Grade 3 |
| Missouri | 3.GM.C.10 | Label area measurements with squared units. | Grade 3 |
| Missouri | 3.GM.C.11 | Demonstrate that tiling a rectangle to find the area and multiplying the side lengths result in the same value. | Grade 3 |
| Missouri | 3.GM.C.12 | Multiply whole-number side lengths to solve problems involving the area of rectangles. | Grade 3 |
| Missouri | 3.GM.C.13 | Find rectangular arrangements that can be formed for a given area. | Grade 3 |
| Missouri | 3.GM.C.14 | Decompose a rectangle into smaller rectangles to find the area of the original rectangle. | Grade 3 |
| Missouri | 3.GM.D.15 | Solve problems involving perimeters of polygons. | Grade 3 |
| Missouri | 3.GM.D.16 | Understand that rectangles can have equal perimeters but different areas, or rectangles can have equal areas but different perimeters. | Grade 3 |
| Missouri | 3.NBT.A.1 | Round whole numbers to the nearest 10 or 100. | Grade 3 |
| Missouri | 3.NBT.A.3 | Demonstrate fluency with addition and subtraction within 1000. | Grade 3 |
| Missouri | 3.NBT.A.4 | Multiply whole numbers by multiples of 10 in the range 10-90. | Grade 3 |
| Missouri | 3.NF.A.1 | Understand a unit fraction as the quantity formed by one part when a whole is partitioned into equal parts. | Grade 3 |
| Missouri | 3.NF.A.2 | Understand that when a whole is partitioned equally, a fraction can be used to represent a portion of the whole. | Grade 3 |
| Missouri | 3.NF.A.3 | Represent fractions on a number line. | Grade 3 |
| Missouri | 3.NF.A.4 | Demonstrate that two fractions are equivalent if they are the same size, or the same point on a number line. | Grade 3 |
| Missouri | 3.NF.A.5 | Recognize and generate equivalent fractions using visual models, and justify why the fractions are equivalent. | Grade 3 |
| Missouri | 3.NF.A.6 | Compare two fractions with the same numerator or denominator using the symbols >, = or <, and justify the solution. | Grade 3 |
| Missouri | 3.NF.A.7 | Explain why fraction comparisons are only valid when the two fractions refer to the same whole. | Grade 3 |
| Missouri | 3.RA.A.1 | Interpret products of whole numbers. | Grade 3 |
| Missouri | 3.RA.A.2 | Interpret quotients of whole numbers. | Grade 3 |
| Missouri | 3.RA.A.3 | Describe in words or drawings a problem that illustrates a multiplication or division situation. | Grade 3 |
| Missouri | 3.RA.A.4 | Use multiplication and division within 100 to solve problems. | Grade 3 |
| Missouri | 3.RA.A.5 | Determine the unknown number in a multiplication or division equation relating three whole numbers. | Grade 3 |
| Missouri | 3.RA.B.6 | Apply properties of operations as strategies to multiply and divide. | Grade 3 |
| Missouri | 3.RA.C.7 | Multiply and divide with numbers and results within 100 using strategies such as the relationship between multiplication and division or properties of operations. Know all products of two one-digit numbers. | Grade 3 |
| Missouri | 3.RA.C.8 | Demonstrate fluency with products within 100. | Grade 3 |
| Missouri | 3.RA.D.9 | Write and solve two-step problems involving variables using any of the four operations. | Grade 3 |
| Missouri | 3.RA.D.10 | Interpret the reasonableness of answers using mental computation and estimation strategies including rounding. | Grade 3 |
| Missouri | 3.RA.E.11 | Identify arithmetic patterns and explain the patterns using properties of operations. | Grade 3 |
| Missouri | 4.DS.A.1 | Create a frequency table and/or line plot to display measurement data. | Grade 4 |
| Missouri | 4.DS.A.2 | Solve problems involving addition and subtraction by using information presented in a data display. | Grade 4 |
| Missouri | 4.GM.A.1 | Draw and identify points, lines, line segments, rays, angles, perpendicular lines and parallel lines. | Grade 4 |
| Missouri | 4.GM.A.2 | Classify two-dimensional shapes by their sides and/or angles. | Grade 4 |
| Missouri | 4.GM.A.3 | Construct lines of symmetry for a two-dimensional figure. | Grade 4 |
| Missouri | 4.GM.B.4 | Identify and estimate angles and their measure. | Grade 4 |
| Missouri | 4.GM.B.5 | Draw and measure angles in whole-number degrees using a protractor. | Grade 4 |
| Missouri | 4.GM.C.6 | Know relative sizes of measurement units within one system of units. | Grade 4 |
| Missouri | 4.GM.C.7 | Use the four operations to solve problems involving distances, intervals of time, liquid volume, weight of objects and money. | Grade 4 |
| Missouri | 4.GM.C.8 | Apply the area and perimeter formulas for rectangles to solve problems. | Grade 4 |
| Missouri | 4.NBT.A.1 | Round multi-digit whole numbers to any place. | Grade 4 |
| Missouri | 4.NBT.A.2 | Read, write and identify multi-digit whole numbers up to one million using number names, base ten numerals and expanded form. | Grade 4 |
| Missouri | 4.NBT.A.3 | Compare two multi-digit numbers using the symbols >, = or <, and justify the solution. | Grade 4 |
| Missouri | 4.NBT.A.4 | Understand that in a multi-digit whole number, a digit represents 10 times what it would represents in the place to its right. | Grade 4 |
| Missouri | 4.NBT.A.5 | Demonstrate fluency with addition and subtraction of whole numbers. | Grade 4 |
| Missouri | 4.NBT.A.6 | Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, and justify the solution. | Grade 4 |
| Missouri | 4.NBT.A.7 | Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, and justify the solution. | Grade 4 |
| Missouri | 4.NF.A.1 | Explain and/or illustrate why two fractions are equivalent. | Grade 4 |
| Missouri | 4.NF.A.2 | Recognize and generate equivalent fractions. | Grade 4 |
| Missouri | 4.NF.A.3 | Compare two fractions using the symbols >, = or <, and justify the solution. | Grade 4 |
| Missouri | 4.NF.B.4 | Understand addition and subtraction of fractions as joining/composing and separating/decomposing parts referring to the same whole. | Grade 4 |
| Missouri | 4.NF.B.5 | Decompose a fraction into a sum of fractions with the same denominator and record each decomposition with an equation and justification. | Grade 4 |
| Missouri | 4.NF.B.6 | Solve problems involving adding and subtracting fractions and mixed numbers with like denominators. | Grade 4 |
| Missouri | 4.NF.B.7 | Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. | Grade 4 |
| Missouri | 4.NF.B.8 | Solve problems involving multiplication of a fraction by a whole number. | Grade 4 |
| Missouri | 4.NF.C.9 | Use decimal notation for fractions with denominators of 10 or 100. | Grade 4 |
| Missouri | 4.NF.C.12 | Compare two decimals to the hundredths place using the symbols >, = or <, and justify the solution. | Grade 4 |
| Missouri | 4.RA.A.1 | Multiply or divide to solve problems involving a multiplicative comparison. | Grade 4 |
| Missouri | 4.RA.A.2 | Solve multi-step whole number problems involving the four operations and variables and using estimation to interpret the reasonableness of the answer. | Grade 4 |
| Missouri | 4.RA.A.3 | Solve whole number division problems involving variables in which remainders need to be interpreted, and justify the solution. | Grade 4 |
| Missouri | 4.RA.B.4 | Recognize that a whole number is a multiple of each of its factors and find the multiples for a given whole number. | Grade 4 |
| Missouri | 4.RA.B.5 | Determine if a whole number within 100 is composite or prime, and find all factor pairs for whole numbers within 100. | Grade 4 |
| Missouri | 4.RA.C.6 | Generate a number pattern that follows a given rule. | Grade 4 |
| Missouri | 4.RA.C.7 | Use words or mathematical symbols to express a rule for a given pattern. | Grade 4 |
| Missouri | 5.DS.A.2 | Create a line plot to represent a given or generated data set, and analyze the data to answer questions and solve problems, recognizing the outliers and generating the median. | Grade 5 |
| Missouri | 5.GM.A.1 | Understand that attributes belonging to a category of figures also belong to all subcategories. | Grade 5 |
| Missouri | 5.GM.A.2 | Classify figures in a hierarchy based on properties. | Grade 5 |
| Missouri | 5.GM.B.4 | Understand the concept of volume and recognize that volume is measured in cubic units. | Grade 5 |
| Missouri | 5.GM.B.5 | Apply the formulas for volume of right rectangular prisms with whole-number edge lengths. | Grade 5 |
| Missouri | 5.GM.C.6 | Define a first quadrant Cartesian coordinate system. | Grade 5 |
| Missouri | 5.GM.C.7 | Plot and interpret points in the first quadrant of the Cartesian coordinate plane. | Grade 5 |
| Missouri | 5.GM.D.8 | Convert measurements of capacity, length and weight within a given measurement system. | Grade 5 |
| Missouri | 5.GM.D.9 | Solve multi-step problems that require measurement conversions. | Grade 5 |
| Missouri | 5.NBT.A.1 | Read, write and identify numbers from billions to thousandths using number names, base ten numerals and expanded form. | Grade 5 |
| Missouri | 5.NBT.A.2 | Compare two numbers from billions to thousandths using the symbols >, = or <, and justify the solution. | Grade 5 |
| Missouri | 5.NBT.A.3 | Understand that in a multi-digit number, a digit represents 1/10 times what it would represents in the place to its left. | Grade 5 |
| Missouri | 5.NBT.A.4 | Evaluate the value of powers of 10 and understand the relationship to the place value system. | Grade 5 |
| Missouri | 5.NBT.A.5 | Round numbers from billions to thousandths place. | Grade 5 |
| Missouri | 5.NBT.A.6 | Add and subtract multi-digit whole numbers and decimals to the thousandths place, and justify the solution. | Grade 5 |
| Missouri | 5.NBT.A.7 | Multiply multi-digit whole numbers and decimals to the hundredths place, and justify the solution. | Grade 5 |
| Missouri | 5.NBT.A.8 | Divide multi-digit whole numbers and decimals to the hundredths place using up to two-digit divisors and four-digit dividends, and justify the solution. | Grade 5 |
| Missouri | 5.NF.A.2 | Convert decimals to fractions and fractions to decimals. | Grade 5 |
| Missouri | 5.NF.A.3 | Compare and order fractions and/or decimals to the thousandths place using the symbols >, = or <, and justify the solution. | Grade 5 |
| Missouri | 5.NF.B.4 | Estimate results of sums, differences and products with fractions and decimals to the thousandths. | Grade 5 |
| Missouri | 5.NF.B.5 | Justify the reasonableness of a product when multiplying with fractions. | Grade 5 |
| Missouri | 5.NF.B.6 | Solve problems involving addition and subtraction of fractions and mixed numbers with unlike denominators, and justify the solution. | Grade 5 |
| Missouri | 5.NF.B.7 | Extend the concept of multiplication to multiply a fraction or whole number by a fraction. | Grade 5 |
| Missouri | 5.NF.B.8 | Extend the concept of division to divide unit fractions and whole numbers by using visual fraction models and equations. | Grade 5 |
| Missouri | 5.RA.A.1 | Investigate the relationship between two numeric patterns. | Grade 5 |
| Missouri | 5.RA.A.2 | Write a rule to describe or explain a given numeric pattern. | Grade 5 |
| Missouri | 5.RA.B.3 | Write, evaluate and interpret numeric expressions using the order of operations. | Grade 5 |
| Missouri | 5.RA.B.4 | Translate written expressions into algebraic expressions. | Grade 5 |
| Missouri | 5.RA.C.5 | Solve and justify multi-step problems involving variables, whole numbers, fractions and decimals. | Grade 5 |
| Missouri | 6.DSP.B.5 | Summarize numerical data sets in relation to the context. | Grade 6 |
| Missouri | 6.EEI.A.2 | Create and evaluate expressions involving variables and whole number exponents. | Grade 6 |
| Missouri | 6.EEI.A.3 | Identify and generate equivalent algebraic expressions using mathematical properties. | Grade 6 |
| Missouri | 6.EEI.B.4 | Use substitution to determine whether a given number in a specified set makes a one-variable equation or inequality true. | Grade 6 |
| Missouri | 6.EEI.B.5 | Understand that if any solutions exist, the solution set for an equation or inequality consists of values that make the equation or inequality true. | Grade 6 |
| Missouri | 6.EEI.B.6 | Write and solve equations using variables to represent quantities, and understand the meaning of the variable in the context of the situation. | Grade 6 |
| Missouri | 6.EEI.B.7 | Solve one-step linear equations in one variable involving non-negative rational numbers. | Grade 6 |
| Missouri | 6.EEI.B.8 | Recognize that inequalities may have infinitely many solutions. | Grade 6 |
| Missouri | 6.EEI.C.9 | Identify and describe relationships between two variables that change in relationship to one another. | Grade 6 |
| Missouri | 6.GM.A.1 | Find the area of polygons by composing or decomposing the shapes into rectangles or triangles. | Grade 6 |
| Missouri | 6.GM.A.2 | Find the volume of right rectangular prisms. | Grade 6 |
| Missouri | 6.GM.A.3 | Solve problems by graphing points in all four quadrants of the Cartesian coordinate plane. | Grade 6 |
| Missouri | 6.GM.A.4 | Solve problems using nets. | Grade 6 |
| Missouri | 6.NS.A.1 | Compute and interpret quotients of positive fractions. | Grade 6 |
| Missouri | 6.NS.B.2 | Demonstrate fluency with division of multi-digit whole numbers. | Grade 6 |
| Missouri | 6.NS.B.3 | Demonstrate fluency with addition, subtraction, multiplication and division of decimals. | Grade 6 |
| Missouri | 6.NS.C.5 | Use positive and negative numbers to represent quantities. | Grade 6 |
| Missouri | 6.NS.C.6 | Locate a rational number as a point on the number line. | Grade 6 |
| Missouri | 6.NS.C.7 | Understand that the absolute value of a rational number is its distance from 0 on the number line. | Grade 6 |
| Missouri | 6.RP.A.1 | Understand a ratio as a comparison of two quantities and represent these comparisons. | Grade 6 |
| Missouri | 6.RP.A.2 | Understand the concept of a unit rate associated with a ratio, and describe the meaning of unit rate. | Grade 6 |
| Missouri | 6.RP.A.3 | Solve problems involving ratios and rates. | Grade 6 |
| Missouri | 7.EEI.A.1 | Apply properties of operations to simplify and to factor linear algebraic expressions with rational coefficients. | Grade 7 |
| Missouri | 7.EEI.A.2 | Understand how to use equivalent expressions to clarify quantities in a problem. | Grade 7 |
| Missouri | 7.EEI.B.3 | Solve multi-step problems posed with rational numbers. | Grade 7 |
| Missouri | 7.EEI.B.4 | Write and/or solve linear equations and inequalities in one variable. | Grade 7 |
| Missouri | 7.GM.A.1 | Solve problems involving scale drawings of real objects and geometric figures, including computing actual lengths and areas from a scale drawing and reproducing the drawing at a different scale. | Grade 7 |
| Missouri | 7.GM.A.2 | Use a variety of tools to construct geometric shapes. | Grade 7 |
| Missouri | 7.GM.A.3 | Describe two-dimensional cross sections of pyramids, prisms, cones and cylinders. | Grade 7 |
| Missouri | 7.GM.B.5 | Use angle properties to write and solve equations for an unknown angle. | Grade 7 |
| Missouri | 7.GM.B.6 | Understand the relationship between area, surface area and volume. | Grade 7 |
| Missouri | 7.NS.A.1 | Apply and extend previous understandings of numbers to add and subtract rational numbers. | Grade 7 |
| Missouri | 7.NS.A.2 | Apply and extend previous understandings of numbers to multiply and divide rational numbers. | Grade 7 |
| Missouri | 7.NS.A.3 | Solve problems involving the four arithmetic operations with rational numbers. | Grade 7 |
| Missouri | 7.RP.A.1 | Compute unit rates, including those that involve complex fractions, with like or different units. | Grade 7 |
| Missouri | 7.RP.A.2 | Recognize and represent proportional relationships between quantities. | Grade 7 |
| Missouri | 7.RP.A.3 | Solve problems involving ratios, rates, percentages and proportional relationships. | Grade 7 |
| Missouri | 8.DSP.A.1 | Construct and interpret scatter plots of bivariate measurement data to investigate patterns of association between two quantities. | Grade 8 |
| Missouri | 8.DSP.A.2 | Generate and use a trend line for bivariate data, and informally assess the fit of the line. | Grade 8 |
| Missouri | 8.EEI.A.1 | Know and apply the properties of integer exponents to generate equivalent expressions. | Grade 8 |
| Missouri | 8.EEI.A.2 | Investigate concepts of square and cube roots. | Grade 8 |
| Missouri | 8.EEI.A.3 | Express very large and very small quantities in scientific notation and approximate how many times larger one is than the other. | Grade 8 |
| Missouri | 8.EEI.A.4 | Use scientific notation to solve problems. | Grade 8 |
| Missouri | 8.EEI.B.5 | Graph proportional relationships. | Grade 8 |
| Missouri | 8.EEI.B.6 | Apply concepts of slope and y-intercept to graphs, equations and proportional relationships. | Grade 8 |
| Missouri | 8.EEI.C.7 | Solve linear equations and inequalities in one variable. | Grade 8 |
| Missouri | 8.EEI.C.8 | Analyze and solve systems of linear equations. | Grade 8 |
| Missouri | 8.F.A.1 | Explore the concept of functions (The use of function notation is not required). | Grade 8 |
| Missouri | 8.F.A.2 | Compare characteristics of two functions each represented in a different way. | Grade 8 |
| Missouri | 8.F.A.3 | Investigate the differences between linear and nonlinear functions. | Grade 8 |
| Missouri | 8.F.B.4 | Use functions to model linear relationships between quantities. | Grade 8 |
| Missouri | 8.F.B.5 | Describe the functional relationship between two quantities from a graph or a verbal description. | Grade 8 |
| Missouri | 8.GM.A.1 | Verify experimentally the congruence properties of rigid transformations. | Grade 8 |
| Missouri | 8.GM.A.2 | Understand that two-dimensional figures are congruent if a series of rigid transformations can be performed to map the pre-image to the image. | Grade 8 |
| Missouri | 8.GM.A.3 | Describe the effect of dilations, translations, rotations and reflections on two-dimensional figures using coordinates. | Grade 8 |
| Missouri | 8.GM.A.4 | Understand that two-dimensional figures are similar if a series of transformations (rotations, reflections, translations and dilations) can be performed to map the pre-image to the image. | Grade 8 |
| Missouri | 8.GM.A.5 | Explore angle relationships and establish informal arguments. | Grade 8 |
| Missouri | 8.GM.B.7 | Use the Pythagorean Theorem to determine unknown side lengths in right triangles in problems in two- and three-dimensional contexts. | Grade 8 |
| Missouri | 8.GM.B.8 | Use the Pythagorean Theorem to find the distance between points in a Cartesian coordinate system. | Grade 8 |
| Missouri | 8.GM.C.9 | Solve problems involving surface area and volume. | Grade 8 |
| Missouri | 8.NS.A.2 | Estimate the value and compare the size of irrational numbers and approximate their locations on a number line. | Grade 8 |
| Missouri | A2.APR.A.5 | Identify zeros of polynomials when suitable factorizations are available, and use the zeros to sketch the function defined by the polynomial. | Algebra |
| Missouri | A1.CED.A.2 | Create and graph linear, quadratic and exponential equations in two variables. | Algebra |
| Missouri | A1.CED.A.3 | Represent constraints by equations or inequalitiesand by systems of equations or inequalities, and interpret the data points as a solution or non-solution in a modeling context. | Algebra |
| Missouri | A1.DS.A.5 | Construct a scatter plot of bivariate quantitative data describing how the variables are related; determine and use a function that models the relationship. | Algebra |
| Missouri | A1.IF.A.2 | Use function notation to evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. | Algebra |
| Missouri | A1.IF.B.3 | Using tables, graphs and verbal descriptions, interpret key characteristics of a function that models the relationship between two quantities. | Algebra |
| Missouri | A1.IF.C.7 | Graph functions expressed symbolically and identify and interpret key features of the graph. | Algebra |
| Missouri | A1.LQE.A.3 | Construct linear, quadratic and exponential equations given graphs, verbal descriptions or tables. | Algebra |
| Missouri | A1.SSE.A.2 | Analyze the structure of polynomials to create equivalent expressions or equations. | Algebra |
| Missouri | A1.SSE.A.3 | Choose and produce equivalent forms of a quadratic expression or equations to reveal and explain properties. | Algebra |
| Montana | K.CC.1 | Count to 100 by ones and by tens. | Kindergarten |
| Montana | K.CC.2 | Count forward beginning from a given number within the known sequence (instead of having to begin at 1). | Kindergarten |
| Montana | K.CC.3 | Write numbers from 0 to 20. Represent a number of objects with a written numeral 0-20 (with 0 representing a count of no objects). | Kindergarten |
| Montana | K.CC.4 | Understand the relationship between numbers and quantities; connect counting to cardinality. | Kindergarten |
| Montana | K.CC.5 | Count to answer “how many?” questions about as many as 20 things arranged in a line, a rectangular array, or a circle, or as many as 10 things in a scattered configuration; given a number from 1–20, count out that many objects from a variety of cultural contexts, including those of Montana American Indians. | Kindergarten |
| Montana | K.CC.6 | Identify whether the number of objects in one group is greater than, less than, or equal to the number of objects in another group, e.g., by using matching and counting strategies. | Kindergarten |
| Montana | K.CC.7 | Compare two numbers between 1 and 10 presented as written numerals. | Kindergarten |
| Montana | K.G.1 | Describe objects, including those of Montana American Indians, in the environment using names of shapes, and describe the relative positions of these objects using terms such as above, below, beside, in front of, behind, and next to. | Kindergarten |
| Montana | K.G.2 | Correctly name shapes regardless of their orientations or overall size. | Kindergarten |
| Montana | K.G.3 | Identify shapes as two-dimensional (lying in a plane, “flat”) or three-dimensional (“solid”). | Kindergarten |
| Montana | K.G.4 | Analyze and compare two- and three-dimensional shapes, in different sizes and orientations, using informal language to describe their similarities, differences, parts (e.g., number of sides and vertices/“corners”) and other attributes (e.g., having sides of equal length). | Kindergarten |
| Montana | K.G.6 | Compose simple shapes to form larger shapes. | Kindergarten |
| Montana | K.MD.1 | Describe measurable attributes of objects, such as length or weight. Describe several measurable attributes of a single object. | Kindergarten |
| Montana | K.MD.2 | Directly compare two objects with a measurable attribute in common, to see which object has “more of”/“less of” the attribute, and describe the difference. | Kindergarten |
| Montana | K.MD.3 | Classify objects from a variety of cultural contexts, including those of Montana American Indians, into given categories; count the numbers of objects in each category and sort the categories by count. | Kindergarten |
| Montana | K.NBT.1 | Compose and decompose numbers from 11 to 19 into ten ones and some further ones, e.g., by using objects or drawings, and record each composition or decomposition by a drawing or equation (e.g., 18 = 10 + 8); understand that these numbers are composed of ten ones and one, two, three, four, five, six, seven, eight, or nine ones. | Kindergarten |
| Montana | K.OA.1 | Represent addition and subtraction with objects, fingers, mental images, drawings, sounds (e.g., claps), acting out situations, verbal explanations, expressions, or equations. | Kindergarten |
| Montana | K.OA.2 | Solve addition and subtraction word problems from a variety of cultural contexts, including those of Montana American Indians, and add and subtract within 10, e.g., by using objects or drawings to represent the problem. | Kindergarten |
| Montana | K.OA.3 | Decompose numbers less than or equal to 10 into pairs in more than one way, e.g., by using objects or drawings, and record each decomposition by a drawing or equation (e.g., 5 = 2 + 3 and 5 = 4 + 1). | Kindergarten |
| Montana | K.OA.4 | For any number from 1 to 9, find the number that makes 10 when added to the given number, e.g., by using objects or drawings, and record the answer with a drawing or equation. | Kindergarten |
| Montana | K.OA.5 | Fluently add and subtract within 5. | Kindergarten |
| Montana | 1.G.1 | Distinguish between defining attributes (e.g., triangles are closed and three-sided) versus non-defining attributes (e.g., color, orientation, overall size); build and draw shapes to possess defining attributes. | Grade 1 |
| Montana | 1.G.2 | Compose two-dimensional shapes (rectangles, squares, trapezoids, triangles, half-circles, and quarter-circles) or three-dimensional shapes (cubes, right rectangular prisms, right circular cones, and right circular cylinders) to create a composite shape, and compose new shapes from the composite shape. | Grade 1 |
| Montana | 1.G.3 | Partition circles and rectangles into two and four equal shares, describe the shares using the words halves, fourths, and quarters, and use the phrases half of, fourth of, and quarter of. Describe the whole as two of, or four of the shares. Understand for these examples that decomposing into more equal shares creates smaller shares. | Grade 1 |
| Montana | 1.MD.1 | Order three objects from a variety of cultural contexts, including those of Montana American Indians, by length; compare the lengths of two objects indirectly by using a third object. | Grade 1 |
| Montana | 1.MD.2 | Express the length of an object as a whole number of length units, by laying multiple copies of a shorter object (the length unit) end to end; understand that the length measurement of an object is the number of same-size length units that span it with no gaps or overlaps. | Grade 1 |
| Montana | 1.MD.3 | Tell and write time in hours and half-hours using analog and digital clocks. | Grade 1 |
| Montana | 1.MD.4 | Organize, represent, and interpret data with up to three categories; ask and answer questions about the total number of data points, how many in each category, and how many more or less are in one category than in another. | Grade 1 |
| Montana | 1.NBT.1 | Count to 120, starting at any number less than 120. In this range, read and write numerals and represent a number of objects with a written numeral. | Grade 1 |
| Montana | 1.NBT.2 | Understand that the two digits of a two-digit number represent amounts of tens and ones. | Grade 1 |
| Montana | 1.NBT.3 | Compare two two-digit numbers based on meanings of the tens and ones digits, recording the results of comparisons with the symbols >, =, and <. | Grade 1 |
| Montana | 1.NBT.4 | Add within 100, including adding a two-digit number and a one-digit number, and adding a two-digit number and a multiple of 10, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Understand that in adding two-digit numbers, one adds tens and tens, ones and ones; and sometimes it is necessary to compose a ten. | Grade 1 |
| Montana | 1.NBT.5 | Given a two-digit number, mentally find 10 more or 10 less than the number, without having to count; explain the reasoning used. | Grade 1 |
| Montana | 1.NBT.6 | Subtract multiples of 10 in the range 10-90 from multiples of 10 in the range 10-90 (positive or zero differences), using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. | Grade 1 |
| Montana | 1.OA.1 | Use addition and subtraction within 20 to solve word problems within a cultural context, including those of Montana American Indians, involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem | Grade 1 |
| Montana | 1.OA.3 | Apply properties of operations as strategies to add and subtract. | Grade 1 |
| Montana | 1.OA.4 | Understand subtraction as an unknown-addend problem. | Grade 1 |
| Montana | 1.OA.5 | Relate counting to addition and subtraction (e.g., by counting on 2 to add 2). | Grade 1 |
| Montana | 1.OA.6 | Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to a ten (e.g., 13 - 4 = 13 - 3 - 1 = 10 - 1 = 9); using the relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 - 8 = 4); and creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13). | Grade 1 |
| Montana | 1.OA.7 | Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false. | Grade 1 |
| Montana | 1.OA.8 | Determine the unknown whole number in an addition or subtraction equation relating three whole numbers. | Grade 1 |
| Montana | 2.G.1 | Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces. Identify triangles, quadrilaterals, pentagons, hexagons, and cubes. | Grade 2 |
| Montana | 2.G.2 | Partition a rectangle into rows and columns of same-size squares and count to find the total number of them. | Grade 2 |
| Montana | 2.G.3 | Partition circles and rectangles into two, three, or four equal shares, describe the shares using the words halves, thirds, half of, a third of, etc., and describe the whole as two halves, three thirds, four fourths. Recognize that equal shares of identical wholes need not have the same shape. | Grade 2 |
| Montana | 2.MD.1 | Measure the length of an object by selecting and using appropriate tools such as rulers, yardsticks, meter sticks, and measuring tapes. | Grade 2 |
| Montana | 2.MD.2 | Measure the length of an object twice, using length units of different lengths for the two measurements; describe how the two measurements relate to the size of the unit chosen. | Grade 2 |
| Montana | 2.MD.4 | Measure to determine how much longer one object is than another, expressing the length difference in terms of a standard length unit. | Grade 2 |
| Montana | 2.MD.5 | Use addition and subtraction within 100 to solve word problems within a cultural context, including those of Montana American Indians, involving lengths that are given in the same units, e.g., by using drawings (such as drawings of rulers) and equations with a symbol for the unknown number to represent the problem. | Grade 2 |
| Montana | 2.MD.7 | Tell and write time from analog and digital clocks to the nearest five minutes, using a.m. and p.m. | Grade 2 |
| Montana | 2.MD.8 | Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies, using $ and ¢ symbols appropriately. | Grade 2 |
| Montana | 2.MD.9 | Generate measurement data by measuring lengths of several objects to the nearest whole unit, or by making repeated measurements of the same object. Show the measurements by making a line plot, where the horizontal scale is marked off in whole-number units. | Grade 2 |
| Montana | 2.MD.10 | Draw a picture graph and a bar graph (with single-unit scale) to represent a data set from a variety of cultural contexts, including those of Montana American Indians, with up to four categories. Solve simple put-together, take-apart, and compare problems using information presented in a bar graph. | Grade 2 |
| Montana | 2.NBT.1 | Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones. | Grade 2 |
| Montana | 2.NBT.2 | Count within 1000; skip-count by 5s, 10s, and 100s. | Grade 2 |
| Montana | 2.NBT.3 | Read and write numbers to 1000 using base-ten numerals, number names, and expanded form. | Grade 2 |
| Montana | 2.NBT.4 | Compare two three-digit numbers based on meanings of the hundreds, tens, and ones digits, using >, =, and < symbols to record the results of comparisons. | Grade 2 |
| Montana | 2.NBT.5 | Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction. | Grade 2 |
| Montana | 2.NBT.6 | Add up to four two-digit numbers using strategies based on place value and properties of operations. | Grade 2 |
| Montana | 2.NBT.7 | Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method. Understand that in adding or subtracting three-digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds. | Grade 2 |
| Montana | 2.NBT.8 | Mentally add 10 or 100 to a given number 100–900, and mentally subtract 10 or 100 from a given number 100–900. | Grade 2 |
| Montana | 2.OA.1 | Use addition and subtraction within 100 to solve one- and two-step word problems involving situations within a cultural context, including those of Montana American Indians, of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem. | Grade 2 |
| Montana | 2.OA.2 | Fluently add and subtract within 20 using mental strategies. By end of Grade 2, know from memory all sums of two one-digit numbers. | Grade 2 |
| Montana | 2.OA.3 | Determine whether a group of objects (up to 20) has an odd or even number of members, e.g., by pairing objects or counting them by 2s; write an equation to express an even number as a sum of two equal addends. | Grade 2 |
| Montana | 2.OA.4 | Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends. | Grade 2 |
| Montana | 3.G.1 | Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories. | Grade 3 |
| Montana | 3.G.2 | Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole. | Grade 3 |
| Montana | 3.MD.1 | Tell and write time to the nearest minute and measure time intervals in minutes. Solve word problems involving addition and subtraction of time intervals in minutes, e.g., by representing the problem on a number line diagram. | Grade 3 |
| Montana | 3.MD.2 | Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l). Add, subtract, multiply, or divide to solve one-step word problems involving masses or volumes that are given in the same units, e.g., by using drawings (such as a beaker with a measurement scale) to represent the problem. | Grade 3 |
| Montana | 3.MD.3 | Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories, within cultural contexts, including those of Montana American Indians. Solve one- and two-step “how many more” and “how many less” problems using information presented in scaled bar graphs. | Grade 3 |
| Montana | 3.MD.4 | Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Show the data by making a line plot, where the horizontal scale is marked off in appropriate units-whole numbers, halves, or quarters. | Grade 3 |
| Montana | 3.MD.5 | Recognize area as an attribute of plane figures and understand concepts of area measurement. | Grade 3 |
| Montana | 3.MD.6 | Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units). | Grade 3 |
| Montana | 3.MD.7 | Relate area to the operations of multiplication and addition. | Grade 3 |
| Montana | 3.MD.8 | Solve real world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters. | Grade 3 |
| Montana | 3.NBT.1 | Use place value understanding to round whole numbers to the nearest 10 or 100. | Grade 3 |
| Montana | 3.NBT.2 | Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction. | Grade 3 |
| Montana | 3.NBT.3 | Multiply one-digit whole numbers by multiples of 10 in the range 10–90 (e.g., 9 × 80, 5 × 60) using strategies based on place value and properties of operations. | Grade 3 |
| Montana | 3.NF.1 | Understand a fraction 1/𝘣 as the quantity formed by 1 part when a whole is partitioned into 𝘣 equal parts; understand a fraction 𝘢/𝑏 as the quantity formed by 𝘢 parts of size 1/𝘣. | Grade 3 |
| Montana | 3.NF.2 | Understand a fraction as a number on the number line; represent fractions on a number line diagram. | Grade 3 |
| Montana | 3.NF.3 | Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size. | Grade 3 |
| Montana | 3.OA.1 | Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each. | Grade 3 |
| Montana | 3.OA.2 | Interpret whole-number quotients of whole numbers, e.g., interpret 56 ÷ 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each. | Grade 3 |
| Montana | 3.OA.3 | Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem. | Grade 3 |
| Montana | 3.OA.4 | Determine the unknown whole number in a multiplication or division equation relating three whole numbers. | Grade 3 |
| Montana | 3.OA.5 | Apply properties of operations as strategies to multiply and divide. | Grade 3 |
| Montana | 3.OA.6 | Understand division as an unknown-factor problem. | Grade 3 |
| Montana | 3.OA.7 | Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 × 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers. | Grade 3 |
| Montana | 3.OA.8 | Solve two-step word problems using the four operations within cultural contexts, including those of Montana American Indians. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. | Grade 3 |
| Montana | 3.OA.9 | Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations. | Grade 3 |
| Montana | 4.G.1 | Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures. | Grade 4 |
| Montana | 4.G.2 | Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles. | Grade 4 |
| Montana | 4.G.3 | Recognize a line of symmetry for a two-dimensional figure, including those found in Montana American Indian designs, as a line across the figure such that the figure can be folded along the line into matching parts. Identify line-symmetric figures and draw lines of symmetry. | Grade 4 |
| Montana | 4.MD.1 | Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table. | Grade 4 |
| Montana | 4.MD.2 | Use the four operations to solve word problems within cultural contexts, including those of Montana American Indians, involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. | Grade 4 |
| Montana | 4.MD.3 | Apply the area and perimeter formulas for rectangles in real world and mathematical problems. | Grade 4 |
| Montana | 4.MD.4 | Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots. | Grade 4 |
| Montana | 4.MD.5 | Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement. | Grade 4 |
| Montana | 4.MD.6 | Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure. | Grade 4 |
| Montana | 4.MD.7 | Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems, e.g., by using an equation with a symbol for the unknown angle measure. | Grade 4 |
| Montana | 4.NBT.1 | Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. | Grade 4 |
| Montana | 4.NBT.2 | Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. | Grade 4 |
| Montana | 4.NBT.3 | Use place value understanding to round multi-digit whole numbers to any place. | Grade 4 |
| Montana | 4.NBT.4 | Fluently add and subtract multi-digit whole numbers using the standard algorithm. | Grade 4 |
| Montana | 4.NBT.5 | Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. | Grade 4 |
| Montana | 4.NBT.6 | Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. | Grade 4 |
| Montana | 4.NF.1 | Explain why a fraction 𝘢/𝘣 is equivalent to a fraction (𝘯 × 𝘢)/(𝘯 × 𝘣) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. | Grade 4 |
| Montana | 4.NF.2 | Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model. | Grade 4 |
| Montana | 4.NF.3 | Understand a fraction 𝘢/𝘣 with 𝘢 > 1 as a sum of fractions 1/𝘣. | Grade 4 |
| Montana | 4.NF.4 | Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. | Grade 4 |
| Montana | 4.NF.5 | Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100. | Grade 4 |
| Montana | 4.NF.6 | Use decimal notation for fractions with denominators 10 or 100. | Grade 4 |
| Montana | 4.NF.7 | Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual model. | Grade 4 |
| Montana | 4.OA.1 | Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 × 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations. | Grade 4 |
| Montana | 4.OA.2 | Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison. | Grade 4 |
| Montana | 4.OA.3 | Solve multistep word problems within cultural contexts, including those of Montana American Indians, with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. | Grade 4 |
| Montana | 4.OA.4 | Find all factor pairs for a whole number in the range 1-100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1-100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1-100 is prime or composite. | Grade 4 |
| Montana | 4.OA.5 | Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. | Grade 4 |
| Montana | 5.G.1 | Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., 𝘹-axis and 𝘹-coordinate, 𝘺-axis and 𝘺-coordinate). | Grade 5 |
| Montana | 5.G.2 | Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation including those found in Montana American Indian designs. | Grade 5 |
| Montana | 5.G.3 | Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. | Grade 5 |
| Montana | 5.G.4 | Classify two-dimensional figures in a hierarchy based on properties. | Grade 5 |
| Montana | 5.MD.1 | Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems within a cultural context, including those of Montana American Indians. | Grade 5 |
| Montana | 5.MD.2 | Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. | Grade 5 |
| Montana | 5.MD.3 | Recognize volume as an attribute of solid figures and understand concepts of volume measurement. | Grade 5 |
| Montana | 5.MD.4 | Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. | Grade 5 |
| Montana | 5.MD.5 | Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume within cultural contexts, including those of Montana American Indians. | Grade 5 |
| Montana | 5.NBT.1 | Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. | Grade 5 |
| Montana | 5.NBT.2 | Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. | Grade 5 |
| Montana | 5.NBT.3 | Read, write, and compare decimals to thousandths. | Grade 5 |
| Montana | 5.NBT.4 | Use place value understanding to round decimals to any place. | Grade 5 |
| Montana | 5.NBT.5 | Fluently multiply multi-digit whole numbers using the standard algorithm. | Grade 5 |
| Montana | 5.NBT.6 | Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. | Grade 5 |
| Montana | 5.NBT.7 | Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings within cultural contexts, including those of Montana American Indians, and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. | Grade 5 |
| Montana | 5.NF.1 | Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. | Grade 5 |
| Montana | 5.NF.2 | Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. | Grade 5 |
| Montana | 5.NF.3 | Interpret a fraction as division of the numerator by the denominator (𝘢/𝘣 = 𝘢 ÷ 𝘣). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. | Grade 5 |
| Montana | 5.NF.4 | Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. | Grade 5 |
| Montana | 5.NF.5 | Interpret multiplication as scaling (resizing). | Grade 5 |
| Montana | 5.NF.6 | Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem within cultural contexts, including those of Montana American Indians. | Grade 5 |
| Montana | 5.NF.7 | Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. | Grade 5 |
| Montana | 5.OA.1 | Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. | Grade 5 |
| Montana | 5.OA.2 | Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. | Grade 5 |
| Montana | 5.OA.3 | Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. | Grade 5 |
| Montana | 6.EE.1 | Write and evaluate numerical expressions involving whole-number exponents. | Grade 6 |
| Montana | 6.EE.2 | Write, read, and evaluate expressions in which letters stand for numbers. | Grade 6 |
| Montana | 6.EE.3 | Apply the properties of operations to generate equivalent expressions. | Grade 6 |
| Montana | 6.EE.4 | Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). | Grade 6 |
| Montana | 6.EE.5 | Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true. | Grade 6 |
| Montana | 6.EE.6 | Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set. | Grade 6 |
| Montana | 6.EE.7 | Solve real-world and mathematical problems by writing and solving equations of the form 𝘹 + 𝘱 = 𝘲 and 𝘱𝘹 = 𝘲 for cases in which 𝘱, 𝘲 and 𝘹 are all nonnegative rational numbers. | Grade 6 |
| Montana | 6.EE.8 | Write an inequality of the form 𝘹 > 𝘤 or 𝘹 𝘤 or 𝘹 < 𝘤 have infinitely many solutions; represent solutions of such inequalities on number line diagrams. | Grade 6 |
| Montana | 6.EE.9 | Use variables to represent two quantities in a real-world problem from a variety of cultural contexts, including those of Montana American Indians, that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. | Grade 6 |
| Montana | 6.G.1 | Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems within cultural contexts, including those of Montana American Indians. | Grade 6 |
| Montana | 6.G.2 | Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas 𝘝 = 𝘭 𝘸 𝘩 and 𝘝 = 𝘣 𝘩 to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems. | Grade 6 |
| Montana | 6.G.3 | Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems. | Grade 6 |
| Montana | 6.G.4 | Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems within cultural contexts, including those of Montana American Indians. | Grade 6 |
| Montana | 6.RP.1 | Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. | Grade 6 |
| Montana | 6.RP.2 | Understand the concept of a unit rate 𝘢/𝘣 associated with a ratio 𝘢:𝘣 with 𝘣 ≠ 0, and use rate language in the context of a ratio relationship. | Grade 6 |
| Montana | 6.RP.3 | Use ratio and rate reasoning to solve real-world and mathematical problems from a variety of cultural contexts, including those of Montana American Indians, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. | Grade 6 |
| Montana | 6.SP.5 | Summarize numerical data sets in relation to their context, such as by: | Grade 6 |
| Montana | 6.NS.1 | Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. | Grade 6 |
| Montana | 6.NS.2 | Fluently divide multi-digit numbers using the standard algorithm. | Grade 6 |
| Montana | 6.NS.3 | Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation. | Grade 6 |
| Montana | 6.NS.5 | Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation. | Grade 6 |
| Montana | 6.NS.6 | Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates. | Grade 6 |
| Montana | 6.NS.7 | Understand ordering and absolute value of rational numbers. | Grade 6 |
| Montana | 6.NS.8 | Solve real-world and mathematical problems from a variety of cultural contexts, including those of Montana American Indians, by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. | Grade 6 |
| Montana | 7.EE.1 | Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients. | Grade 7 |
| Montana | 7.EE.2 | Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. | Grade 7 |
| Montana | 7.EE.3 | Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. | Grade 7 |
| Montana | 7.EE.4 | Use variables to represent quantities in a real-world or mathematical problem, including those represented in Montana American Indian cultural contexts, and construct simple equations and inequalities to solve problems by reasoning about the quantities. | Grade 7 |
| Montana | 7.G.1 | Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale. | Grade 7 |
| Montana | 7.G.2 | Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle. | Grade 7 |
| Montana | 7.G.3 | Describe the two-dimensional figures that result from slicing three-dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids. | Grade 7 |
| Montana | 7.G.4 | Know the formulas for the area and circumference of a circle and use them to solve problems from a variety of cultural contexts, including those of Montana American Indians; give an informal derivation of the relationship between the circumference and area of a circle. | Grade 7 |
| Montana | 7.G.5 | Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure. | Grade 7 |
| Montana | 7.G.6 | Solve real-world and mathematical problems from a variety of cultural contexts, including those of Montana American Indians, involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. | Grade 7 |
| Montana | 7.RP.1 | Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. | Grade 7 |
| Montana | 7.RP.2 | Recognize and represent proportional relationships between quantities including those represented in Montana American Indian cultural contexts. | Grade 7 |
| Montana | 7.RP.3 | Use proportional relationships to solve multistep ratio and percent problems within cultural contexts, including those of Montana American Indians (e.g., percent of increase and decrease of tribal land). | Grade 7 |
| Montana | 7.NS.1 | Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram. | Grade 7 |
| Montana | 7.NS.2 | Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers. | Grade 7 |
| Montana | 7.NS.3 | Solve real-world and mathematical problems from a variety of cultural contexts, including those of Montana American Indians, involving the four operations with rational numbers. | Grade 7 |
| Montana | 8.EE.1 | Know and apply the properties of integer exponents to generate equivalent numerical expressions. | Grade 8 |
| Montana | 8.EE.2 | Use square root and cube root symbols to represent solutions to equations of the form 𝘹² = 𝘱 and 𝘹³ = 𝘱, where 𝘱 is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that √2 is irrational. | Grade 8 |
| Montana | 8.EE.3 | Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other. | Grade 8 |
| Montana | 8.EE.4 | Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology. | Grade 8 |
| Montana | 8.EE.5 | Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. | Grade 8 |
| Montana | 8.EE.6 | Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation 𝘺 = 𝘮𝘹 for a line through the origin and the equation 𝘺 = 𝘮𝘹 + 𝘣 for a line intercepting the vertical axis at 𝘣. | Grade 8 |
| Montana | 8.EE.7 | Solve linear equations in one variable. | Grade 8 |
| Montana | 8.EE.8 | Analyze and solve pairs of simultaneous linear equations. | Grade 8 |
| Montana | 8.F.1 | Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output. | Grade 8 |
| Montana | 8.F.2 | Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). | Grade 8 |
| Montana | 8.F.3 | Interpret the equation 𝘺 = 𝘮𝘹 + 𝘣 as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. | Grade 8 |
| Montana | 8.F.4 | Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (𝘹, 𝘺) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values. | Grade 8 |
| Montana | 8.F.5 | Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally. | Grade 8 |
| Montana | 8.G.1 | Verify experimentally the properties of rotations, reflections, and translations from a variety of cultural contexts, including those of Montana American Indians. | Grade 8 |
| Montana | 8.G.2 | Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them. | Grade 8 |
| Montana | 8.G.3 | Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures from a variety of cultural contexts, including those of Montana American Indians: using coordinates. | Grade 8 |
| Montana | 8.G.4 | Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two-dimensional figures, describe a sequence that exhibits the similarity between them. | Grade 8 |
| Montana | 8.G.5 | Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. | Grade 8 |
| Montana | 8.G.7 | Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions. | Grade 8 |
| Montana | 8.G.8 | Apply the Pythagorean Theorem to find the distance between two points in a coordinate system. | Grade 8 |
| Montana | 8.G.9 | Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems. | Grade 8 |
| Montana | 8.SP.1 | Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association. | Grade 8 |
| Montana | 8.SP.2 | Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line. | Grade 8 |
| Montana | 8.NS.2 | Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g., π²). | Grade 8 |
| Montana | A-APR.3 | Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial. | High School |
| Montana | A-CED.2 | Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. | High School |
| Montana | A-CED.3 | Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context. | High School |
| Montana | A-REI.3 | Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. | High School |
| Montana | A-SSE.2 | Use the structure of an expression to identify ways to rewrite it. | High School |
| Montana | A-SSE.3 | Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression. | High School |
| Montana | F-BF.1 | Write a function that describes a relationship between two quantities. | High School |
| Montana | F-IF.2 | Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. | High School |
| Montana | F-IF.4 | For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. | High School |
| Montana | F-IF.7 | Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. | High School |
| Montana | S-ID.6 | Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. | High School |
| Nebraska | K.N.2.a | Use one-to-one correspondence when counting objects to show the relationship between numbers and quantities and understand the last number counted is a direct representation of the total objects in a given set. | Kindergarten |
| Nebraska | K.N.2.d | Count up to 20 objects arranged in a line, a rectangular array, or a circle, and count up to 10 objects in a scattered configuration. | Kindergarten |
| Nebraska | K.N.2.e | Count verbally forward and backward from any given number within 20. | Kindergarten |
| Nebraska | K.N.2.f | Count verbally in sequential order by ones and by tens to 100, making accurate decade transitions (e.g., 89 to 90). | Kindergarten |
| Nebraska | K.N.2.g | Write and name numbers 0 to 20. Represent a number of objects with a written numeral 0 to 20. | Kindergarten |
| Nebraska | K.N.2.h | Compare the number of objects in two groups, up to 20, using the words fewer than, more than, the same as. | Kindergarten |
| Nebraska | K.N.3.a | Compose and decompose numbers from 11 to 19 into a group of ten ones and some more ones using a model, drawing, or equation. | Kindergarten |
| Nebraska | K.N.4.a | Represent and explain addition and subtraction as part-whole relationships, with addition as putting together and/or adding to and subtraction as taking apart and/or taking from, using objects, drawings, numbers, and equations. | Kindergarten |
| Nebraska | K.N.4.b | Compose and decompose numbers less than or equal to 10 into pairs in more than one way using verbal explanations, objects, or drawings. | Kindergarten |
| Nebraska | K.N.4.c | For any number from 1 to 9, find the number that makes 10 when added to the given number, sharing the answer with a model, drawing, or equation. | Kindergarten |
| Nebraska | K.N.4.d | Efficiently, flexibly, and accurately add and subtract within 5. | Kindergarten |
| Nebraska | K.N.4.e | Solve authentic problems that involve addition and subtraction within 10 (e.g., by using objects, drawings, and equations to represent the problem). | Kindergarten |
| Nebraska | K.G.1.a | Identify and name two-dimensional shapes including circles, triangles, squares, and rectangles regardless of orientation or size. | Kindergarten |
| Nebraska | K.G.1.b | Identify and name three-dimensional shapes including spheres, cubes, cylinders, and cones regardless of orientation or size. | Kindergarten |
| Nebraska | K.G.1.c | Describe the relative positions of shapes in relation to other objects or shapes using terms such as above, below, in front of, behind, and next to. | Kindergarten |
| Nebraska | K.G.1.d | Create shapes using given materials and describe one or more of the attributes such as number of sides/corners. | Kindergarten |
| Nebraska | K.G.1.e | Combine simple shapes to compose larger shapes. | Kindergarten |
| Nebraska | K.G.2.a | Describe measurable attributes of authentic objects including length, capacity, and weight. | Kindergarten |
| Nebraska | K.G.2.b | Directly compare two objects with a measurable attribute in common to describe which object is longer/shorter, heavier/lighter, and has more/less-capacity. | Kindergarten |
| Nebraska | K.G.3.a | Identify the name and value of pennies, nickels, and dimes. | Kindergarten |
| Nebraska | K.D.1.a | Identify, sort, and classify objects by size, shape, color, and other attributes. | Kindergarten |
| Nebraska | 1.N.2.a | Count verbally by ones and tens within 120 starting at any given number. | Grade 1 |
| Nebraska | 1.N.3.a | Understand 10 as a bundle, collection, or (more abstractly) composition of ten ones and that the two digits of a two-digit number represent a composition of some tens and some ones. | Grade 1 |
| Nebraska | 1.N.3.b | Compare two, two-digit numbers using words greater than, less than, equal to, and symbols , =. Justify comparisons based on the number of tens and ones. | Grade 1 |
| Nebraska | 1.N.4.a | Add and subtract within 20, using flexible strategies such as counting on or counting back, making ten, using ten, and using doubles and near doubles. | Grade 1 |
| Nebraska | 1.N.4.d | Mentally find 10 more or 10 less than a two-digit number without having to count and explain the reasoning used. | Grade 1 |
| Nebraska | 1.N.4.e | Add within 100, including adding a two-digit number and a one-digit number, adding a two-digit number and a multiple of ten, using concrete models, drawings, and strategies that reflect an understanding of place value, the relationship between addition and subtraction, and the properties of operations. Relate the strategy to a written method and explain the reasoning used to solve. | Grade 1 |
| Nebraska | 1.N.4.g | Subtract multiples of ten from two-digit numbers (positive or zero differences) using concrete models, drawings, and strategies that reflect an understanding of place value, the relationship between addition and subtraction, and the properties of operations. Relate the strategy to a written method and explain the reasoning used to solve. | Grade 1 |
| Nebraska | 1.N.5.a | Use the meaning of the equal sign to determine if equations are true and give examples of equations that are true (e.g., 4 = 4, 6 = 7 – 1, 6 + 3 = 3 + 6, 7 + 2 = 5 + 4). | Grade 1 |
| Nebraska | 1.N.5.b | Use the relationship of addition and subtraction to solve subtraction problems (e.g., find 12 – 9 = , using the addition fact 9 + 3 = 12). | Grade 1 |
| Nebraska | 1.N.5.d | Use the commutative property of addition to develop addition strategies and compose/decompose numbers to develop addition and subtraction strategies. (See other flexible strategies in 1.N.4.a). | Grade 1 |
| Nebraska | 1.N.5.e | Solve problems that call for addition of three whole numbers whose sum is less than or equal to 20 using flexible strategies with objects, drawings, and/or equations. | Grade 1 |
| Nebraska | 1.N.5.f | Solve authentic problems involving addition and subtraction within 20 in situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all parts of the addition or subtraction problem by using objects, drawings, and/or equations with a symbol for the unknown number to represent the problem. | Grade 1 |
| Nebraska | 1.G.1.a | Determine geometric attributes of two-dimensional shapes regardless of orientation or size for rhombi, trapezoids, and hexagons (e.g., a hexagon is closed with six sides). | Grade 1 |
| Nebraska | 1.G.1.b | Determine geometric attributes of three-dimensional shapes including cones, cylinders, cubes, and rectangular prisms regardless of orientation or size. | Grade 1 |
| Nebraska | 1.G.1.d | Partition circles and rectangles into two and four equal parts using the language halves and fourths. | Grade 1 |
| Nebraska | 1.G.2.a | Measure the length of an object as a whole number of same-size, non-standard units by placing them end to end. | Grade 1 |
| Nebraska | 1.G.2.b | Order three objects by directly comparing their lengths or indirectly by using a third object. | Grade 1 |
| Nebraska | 1.G.3.b | Count collections of like coins (penny, nickel, and dime) relating to patterns of counting by 1s, 5s, and 10s. | Grade 1 |
| Nebraska | 1.G.3.c | Tell and write time to the half hour and hour using analog and digital clocks. | Grade 1 |
| Nebraska | 1.D.2.a | Ask and answer questions about the total number of data points, how many in each category, and compare categories by identifying how many more or less are in a particular category using a picture graph. | Grade 1 |
| Nebraska | 2.N.2.a | Count within 1,000, including skip counting by 5s, 10s, and 100s starting at a variety of multiples of 5, 10, or 100. | Grade 2 |
| Nebraska | 2.N.3.a | Read and write numbers within the range of 0 to 1,000 using standard, word, and expanded forms. | Grade 2 |
| Nebraska | 2.N.3.b | Understand 100 as a bundle, collection, or (more abstractly) composition of ten tens and that the three digits of a three-digit number represent a composition of some hundreds, some tens, and some ones. | Grade 2 |
| Nebraska | 2.N.3.c | Compare two three-digit numbers by using symbols , = and justify the comparison based on the value of the hundreds, tens, and ones. | Grade 2 |
| Nebraska | 2.N.4.a | Fluently add and subtract within 20. | Grade 2 |
| Nebraska | 2.N.4.b | Add and subtract using 100 strategies based on place value including properties of operations, relationships between addition and subtraction, and algorithms. | Grade 2 |
| Nebraska | 2.N.4.c | Mentally add or subtract 10 or 100 to or from a given number 100 to 900. | Grade 2 |
| Nebraska | 2.N.4.d | Add up to three two-digit numbers using strategies based on place value and understanding of properties. | Grade 2 |
| Nebraska | 2.N.4.e | Add and subtract within 1,000 using concrete models, drawings, and strategies that reflect an understanding of place value and the properties of operations. | Grade 2 |
| Nebraska | 2.N.5.a | Solve authentic problems involving addition and subtraction within 100 in situations of addition and subtraction, including adding to, subtracting from, joining and separating, and comparing situations with unknowns in all positions using objects, models, drawings, verbal explanations, expressions, and equations. | Grade 2 |
| Nebraska | 2.N.5.c | Use repeated addition to find the total number of objects arranged in an array no larger than five rows and five columns and write an equation to express the total. | Grade 2 |
| Nebraska | 2.N.5.d | Identify a group of objects from 0 to 20 as even or odd by counting by 2s or by showing even numbers as a sum of two equal parts. | Grade 2 |
| Nebraska | 2.G.1.b | Recognize and draw two-dimensional shapes having a specific number of sides, angles, and vertices including triangles, quadrilaterals, pentagons, and hexagons. | Grade 2 |
| Nebraska | 2.G.1.c | Partition a rectangle into rows and columns of equal-sized squares and count to find the total. | Grade 2 |
| Nebraska | 2.G.1.d | Divide circles and rectangles into two, three, or four equal parts and describe the parts using the language of halves, thirds, fourths, half of, a third of, and a fourth of. | Grade 2 |
| Nebraska | 2.G.1.e | Recognize that equal shares of identical wholes need not have the same shape. | Grade 2 |
| Nebraska | 2.G.2.a | Measure the length of an object using two different length units and describe how the measurements relate to the size of the specific unit. | Grade 2 |
| Nebraska | 2.G.2.b | Compare the difference in length of objects using inches and feet or centimeters and meters. | Grade 2 |
| Nebraska | 2.G.3.a | Identify and use appropriate tools for measuring length. | Grade 2 |
| Nebraska | 2.G.4.b | Use addition and subtraction within 100 to solve problems using the same standard-length units. | Grade 2 |
| Nebraska | 2.G.5.a | Solve problems involving dollar bills, quarters, dimes, nickels, and pennies using $ and ¢ symbols appropriately. | Grade 2 |
| Nebraska | 2.G.5.b | Identify and write time to five-minute intervals using analog and digital clocks and both a.m. and p.m. | Grade 2 |
| Nebraska | 2.D.1.a | Ask authentic questions to generate data and represent the data using scaled picture graphs with up to four categories. | Grade 2 |
| Nebraska | 2.D.1.b | Ask authentic questions to generate data and represent the data using bar graphs with up to four categories. | Grade 2 |
| Nebraska | 2.D.1.c | Create and represent a data set by making a line plot using whole numbers. | Grade 2 |
| Nebraska | 2.D.2.a | Analyze data using scaled picture graphs or bar graphs with up to four categories. Solve problems including one-step comparison problems, using information from the graphs. | Grade 2 |
| Nebraska | 3.N.2.a | Partition two-dimensional figures into equal areas and express the area of each part as a unit fraction of the whole. | Grade 3 |
| Nebraska | 3.N.2.b | Find parts of a whole using visual fraction models. | Grade 3 |
| Nebraska | 3.N.2.c | Represent and understand a fraction as a number on a number line. | Grade 3 |
| Nebraska | 3.N.2.f | Compare and order fractions having the same numerators or denominators by reasoning about their size. | Grade 3 |
| Nebraska | 3.A.1.a | Add and subtract up to four-digit whole numbers with or without regrouping using strategies based on place value and algorithms. | Grade 3 |
| Nebraska | 3.A.1.c | Solve and write one-step whole number equations to represent authentic problems using the four operations including equations with an unknown start, unknown change, or unknown result. | Grade 3 |
| Nebraska | 3.A.1.d | Interpret and solve two-step authentic problems involving whole numbers and the four operations. | Grade 3 |
| Nebraska | 3.A.1.e | Apply commutative, associative, distributive, identity, and zero properties as strategies to multiply and divide. | Grade 3 |
| Nebraska | 3.A.1.f | Use drawings, words, arrays, symbols, repeated addition, equal groups, and number lines to interpret and explain the meaning of multiplication and division and their relationship. | Grade 3 |
| Nebraska | 3.A.1.g | Fluently multiply and divide within 100 using strategies based on understanding and properties of operations. | Grade 3 |
| Nebraska | 3.A.1.h | Multiply one-digit whole numbers by multiples of 10 in the range of 10 to 90 using strategies based on place value and properties of operations. | Grade 3 |
| Nebraska | 3.G.1.1 | Sort quadrilaterals into categories according to their attributes. | Grade 3 |
| Nebraska | 3.G.2.a | Solve authentic problems involving perimeters of polygons when given the side lengths or when given the perimeter and unknown side length(s). | Grade 3 |
| Nebraska | 3.G.2.b | Use concrete and pictorial models to measure areas in square units by counting square units. | Grade 3 |
| Nebraska | 3.G.2.c | Find the area of a rectangle with whole-number side lengths by modeling with unit squares; show that area can be additive and is the same as would be found by multiplying the side lengths. | Grade 3 |
| Nebraska | 3.G.3.a | Identify and use the appropriate tools and units of measurement, both customary and metric, to solve authentic problems involving length, weight, mass, liquid volume, and capacity (within the same system and unit). | Grade 3 |
| Nebraska | 3.G.4.a | Tell and write time to the minute using both analog and digital clocks. | Grade 3 |
| Nebraska | 3.G.4.b | Solve authentic problems involving addition and subtraction of time intervals and find elapsed time. | Grade 3 |
| Nebraska | 3.D.1.a | Create scaled picture graphs and scaled bar graphs to represent a data set with more than four categories, including data collected through observations, surveys, and experiments. | Grade 3 |
| Nebraska | 3.D.1.b | Generate and represent data using line plots where the horizontal scale is marked off in halves and whole number units. | Grade 3 |
| Nebraska | 3.D.2.a | Analyze data and make simple statements using information represented in picture graphs, line plots, and bar graphs. | Grade 3 |
| Nebraska | 4.N.1.a | Read, write, and demonstrate multiple equivalent representations for whole numbers up to 1,000,000 and decimals to the hundredths using visual representations, standard form, and expanded form. | Grade 4 |
| Nebraska | 4.N.1.b | Represent and justify comparisons of whole numbers up to 1,000,000 and decimals through the hundredths place using number lines and reasoning strategies. | Grade 4 |
| Nebraska | 4.N.1.c | Recognize a digit in one place represents ten times what it represents in the place to its right. | Grade 4 |
| Nebraska | 4.N.1.d | Use decimal notation for fractions with denominators of 10 or 100 (e.g., 43/100 = 0.43). | Grade 4 |
| Nebraska | 4.N.2.b | Explain and demonstrate how equivalent fractions are generated by multiplying by a fraction equivalent to 1 using visual fraction models and the Identity Property of Multiplication. | Grade 4 |
| Nebraska | 4.N.2.c | Compare and order fractions having unlike numerators or denominators using number lines, benchmarks, reasoning strategies, and/or equivalence. | Grade 4 |
| Nebraska | 4.N.3.a | Decompose a fraction into a sum of fractions with the same denominator in more than one way and record each decomposition with an equation and a visual representation. | Grade 4 |
| Nebraska | 4.N.3.e | Multiply a fraction by a whole number using visual fraction models and properties of operations. | Grade 4 |
| Nebraska | 4.N.4.b | Determine factors of any whole number up to 100 and classify a number up to 100 as prime or composite. | Grade 4 |
| Nebraska | 4.A.1.a | Add and subtract multi-digit numbers using an algorithm. | Grade 4 |
| Nebraska | 4.A.1.b | Multiply up to a four-digit whole number by a one-digit whole number and multiply a two-digit whole number by a two-digit whole number, using strategies based on place value, properties of operations, and algorithms. | Grade 4 |
| Nebraska | 4.A.1.c | Divide up to a four-digit whole number by a one-digit divisor with and without a remainder using strategies based on place value. | Grade 4 |
| Nebraska | 4.A.1.e | Create a simple algebraic expression or equation using a variable for an unknown number to represent an authentic mathematical situation (e.g., 3 + n = 15, 81 ÷ n = 9). | Grade 4 |
| Nebraska | 4.A.1.f | Solve one- and two-step authentic problems using the four operations including interpreting remainders and the use of a letter to represent the unknown quantity. | Grade 4 |
| Nebraska | 4.G.1.a | Identify, create, and describe points, lines, line segments, rays, angles, parallel lines, perpendicular lines, and intersecting lines. | Grade 4 |
| Nebraska | 4.G.1.b | Justify the classification of angles as acute, obtuse, or right. | Grade 4 |
| Nebraska | 4.G.1.c | Justify the classification of two-dimensional shapes based on the presence or absence of parallel and perpendicular lines or the presence or absence of specific angles. | Grade 4 |
| Nebraska | 4.G.1.d | Recognize, draw, and justify lines of symmetry in two-dimensional shapes. | Grade 4 |
| Nebraska | 4.G.2.c | Generate simple conversions from a larger unit to a smaller unit within the customary and metric systems of measurement. | Grade 4 |
| Nebraska | 4.G.2.d | Measure angles in whole number degrees using a protractor and relate benchmark angle measurements to their rotation through a circle (e.g., 180º = 1/2 of a circle). | Grade 4 |
| Nebraska | 4.G.2.e | Recognize angle measures as additive and solve problems involving addition and subtraction to find unknown angles on a diagram. | Grade 4 |
| Nebraska | 4.G.3.a | Apply perimeter and area formulas for rectangles to solve authentic problems. | Grade 4 |
| Nebraska | 4.D.1.a | Generate and represent data using line plots where the horizontal scale is marked off in appropriate units—whole numbers, halves, fourths, or eighths. | Grade 4 |
| Nebraska | 5.N.1.a | Read, write, and demonstrate multiple equivalent representations for multi-digit whole numbers and decimals through the thousandths place using standard form and expanded form. | Grade 5 |
| Nebraska | 5.N.1.b | Recognize a digit in one place represents 1/10 of what it represents in the place to its left. | Grade 5 |
| Nebraska | 5.N.1.c | Use whole number exponents to denote powers of 10. | Grade 5 |
| Nebraska | 5.N.3.a | Interpret a fraction as division of the numerator by the denominator. | Grade 5 |
| Nebraska | 5.N.3.b | Multiply a whole number by a fraction or a fraction by a fraction, including mixed numbers, using visual fraction models and properties of operations. | Grade 5 |
| Nebraska | 5.N.3.d | Solve authentic problems involving addition, subtraction, and multiplication of fractions and mixed numbers with like and unlike denominators. | Grade 5 |
| Nebraska | 5.N.3.e | Add and subtract fractions and mixed numbers with unlike denominators without simplifying. | Grade 5 |
| Nebraska | 5.N.3.f | Solve authentic problems involving division of unit fractions by whole numbers and division of whole numbers by unit fractions. | Grade 5 |
| Nebraska | 5.N.3.g | Add, subtract, multiply, and divide decimals to hundredths using strategies based on place value, properties of operations, and/or algorithms. | Grade 5 |
| Nebraska | 5.A.1.a | Multiply multi-digit whole numbers using an algorithm. | Grade 5 |
| Nebraska | 5.A.1.b | Divide four-digit whole numbers by a two-digit divisor, with and without remainders, using strategies based on place value. | Grade 5 |
| Nebraska | 5.A.1.d | Simplify authentic numerical or algebraic expressions using order of operations (excluding exponents). | Grade 5 |
| Nebraska | 5.G.1.b | Recognize volume as an attribute of solid figures that is measured in cubic units. | Grade 5 |
| Nebraska | 5.G.1.c | Justify the classification of two and three-dimensional figures in a hierarchy based on their properties. | Grade 5 |
| Nebraska | 5.G.2.a | Identify the origin, x axis, and y axis of the coordinate plane. | Grade 5 |
| Nebraska | 5.G.2.b | Graph and name points in the first quadrant of the coordinate plane using ordered pairs of whole numbers. | Grade 5 |
| Nebraska | 5.G.2.c | Form ordered pairs from authentic problems involving rules or patterns, graph the ordered pairs in the first quadrant on a coordinate plane, and interpret coordinate values in the context of the situation. | Grade 5 |
| Nebraska | 5.G.3.a | Generate conversions in authentic mathematical situations from larger units to smaller units and smaller units to larger units, within the customary and metric systems of measurement. | Grade 5 |
| Nebraska | 5.G.4.c | Use concrete models to measure the volume of rectangular prisms by counting cubic units. | Grade 5 |
| Nebraska | 5.G.4.d | Find the volume of a rectangular prism with whole-number side lengths by modeling with unit cubes and show that the volume can be additive and is the same as would be found by multiplying the area of the base times height. | Grade 5 |
| Nebraska | 5.D.2.a | Represent, analyze, and solve authentic problems using information presented in one or more tables or line plots including whole numbers and fractions. | Grade 5 |
| Nebraska | 6.N.1.d | Determine absolute value of rational numbers. | Grade 6 |
| Nebraska | 6.N.1.e | Compare and order numbers including non-negative fractions and decimals, integers, and absolute values and locate them on the number line. | Grade 6 |
| Nebraska | 6.N.2.a | Divide multi-digit whole numbers and decimals using an algorithm. | Grade 6 |
| Nebraska | 6.N.2.b | Divide non-negative fractions and mixed numbers. | Grade 6 |
| Nebraska | 6.N.2.c | Evaluate numerical expressions including absolute value and/or positive exponents with respect to order of operations. | Grade 6 |
| Nebraska | 6.R.1.b | Explain and determine unit rates. | Grade 6 |
| Nebraska | 6.R.1.c | Find a percent of a quantity as a rate per 100 and solve problems involving finding the whole, given a part and the percent. | Grade 6 |
| Nebraska | 6.R.1.e | Solve authentic problems using ratios, unit rates, and percents. | Grade 6 |
| Nebraska | 6.R.1.f | Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities. | Grade 6 |
| Nebraska | 6.R.2.a | Identify the ordered pair of a given point in the coordinate plane. | Grade 6 |
| Nebraska | 6.R.2.b | Plot the location of an ordered pair in the coordinate plane. | Grade 6 |
| Nebraska | 6.R.2.c | Identify the location of a given point in the coordinate plane (e.g., axis, origin, quadrant). | Grade 6 |
| Nebraska | 6.R.2.d | Make tables of equivalent ratios relating quantities with whole number measurements. | Grade 6 |
| Nebraska | 6.R.2.e | Use the constant of proportionality to find the missing value in ratio tables. | Grade 6 |
| Nebraska | 6.R.2.g | Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation. | Grade 6 |
| Nebraska | 6.A.1.a | Recognize and generate equivalent algebraic expressions involving the distributive property and combining like terms. | Grade 6 |
| Nebraska | 6.A.1.b | Given the value of the variable, evaluate algebraic expressions with non-negative rational numbers with respect to order of operations, which may include absolute value. | Grade 6 |
| Nebraska | 6.A.1.c | Use substitution to determine if a given value for a variable makes an equation or inequality true. | Grade 6 |
| Nebraska | 6.A.1.d | Solve one-step equations with non-negative rational numbers using addition, subtraction, multiplication, and division. | Grade 6 |
| Nebraska | 6.A.1.e | Solve one-step inequalities with whole numbers using addition, subtraction, multiplication, and division and represent solutions on a number line (e.g., graph 3x > 3). | Grade 6 |
| Nebraska | 6.A.2.b | Write equations (e.g., one operation, one variable) to represent authentic situations involving non- negative rational numbers. | Grade 6 |
| Nebraska | 6.A.2.c | Write inequalities (e.g., one operation, one variable) to represent authentic situations involving whole numbers. | Grade 6 |
| Nebraska | 6.G.3.a | Determine the area of quadrilaterals and triangles by composition and decomposition of these shapes, as well as applications of properties and formulas. Quadrilaterals include parallelograms and trapezoids. | Grade 6 |
| Nebraska | 6.G.3.b | Determine the surface area of rectangular prisms and triangular prisms using nets as well as application of formulas. | Grade 6 |
| Nebraska | 6.G.3.c | Apply volume formulas for triangular prisms. | Grade 6 |
| Nebraska | 6.D.2.a | Represent data using dot plots, box-and-whisker plots, and histograms. | Grade 6 |
| Nebraska | 6.D.2.b | Solve problems using information presented in dot plots, box-and-whisker plots, histograms, and circle graphs. | Grade 6 |
| Nebraska | 6.D.2.d | Compare the mean, median, mode, and range from two sets of data. | Grade 6 |
| Nebraska | 6.D.2.e | Compare and interpret data sets based upon their measures of central tendency and graphical representations (e.g., center, spread, shape). | Grade 6 |
| Nebraska | 7.N.2.a | Add, subtract, multiply, and divide rational numbers (e.g., positive and negative fractions, decimals, and integers). | Grade 7 |
| Nebraska | 7.N.2.b | Apply properties of operations (commutative, associative, distributive, identity, inverse, zero) as strategies for problem solving with rational numbers. | Grade 7 |
| Nebraska | 7.R.1.a | Decide whether two quantities are in a proportional relationship (e.g., by testing for equivalent ratios in a table). | Grade 7 |
| Nebraska | 7.R.1.c | Use proportional relationships to solve authentic percent problems (e.g., percent change, sales tax, mark-up, discount, tip). | Grade 7 |
| Nebraska | 7.R.1.d | Solve authentic problems involving scale drawings. | Grade 7 |
| Nebraska | 7.A.1.c | Solve one- and two-step equations involving rational numbers. | Grade 7 |
| Nebraska | 7.A.1.d | Solve equations using the distributive property and combining like terms. | Grade 7 |
| Nebraska | 7.A.2.a | Write one- and two-step equations involving rational numbers from words, tables, and authentic situations. | Grade 7 |
| Nebraska | 7.A.2.b | Write one- and two-step inequalities to represent authentic situations involving integers. | Grade 7 |
| Nebraska | 7.G.1.a | Apply properties of adjacent, complementary, supplementary, linear pair, and vertical angles to find missing angle measures. | Grade 7 |
| Nebraska | 7.G.2.a | Draw polygons in the coordinate plane given coordinates for the vertices. | Grade 7 |
| Nebraska | 7.G.3.a | Solve authentic problems involving perimeter and area of composite shapes made from triangles and quadrilaterals. | Grade 7 |
| Nebraska | 7.G.3.b | Determine surface area and volume of composite rectangular and triangular prisms. | Grade 7 |
| Nebraska | 7.G.3.c | Determine the area and circumference of circles both on and off the coordinate plane using 3.14 for the value of Pi. | Grade 7 |
| Nebraska | 8.N.1.b | Represent numbers with positive and negative exponents and in scientific notation. | Grade 8 |
| Nebraska | 8.N.1.d | Approximate, compare, and order real numbers, both rational and irrational, and locate them on the number line. | Grade 8 |
| Nebraska | 8.N.2.b | Simplify numerical expressions involving integer exponents, square roots, and cube roots (e.g., 4-2 is the same as 1/16). | Grade 8 |
| Nebraska | 8.N.2.d | Multiply and divide numbers using scientific notation. | Grade 8 |
| Nebraska | 8.A.1.a | Describe single variable equations as having one solution, no solution, or infinitely many solutions. | Grade 8 |
| Nebraska | 8.A.1.b | Solve multi-step equations involving rational numbers with the same variable appearing on both sides of the equation. | Grade 8 |
| Nebraska | 8.A.1.c | Solve equations of the form x² = k(k ≤ 400) and x³ = k(k ≤ 125), where k is a positive rational number, using square root and cube root symbols. | Grade 8 |
| Nebraska | 8.A.2.c | Graph proportional relationships and interpret the rate of change. | Grade 8 |
| Nebraska | 8.G.1.b | Identify and apply geometric properties of parallel lines cut by a transversal and the resulting corresponding same side interior, alternate interior, and alternate exterior angles to find missing measures. | Grade 8 |
| Nebraska | 8.G.2.a | Perform and describe positions and orientations of shapes under single transformations including rotations in multiples of 90 degrees about the origin, translations, reflections, and dilations on and off the coordinate plane. | Grade 8 |
| Nebraska | 8.G.2.b | Determine if two-dimensional figures are congruent or similar. | Grade 8 |
| Nebraska | 8.G.3.a | Explain a model of the Pythagorean Theorem. | Grade 8 |
| Nebraska | 8.G.3.b | Apply the Pythagorean Theorem to find side lengths of triangles and to solve authentic problems. | Grade 8 |
| Nebraska | 8.G.3.c | Find the distance between any two points on the coordinate plane using the Pythagorean Theorem. | Grade 8 |
| Nebraska | 8.G.3.d | Determine the volume of cones, cylinders, and spheres and solve authentic problems using volumes. | Grade 8 |
| Nebraska | 8.D.2.a | Represent and interpret bivariate data (e.g., ordered pairs) using scatter plots. | Grade 8 |
| Nebraska | 8.D.2.b | Describe patterns such as positive or negative association, linear or nonlinear association, clustering, and outliers when bivariate data is represented on a coordinate plane. | Grade 8 |
| Nebraska | 8.D.2.c | Draw an informal line of best fit based on the closeness of the data points to the line. | Grade 8 |
| Nebraska | 8.D.2.d | Use a linear model to make predictions and interpret the rate of change and y-intercept in context. | Grade 8 |
| Nebraska | HS.N.1.f | Convert equivalent rates (e.g., miles per hour to feet per second). | High School |
| Nebraska | HS.N.1.h | Use scientific notation to appropriately represent large and small quantities. | High School |
| Nebraska | HS.N.2.b | Use properties of rational and irrational numbers. | High School |
| Nebraska | HS.A.1.b | Analyze a relation to determine if it is a function given mapping diagrams, function notation (e.g., f(x)=𝘹²), a table, or a graph. | High School |
| Nebraska | HS.A.1.c | Classify a function given its mapping diagram, function notation, table, or graph as a linear, quadratic, absolute value, exponential, or other function. | High School |
| Nebraska | HS.A.1.d | Analyze a function’s domain and range to determine if it is one-to-one and has an inverse function both algebraically and graphically. | High School |
| Nebraska | HS.A.2.a | Analyze and explain the properties used in solving equations, inequalities, systems of linear equations, systems of linear inequalities, and literal equations. | High School |
| Nebraska | HS.A.2.b | Generate expressions in equivalent forms by using algebraic properties to make different characteristics or features visible. | High School |
| Nebraska | HS.A.2.e | Write and graph equations of functions (linear, absolute value, quadratic, and exponential) using the points of interest of the function. | High School |
| Nebraska | HS.A.2.h | Explain the connection between the factors of a polynomial and the zeros of a polynomial. | High School |
| Nebraska | HS.A.3.b | Identify, interpret, relate, and graph the factors, x-intercepts, roots, and zeros of polynomial functions using algebraic and graphing methods. | High School |
| Nebraska | HS.G.1.a | Demonstrate that two figures are similar or congruent by using a sequence of rigid motions and dilations that map a figure onto the other in problems both with and without coordinates. | High School |
| Nebraska | HS.D.2.f | Represent data on two quantitative variables on a scatter plot and describe how the variables are related. | High School |
| Nebraska | AT.A.1.c | Given a function, list the sequence of algebraic transformations that changes a parent function to the given function. | Advanced Topics |
| Nebraska | AT.G.2.b | Determine the shape of a two-dimensional cross-section of a three-dimensional object. | Advanced Topics |
| Nevada | K.CC.A.1 | Count to 100 by ones and by tens. | Kindergarten |
| Nevada | K.CC.A.2 | Count forward beginning from a given number within the known sequence (instead of having to begin at 1). | Kindergarten |
| Nevada | K.CC.A.3 | Write numbers from 0 to 20. Represent a number of objects with a written numeral 0-20 (with 0 representing a count of no objects). | Kindergarten |
| Nevada | K.CC.B.4 | Understand the relationship between numbers and quantities; connect counting to cardinality. | Kindergarten |
| Nevada | K.CC.B.5 | Count to answer “how many?” questions about as many as 20 things arranged in a line, a rectangular array, or a circle, or as many as 10 things in a scattered configuration; given a number from 1-20, count out that many objects. | Kindergarten |
| Nevada | K.CC.C.6 | Identify whether the number of objects in one group is greater than, less than, or equal to the number of objects in another group, e.g., by using matching and counting strategies. | Kindergarten |
| Nevada | K.CC.C.7 | Compare two numbers between 1 and 10 presented as written numerals. | Kindergarten |
| Nevada | K.G.A.1 | Describe objects in the environment using names of shapes, and describe the relative positions of these objects using terms such as above, below, beside, in front of, behind, and next to. | Kindergarten |
| Nevada | K.G.A.2 | Correctly name shapes regardless of their orientations or overall size. | Kindergarten |
| Nevada | K.G.A.3 | Identify shapes as two-dimensional (lying in a plane, “flat”) or three-dimensional (“solid”). | Kindergarten |
| Nevada | K.G.B.4 | Analyze and compare two- and three-dimensional shapes, in different sizes and orientations, using informal language to describe their similarities, differences, parts (e.g., number of sides and vertices/“corners”) and other attributes (e.g., having sides of equal length). | Kindergarten |
| Nevada | K.G.B.6 | Compose simple shapes to form larger shapes. | Kindergarten |
| Nevada | K.MD.A.1 | Describe measurable attributes of objects, such as length or weight. Describe several measurable attributes of a single object. | Kindergarten |
| Nevada | K.MD.A.2 | Directly compare two objects with a measurable attribute in common, to see which object has “more of”/“less of” the attribute, and describe the difference. | Kindergarten |
| Nevada | K.MD.B.3 | Classify objects into given categories; count the numbers of objects in each category and sort the categories by count. | Kindergarten |
| Nevada | K.NBT.A.1 | Compose and decompose numbers from 11 to 19 into ten ones and some further ones, e.g., by using objects or drawings, and record each composition or decomposition by a drawing or equation (e.g., 18 = 10 + 8); understand that these numbers are composed of ten ones and one, two, three, four, five, six, seven, eight, or nine ones. | Kindergarten |
| Nevada | K.OA.A.1 | Represent addition and subtraction with objects, fingers, mental images, drawings, sounds (e.g., claps), acting out situations, verbal explanations, expressions, or equations. | Kindergarten |
| Nevada | K.OA.A.2 | Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem. | Kindergarten |
| Nevada | K.OA.A.3 | Decompose numbers less than or equal to 10 into pairs in more than one way, e.g., by using objects or drawings, and record each decomposition by a drawing or equation (e.g., 5 = 2 + 3 and 5 = 4 + 1). | Kindergarten |
| Nevada | K.OA.A.4 | For any number from 1 to 9, find the number that makes 10 when added to the given number, e.g., by using objects or drawings, and record the answer with a drawing or equation. | Kindergarten |
| Nevada | K.OA.A.5 | Fluently add and subtract within 5. | Kindergarten |
| Nevada | 1.G.A.1 | Distinguish between defining attributes (e.g., triangles are closed and three-sided) versus non-defining attributes (e.g., color, orientation, overall size); build and draw shapes to possess defining attributes. | Grade 1 |
| Nevada | 1.G.A.2 | Compose two-dimensional shapes (rectangles, squares, trapezoids, triangles, half-circles, and quarter-circles) or three-dimensional shapes (cubes, right rectangular prisms, right circular cones, and right circular cylinders) to create a composite shape, and compose new shapes from the composite shape. | Grade 1 |
| Nevada | 1.G.A.3 | Partition circles and rectangles into two and four equal shares, describe the shares using the words halves, fourths, and quarters, and use the phrases half of, fourth of, and quarter of. Describe the whole as two of, or four of the shares. Understand for these examples that decomposing into more equal shares creates smaller shares. | Grade 1 |
| Nevada | 1.MD.A.1 | Order three objects by length; compare the lengths of two objects indirectly by using a third object. | Grade 1 |
| Nevada | 1.MD.A.2 | Express the length of an object as a whole number of length units, by laying multiple copies of a shorter object (the length unit) end to end; understand that the length measurement of an object is the number of same-size length units that span it with no gaps or overlaps. | Grade 1 |
| Nevada | 1.MD.B.3 | Tell and write time in hours and half-hours using analog and digital clocks. | Grade 1 |
| Nevada | 1.MD.C.4 | Organize, represent, and interpret data with up to three categories; ask and answer questions about the total number of data points, how many in each category, and how many more or less are in one category than in another. | Grade 1 |
| Nevada | 1.NBT.A.1 | Count to 120, starting at any number less than 120. In this range, read and write numerals and represent a number of objects with a written numeral. | Grade 1 |
| Nevada | 1.NBT.B.2 | Understand that the two digits of a two-digit number represent amounts of tens and ones. | Grade 1 |
| Nevada | 1.NBT.B.3 | Compare two two-digit numbers based on meanings of the tens and ones digits, recording the results of comparisons with the symbols >, =, and <. | Grade 1 |
| Nevada | 1.NBT.C.4 | Add within 100, including adding a two-digit number and a one-digit number, and adding a two-digit number and a multiple of 10, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Understand that in adding two-digit numbers, one adds tens and tens, ones and ones; and sometimes it is necessary to compose a ten. | Grade 1 |
| Nevada | 1.NBT.C.5 | Given a two-digit number, mentally find 10 more or 10 less than the number, without having to count; explain the reasoning used. | Grade 1 |
| Nevada | 1.NBT.C.6 | Subtract multiples of 10 in the range 10-90 from multiples of 10 in the range 10-90 (positive or zero differences), using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. | Grade 1 |
| Nevada | 1.OA.A.1 | Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem. | Grade 1 |
| Nevada | 1.OA.B.3 | Apply properties of operations as strategies to add and subtract. | Grade 1 |
| Nevada | 1.OA.B.4 | Understand subtraction as an unknown-addend problem. | Grade 1 |
| Nevada | 1.OA.C.5 | Relate counting to addition and subtraction (e.g., by counting on 2 to add 2). | Grade 1 |
| Nevada | 1.OA.C.6 | Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to a ten (e.g., 13 - 4 = 13 - 3 - 1 = 10 - 1 = 9); using the relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 - 8 = 4); and creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13). | Grade 1 |
| Nevada | 1.OA.D.7 | Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false. | Grade 1 |
| Nevada | 1.OA.D.8 | Determine the unknown whole number in an addition or subtraction equation relating three whole numbers. | Grade 1 |
| Nevada | 2.G.A.1 | Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces. Identify triangles, quadrilaterals, pentagons, hexagons, and cubes. | Grade 2 |
| Nevada | 2.G.A.2 | Partition a rectangle into rows and columns of same-size squares and count to find the total number of them. | Grade 2 |
| Nevada | 2.G.A.3 | Partition circles and rectangles into two, three, or four equal shares, describe the shares using the words halves, thirds, half of, a third of, etc., and describe the whole as two halves, three thirds, four fourths. Recognize that equal shares of identical wholes need not have the same shape. | Grade 2 |
| Nevada | 2.MD.A.1 | Measure the length of an object by selecting and using appropriate tools such as rulers, yardsticks, meter sticks, and measuring tapes. | Grade 2 |
| Nevada | 2.MD.A.2 | Measure the length of an object twice, using length units of different lengths for the two measurements; describe how the two measurements relate to the size of the unit chosen. | Grade 2 |
| Nevada | 2.MD.A.4 | Measure to determine how much longer one object is than another, expressing the length difference in terms of a standard length unit. | Grade 2 |
| Nevada | 2.MD.B.5 | Use addition and subtraction within 100 to solve word problems involving lengths that are given in the same units, e.g., by using drawings (such as drawings of rulers) and equations with a symbol for the unknown number to represent the problem. | Grade 2 |
| Nevada | 2.MD.C.7 | Tell and write time from analog and digital clocks to the nearest five minutes, using a.m. and p.m. | Grade 2 |
| Nevada | 2.MD.C.8 | Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies, using $ and ¢ symbols appropriately. | Grade 2 |
| Nevada | 2.MD.D.9 | Generate measurement data by measuring lengths of several objects to the nearest whole unit, or by making repeated measurements of the same object. Show the measurements by making a line plot, where the horizontal scale is marked off in whole-number units. | Grade 2 |
| Nevada | 2.MD.D.10 | Draw a picture graph and a bar graph (with single-unit scale) to represent a data set with up to four categories. Solve simple put-together, take-apart, and compare problems using information presented in a bar graph. | Grade 2 |
| Nevada | 2.NBT.A.1 | Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones. | Grade 2 |
| Nevada | 2.NBT.A.2 | Count within 1000; skip-count by 5s, 10s, and 100s. | Grade 2 |
| Nevada | 2.NBT.A.3 | Read and write numbers to 1000 using base-ten numerals, number names, and expanded form. | Grade 2 |
| Nevada | 2.NBT.A.4 | Compare two three-digit numbers based on meanings of the hundreds, tens, and ones digits, using >, =, and < symbols to record the results of comparisons. | Grade 2 |
| Nevada | 2.NBT.B.5 | Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction. | Grade 2 |
| Nevada | 2.NBT.B.6 | Add up to four two-digit numbers using strategies based on place value and properties of operations. | Grade 2 |
| Nevada | 2.NBT.B.7 | Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method. Understand that in adding or subtracting three-digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds. | Grade 2 |
| Nevada | 2.NBT.B.8 | Mentally add 10 or 100 to a given number 100–900, and mentally subtract 10 or 100 from a given number 100–900. | Grade 2 |
| Nevada | 2.OA.A.1 | Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem. | Grade 2 |
| Nevada | 2.OA.B.2 | Fluently add and subtract within 20 using mental strategies. By end of Grade 2, know from memory all sums of two one-digit numbers. | Grade 2 |
| Nevada | 2.OA.C.3 | Determine whether a group of objects (up to 20) has an odd or even number of members, e.g., by pairing objects or counting them by 2s; write an equation to express an even number as a sum of two equal addends. | Grade 2 |
| Nevada | 2.OA.C.4 | Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends. | Grade 2 |
| Nevada | 3.G.A.1 | Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories. | Grade 3 |
| Nevada | 3.G.A.2 | Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole. | Grade 3 |
| Nevada | 3.MD.A.1 | Tell and write time to the nearest minute and measure time intervals in minutes. Solve word problems involving addition and subtraction of time intervals in minutes, e.g., by representing the problem on a number line diagram. | Grade 3 |
| Nevada | 3.MD.A.2 | Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l). Add, subtract, multiply, or divide to solve one-step word problems involving masses or volumes that are given in the same units, e.g., by using drawings (such as a beaker with a measurement scale) to represent the problem. | Grade 3 |
| Nevada | 3.MD.B.3 | Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and two-step “how many more” and “how many less” problems using information presented in scaled bar graphs. | Grade 3 |
| Nevada | 3.MD.B.4 | Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Show the data by making a line plot, where the horizontal scale is marked off in appropriate units-whole numbers, halves, or quarters. | Grade 3 |
| Nevada | 3.MD.C.5 | Recognize area as an attribute of plane figures and understand concepts of area measurement. | Grade 3 |
| Nevada | 3.MD.C.6 | Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units). | Grade 3 |
| Nevada | 3.MD.C.7 | Relate area to the operations of multiplication and addition. | Grade 3 |
| Nevada | 3.MD.D.8 | Solve real world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters. | Grade 3 |
| Nevada | 3.NBT.A.1 | Use place value understanding to round whole numbers to the nearest 10 or 100. | Grade 3 |
| Nevada | 3.NBT.A.2 | Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction. | Grade 3 |
| Nevada | 3.NBT.A.3 | Multiply one-digit whole numbers by multiples of 10 in the range 10–90 (e.g., 9 × 80, 5 × 60) using strategies based on place value and properties of operations. | Grade 3 |
| Nevada | 3.NF.A.1 | Understand a fraction 1/𝘣 as the quantity formed by 1 part when a whole is partitioned into 𝘣 equal parts; understand a fraction 𝘢/𝑏 as the quantity formed by 𝘢 parts of size 1/𝘣. | Grade 3 |
| Nevada | 3.NF.A.2 | Understand a fraction as a number on the number line; represent fractions on a number line diagram. | Grade 3 |
| Nevada | 3.NF.A.3 | Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size. | Grade 3 |
| Nevada | 3.OA.A.1 | Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each. | Grade 3 |
| Nevada | 3.OA.A.2 | Interpret whole-number quotients of whole numbers, e.g., interpret 56 ÷ 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each. | Grade 3 |
| Nevada | 3.OA.A.3 | Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem. | Grade 3 |
| Nevada | 3.OA.A.4 | Determine the unknown whole number in a multiplication or division equation relating three whole numbers. | Grade 3 |
| Nevada | 3.OA.B.5 | Apply properties of operations as strategies to multiply and divide. | Grade 3 |
| Nevada | 3.OA.B.6 | Understand division as an unknown-factor problem. | Grade 3 |
| Nevada | 3.OA.C.7 | Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 × 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers. | Grade 3 |
| Nevada | 3.OA.D.8 | Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. | Grade 3 |
| Nevada | 3.OA.D.9 | Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations. | Grade 3 |
| Nevada | 4.G.A.1 | Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures. | Grade 4 |
| Nevada | 4.G.A.2 | Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles. | Grade 4 |
| Nevada | 4.G.A.3 | Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify line-symmetric figures and draw lines of symmetry. | Grade 4 |
| Nevada | 4.MD.A.1 | Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table. | Grade 4 |
| Nevada | 4.MD.A.2 | Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. | Grade 4 |
| Nevada | 4.MD.A.3 | Apply the area and perimeter formulas for rectangles in real world and mathematical problems. | Grade 4 |
| Nevada | 4.MD.B.4 | Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots. | Grade 4 |
| Nevada | 4.MD.C.5 | Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement. | Grade 4 |
| Nevada | 4.MD.C.6 | Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure. | Grade 4 |
| Nevada | 4.MD.C.7 | Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems, e.g., by using an equation with a symbol for the unknown angle measure. | Grade 4 |
| Nevada | 4.NBT.A.1 | Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. | Grade 4 |
| Nevada | 4.NBT.A.2 | Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. | Grade 4 |
| Nevada | 4.NBT.A.3 | Use place value understanding to round multi-digit whole numbers to any place. | Grade 4 |
| Nevada | 4.NBT.B.4 | Fluently add and subtract multi-digit whole numbers using the standard algorithm. | Grade 4 |
| Nevada | 4.NBT.B.5 | Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. | Grade 4 |
| Nevada | 4.NBT.B.6 | Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. | Grade 4 |
| Nevada | 4.NF.A.1 | Explain why a fraction 𝘢/𝘣 is equivalent to a fraction (𝘯 × 𝘢)/(𝘯 × 𝘣) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. | Grade 4 |
| Nevada | 4.NF.A.2 | Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model. | Grade 4 |
| Nevada | 4.NF.B.3 | Understand a fraction 𝘢/𝘣 with 𝘢 > 1 as a sum of fractions 1/𝘣. | Grade 4 |
| Nevada | 4.NF.B.4 | Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. | Grade 4 |
| Nevada | 4.NF.C.5 | Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100. | Grade 4 |
| Nevada | 4.NF.C.6 | Use decimal notation for fractions with denominators 10 or 100. | Grade 4 |
| Nevada | 4.NF.C.7 | Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual model. | Grade 4 |
| Nevada | 4.OA.A.1 | Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 × 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations. | Grade 4 |
| Nevada | 4.OA.A.2 | Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison. | Grade 4 |
| Nevada | 4.OA.A.3 | Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. | Grade 4 |
| Nevada | 4.OA.B.4 | Find all factor pairs for a whole number in the range 1-100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1-100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1-100 is prime or composite. | Grade 4 |
| Nevada | 4.OA.C.5 | Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. | Grade 4 |
| Nevada | 5.G.A.1 | Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., 𝘹-axis and 𝘹-coordinate, 𝘺-axis and 𝘺-coordinate). | Grade 5 |
| Nevada | 5.G.A.2 | Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. | Grade 5 |
| Nevada | 5.G.B.3 | Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. | Grade 5 |
| Nevada | 5.G.B.4 | Classify two-dimensional figures in a hierarchy based on properties. | Grade 5 |
| Nevada | 5.MD.A.1 | Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. | Grade 5 |
| Nevada | 5.MD.B.2 | Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. | Grade 5 |
| Nevada | 5.MD.C.3 | Recognize volume as an attribute of solid figures and understand concepts of volume measurement. | Grade 5 |
| Nevada | 5.MD.C.4 | Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. | Grade 5 |
| Nevada | 5.MD.C.5 | Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume. | Grade 5 |
| Nevada | 5.NBT.A.1 | Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. | Grade 5 |
| Nevada | 5.NBT.A.2 | Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. | Grade 5 |
| Nevada | 5.NBT.A.3 | Read, write, and compare decimals to thousandths. | Grade 5 |
| Nevada | 5.NBT.A.4 | Use place value understanding to round decimals to any place. | Grade 5 |
| Nevada | 5.NBT.B.5 | Fluently multiply multi-digit whole numbers using the standard algorithm. | Grade 5 |
| Nevada | 5.NBT.B.6 | Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. | Grade 5 |
| Nevada | 5.NBT.B.7 | Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. | Grade 5 |
| Nevada | 5.NF.A.1 | Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. | Grade 5 |
| Nevada | 5.NF.A.2 | Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. | Grade 5 |
| Nevada | 5.NF.B.3 | Interpret a fraction as division of the numerator by the denominator (𝘢/𝘣 = 𝘢 ÷ 𝘣). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. | Grade 5 |
| Nevada | 5.NF.B.4 | Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. | Grade 5 |
| Nevada | 5.NF.B.5 | Interpret multiplication as scaling (resizing). | Grade 5 |
| Nevada | 5.NF.B.6 | Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. | Grade 5 |
| Nevada | 5.NF.B.7 | Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. | Grade 5 |
| Nevada | 5.OA.A.1 | Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. | Grade 5 |
| Nevada | 5.OA.A.2 | Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. | Grade 5 |
| Nevada | 5.OA.B.3 | Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. | Grade 5 |
| Nevada | 6.EE.A.1 | Write and evaluate numerical expressions involving whole-number exponents. | Grade 6 |
| Nevada | 6.EE.A.2 | Write, read, and evaluate expressions in which letters stand for numbers. | Grade 6 |
| Nevada | 6.EE.A.3 | Apply the properties of operations to generate equivalent expressions. | Grade 6 |
| Nevada | 6.EE.A.4 | Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). | Grade 6 |
| Nevada | 6.EE.B.5 | Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true. | Grade 6 |
| Nevada | 6.EE.B.6 | Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set. | Grade 6 |
| Nevada | 6.EE.B.7 | Solve real-world and mathematical problems by writing and solving equations of the form 𝘹 + 𝘱 = 𝘲 and 𝘱𝘹 = 𝘲 for cases in which 𝘱, 𝘲 and 𝘹 are all nonnegative rational numbers. | Grade 6 |
| Nevada | 6.EE.B.8 | Write an inequality of the form 𝘹 > 𝘤 or 𝘹 𝘤 or 𝘹 < 𝘤 have infinitely many solutions; represent solutions of such inequalities on number line diagrams. | Grade 6 |
| Nevada | 6.EE.C.9 | Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. | Grade 6 |
| Nevada | 6.G.A.1 | Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems. | Grade 6 |
| Nevada | 6.G.A.2 | Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas 𝘝 = 𝘭 𝘸 𝘩 and 𝘝 = 𝘣 𝘩 to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems. | Grade 6 |
| Nevada | 6.G.A.3 | Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems. | Grade 6 |
| Nevada | 6.G.A.4 | Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems. | Grade 6 |
| Nevada | 6.RP.A.1 | Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. | Grade 6 |
| Nevada | 6.RP.A.2 | Understand the concept of a unit rate 𝘢/𝘣 associated with a ratio 𝘢:𝘣 with 𝘣 ≠ 0, and use rate language in the context of a ratio relationship. | Grade 6 |
| Nevada | 6.RP.A.3 | Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. | Grade 6 |
| Nevada | 6.SP.B.5 | Summarize numerical data sets in relation to their context, such as by: | Grade 6 |
| Nevada | 6.NS.A.1 | Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. | Grade 6 |
| Nevada | 6.NS.B.2 | Fluently divide multi-digit numbers using the standard algorithm. | Grade 6 |
| Nevada | 6.NS.B.3 | Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation. | Grade 6 |
| Nevada | 6.NS.C.5 | Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation. | Grade 6 |
| Nevada | 6.NS.C.6 | Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates. | Grade 6 |
| Nevada | 6.NS.C.7 | Understand ordering and absolute value of rational numbers. | Grade 6 |
| Nevada | 6.NS.C.8 | Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. | Grade 6 |
| Nevada | 7.EE.A.1 | Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients. | Grade 7 |
| Nevada | 7.EE.A.2 | Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. | Grade 7 |
| Nevada | 7.EE.B.3 | Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. | Grade 7 |
| Nevada | 7.EE.B.4 | Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. | Grade 7 |
| Nevada | 7.G.A.1 | Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale. | Grade 7 |
| Nevada | 7.G.A.2 | Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle. | Grade 7 |
| Nevada | 7.G.A.3 | Describe the two-dimensional figures that result from slicing three-dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids. | Grade 7 |
| Nevada | 7.G.B.4 | Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle. | Grade 7 |
| Nevada | 7.G.B.5 | Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure. | Grade 7 |
| Nevada | 7.G.B.6 | Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. | Grade 7 |
| Nevada | 7.RP.A.1 | Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. | Grade 7 |
| Nevada | 7.RP.A.2 | Recognize and represent proportional relationships between quantities. | Grade 7 |
| Nevada | 7.RP.A.3 | Use proportional relationships to solve multistep ratio and percent problems. | Grade 7 |
| Nevada | 7.NS.A.1 | Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram. | Grade 7 |
| Nevada | 7.NS.A.2 | Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers. | Grade 7 |
| Nevada | 7.NS.A.3 | Solve real-world and mathematical problems involving the four operations with rational numbers. | Grade 7 |
| Nevada | 8.EE.A.1 | Know and apply the properties of integer exponents to generate equivalent numerical expressions. | Grade 8 |
| Nevada | 8.EE.A.2 | Use square root and cube root symbols to represent solutions to equations of the form 𝘹² = 𝘱 and 𝘹³ = 𝘱, where 𝘱 is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that √2 is irrational. | Grade 8 |
| Nevada | 8.EE.A.3 | Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other. | Grade 8 |
| Nevada | 8.EE.A.4 | Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology. | Grade 8 |
| Nevada | 8.EE.B.5 | Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. | Grade 8 |
| Nevada | 8.EE.B.6 | Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation 𝘺 = 𝘮𝘹 for a line through the origin and the equation 𝘺 = 𝘮𝘹 + 𝘣 for a line intercepting the vertical axis at 𝘣. | Grade 8 |
| Nevada | 8.EE.C.7 | Solve linear equations in one variable. | Grade 8 |
| Nevada | 8.EE.C.8 | Analyze and solve pairs of simultaneous linear equations. | Grade 8 |
| Nevada | 8.F.A.1 | Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output. | Grade 8 |
| Nevada | 8.F.A.2 | Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). | Grade 8 |
| Nevada | 8.F.A.3 | Interpret the equation 𝘺 = 𝘮𝘹 + 𝘣 as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. | Grade 8 |
| Nevada | 8.F.B.4 | Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (𝘹, 𝘺) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values. | Grade 8 |
| Nevada | 8.F.B.5 | Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally. | Grade 8 |
| Nevada | 8.G.A.1 | Verify experimentally the properties of rotations, reflections, and translations. | Grade 8 |
| Nevada | 8.G.A.2 | Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them. | Grade 8 |
| Nevada | 8.G.A.3 | Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates. | Grade 8 |
| Nevada | 8.G.A.4 | Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two-dimensional figures, describe a sequence that exhibits the similarity between them. | Grade 8 |
| Nevada | 8.G.A.5 | Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. | Grade 8 |
| Nevada | 8.G.B.7 | Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions. | Grade 8 |
| Nevada | 8.G.B.8 | Apply the Pythagorean Theorem to find the distance between two points in a coordinate system. | Grade 8 |
| Nevada | 8.G.C.9 | Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems. | Grade 8 |
| Nevada | 8.SP.A.1 | Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association. | Grade 8 |
| Nevada | 8.SP.A.2 | Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line. | Grade 8 |
| Nevada | 8.NS.A.2 | Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g., π²). | Grade 8 |
| Nevada | A-APR.B.3 | Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial. | High School |
| Nevada | A-CED.A.2 | Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. | High School |
| Nevada | A-CED.A.3 | Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context. | High School |
| Nevada | A-REI.B.3 | Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. | High School |
| Nevada | A-SSE.A.2 | Use the structure of an expression to identify ways to rewrite it. | High School |
| Nevada | A-SSE.B.3 | Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression. | High School |
| Nevada | F-BF.A.1 | Write a function that describes a relationship between two quantities. | High School |
| Nevada | F-IF.A.2 | Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. | High School |
| Nevada | F-IF.B.4 | For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. | High School |
| Nevada | F-IF.C.7 | Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. | High School |
| Nevada | S-ID.B.6 | Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. | High School |
| New Hampshire | K.CC.A.1 | Count to 100 by ones and by tens. | Kindergarten |
| New Hampshire | K.CC.A.2 | Count forward beginning from a given number within the known sequence (instead of having to begin at 1). | Kindergarten |
| New Hampshire | K.CC.A.3 | Write numbers from 0 to 20. Represent a number of objects with a written numeral 0-20 (with 0 representing a count of no objects). | Kindergarten |
| New Hampshire | K.CC.B.4 | Understand the relationship between numbers and quantities; connect counting to cardinality. | Kindergarten |
| New Hampshire | K.CC.B.5 | Count to answer “how many?” questions about as many as 20 things arranged in a line, a rectangular array, or a circle, or as many as 10 things in a scattered configuration; given a number from 1-20, count out that many objects. | Kindergarten |
| New Hampshire | K.CC.C.6 | Identify whether the number of objects in one group is greater than, less than, or equal to the number of objects in another group, e.g., by using matching and counting strategies. | Kindergarten |
| New Hampshire | K.CC.C.7 | Compare two numbers between 1 and 10 presented as written numerals. | Kindergarten |
| New Hampshire | K.G.A.1 | Describe objects in the environment using names of shapes, and describe the relative positions of these objects using terms such as above, below, beside, in front of, behind, and next to. | Kindergarten |
| New Hampshire | K.G.A.2 | Correctly name shapes regardless of their orientations or overall size. | Kindergarten |
| New Hampshire | K.G.A.3 | Identify shapes as two-dimensional (lying in a plane, “flat”) or three-dimensional (“solid”). | Kindergarten |
| New Hampshire | K.G.B.4 | Analyze and compare two- and three-dimensional shapes, in different sizes and orientations, using informal language to describe their similarities, differences, parts (e.g., number of sides and vertices/“corners”) and other attributes (e.g., having sides of equal length). | Kindergarten |
| New Hampshire | K.G.B.6 | Compose simple shapes to form larger shapes. | Kindergarten |
| New Hampshire | K.MD.A.1 | Describe measurable attributes of objects, such as length or weight. Describe several measurable attributes of a single object. | Kindergarten |
| New Hampshire | K.MD.A.2 | Directly compare two objects with a measurable attribute in common, to see which object has “more of”/“less of” the attribute, and describe the difference. | Kindergarten |
| New Hampshire | K.MD.B.3 | Classify objects into given categories; count the numbers of objects in each category and sort the categories by count. | Kindergarten |
| New Hampshire | K.NBT.A.1 | Compose and decompose numbers from 11 to 19 into ten ones and some further ones, e.g., by using objects or drawings, and record each composition or decomposition by a drawing or equation (e.g., 18 = 10 + 8); understand that these numbers are composed of ten ones and one, two, three, four, five, six, seven, eight, or nine ones. | Kindergarten |
| New Hampshire | K.OA.A.1 | Represent addition and subtraction with objects, fingers, mental images, drawings, sounds (e.g., claps), acting out situations, verbal explanations, expressions, or equations. | Kindergarten |
| New Hampshire | K.OA.A.2 | Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem. | Kindergarten |
| New Hampshire | K.OA.A.3 | Decompose numbers less than or equal to 10 into pairs in more than one way, e.g., by using objects or drawings, and record each decomposition by a drawing or equation (e.g., 5 = 2 + 3 and 5 = 4 + 1). | Kindergarten |
| New Hampshire | K.OA.A.4 | For any number from 1 to 9, find the number that makes 10 when added to the given number, e.g., by using objects or drawings, and record the answer with a drawing or equation. | Kindergarten |
| New Hampshire | K.OA.A.5 | Fluently add and subtract within 5. | Kindergarten |
| New Hampshire | 1.G.A.1 | Distinguish between defining attributes (e.g., triangles are closed and three-sided) versus non-defining attributes (e.g., color, orientation, overall size); build and draw shapes to possess defining attributes. | Grade 1 |
| New Hampshire | 1.G.A.2 | Compose two-dimensional shapes (rectangles, squares, trapezoids, triangles, half-circles, and quarter-circles) or three-dimensional shapes (cubes, right rectangular prisms, right circular cones, and right circular cylinders) to create a composite shape, and compose new shapes from the composite shape. | Grade 1 |
| New Hampshire | 1.G.A.3 | Partition circles and rectangles into two and four equal shares, describe the shares using the words halves, fourths, and quarters, and use the phrases half of, fourth of, and quarter of. Describe the whole as two of, or four of the shares. Understand for these examples that decomposing into more equal shares creates smaller shares. | Grade 1 |
| New Hampshire | 1.MD.A.1 | Order three objects by length; compare the lengths of two objects indirectly by using a third object. | Grade 1 |
| New Hampshire | 1.MD.A.2 | Express the length of an object as a whole number of length units, by laying multiple copies of a shorter object (the length unit) end to end; understand that the length measurement of an object is the number of same-size length units that span it with no gaps or overlaps. | Grade 1 |
| New Hampshire | 1.MD.B.3 | Tell and write time in hours and half-hours using analog and digital clocks. | Grade 1 |
| New Hampshire | 1.MD.C.4 | Organize, represent, and interpret data with up to three categories; ask and answer questions about the total number of data points, how many in each category, and how many more or less are in one category than in another. | Grade 1 |
| New Hampshire | 1.NBT.A.1 | Count to 120, starting at any number less than 120. In this range, read and write numerals and represent a number of objects with a written numeral. | Grade 1 |
| New Hampshire | 1.NBT.B.2 | Understand that the two digits of a two-digit number represent amounts of tens and ones. | Grade 1 |
| New Hampshire | 1.NBT.B.3 | Compare two two-digit numbers based on meanings of the tens and ones digits, recording the results of comparisons with the symbols >, =, and <. | Grade 1 |
| New Hampshire | 1.NBT.C.4 | Add within 100, including adding a two-digit number and a one-digit number, and adding a two-digit number and a multiple of 10, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Understand that in adding two-digit numbers, one adds tens and tens, ones and ones; and sometimes it is necessary to compose a ten. | Grade 1 |
| New Hampshire | 1.NBT.C.5 | Given a two-digit number, mentally find 10 more or 10 less than the number, without having to count; explain the reasoning used. | Grade 1 |
| New Hampshire | 1.NBT.C.6 | Subtract multiples of 10 in the range 10-90 from multiples of 10 in the range 10-90 (positive or zero differences), using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. | Grade 1 |
| New Hampshire | 1.OA.A.1 | Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem. | Grade 1 |
| New Hampshire | 1.OA.B.3 | Apply properties of operations as strategies to add and subtract. | Grade 1 |
| New Hampshire | 1.OA.B.4 | Understand subtraction as an unknown-addend problem. | Grade 1 |
| New Hampshire | 1.OA.C.5 | Relate counting to addition and subtraction (e.g., by counting on 2 to add 2). | Grade 1 |
| New Hampshire | 1.OA.C.6 | Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to a ten (e.g., 13 - 4 = 13 - 3 - 1 = 10 - 1 = 9); using the relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 - 8 = 4); and creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13). | Grade 1 |
| New Hampshire | 1.OA.D.7 | Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false. | Grade 1 |
| New Hampshire | 1.OA.D.8 | Determine the unknown whole number in an addition or subtraction equation relating three whole numbers. | Grade 1 |
| New Hampshire | 2.G.A.1 | Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces. Identify triangles, quadrilaterals, pentagons, hexagons, and cubes. | Grade 2 |
| New Hampshire | 2.G.A.2 | Partition a rectangle into rows and columns of same-size squares and count to find the total number of them. | Grade 2 |
| New Hampshire | 2.G.A.3 | Partition circles and rectangles into two, three, or four equal shares, describe the shares using the words halves, thirds, half of, a third of, etc., and describe the whole as two halves, three thirds, four fourths. Recognize that equal shares of identical wholes need not have the same shape. | Grade 2 |
| New Hampshire | 2.MD.A.1 | Measure the length of an object by selecting and using appropriate tools such as rulers, yardsticks, meter sticks, and measuring tapes. | Grade 2 |
| New Hampshire | 2.MD.A.2 | Measure the length of an object twice, using length units of different lengths for the two measurements; describe how the two measurements relate to the size of the unit chosen. | Grade 2 |
| New Hampshire | 2.MD.A.4 | Measure to determine how much longer one object is than another, expressing the length difference in terms of a standard length unit. | Grade 2 |
| New Hampshire | 2.MD.B.5 | Use addition and subtraction within 100 to solve word problems involving lengths that are given in the same units, e.g., by using drawings (such as drawings of rulers) and equations with a symbol for the unknown number to represent the problem. | Grade 2 |
| New Hampshire | 2.MD.C.7 | Tell and write time from analog and digital clocks to the nearest five minutes, using a.m. and p.m. | Grade 2 |
| New Hampshire | 2.MD.C.8 | Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies, using $ and ¢ symbols appropriately. | Grade 2 |
| New Hampshire | 2.MD.D.9 | Generate measurement data by measuring lengths of several objects to the nearest whole unit, or by making repeated measurements of the same object. Show the measurements by making a line plot, where the horizontal scale is marked off in whole-number units. | Grade 2 |
| New Hampshire | 2.MD.D.10 | Draw a picture graph and a bar graph (with single-unit scale) to represent a data set with up to four categories. Solve simple put-together, take-apart, and compare problems using information presented in a bar graph. | Grade 2 |
| New Hampshire | 2.NBT.A.1 | Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones. | Grade 2 |
| New Hampshire | 2.NBT.A.2 | Count within 1000; skip-count by 5s, 10s, and 100s. | Grade 2 |
| New Hampshire | 2.NBT.A.3 | Read and write numbers to 1000 using base-ten numerals, number names, and expanded form. | Grade 2 |
| New Hampshire | 2.NBT.A.4 | Compare two three-digit numbers based on meanings of the hundreds, tens, and ones digits, using >, =, and < symbols to record the results of comparisons. | Grade 2 |
| New Hampshire | 2.NBT.B.5 | Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction. | Grade 2 |
| New Hampshire | 2.NBT.B.6 | Add up to four two-digit numbers using strategies based on place value and properties of operations. | Grade 2 |
| New Hampshire | 2.NBT.B.7 | Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method. Understand that in adding or subtracting three-digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds. | Grade 2 |
| New Hampshire | 2.NBT.B.8 | Mentally add 10 or 100 to a given number 100–900, and mentally subtract 10 or 100 from a given number 100–900. | Grade 2 |
| New Hampshire | 2.OA.A.1 | Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem. | Grade 2 |
| New Hampshire | 2.OA.B.2 | Fluently add and subtract within 20 using mental strategies. By end of Grade 2, know from memory all sums of two one-digit numbers. | Grade 2 |
| New Hampshire | 2.OA.C.3 | Determine whether a group of objects (up to 20) has an odd or even number of members, e.g., by pairing objects or counting them by 2s; write an equation to express an even number as a sum of two equal addends. | Grade 2 |
| New Hampshire | 2.OA.C.4 | Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends. | Grade 2 |
| New Hampshire | 3.G.A.1 | Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories. | Grade 3 |
| New Hampshire | 3.G.A.2 | Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole. | Grade 3 |
| New Hampshire | 3.MD.A.1 | Tell and write time to the nearest minute and measure time intervals in minutes. Solve word problems involving addition and subtraction of time intervals in minutes, e.g., by representing the problem on a number line diagram. | Grade 3 |
| New Hampshire | 3.MD.A.2 | Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l). Add, subtract, multiply, or divide to solve one-step word problems involving masses or volumes that are given in the same units, e.g., by using drawings (such as a beaker with a measurement scale) to represent the problem. | Grade 3 |
| New Hampshire | 3.MD.B.3 | Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and two-step “how many more” and “how many less” problems using information presented in scaled bar graphs. | Grade 3 |
| New Hampshire | 3.MD.B.4 | Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Show the data by making a line plot, where the horizontal scale is marked off in appropriate units-whole numbers, halves, or quarters. | Grade 3 |
| New Hampshire | 3.MD.C.5 | Recognize area as an attribute of plane figures and understand concepts of area measurement. | Grade 3 |
| New Hampshire | 3.MD.C.6 | Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units). | Grade 3 |
| New Hampshire | 3.MD.C.7 | Relate area to the operations of multiplication and addition. | Grade 3 |
| New Hampshire | 3.MD.D.8 | Solve real world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters. | Grade 3 |
| New Hampshire | 3.NBT.A.1 | Use place value understanding to round whole numbers to the nearest 10 or 100. | Grade 3 |
| New Hampshire | 3.NBT.A.2 | Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction. | Grade 3 |
| New Hampshire | 3.NBT.A.3 | Multiply one-digit whole numbers by multiples of 10 in the range 10–90 (e.g., 9 × 80, 5 × 60) using strategies based on place value and properties of operations. | Grade 3 |
| New Hampshire | 3.NF.A.1 | Understand a fraction 1/𝘣 as the quantity formed by 1 part when a whole is partitioned into 𝘣 equal parts; understand a fraction 𝘢/𝑏 as the quantity formed by 𝘢 parts of size 1/𝘣. | Grade 3 |
| New Hampshire | 3.NF.A.2 | Understand a fraction as a number on the number line; represent fractions on a number line diagram. | Grade 3 |
| New Hampshire | 3.NF.A.3 | Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size. | Grade 3 |
| New Hampshire | 3.OA.A.1 | Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each. | Grade 3 |
| New Hampshire | 3.OA.A.2 | Interpret whole-number quotients of whole numbers, e.g., interpret 56 ÷ 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each. | Grade 3 |
| New Hampshire | 3.OA.A.3 | Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem. | Grade 3 |
| New Hampshire | 3.OA.A.4 | Determine the unknown whole number in a multiplication or division equation relating three whole numbers. | Grade 3 |
| New Hampshire | 3.OA.B.5 | Apply properties of operations as strategies to multiply and divide. | Grade 3 |
| New Hampshire | 3.OA.B.6 | Understand division as an unknown-factor problem. | Grade 3 |
| New Hampshire | 3.OA.C.7 | Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 × 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers. | Grade 3 |
| New Hampshire | 3.OA.D.8 | Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. | Grade 3 |
| New Hampshire | 3.OA.D.9 | Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations. | Grade 3 |
| New Hampshire | 4.G.A.1 | Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures. | Grade 4 |
| New Hampshire | 4.G.A.2 | Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles. | Grade 4 |
| New Hampshire | 4.G.A.3 | Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify line-symmetric figures and draw lines of symmetry. | Grade 4 |
| New Hampshire | 4.MD.A.1 | Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table. | Grade 4 |
| New Hampshire | 4.MD.A.2 | Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. | Grade 4 |
| New Hampshire | 4.MD.A.3 | Apply the area and perimeter formulas for rectangles in real world and mathematical problems. | Grade 4 |
| New Hampshire | 4.MD.B.4 | Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots. | Grade 4 |
| New Hampshire | 4.MD.C.5 | Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement. | Grade 4 |
| New Hampshire | 4.MD.C.6 | Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure. | Grade 4 |
| New Hampshire | 4.MD.C.7 | Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems, e.g., by using an equation with a symbol for the unknown angle measure. | Grade 4 |
| New Hampshire | 4.NBT.A.1 | Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. | Grade 4 |
| New Hampshire | 4.NBT.A.2 | Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. | Grade 4 |
| New Hampshire | 4.NBT.A.3 | Use place value understanding to round multi-digit whole numbers to any place. | Grade 4 |
| New Hampshire | 4.NBT.B.4 | Fluently add and subtract multi-digit whole numbers using the standard algorithm. | Grade 4 |
| New Hampshire | 4.NBT.B.5 | Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. | Grade 4 |
| New Hampshire | 4.NBT.B.6 | Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. | Grade 4 |
| New Hampshire | 4.NF.A.1 | Explain why a fraction 𝘢/𝘣 is equivalent to a fraction (𝘯 × 𝘢)/(𝘯 × 𝘣) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. | Grade 4 |
| New Hampshire | 4.NF.A.2 | Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model. | Grade 4 |
| New Hampshire | 4.NF.B.3 | Understand a fraction 𝘢/𝘣 with 𝘢 > 1 as a sum of fractions 1/𝘣. | Grade 4 |
| New Hampshire | 4.NF.B.4 | Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. | Grade 4 |
| New Hampshire | 4.NF.C.5 | Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100. | Grade 4 |
| New Hampshire | 4.NF.C.6 | Use decimal notation for fractions with denominators 10 or 100. | Grade 4 |
| New Hampshire | 4.NF.C.7 | Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual model. | Grade 4 |
| New Hampshire | 4.OA.A.1 | Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 × 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations. | Grade 4 |
| New Hampshire | 4.OA.A.2 | Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison. | Grade 4 |
| New Hampshire | 4.OA.A.3 | Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. | Grade 4 |
| New Hampshire | 4.OA.B.4 | Find all factor pairs for a whole number in the range 1-100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1-100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1-100 is prime or composite. | Grade 4 |
| New Hampshire | 4.OA.C.5 | Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. | Grade 4 |
| New Hampshire | 5.G.A.1 | Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., 𝘹-axis and 𝘹-coordinate, 𝘺-axis and 𝘺-coordinate). | Grade 5 |
| New Hampshire | 5.G.A.2 | Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. | Grade 5 |
| New Hampshire | 5.G.B.3 | Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. | Grade 5 |
| New Hampshire | 5.G.B.4 | Classify two-dimensional figures in a hierarchy based on properties. | Grade 5 |
| New Hampshire | 5.MD.A.1 | Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. | Grade 5 |
| New Hampshire | 5.MD.B.2 | Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. | Grade 5 |
| New Hampshire | 5.MD.C.3 | Recognize volume as an attribute of solid figures and understand concepts of volume measurement. | Grade 5 |
| New Hampshire | 5.MD.C.4 | Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. | Grade 5 |
| New Hampshire | 5.MD.C.5 | Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume. | Grade 5 |
| New Hampshire | 5.NBT.A.1 | Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. | Grade 5 |
| New Hampshire | 5.NBT.A.2 | Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. | Grade 5 |
| New Hampshire | 5.NBT.A.3 | Read, write, and compare decimals to thousandths. | Grade 5 |
| New Hampshire | 5.NBT.A.4 | Use place value understanding to round decimals to any place. | Grade 5 |
| New Hampshire | 5.NBT.B.5 | Fluently multiply multi-digit whole numbers using the standard algorithm. | Grade 5 |
| New Hampshire | 5.NBT.B.6 | Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. | Grade 5 |
| New Hampshire | 5.NBT.B.7 | Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. | Grade 5 |
| New Hampshire | 5.NF.A.1 | Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. | Grade 5 |
| New Hampshire | 5.NF.A.2 | Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. | Grade 5 |
| New Hampshire | 5.NF.B.3 | Interpret a fraction as division of the numerator by the denominator (𝘢/𝘣 = 𝘢 ÷ 𝘣). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. | Grade 5 |
| New Hampshire | 5.NF.B.4 | Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. | Grade 5 |
| New Hampshire | 5.NF.B.5 | Interpret multiplication as scaling (resizing). | Grade 5 |
| New Hampshire | 5.NF.B.6 | Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. | Grade 5 |
| New Hampshire | 5.NF.B.7 | Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. | Grade 5 |
| New Hampshire | 5.OA.A.1 | Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. | Grade 5 |
| New Hampshire | 5.OA.A.2 | Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. | Grade 5 |
| New Hampshire | 5.OA.B.3 | Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. | Grade 5 |
| New Hampshire | 6.EE.A.1 | Write and evaluate numerical expressions involving whole-number exponents. | Grade 6 |
| New Hampshire | 6.EE.A.2 | Write, read, and evaluate expressions in which letters stand for numbers. | Grade 6 |
| New Hampshire | 6.EE.A.3 | Apply the properties of operations to generate equivalent expressions. | Grade 6 |
| New Hampshire | 6.EE.A.4 | Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). | Grade 6 |
| New Hampshire | 6.EE.B.5 | Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true. | Grade 6 |
| New Hampshire | 6.EE.B.6 | Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set. | Grade 6 |
| New Hampshire | 6.EE.B.7 | Solve real-world and mathematical problems by writing and solving equations of the form 𝘹 + 𝘱 = 𝘲 and 𝘱𝘹 = 𝘲 for cases in which 𝘱, 𝘲 and 𝘹 are all nonnegative rational numbers. | Grade 6 |
| New Hampshire | 6.EE.B.8 | Write an inequality of the form 𝘹 > 𝘤 or 𝘹 𝘤 or 𝘹 < 𝘤 have infinitely many solutions; represent solutions of such inequalities on number line diagrams. | Grade 6 |
| New Hampshire | 6.EE.C.9 | Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. | Grade 6 |
| New Hampshire | 6.G.A.1 | Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems. | Grade 6 |
| New Hampshire | 6.G.A.2 | Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas 𝘝 = 𝘭 𝘸 𝘩 and 𝘝 = 𝘣 𝘩 to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems. | Grade 6 |
| New Hampshire | 6.G.A.3 | Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems. | Grade 6 |
| New Hampshire | 6.G.A.4 | Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems. | Grade 6 |
| New Hampshire | 6.RP.A.1 | Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. | Grade 6 |
| New Hampshire | 6.RP.A.2 | Understand the concept of a unit rate 𝘢/𝘣 associated with a ratio 𝘢:𝘣 with 𝘣 ≠ 0, and use rate language in the context of a ratio relationship. | Grade 6 |
| New Hampshire | 6.RP.A.3 | Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. | Grade 6 |
| New Hampshire | 6.SP.B.5 | Summarize numerical data sets in relation to their context, such as by: | Grade 6 |
| New Hampshire | 6.NS.A.1 | Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. | Grade 6 |
| New Hampshire | 6.NS.B.2 | Fluently divide multi-digit numbers using the standard algorithm. | Grade 6 |
| New Hampshire | 6.NS.B.3 | Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation. | Grade 6 |
| New Hampshire | 6.NS.C.5 | Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation. | Grade 6 |
| New Hampshire | 6.NS.C.6 | Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates. | Grade 6 |
| New Hampshire | 6.NS.C.7 | Understand ordering and absolute value of rational numbers. | Grade 6 |
| New Hampshire | 6.NS.C.8 | Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. | Grade 6 |
| New Hampshire | 7.EE.A.1 | Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients. | Grade 7 |
| New Hampshire | 7.EE.A.2 | Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. | Grade 7 |
| New Hampshire | 7.EE.B.3 | Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. | Grade 7 |
| New Hampshire | 7.EE.B.4 | Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. | Grade 7 |
| New Hampshire | 7.G.A.1 | Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale. | Grade 7 |
| New Hampshire | 7.G.A.2 | Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle. | Grade 7 |
| New Hampshire | 7.G.A.3 | Describe the two-dimensional figures that result from slicing three-dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids. | Grade 7 |
| New Hampshire | 7.G.B.4 | Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle. | Grade 7 |
| New Hampshire | 7.G.B.5 | Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure. | Grade 7 |
| New Hampshire | 7.G.B.6 | Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. | Grade 7 |
| New Hampshire | 7.RP.A.1 | Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. | Grade 7 |
| New Hampshire | 7.RP.A.2 | Recognize and represent proportional relationships between quantities. | Grade 7 |
| New Hampshire | 7.RP.A.3 | Use proportional relationships to solve multistep ratio and percent problems. | Grade 7 |
| New Hampshire | 7.NS.A.1 | Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram. | Grade 7 |
| New Hampshire | 7.NS.A.2 | Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers. | Grade 7 |
| New Hampshire | 7.NS.A.3 | Solve real-world and mathematical problems involving the four operations with rational numbers. | Grade 7 |
| New Hampshire | 8.EE.A.1 | Know and apply the properties of integer exponents to generate equivalent numerical expressions. | Grade 8 |
| New Hampshire | 8.EE.A.2 | Use square root and cube root symbols to represent solutions to equations of the form 𝘹² = 𝘱 and 𝘹³ = 𝘱, where 𝘱 is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that √2 is irrational. | Grade 8 |
| New Hampshire | 8.EE.A.3 | Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other. | Grade 8 |
| New Hampshire | 8.EE.A.4 | Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology. | Grade 8 |
| New Hampshire | 8.EE.B.5 | Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. | Grade 8 |
| New Hampshire | 8.EE.B.6 | Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation 𝘺 = 𝘮𝘹 for a line through the origin and the equation 𝘺 = 𝘮𝘹 + 𝘣 for a line intercepting the vertical axis at 𝘣. | Grade 8 |
| New Hampshire | 8.EE.C.7 | Solve linear equations in one variable. | Grade 8 |
| New Hampshire | 8.EE.C.8 | Analyze and solve pairs of simultaneous linear equations. | Grade 8 |
| New Hampshire | 8.F.A.1 | Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output. | Grade 8 |
| New Hampshire | 8.F.A.2 | Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). | Grade 8 |
| New Hampshire | 8.F.A.3 | Interpret the equation 𝘺 = 𝘮𝘹 + 𝘣 as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. | Grade 8 |
| New Hampshire | 8.F.B.4 | Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (𝘹, 𝘺) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values. | Grade 8 |
| New Hampshire | 8.F.B.5 | Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally. | Grade 8 |
| New Hampshire | 8.G.A.1 | Verify experimentally the properties of rotations, reflections, and translations. | Grade 8 |
| New Hampshire | 8.G.A.2 | Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them. | Grade 8 |
| New Hampshire | 8.G.A.3 | Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates. | Grade 8 |
| New Hampshire | 8.G.A.4 | Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two-dimensional figures, describe a sequence that exhibits the similarity between them. | Grade 8 |
| New Hampshire | 8.G.A.5 | Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. | Grade 8 |
| New Hampshire | 8.G.B.7 | Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions. | Grade 8 |
| New Hampshire | 8.G.B.8 | Apply the Pythagorean Theorem to find the distance between two points in a coordinate system. | Grade 8 |
| New Hampshire | 8.G.C.9 | Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems. | Grade 8 |
| New Hampshire | 8.SP.A.1 | Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association. | Grade 8 |
| New Hampshire | 8.SP.A.2 | Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line. | Grade 8 |
| New Hampshire | 8.NS.A.2 | Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g., π²). | Grade 8 |
| New Hampshire | A-APR.B.3 | Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial. | High School |
| New Hampshire | A-CED.A.2 | Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. | High School |
| New Hampshire | A-CED.A.3 | Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context. | High School |
| New Hampshire | A-REI.B.3 | Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. | High School |
| New Hampshire | A-SSE.A.2 | Use the structure of an expression to identify ways to rewrite it. | High School |
| New Hampshire | A-SSE.B.3 | Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression. | High School |
| New Hampshire | F-BF.A.1 | Write a function that describes a relationship between two quantities. | High School |
| New Hampshire | F-IF.A.2 | Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. | High School |
| New Hampshire | F-IF.B.4 | For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. | High School |
| New Hampshire | F-IF.C.7 | Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. | High School |
| New Hampshire | S-ID.B.6 | Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. | High School |
| New Jersey | K.CC.A.1 | Count to 100 by ones and by tens. | Kindergarten |
| New Jersey | K.CC.A.2 | Count forward beginning from a given number within the known sequence (instead of having to begin at 1). | Kindergarten |
| New Jersey | K.CC.A.3 | Write numbers from 0 to 20. Represent a number of objects with a written numeral 0-20 (with 0 representing a count of no objects). | Kindergarten |
| New Jersey | K.CC.B.4 | Understand the relationship between numbers and quantities; connect counting to cardinality. | Kindergarten |
| New Jersey | K.CC.B.5 | Count to answer “how many?” questions about as many as 20 things arranged in a line, a rectangular array, or a circle, or as many as 10 things in a scattered configuration; given a number from 1–20, count out that many objects. | Kindergarten |
| New Jersey | K.CC.C.6 | Identify whether the number of objects in one group is greater than, less than, or equal to the number of objects in another group, e.g., by using matching and counting strategies. | Kindergarten |
| New Jersey | K.CC.C.7 | Compare two numbers between 1 and 10 presented as written numerals. | Kindergarten |
| New Jersey | K.G.A.1 | Describe objects in the environment using names of shapes, and describe the relative positions of these objects using terms such as above, below, beside, in front of, behind, and next to. | Kindergarten |
| New Jersey | K.G.A.2 | Correctly name shapes regardless of their orientations or overall size. | Kindergarten |
| New Jersey | K.G.A.3 | Identify shapes as two-dimensional (lying in a plane, “flat”) or three-dimensional (“solid”). | Kindergarten |
| New Jersey | K.G.B.4 | Analyze and compare two- and three-dimensional shapes, in different sizes and orientations, using informal language to describe their similarities, differences, parts (e.g., number of sides and vertices/“corners”) and other attributes (e.g., having sides of equal length). | Kindergarten |
| New Jersey | K.G.B.6 | Compose simple shapes to form larger shapes. | Kindergarten |
| New Jersey | K.MD.A.1 | Describe measurable attributes of objects, such as length or weight. Describe several measurable attributes of a single object. | Kindergarten |
| New Jersey | K.MD.A.2 | Directly compare two objects with a measurable attribute in common, to see which object has “more of”/“less of” the attribute, and describe the difference. | Kindergarten |
| New Jersey | K.MD.B.3 | Classify objects into given categories; count the numbers of objects in each category and sort the categories by count. | Kindergarten |
| New Jersey | K.NBT.A.1 | Compose and decompose numbers from 11 to 19 into ten ones and some further ones, e.g., by using objects or drawings, and record each composition or decomposition by a drawing or equation (e.g., 18 = 10 + 8); understand that these numbers are composed of ten ones and one, two, three, four, five, six, seven, eight, or nine ones. | Kindergarten |
| New Jersey | K.OA.A.1 | Represent addition and subtraction up to 10 with objects, fingers, mental images, drawings, sounds (e.g., claps), acting out situations, verbal explanations, expressions, or equations. | Kindergarten |
| New Jersey | K.OA.A.2 | Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem. | Kindergarten |
| New Jersey | K.OA.A.3 | Decompose numbers less than or equal to 10 into pairs in more than one way, e.g., by using objects or drawings, and record each decomposition by a drawing or equation (e.g., 5 = 2 + 3 and 5 = 4 + 1). | Kindergarten |
| New Jersey | K.OA.A.4 | For any number from 1 to 9, find the number that makes 10 when added to the given number, e.g., by using objects or drawings, and record the answer with a drawing or equation. | Kindergarten |
| New Jersey | K.OA.A.5 | Demonstrate fluency for addition and subtraction within 5. | Kindergarten |
| New Jersey | 1.G.A.1 | Distinguish between defining attributes (e.g., triangles are closed and three-sided) versus non-defining attributes (e.g., color, orientation, overall size); build and draw shapes to possess defining attributes. | Grade 1 |
| New Jersey | 1.G.A.2 | Compose two-dimensional shapes (rectangles, squares, trapezoids, triangles, half-circles, and quarter-circles) or three-dimensional shapes (cubes, right rectangular prisms, right circular cones, and right circular cylinders) to create a composite shape, and compose new shapes from the composite shape. | Grade 1 |
| New Jersey | 1.G.A.3 | Partition circles and rectangles into two and four equal shares, describe the shares using the words halves, fourths, and quarters, and use the phrases half of, fourth of, and quarter of. Describe the whole as two of, or four of the shares. Understand for these examples that decomposing into more equal shares creates smaller shares. | Grade 1 |
| New Jersey | 1.MD.A.1 | Order three objects by length; compare the lengths of two objects indirectly by using a third object. | Grade 1 |
| New Jersey | 1.MD.A.2 | Express the length of an object as a whole number of length units, by laying multiple copies of a shorter object (the length unit) end to end; understand that the length measurement of an object is the number of same-size length units that span it with no gaps or overlaps. | Grade 1 |
| New Jersey | 1.MD.B.3 | Tell and write time in hours and half-hours using analog and digital clocks. | Grade 1 |
| New Jersey | 1.MD.C.4 | Organize, represent, and interpret data with up to three categories; ask and answer questions about the total number of data points, how many in each category, and how many more or less are in one category than in another. | Grade 1 |
| New Jersey | 1.NBT.A.1 | Count to 120, starting at any number less than 120. In this range, read and write numerals and represent a number of objects with a written numeral. | Grade 1 |
| New Jersey | 1.NBT.B.2 | Understand that the two digits of a two-digit number represent amounts of tens and ones. | Grade 1 |
| New Jersey | 1.NBT.B.3 | Compare two two-digit numbers based on meanings of the tens and ones digits, recording the results of comparisons with the symbols >, =, and <. | Grade 1 |
| New Jersey | 1.NBT.C.4 | Add within 100, including adding a two-digit number and a one-digit number, and adding a two-digit number and a multiple of 10, using concrete models (e.g., base ten blocks) or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Understand that in adding two-digit numbers, one adds tens and tens, ones and ones; and sometimes it is necessary to compose a ten. | Grade 1 |
| New Jersey | 1.NBT.C.5 | Given a two-digit number, mentally find 10 more or 10 less than the number, without having to count; explain the reasoning used. | Grade 1 |
| New Jersey | 1.NBT.C.6 | Subtract multiples of 10 in the range 10-90 from multiples of 10 in the range 10-90 (positive or zero differences), using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. | Grade 1 |
| New Jersey | 1.OA.A.1 | Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem. | Grade 1 |
| New Jersey | 1.OA.B.3 | Apply properties of operations as strategies to add and subtract. | Grade 1 |
| New Jersey | 1.OA.B.4 | Understand subtraction as an unknown-addend problem. | Grade 1 |
| New Jersey | 1.OA.C.5 | Relate counting to addition and subtraction (e.g., by counting on 2 to add 2). | Grade 1 |
| New Jersey | 1.OA.C.6 | Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to a ten (e.g., 13 – 4 = 13 – 3 – 1 = 10 – 1 = 9); using the relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 – 8 = 4); and creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13). | Grade 1 |
| New Jersey | 1.OA.D.7 | Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false. | Grade 1 |
| New Jersey | 1.OA.D.8 | Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers. | Grade 1 |
| New Jersey | 2.G.A.1 | Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces. Identify triangles, quadrilaterals, pentagons, hexagons, and cubes. | Grade 2 |
| New Jersey | 2.G.A.2 | Partition a rectangle into rows and columns of same-size squares and count to find the total number of them. | Grade 2 |
| New Jersey | 2.G.A.3 | Partition circles and rectangles into two, three, or four equal shares, describe the shares using the words halves, thirds, half of, a third of, etc., and describe the whole as two halves, three thirds, four fourths. Recognize that equal shares of identical wholes need not have the same shape. | Grade 2 |
| New Jersey | 2.MD.A.1 | Measure the length of an object by selecting and using appropriate tools such as rulers, yardsticks, meter sticks, and measuring tapes. | Grade 2 |
| New Jersey | 2.MD.A.2 | Measure the length of an object twice, using length units of different lengths for the two measurements; describe how the two measurements relate to the size of the unit chosen. | Grade 2 |
| New Jersey | 2.MD.A.4 | Measure to determine how much longer one object is than another, expressing the length difference in terms of a standard length unit. | Grade 2 |
| New Jersey | 2.MD.B.5 | Use addition and subtraction within 100 to solve word problems involving lengths that are given in the same units, e.g., by using drawings (such as drawings of rulers) and equations with a symbol for the unknown number to represent the problem. | Grade 2 |
| New Jersey | 2.MD.C.7 | Tell and write time from analog and digital clocks to the nearest five minutes, using a.m. and p.m. | Grade 2 |
| New Jersey | 2.MD.C.8 | Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies, using $ and ¢ symbols appropriately. | Grade 2 |
| New Jersey | 2.MD.D.9 | Generate measurement data by measuring lengths of several objects to the nearest whole unit, or by making repeated measurements of the same object. Show the measurements by making a line plot, where the horizontal scale is marked off in whole-number units. | Grade 2 |
| New Jersey | 2.MD.D.10 | Draw a picture graph and a bar graph (with single-unit scale) to represent a data set with up to four categories. Solve simple put together, take-apart, and compare problems using information presented in a bar graph. | Grade 2 |
| New Jersey | 2.NBT.A.1 | Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones. | Grade 2 |
| New Jersey | 2.NBT.A.2 | Count within 1000; skip-count by 5s, 10s, and 100s. | Grade 2 |
| New Jersey | 2.NBT.A.3 | Read and write numbers to 1000 using base-ten numerals, number names, and expanded form. | Grade 2 |
| New Jersey | 2.NBT.A.4 | Compare two three-digit numbers based on meanings of the hundreds, tens, and ones digits, using >, =, and < symbols to record the results of comparisons. | Grade 2 |
| New Jersey | 2.NBT.B.5 | Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction. | Grade 2 |
| New Jersey | 2.NBT.B.6 | Add up to four two-digit numbers using strategies based on place value and properties of operations. | Grade 2 |
| New Jersey | 2.NBT.B.7 | Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method. Understand that in adding or subtracting three-digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds. | Grade 2 |
| New Jersey | 2.NBT.B.8 | Mentally add 10 or 100 to a given number 100–900, and mentally subtract 10 or 100 from a given number 100–900. | Grade 2 |
| New Jersey | 2.OA.A.1 | Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem. | Grade 2 |
| New Jersey | 2.OA.B.2 | Fluently add and subtract within 20 using mental strategies. By end of Grade 2, know from memory all sums of two one-digit numbers. | Grade 2 |
| New Jersey | 2.OA.C.3 | Determine whether a group of objects (up to 20) has an odd or even number of members, e.g., by pairing objects or counting them by 2s; write an equation to express an even number as a sum of two equal addends. | Grade 2 |
| New Jersey | 2.OA.C.4 | Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends. | Grade 2 |
| New Jersey | 3.G.A.1 | Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories. | Grade 3 |
| New Jersey | 3.G.A.2 | Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole. | Grade 3 |
| New Jersey | 3.MD.A.1 | Tell and write time to the nearest minute and measure time intervals in minutes. Solve word problems involving addition and subtraction of time intervals in minutes, e.g., by representing the problem on a number line diagram. | Grade 3 |
| New Jersey | 3.MD.A.2 | Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l). Add, subtract, multiply, or divide to solve one-step word problems involving masses or volumes that are given in the same units, e.g., by using drawings (such as a beaker with a measurement scale) to represent the problem. | Grade 3 |
| New Jersey | 3.MD.B.3 | Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and two-step “how many more” and “how many less” problems using information presented in scaled bar graphs. | Grade 3 |
| New Jersey | 3.MD.B.4 | Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Show the data by making a line plot, where the horizontal scale is marked off in appropriate units— whole numbers, halves, or quarters. | Grade 3 |
| New Jersey | 3.MD.C.5 | Recognize area as an attribute of plane figures and understand concepts of area measurement. | Grade 3 |
| New Jersey | 3.MD.C.6 | Measure areas by counting unit squares (square cm, square m, square in, square ft, and non-standard units). | Grade 3 |
| New Jersey | 3.MD.C.7 | Relate area to the operations of multiplication and addition. | Grade 3 |
| New Jersey | 3.MD.D.8 | Solve real world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters. | Grade 3 |
| New Jersey | 3.NBT.A.1 | Use place value understanding to round whole numbers to the nearest 10 or 100. | Grade 3 |
| New Jersey | 3.NBT.A.2 | Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction. | Grade 3 |
| New Jersey | 3.NBT.A.3 | Multiply one-digit whole numbers by multiples of 10 in the range 10–90 (e.g., 9 × 80, 5 × 60) using strategies based on place value and properties of operations. | Grade 3 |
| New Jersey | 3.NF.A.1 | Understand a fraction 1/𝑏 as the quantity formed by 1 part when a whole is partitioned into 𝑏 equal parts; understand a fraction 𝑎/𝑏 as the quantity formed by a parts of size 1/𝑏. | Grade 3 |
| New Jersey | 3.NF.A.2 | Understand a fraction as a number on the number line; represent fractions on a number line diagram. | Grade 3 |
| New Jersey | 3.NF.A.3 | Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size. | Grade 3 |
| New Jersey | 3.OA.A.1 | Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each. | Grade 3 |
| New Jersey | 3.OA.A.2 | Interpret whole-number quotients of whole numbers, e.g., interpret 56 ÷ 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each. | Grade 3 |
| New Jersey | 3.OA.A.3 | Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem. | Grade 3 |
| New Jersey | 3.OA.A.4 | Determine the unknown whole number in a multiplication or division equation relating three whole numbers. | Grade 3 |
| New Jersey | 3.OA.B.5 | Apply properties of operations as strategies to multiply and divide. | Grade 3 |
| New Jersey | 3.OA.B.6 | Understand division as an unknown-factor problem. | Grade 3 |
| New Jersey | 3.OA.C.7 | Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 × 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers. | Grade 3 |
| New Jersey | 3.OA.D.8 | Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. | Grade 3 |
| New Jersey | 3.OA.D.9 | Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations. | Grade 3 |
| New Jersey | 4.G.A.1 | Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures. | Grade 4 |
| New Jersey | 4.G.A.2 | Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles. | Grade 4 |
| New Jersey | 4.G.A.3 | Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify line-symmetric figures and draw lines of symmetry. | Grade 4 |
| New Jersey | 4.MD.A.1 | Know relative sizes of measurement units within one system of units including km, m, cm, mm; kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two column table. | Grade 4 |
| New Jersey | 4.MD.A.2 | Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. | Grade 4 |
| New Jersey | 4.MD.A.3 | Apply the area and perimeter formulas for rectangles in real world and mathematical problems. | Grade 4 |
| New Jersey | 4.MD.B.4 | Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots. | Grade 4 |
| New Jersey | 4.MD.C.5 | Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement. | Grade 4 |
| New Jersey | 4.MD.C.6 | Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure. | Grade 4 |
| New Jersey | 4.MD.C.7 | Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems, e.g., by using an equation with a symbol for the unknown angle measure. | Grade 4 |
| New Jersey | 4.NBT.A.1 | Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. | Grade 4 |
| New Jersey | 4.NBT.A.2 | Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. | Grade 4 |
| New Jersey | 4.NBT.A.3 | Use place value understanding to round multi-digit whole numbers to any place. | Grade 4 |
| New Jersey | 4.NBT.B.4 | Fluently add and subtract multi-digit whole numbers using the standard algorithm. | Grade 4 |
| New Jersey | 4.NBT.B.5 | Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. | Grade 4 |
| New Jersey | 4.NBT.B.6 | Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. | Grade 4 |
| New Jersey | 4.NF.A.1 | Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. | Grade 4 |
| New Jersey | 4.NF.A.2 | Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model. | Grade 4 |
| New Jersey | 4.NF.B.3 | Understand a fraction 𝑎/𝑏 with 𝑎 > 1 as a sum of fractions 1/𝑏. | Grade 4 |
| New Jersey | 4.NF.B.4 | Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. | Grade 4 |
| New Jersey | 4.NF.C.5 | Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100. | Grade 4 |
| New Jersey | 4.NF.C.6 | Use decimal notation for fractions with denominators 10 or 100. | Grade 4 |
| New Jersey | 4.NF.C.7 | Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual model. | Grade 4 |
| New Jersey | 4.OA.A.1 | Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 × 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations. | Grade 4 |
| New Jersey | 4.OA.A.2 | Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison. | Grade 4 |
| New Jersey | 4.OA.A.3 | Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. | Grade 4 |
| New Jersey | 4.OA.B.4 | Find all factor pairs for a whole number in the range 1–100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1–100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1–100 is prime or composite. | Grade 4 |
| New Jersey | 4.OA.C.5 | Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. | Grade 4 |
| New Jersey | 5.G.A.1 | Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., 𝑥-axis and 𝑥-coordinate, 𝑦-axis and 𝑦-coordinate). | Grade 5 |
| New Jersey | 5.G.A.2 | Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. | Grade 5 |
| New Jersey | 5.G.B.3 | Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. | Grade 5 |
| New Jersey | 5.G.B.4 | Classify two-dimensional figures in a hierarchy based on properties. | Grade 5 |
| New Jersey | 5.MD.A.1 | Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. | Grade 5 |
| New Jersey | 5.MD.B.2 | Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. | Grade 5 |
| New Jersey | 5.MD.C.3 | Recognize volume as an attribute of solid figures and understand concepts of volume measurement. | Grade 5 |
| New Jersey | 5.MD.C.4 | Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and non-standard units. | Grade 5 |
| New Jersey | 5.MD.C.5 | Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume. | Grade 5 |
| New Jersey | 5.NBT.A.1 | Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. | Grade 5 |
| New Jersey | 5.NBT.A.2 | Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. | Grade 5 |
| New Jersey | 5.NBT.A.3 | Read, write, and compare decimals to thousandths. | Grade 5 |
| New Jersey | 5.NBT.A.4 | Use place value understanding to round decimals to any place. | Grade 5 |
| New Jersey | 5.NBT.B.5 | Fluently multiply multi-digit whole numbers using the standard algorithm. | Grade 5 |
| New Jersey | 5.NBT.B.6 | Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. | Grade 5 |
| New Jersey | 5.NBT.B.7 | Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. | Grade 5 |
| New Jersey | 5.NF.A.1 | Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. | Grade 5 |
| New Jersey | 5.NF.A.2 | Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. | Grade 5 |
| New Jersey | 5.NF.B.3 | Interpret a fraction as division of the numerator by the denominator (𝑎/𝑏 = 𝑎 ÷ 𝑏). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. | Grade 5 |
| New Jersey | 5.NF.B.4 | Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. | Grade 5 |
| New Jersey | 5.NF.B.5 | Interpret multiplication as scaling (resizing). | Grade 5 |
| New Jersey | 5.NF.B.6 | Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. | Grade 5 |
| New Jersey | 5.NF.B.7 | Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. | Grade 5 |
| New Jersey | 5.OA.A.1 | Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. | Grade 5 |
| New Jersey | 5.OA.A.2 | Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. | Grade 5 |
| New Jersey | 5.OA.B.3 | Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. | Grade 5 |
| New Jersey | 6.EE.A.1 | Write and evaluate numerical expressions involving whole-number exponents. | Grade 6 |
| New Jersey | 6.EE.A.2 | Write, read, and evaluate expressions in which letters stand for numbers. | Grade 6 |
| New Jersey | 6.EE.A.3 | Apply the properties of operations to generate equivalent expressions. | Grade 6 |
| New Jersey | 6.EE.A.4 | Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). | Grade 6 |
| New Jersey | 6.EE.B.5 | Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true. | Grade 6 |
| New Jersey | 6.EE.B.6 | Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set. | Grade 6 |
| New Jersey | 6.EE.B.7 | Solve real-world and mathematical problems by writing and solving equations of the form 𝑥 + 𝑝 = 𝑞 and 𝑝𝑥 = 𝑞 for cases in which 𝑝, 𝑞 and 𝑥 are all nonnegative rational numbers. | Grade 6 |
| New Jersey | 6.EE.B.8 | Write an inequality of the form 𝑥 > 𝑐 or 𝑥 𝑐 or 𝑥 < 𝑐 have infinitely many solutions; represent solutions of such inequalities on number line diagrams. | Grade 6 |
| New Jersey | 6.EE.C.9 | Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. | Grade 6 |
| New Jersey | 6.G.A.1 | Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems. | Grade 6 |
| New Jersey | 6.G.A.2 | Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas 𝑉 = 𝑙𝑤ℎ and 𝑉 = 𝐵ℎ to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems. | Grade 6 |
| New Jersey | 6.G.A.3 | Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems. | Grade 6 |
| New Jersey | 6.G.A.4 | Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems. | Grade 6 |
| New Jersey | 6.RP.A.1 | Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. | Grade 6 |
| New Jersey | 6.RP.A.2 | Understand the concept of a unit rate 𝑎/𝑏 associated with a ratio 𝑎:𝑏 with 𝑏 ≠ 0, and use rate language in the context of a ratio relationship. | Grade 6 |
| New Jersey | 6.RP.A.3 | Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. | Grade 6 |
| New Jersey | 6.SP.B.5 | Summarize numerical data sets in relation to their context, such as by: | Grade 6 |
| New Jersey | 6.NS.A.1 | Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. | Grade 6 |
| New Jersey | 6.NS.B.2 | Fluently divide multi-digit numbers using the standard algorithm. | Grade 6 |
| New Jersey | 6.NS.B.3 | Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation. | Grade 6 |
| New Jersey | 6.NS.C.5 | Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation. | Grade 6 |
| New Jersey | 6.NS.C.6 | Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates. | Grade 6 |
| New Jersey | 6.NS.C.7 | Understand ordering and absolute value of rational numbers. | Grade 6 |
| New Jersey | 6.NS.C.8 | Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. | Grade 6 |
| New Jersey | 7.EE.A.1 | Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients. | Grade 7 |
| New Jersey | 7.EE.A.2 | Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. | Grade 7 |
| New Jersey | 7.EE.B.3 | Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. | Grade 7 |
| New Jersey | 7.EE.B.4 | Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. | Grade 7 |
| New Jersey | 7.G.A.1 | Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale. | Grade 7 |
| New Jersey | 7.G.A.2 | Draw (with technology, with ruler and protractor, as well as freehand) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle. | Grade 7 |
| New Jersey | 7.G.A.3 | Describe the two-dimensional figures that result from slicing three-dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids. | Grade 7 |
| New Jersey | 7.G.B.4 | Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle. | Grade 7 |
| New Jersey | 7.G.B.5 | Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure. | Grade 7 |
| New Jersey | 7.G.B.6 | Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. | Grade 7 |
| New Jersey | 7.RP.A.1 | Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. | Grade 7 |
| New Jersey | 7.RP.A.2 | Recognize and represent proportional relationships between quantities. | Grade 7 |
| New Jersey | 7.RP.A.3 | Use proportional relationships to solve multistep ratio and percent problems. | Grade 7 |
| New Jersey | 7.NS.A.1 | Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram. | Grade 7 |
| New Jersey | 7.NS.A.2 | Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers. | Grade 7 |
| New Jersey | 7.NS.A.3 | Solve real-world and mathematical problems involving the four operations with rational numbers. | Grade 7 |
| New Jersey | 8.EE.A.1 | Know and apply the properties of integer exponents to generate equivalent numerical expressions. | Grade 8 |
| New Jersey | 8.EE.A.2 | Use square root and cube root symbols to represent solutions to equations of the form 𝑥² = 𝑝 and 𝑥³ = 𝑝, where 𝑝 is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that √2 is irrational. | Grade 8 |
| New Jersey | 8.EE.A.3 | Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other. | Grade 8 |
| New Jersey | 8.EE.A.4 | Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology. | Grade 8 |
| New Jersey | 8.EE.B.5 | Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. | Grade 8 |
| New Jersey | 8.EE.B.6 | Use similar triangles to explain why the slope 𝑚 is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation 𝑦 = 𝑚𝑥 for a line through the origin and the equation 𝑦 = 𝑚𝑥 + 𝑏 for a line intercepting the vertical axis at 𝑏. | Grade 8 |
| New Jersey | 8.EE.C.7 | Solve linear equations in one variable. | Grade 8 |
| New Jersey | 8.EE.C.8 | Analyze and solve pairs of simultaneous linear equations. | Grade 8 |
| New Jersey | 8.F.A.1 | Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output. | Grade 8 |
| New Jersey | 8.F.A.2 | Compare properties (e.g. rate of change, intercepts, domain and range) of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). | Grade 8 |
| New Jersey | 8.F.A.3 | Interpret the equation 𝑦 = 𝑚𝑥 + 𝑏 as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. | Grade 8 |
| New Jersey | 8.F.B.4 | Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (𝑥, 𝑦) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values. | Grade 8 |
| New Jersey | 8.F.B.5 | Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally. | Grade 8 |
| New Jersey | 8.G.A.1 | Verify experimentally the properties of rotations, reflections, and translations. | Grade 8 |
| New Jersey | 8.G.A.2 | Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them. | Grade 8 |
| New Jersey | 8.G.A.3 | Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates. | Grade 8 |
| New Jersey | 8.G.A.4 | Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two-dimensional figures, describe a sequence that exhibits the similarity between them. | Grade 8 |
| New Jersey | 8.G.A.5 | Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. | Grade 8 |
| New Jersey | 8.G.B.7 | Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions. | Grade 8 |
| New Jersey | 8.G.B.8 | Apply the Pythagorean Theorem to find the distance between two points in a coordinate system. | Grade 8 |
| New Jersey | 8.G.C.9 | Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems. | Grade 8 |
| New Jersey | 8.SP.A.1 | Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association. | Grade 8 |
| New Jersey | 8.SP.A.2 | Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit (e.g. line of best fit) by judging the closeness of the data points to the line. | Grade 8 |
| New Jersey | 8.NS.A.2 | Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g., π²). | Grade 8 |
| New Jersey | A-APR.B.3 | Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial. | High School |
| New Jersey | A-CED.A.2 | Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. | High School |
| New Jersey | A-CED.A.3 | Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. | High School |
| New Jersey | A-REI.B.3 | Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. | High School |
| New Jersey | A-SSE.A.2 | Use the structure of an expression to identify ways to rewrite it. For example, see 𝑥⁴ – 𝑦⁴ as (𝑥²)² – (𝑦²)², thus recognizing it as a difference of squares that can be factored as (𝑥² – 𝑦²)(𝑥² + 𝑦²). | High School |
| New Jersey | A-SSE.B.3 | Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression. | High School |
| New Jersey | F-BF.A.1 | Write a function that describes a relationship between two quantities. | High School |
| New Jersey | F-IF.A.2 | Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. | High School |
| New Jersey | F-IF.B.4 | For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. | High School |
| New Jersey | F-IF.C.7 | Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. | High School |
| New Jersey | S-ID.B.6 | Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. | High School |
| New Mexico | K.CC.1 | Count to 100 by ones and by tens. | Kindergarten |
| New Mexico | K.CC.2 | Count forward beginning from a given number within the known sequence (instead of having to begin at 1). | Kindergarten |
| New Mexico | K.CC.3 | Write numbers from 0 to 20. Represent a number of objects with a written numeral 0-20 (with 0 representing a count of no objects). | Kindergarten |
| New Mexico | K.CC.4 | Understand the relationship between numbers and quantities; connect counting to cardinality. | Kindergarten |
| New Mexico | K.CC.5 | Count to answer “how many?” questions about as many as 20 things arranged in a line, a rectangular array, or a circle, or as many as 10 things in a scattered configuration; given a number from 1-20, count out that many objects. | Kindergarten |
| New Mexico | K.CC.6 | Identify whether the number of objects in one group is greater than, less than, or equal to the number of objects in another group, e.g., by using matching and counting strategies. | Kindergarten |
| New Mexico | K.CC.7 | Compare two numbers between 1 and 10 presented as written numerals. | Kindergarten |
| New Mexico | K.G.1 | Describe objects in the environment using names of shapes, and describe the relative positions of these objects using terms such as above, below, beside, in front of, behind, and next to. | Kindergarten |
| New Mexico | K.G.2 | Correctly name shapes regardless of their orientations or overall size. | Kindergarten |
| New Mexico | K.G.3 | Identify shapes as two-dimensional (lying in a plane, “flat”) or three-dimensional (“solid”). | Kindergarten |
| New Mexico | K.G.4 | Analyze and compare two- and three-dimensional shapes, in different sizes and orientations, using informal language to describe their similarities, differences, parts (e.g., number of sides and vertices/“corners”) and other attributes (e.g., having sides of equal length). | Kindergarten |
| New Mexico | K.G.6 | Compose simple shapes to form larger shapes. | Kindergarten |
| New Mexico | K.MD.1 | Describe measurable attributes of objects, such as length or weight. Describe several measurable attributes of a single object. | Kindergarten |
| New Mexico | K.MD.2 | Directly compare two objects with a measurable attribute in common, to see which object has “more of”/“less of” the attribute, and describe the difference. | Kindergarten |
| New Mexico | K.MD.3 | Classify objects into given categories; count the numbers of objects in each category and sort the categories by count. | Kindergarten |
| New Mexico | K.NBT.1 | Compose and decompose numbers from 11 to 19 into ten ones and some further ones, e.g., by using objects or drawings, and record each composition or decomposition by a drawing or equation (e.g., 18 = 10 + 8); understand that these numbers are composed of ten ones and one, two, three, four, five, six, seven, eight, or nine ones. | Kindergarten |
| New Mexico | K.OA.1 | Represent addition and subtraction with objects, fingers, mental images, drawings, sounds (e.g., claps), acting out situations, verbal explanations, expressions, or equations. | Kindergarten |
| New Mexico | K.OA.2 | Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem. | Kindergarten |
| New Mexico | K.OA.3 | Decompose numbers less than or equal to 10 into pairs in more than one way, e.g., by using objects or drawings, and record each decomposition by a drawing or equation (e.g., 5 = 2 + 3 and 5 = 4 + 1). | Kindergarten |
| New Mexico | K.OA.4 | For any number from 1 to 9, find the number that makes 10 when added to the given number, e.g., by using objects or drawings, and record the answer with a drawing or equation. | Kindergarten |
| New Mexico | K.OA.5 | Fluently add and subtract within 5. | Kindergarten |
| New Mexico | 1.G.1 | Distinguish between defining attributes (e.g., triangles are closed and three-sided) versus non-defining attributes (e.g., color, orientation, overall size); build and draw shapes to possess defining attributes. | Grade 1 |
| New Mexico | 1.G.2 | Compose two-dimensional shapes (rectangles, squares, trapezoids, triangles, half-circles, and quarter-circles) or three-dimensional shapes (cubes, right rectangular prisms, right circular cones, and right circular cylinders) to create a composite shape, and compose new shapes from the composite shape. | Grade 1 |
| New Mexico | 1.G.3 | Partition circles and rectangles into two and four equal shares, describe the shares using the words halves, fourths, and quarters, and use the phrases half of, fourth of, and quarter of. Describe the whole as two of, or four of the shares. Understand for these examples that decomposing into more equal shares creates smaller shares. | Grade 1 |
| New Mexico | 1.MD.1 | Order three objects by length; compare the lengths of two objects indirectly by using a third object. | Grade 1 |
| New Mexico | 1.MD.2 | Express the length of an object as a whole number of length units, by laying multiple copies of a shorter object (the length unit) end to end; understand that the length measurement of an object is the number of same-size length units that span it with no gaps or overlaps. | Grade 1 |
| New Mexico | 1.MD.3 | Tell and write time in hours and half-hours using analog and digital clocks. | Grade 1 |
| New Mexico | 1.MD.4 | Organize, represent, and interpret data with up to three categories; ask and answer questions about the total number of data points, how many in each category, and how many more or less are in one category than in another. | Grade 1 |
| New Mexico | 1.NBT.1 | Count to 120, starting at any number less than 120. In this range, read and write numerals and represent a number of objects with a written numeral. | Grade 1 |
| New Mexico | 1.NBT.2 | Understand that the two digits of a two-digit number represent amounts of tens and ones. | Grade 1 |
| New Mexico | 1.NBT.3 | Compare two two-digit numbers based on meanings of the tens and ones digits, recording the results of comparisons with the symbols >, =, and <. | Grade 1 |
| New Mexico | 1.NBT.4 | Add within 100, including adding a two-digit number and a one-digit number, and adding a two-digit number and a multiple of 10, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Understand that in adding two-digit numbers, one adds tens and tens, ones and ones; and sometimes it is necessary to compose a ten. | Grade 1 |
| New Mexico | 1.NBT.5 | Given a two-digit number, mentally find 10 more or 10 less than the number, without having to count; explain the reasoning used. | Grade 1 |
| New Mexico | 1.NBT.6 | Subtract multiples of 10 in the range 10-90 from multiples of 10 in the range 10-90 (positive or zero differences), using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. | Grade 1 |
| New Mexico | 1.OA.1 | Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem. | Grade 1 |
| New Mexico | 1.OA.3 | Apply properties of operations as strategies to add and subtract. | Grade 1 |
| New Mexico | 1.OA.4 | Understand subtraction as an unknown-addend problem. | Grade 1 |
| New Mexico | 1.OA.5 | Relate counting to addition and subtraction (e.g., by counting on 2 to add 2). | Grade 1 |
| New Mexico | 1.OA.6 | Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to a ten (e.g., 13 - 4 = 13 - 3 - 1 = 10 - 1 = 9); using the relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 - 8 = 4); and creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13). | Grade 1 |
| New Mexico | 1.OA.7 | Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false. | Grade 1 |
| New Mexico | 1.OA.8 | Determine the unknown whole number in an addition or subtraction equation relating three whole numbers. | Grade 1 |
| New Mexico | 2.G.1 | Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces. Identify triangles, quadrilaterals, pentagons, hexagons, and cubes. | Grade 2 |
| New Mexico | 2.G.2 | Partition a rectangle into rows and columns of same-size squares and count to find the total number of them. | Grade 2 |
| New Mexico | 2.G.3 | Partition circles and rectangles into two, three, or four equal shares, describe the shares using the words halves, thirds, half of, a third of, etc., and describe the whole as two halves, three thirds, four fourths. Recognize that equal shares of identical wholes need not have the same shape. | Grade 2 |
| New Mexico | 2.MD.1 | Measure the length of an object by selecting and using appropriate tools such as rulers, yardsticks, meter sticks, and measuring tapes. | Grade 2 |
| New Mexico | 2.MD.2 | Measure the length of an object twice, using length units of different lengths for the two measurements; describe how the two measurements relate to the size of the unit chosen. | Grade 2 |
| New Mexico | 2.MD.4 | Measure to determine how much longer one object is than another, expressing the length difference in terms of a standard length unit. | Grade 2 |
| New Mexico | 2.MD.5 | Use addition and subtraction within 100 to solve word problems involving lengths that are given in the same units, e.g., by using drawings (such as drawings of rulers) and equations with a symbol for the unknown number to represent the problem. | Grade 2 |
| New Mexico | 2.MD.7 | Tell and write time from analog and digital clocks to the nearest five minutes, using a.m. and p.m. | Grade 2 |
| New Mexico | 2.MD.8 | Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies, using $ and ¢ symbols appropriately. | Grade 2 |
| New Mexico | 2.MD.9 | Generate measurement data by measuring lengths of several objects to the nearest whole unit, or by making repeated measurements of the same object. Show the measurements by making a line plot, where the horizontal scale is marked off in whole-number units. | Grade 2 |
| New Mexico | 2.MD.10 | Draw a picture graph and a bar graph (with single-unit scale) to represent a data set with up to four categories. Solve simple put-together, take-apart, and compare problems using information presented in a bar graph. | Grade 2 |
| New Mexico | 2.NBT.1 | Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones. | Grade 2 |
| New Mexico | 2.NBT.2 | Count within 1000; skip-count by 5s, 10s, and 100s. | Grade 2 |
| New Mexico | 2.NBT.3 | Read and write numbers to 1000 using base-ten numerals, number names, and expanded form. | Grade 2 |
| New Mexico | 2.NBT.4 | Compare two three-digit numbers based on meanings of the hundreds, tens, and ones digits, using >, =, and < symbols to record the results of comparisons. | Grade 2 |
| New Mexico | 2.NBT.5 | Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction. | Grade 2 |
| New Mexico | 2.NBT.6 | Add up to four two-digit numbers using strategies based on place value and properties of operations. | Grade 2 |
| New Mexico | 2.NBT.7 | Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method. Understand that in adding or subtracting three-digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds. | Grade 2 |
| New Mexico | 2.NBT.8 | Mentally add 10 or 100 to a given number 100–900, and mentally subtract 10 or 100 from a given number 100–900. | Grade 2 |
| New Mexico | 2.OA.1 | Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem. | Grade 2 |
| New Mexico | 2.OA.2 | Fluently add and subtract within 20 using mental strategies. By end of Grade 2, know from memory all sums of two one-digit numbers. | Grade 2 |
| New Mexico | 2.OA.3 | Determine whether a group of objects (up to 20) has an odd or even number of members, e.g., by pairing objects or counting them by 2s; write an equation to express an even number as a sum of two equal addends. | Grade 2 |
| New Mexico | 2.OA.4 | Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends. | Grade 2 |
| New Mexico | 3.G.1 | Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories. | Grade 3 |
| New Mexico | 3.G.2 | Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole. | Grade 3 |
| New Mexico | 3.MD.1 | Tell and write time to the nearest minute and measure time intervals in minutes. Solve word problems involving addition and subtraction of time intervals in minutes, e.g., by representing the problem on a number line diagram. | Grade 3 |
| New Mexico | 3.MD.2 | Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l). Add, subtract, multiply, or divide to solve one-step word problems involving masses or volumes that are given in the same units, e.g., by using drawings (such as a beaker with a measurement scale) to represent the problem. | Grade 3 |
| New Mexico | 3.MD.3 | Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and two-step “how many more” and “how many less” problems using information presented in scaled bar graphs. | Grade 3 |
| New Mexico | 3.MD.4 | Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Show the data by making a line plot, where the horizontal scale is marked off in appropriate units-whole numbers, halves, or quarters. | Grade 3 |
| New Mexico | 3.MD.5 | Recognize area as an attribute of plane figures and understand concepts of area measurement. | Grade 3 |
| New Mexico | 3.MD.6 | Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units). | Grade 3 |
| New Mexico | 3.MD.7 | Relate area to the operations of multiplication and addition. | Grade 3 |
| New Mexico | 3.MD.8 | Solve real world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters. | Grade 3 |
| New Mexico | 3.NBT.1 | Use place value understanding to round whole numbers to the nearest 10 or 100. | Grade 3 |
| New Mexico | 3.NBT.2 | Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction. | Grade 3 |
| New Mexico | 3.NBT.3 | Multiply one-digit whole numbers by multiples of 10 in the range 10–90 (e.g., 9 × 80, 5 × 60) using strategies based on place value and properties of operations. | Grade 3 |
| New Mexico | 3.NF.1 | Understand a fraction 1/𝘣 as the quantity formed by 1 part when a whole is partitioned into 𝘣 equal parts; understand a fraction 𝘢/𝑏 as the quantity formed by 𝘢 parts of size 1/𝘣. | Grade 3 |
| New Mexico | 3.NF.2 | Understand a fraction as a number on the number line; represent fractions on a number line diagram. | Grade 3 |
| New Mexico | 3.NF.3 | Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size. | Grade 3 |
| New Mexico | 3.OA.1 | Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each. | Grade 3 |
| New Mexico | 3.OA.2 | Interpret whole-number quotients of whole numbers, e.g., interpret 56 ÷ 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each. | Grade 3 |
| New Mexico | 3.OA.3 | Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem. | Grade 3 |
| New Mexico | 3.OA.4 | Determine the unknown whole number in a multiplication or division equation relating three whole numbers. | Grade 3 |
| New Mexico | 3.OA.5 | Apply properties of operations as strategies to multiply and divide. | Grade 3 |
| New Mexico | 3.OA.6 | Understand division as an unknown-factor problem. | Grade 3 |
| New Mexico | 3.OA.7 | Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 × 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers. | Grade 3 |
| New Mexico | 3.OA.8 | Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. | Grade 3 |
| New Mexico | 3.OA.9 | Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations. | Grade 3 |
| New Mexico | 4.G.1 | Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures. | Grade 4 |
| New Mexico | 4.G.2 | Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles. | Grade 4 |
| New Mexico | 4.G.3 | Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify line-symmetric figures and draw lines of symmetry. | Grade 4 |
| New Mexico | 4.MD.1 | Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table. | Grade 4 |
| New Mexico | 4.MD.2 | Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. | Grade 4 |
| New Mexico | 4.MD.3 | Apply the area and perimeter formulas for rectangles in real world and mathematical problems. | Grade 4 |
| New Mexico | 4.MD.4 | Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots. | Grade 4 |
| New Mexico | 4.MD.5 | Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement. | Grade 4 |
| New Mexico | 4.MD.6 | Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure. | Grade 4 |
| New Mexico | 4.MD.7 | Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems, e.g., by using an equation with a symbol for the unknown angle measure. | Grade 4 |
| New Mexico | 4.NBT.1 | Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. | Grade 4 |
| New Mexico | 4.NBT.2 | Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. | Grade 4 |
| New Mexico | 4.NBT.3 | Use place value understanding to round multi-digit whole numbers to any place. | Grade 4 |
| New Mexico | 4.NBT.4 | Fluently add and subtract multi-digit whole numbers using the standard algorithm. | Grade 4 |
| New Mexico | 4.NBT.5 | Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. | Grade 4 |
| New Mexico | 4.NBT.6 | Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. | Grade 4 |
| New Mexico | 4.NF.1 | Explain why a fraction 𝘢/𝘣 is equivalent to a fraction (𝘯 × 𝘢)/(𝘯 × 𝘣) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. | Grade 4 |
| New Mexico | 4.NF.2 | Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model. | Grade 4 |
| New Mexico | 4.NF.3 | Understand a fraction 𝘢/𝘣 with 𝘢 > 1 as a sum of fractions 1/𝘣. | Grade 4 |
| New Mexico | 4.NF.4 | Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. | Grade 4 |
| New Mexico | 4.NF.5 | Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100. | Grade 4 |
| New Mexico | 4.NF.6 | Use decimal notation for fractions with denominators 10 or 100. | Grade 4 |
| New Mexico | 4.NF.7 | Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual model. | Grade 4 |
| New Mexico | 4.OA.1 | Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 × 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations. | Grade 4 |
| New Mexico | 4.OA.2 | Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison. | Grade 4 |
| New Mexico | 4.OA.3 | Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. | Grade 4 |
| New Mexico | 4.OA.4 | Find all factor pairs for a whole number in the range 1-100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1-100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1-100 is prime or composite. | Grade 4 |
| New Mexico | 4.OA.5 | Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. | Grade 4 |
| New Mexico | 5.G.1 | Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., 𝘹-axis and 𝘹-coordinate, 𝘺-axis and 𝘺-coordinate). | Grade 5 |
| New Mexico | 5.G.2 | Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. | Grade 5 |
| New Mexico | 5.G.3 | Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. | Grade 5 |
| New Mexico | 5.G.4 | Classify two-dimensional figures in a hierarchy based on properties. | Grade 5 |
| New Mexico | 5.MD.1 | Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. | Grade 5 |
| New Mexico | 5.MD.2 | Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. | Grade 5 |
| New Mexico | 5.MD.3 | Recognize volume as an attribute of solid figures and understand concepts of volume measurement. | Grade 5 |
| New Mexico | 5.MD.4 | Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. | Grade 5 |
| New Mexico | 5.MD.5 | Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume. | Grade 5 |
| New Mexico | 5.NBT.1 | Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. | Grade 5 |
| New Mexico | 5.NBT.2 | Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. | Grade 5 |
| New Mexico | 5.NBT.3 | Read, write, and compare decimals to thousandths. | Grade 5 |
| New Mexico | 5.NBT.4 | Use place value understanding to round decimals to any place. | Grade 5 |
| New Mexico | 5.NBT.5 | Fluently multiply multi-digit whole numbers using the standard algorithm. | Grade 5 |
| New Mexico | 5.NBT.6 | Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. | Grade 5 |
| New Mexico | 5.NBT.7 | Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. | Grade 5 |
| New Mexico | 5.NF.1 | Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. | Grade 5 |
| New Mexico | 5.NF.2 | Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. | Grade 5 |
| New Mexico | 5.NF.3 | Interpret a fraction as division of the numerator by the denominator (𝘢/𝘣 = 𝘢 ÷ 𝘣). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. | Grade 5 |
| New Mexico | 5.NF.4 | Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. | Grade 5 |
| New Mexico | 5.NF.5 | Interpret multiplication as scaling (resizing). | Grade 5 |
| New Mexico | 5.NF.6 | Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. | Grade 5 |
| New Mexico | 5.NF.7 | Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. | Grade 5 |
| New Mexico | 5.OA.1 | Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. | Grade 5 |
| New Mexico | 5.OA.2 | Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. | Grade 5 |
| New Mexico | 5.OA.3 | Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. | Grade 5 |
| New Mexico | 6.EE.1 | Write and evaluate numerical expressions involving whole-number exponents. | Grade 6 |
| New Mexico | 6.EE.2 | Write, read, and evaluate expressions in which letters stand for numbers. | Grade 6 |
| New Mexico | 6.EE.3 | Apply the properties of operations to generate equivalent expressions. | Grade 6 |
| New Mexico | 6.EE.4 | Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). | Grade 6 |
| New Mexico | 6.EE.5 | Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true. | Grade 6 |
| New Mexico | 6.EE.6 | Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set. | Grade 6 |
| New Mexico | 6.EE.7 | Solve real-world and mathematical problems by writing and solving equations of the form 𝘹 + 𝘱 = 𝘲 and 𝘱𝘹 = 𝘲 for cases in which 𝘱, 𝘲 and 𝘹 are all nonnegative rational numbers. | Grade 6 |
| New Mexico | 6.EE.8 | Write an inequality of the form 𝘹 > 𝘤 or 𝘹 𝘤 or 𝘹 < 𝘤 have infinitely many solutions; represent solutions of such inequalities on number line diagrams. | Grade 6 |
| New Mexico | 6.EE.9 | Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. | Grade 6 |
| New Mexico | 6.G.1 | Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems. | Grade 6 |
| New Mexico | 6.G.2 | Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas 𝘝 = 𝘭 𝘸 𝘩 and 𝘝 = 𝘣 𝘩 to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems. | Grade 6 |
| New Mexico | 6.G.3 | Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems. | Grade 6 |
| New Mexico | 6.G.4 | Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems. | Grade 6 |
| New Mexico | 6.RP.1 | Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. | Grade 6 |
| New Mexico | 6.RP.2 | Understand the concept of a unit rate 𝘢/𝘣 associated with a ratio 𝘢:𝘣 with 𝘣 ≠ 0, and use rate language in the context of a ratio relationship. | Grade 6 |
| New Mexico | 6.RP.3 | Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. | Grade 6 |
| New Mexico | 6.SP.5 | Summarize numerical data sets in relation to their context, such as by: | Grade 6 |
| New Mexico | 6.NS.1 | Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. | Grade 6 |
| New Mexico | 6.NS.2 | Fluently divide multi-digit numbers using the standard algorithm. | Grade 6 |
| New Mexico | 6.NS.3 | Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation. | Grade 6 |
| New Mexico | 6.NS.5 | Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation. | Grade 6 |
| New Mexico | 6.NS.6 | Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates. | Grade 6 |
| New Mexico | 6.NS.7 | Understand ordering and absolute value of rational numbers. | Grade 6 |
| New Mexico | 6.NS.8 | Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. | Grade 6 |
| New Mexico | 7.EE.1 | Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients. | Grade 7 |
| New Mexico | 7.EE.2 | Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. | Grade 7 |
| New Mexico | 7.EE.3 | Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. | Grade 7 |
| New Mexico | 7.EE.4 | Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. | Grade 7 |
| New Mexico | 7.G.1 | Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale. | Grade 7 |
| New Mexico | 7.G.2 | Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle. | Grade 7 |
| New Mexico | 7.G.3 | Describe the two-dimensional figures that result from slicing three-dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids. | Grade 7 |
| New Mexico | 7.G.4 | Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle. | Grade 7 |
| New Mexico | 7.G.5 | Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure. | Grade 7 |
| New Mexico | 7.G.6 | Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. | Grade 7 |
| New Mexico | 7.RP.1 | Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. | Grade 7 |
| New Mexico | 7.RP.2 | Recognize and represent proportional relationships between quantities. | Grade 7 |
| New Mexico | 7.RP.3 | Use proportional relationships to solve multistep ratio and percent problems. | Grade 7 |
| New Mexico | 7.NS.1 | Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram. | Grade 7 |
| New Mexico | 7.NS.2 | Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers. | Grade 7 |
| New Mexico | 7.NS.3 | Solve real-world and mathematical problems involving the four operations with rational numbers. | Grade 7 |
| New Mexico | 8.EE.1 | Know and apply the properties of integer exponents to generate equivalent numerical expressions. | Grade 8 |
| New Mexico | 8.EE.2 | Use square root and cube root symbols to represent solutions to equations of the form 𝘹² = 𝘱 and 𝘹³ = 𝘱, where 𝘱 is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that √2 is irrational. | Grade 8 |
| New Mexico | 8.EE.3 | Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other. | Grade 8 |
| New Mexico | 8.EE.4 | Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology. | Grade 8 |
| New Mexico | 8.EE.5 | Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. | Grade 8 |
| New Mexico | 8.EE.6 | Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation 𝘺 = 𝘮𝘹 for a line through the origin and the equation 𝘺 = 𝘮𝘹 + 𝘣 for a line intercepting the vertical axis at 𝘣. | Grade 8 |
| New Mexico | 8.EE.7 | Solve linear equations in one variable. | Grade 8 |
| New Mexico | 8.EE.8 | Analyze and solve pairs of simultaneous linear equations. | Grade 8 |
| New Mexico | 8.F.1 | Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output. | Grade 8 |
| New Mexico | 8.F.2 | Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). | Grade 8 |
| New Mexico | 8.F.3 | Interpret the equation 𝘺 = 𝘮𝘹 + 𝘣 as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. | Grade 8 |
| New Mexico | 8.F.4 | Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (𝘹, 𝘺) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values. | Grade 8 |
| New Mexico | 8.F.5 | Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally. | Grade 8 |
| New Mexico | 8.G.1 | Verify experimentally the properties of rotations, reflections, and translations. | Grade 8 |
| New Mexico | 8.G.2 | Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them. | Grade 8 |
| New Mexico | 8.G.3 | Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates. | Grade 8 |
| New Mexico | 8.G.4 | Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two-dimensional figures, describe a sequence that exhibits the similarity between them. | Grade 8 |
| New Mexico | 8.G.5 | Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. | Grade 8 |
| New Mexico | 8.G.7 | Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions. | Grade 8 |
| New Mexico | 8.G.8 | Apply the Pythagorean Theorem to find the distance between two points in a coordinate system. | Grade 8 |
| New Mexico | 8.G.9 | Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems. | Grade 8 |
| New Mexico | 8.SP.1 | Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association. | Grade 8 |
| New Mexico | 8.SP.2 | Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line. | Grade 8 |
| New Mexico | 8.NS.2 | Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g., π²). | Grade 8 |
| New Mexico | A-APR.3 | Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial. | High School |
| New Mexico | A-CED.2 | Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. | High School |
| New Mexico | A-CED.3 | Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context. | High School |
| New Mexico | A-REI.3 | Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. | High School |
| New Mexico | A-SSE.2 | Use the structure of an expression to identify ways to rewrite it. | High School |
| New Mexico | A-SSE.3 | Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression. | High School |
| New Mexico | F-BF.1 | Write a function that describes a relationship between two quantities. | High School |
| New Mexico | F-IF.2 | Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. | High School |
| New Mexico | F-IF.4 | For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. | High School |
| New Mexico | F-IF.7 | Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. | High School |
| New Mexico | S-ID.6 | Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. | High School |
| New York | NY-K.CC.1 | Count to 100 by ones and by tens. | Kindergarten |
| New York | NY-K.CC.2 | Count to 100 by ones beginning from any given number (instead of beginning at 1). | Kindergarten |
| New York | NY-K.CC.3 | Write numbers from 0 to 20. Represent a number of objects with a written numeral 0–20 (with 0 representing a count of no objects). | Kindergarten |
| New York | NY-K.CC.4 | Understand the relationship between numbers and quantities up to 20; connect counting to cardinality. | Kindergarten |
| New York | NY-K.CC.5a | Answer counting questions using as many as 20 objects arranged in a line, a rectangular array, and a circle. Answer counting questions using as many as 10 objects in a scattered configuration. | Kindergarten |
| New York | NY-K.CC.5b | Given a number from 1–20, count out that many objects. | Kindergarten |
| New York | NY-K.CC.6 | Identify whether the number of objects in one group is greater than (more than), less than (fewer than), or equal to (the same as) the number of objects in another group. | Kindergarten |
| New York | NY-K.CC.7 | Compare two numbers between 1 and 10 presented as written numerals. | Kindergarten |
| New York | NY-K.G.1 | Describe objects in the environment using names of shapes, and describe the relative positions of these objects using terms such as above, below, beside, in front of, behind, and next to. | Kindergarten |
| New York | NY-K.G.2 | Name shapes regardless of their orientation or overall size. | Kindergarten |
| New York | NY-K.G.3 | Understand the difference between two-dimensional (lying in a plane, “flat”) and three-dimensional (“solid”) shapes. | Kindergarten |
| New York | NY-K.G.4 | Analyze, compare, and sort two- and three-dimensional shapes, in different sizes and orientations, using informal language to describe their similarities, differences, parts, and other attributes. | Kindergarten |
| New York | NY-K.G.6 | Compose larger shapes from simple shapes. | Kindergarten |
| New York | NY-K.MD.1 | Describe measurable attributes of an object(s), such as length or weight, using appropriate vocabulary. | Kindergarten |
| New York | NY-K.MD.2 | Directly compare two objects with a common measurable attribute and describe the difference. | Kindergarten |
| New York | NY-K.MD.3 | Classify objects into given categories; count the objects in each category and sort the categories by count. | Kindergarten |
| New York | NY-K.MD.4 | Explore coins (pennies, nickels, dimes, and quarters) and begin identifying pennies and dimes. | Kindergarten |
| New York | NY-K.NBT.1 | Compose and decompose the numbers from 11 to 19 into ten ones and one, two, three, four, five, six, seven, eight, or nine ones. | Kindergarten |
| New York | NY-K.OA.1 | Represent addition and subtraction using objects, fingers, pennies, drawings, sounds, acting out situations, verbal explanations, expressions, equations, or other strategies. | Kindergarten |
| New York | NY-K.OA.2a | Add and subtract within 10. | Kindergarten |
| New York | NY-K.OA.2b | Solve addition and subtraction word problems within 10. | Kindergarten |
| New York | NY-K.OA.3 | Decompose numbers less than or equal to 10 into pairs in more than one way. Record each decomposition with a drawing or equation. | Kindergarten |
| New York | NY-K.OA.4 | Find the number that makes 10 when given a number from 1 to 9. Record the answer with a drawing or equation. | Kindergarten |
| New York | NY-K.OA.5 | Fluently add and subtract within 5. | Kindergarten |
| New York | NY-1.G.1 | Distinguish between defining attributes versus non-defining attributes for a wide variety of shapes. Build and/or draw shapes to possess defining attributes. | Grade 1 |
| New York | NY-1.G.2 | Compose two-dimensional shapes (rectangles, squares, trapezoids, triangles, half-circles, and quarter-circles) or three-dimensional shapes (cubes, right rectangular prisms, right circular cones, and right circular cylinders) to create a composite shape, and compose new shapes from the composite shape. | Grade 1 |
| New York | NY-1.G.3 | Partition circles and rectangles into two and four equal shares, describe the shares using the words halves, fourths, and quarters, and use the phrases half of, fourth of, and quarter of. Describe the whole as two of, or four of the shares. Understand for these examples that decomposing into more equal shares creates smaller shares. | Grade 1 |
| New York | NY-1.MD.1 | Order three objects by length; compare the lengths of two objects indirectly by using a third object. | Grade 1 |
| New York | NY-1.MD.2 | Measure the length of an object using same-size “length units” placed end to end with no gaps or overlaps. Express the length of an object as a whole number of “length units.” | Grade 1 |
| New York | NY-1.MD.3a | Tell and write time in hours and half-hours using analog and digital clocks. Develop an understanding of common terms, such as, but not limited to, o’clock and half past. | Grade 1 |
| New York | NY-1.MD.3b | Recognize and identify coins (penny, nickel, dime, and quarter) and their value and use the cent symbol (¢) appropriately. | Grade 1 |
| New York | NY-1.MD.3c | Count a mixed collection of dimes and pennies and determine the cent value (total not to exceed 100 cents). | Grade 1 |
| New York | NY-1.MD.4 | Organize, represent, and interpret data with up to three categories; ask and answer questions about the total number of data points, how many in each category, and how many more or less are in one category than in another. | Grade 1 |
| New York | NY-1.NBT.1 | Count to 120, starting at any number less than 120. In this range, read and write numerals and represent a number of objects with a written numeral. | Grade 1 |
| New York | NY-1.NBT.2 | Understand that the two digits of a two-digit number represent amounts of tens and ones. | Grade 1 |
| New York | NY-1.NBT.3 | Compare two two-digit numbers based on meanings of the tens and ones digits, recording the results of comparisons with the symbols >, =, and <. | Grade 1 |
| New York | NY-1.NBT.4 | Add within 100, including a two-digit number and a one-digit number; a two-digit number and a multiple of 10. Use concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction. Understand that in adding two-digit numbers, one adds tens and tens, ones and ones, and sometimes it is necessary to compose a ten. Relate the strategy to a written representation and explain the reasoning used. | Grade 1 |
| New York | NY-1.NBT.5 | Given a two-digit number, mentally find 10 more or 10 less than the number, without having to count; explain the reasoning used. | Grade 1 |
| New York | NY-1.NBT.6 | Subtract multiples of 10 from multiples of 10 in the range 10–90 using concrete models or drawings, and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction. Relate the strategy used to a written representation and explain the reasoning. | Grade 1 |
| New York | NY-1.OA.1 | Use addition and subtraction within 20 to solve one step word problems involving situations of adding to, taking from, putting together, taking apart, and/or comparing, with unknowns in all positions. | Grade 1 |
| New York | NY-1.OA.3 | Apply properties of operations as strategies to add and subtract. | Grade 1 |
| New York | NY-1.OA.4 | Understand subtraction as an unknown-addend problem within 20. | Grade 1 |
| New York | NY-1.OA.5 | Relate counting to addition and subtraction. | Grade 1 |
| New York | NY-1.OA.6a | Add and subtract within 20. Use strategies such as: | Grade 1 |
| New York | NY-1.OA.6b | Fluently add and subtract within 10. | Grade 1 |
| New York | NY-1.OA.7 | Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false. | Grade 1 |
| New York | NY-1.OA.8 | Determine the unknown whole number in an addition or subtraction equation with the unknown in all positions. | Grade 1 |
| New York | NY-2.G.2 | Partition a rectangle into rows and columns of same-size squares and count to find the total number of them. | Grade 2 |
| New York | NY-2.G.3 | Partition circles and rectangles into two, three, or four equal shares. Describe the shares using the words halves, thirds, half of, a third of, etc. Describe the whole as two halves, three thirds, four fourths. Recognize that equal shares of identical wholes need not have the same shape. | Grade 2 |
| New York | NY-2.MD.1 | Measure the length of an object to the nearest whole by selecting and using appropriate tools such as rulers, yardsticks, meter sticks, and measuring tapes. | Grade 2 |
| New York | NY-2.MD.2 | Measure the length of an object twice, using different “length units” for the two measurements; describe how the two measurements relate to the size of the unit chosen. | Grade 2 |
| New York | NY-2.MD.4 | Measure to determine how much longer one object is than another, expressing the length difference in terms of a standard “length unit.” | Grade 2 |
| New York | NY-2.MD.5 | Use addition and subtraction within 100 to solve word problems involving lengths that are given in the same units. | Grade 2 |
| New York | NY-2.MD.7 | Tell and write time from analog and digital clocks in five minute increments, using a.m. and p.m. Develop an understanding of common terms, such as, but not limited to, quarter past, half past, and quarter to. | Grade 2 |
| New York | NY-2.MD.8b | Solve real world and mathematical problems within one dollar involving quarters, dimes, nickels, and pennies, using the ¢ (cent) symbol appropriately. | Grade 2 |
| New York | NY-2.MD.9 | Generate measurement data by measuring lengths of several objects to the nearest whole unit, or by making repeated measurements of the same object. Present the measurement data in a line plot, where the horizontal scale is marked off in whole-number units. | Grade 2 |
| New York | NY-2.MD.10 | Draw a picture graph and a bar graph (with single-unit scale) to represent a data set with up to four categories. Solve simple put-together, take-apart, and compare problems using information presented in a picture graph or a bar graph. | Grade 2 |
| New York | NY-2.NBT.1 | Understand that the digits of a three-digit number represent amounts of hundreds, tens, and ones. | Grade 2 |
| New York | NY-2.NBT.2 | Count within 1000; skip-count by 5s, 10s, and 100s. | Grade 2 |
| New York | NY-2.NBT.3 | Read and write numbers to 1000 using base-ten numerals, number names, and expanded form. | Grade 2 |
| New York | NY-2.NBT.4 | Compare two three-digit numbers based on meanings of the hundreds, tens, and ones digits, using >, =, and < symbols to record the results of comparisons. | Grade 2 |
| New York | NY-2.NBT.5 | Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction. | Grade 2 |
| New York | NY-2.NBT.6 | Add up to four two-digit numbers using strategies based on place value and properties of operations. | Grade 2 |
| New York | NY-2.NBT.7a | Add and subtract within 1000, using concrete models or drawings, and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction. Relate the strategy to a written representation. | Grade 2 |
| New York | NY-2.NBT.7b | Understand that in adding or subtracting up to three-digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones, and sometimes it is necessary to compose or decompose tens or hundreds. | Grade 2 |
| New York | NY-2.NBT.8 | Mentally add 10 or 100 to a given number 100–900, and mentally subtract 10 or 100 from a given number 100–900. | Grade 2 |
| New York | NY-2.OA.1a | Use addition and subtraction within 100 to solve one-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions. | Grade 2 |
| New York | NY-2.OA.1b | Use addition and subtraction within 100 to develop an understanding of solving two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions. | Grade 2 |
| New York | NY-2.OA.2a | Fluently add and subtract within 20 using mental strategies. Strategies could include: | Grade 2 |
| New York | NY-2.OA.2b | Know from memory all sums within 20 of two one-digit numbers. | Grade 2 |
| New York | NY-2.OA.3a | Determine whether a group of objects (up to 20) has an odd or even number of members. | Grade 2 |
| New York | NY-2.OA.3b | Write an equation to express an even number as a sum of two equal addends. | Grade 2 |
| New York | NY-2.OA.4 | Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns. Write an equation to express the total as a sum of equal addends. | Grade 2 |
| New York | NY-3.G.1 | Recognize and classify polygons based on the number of sides and vertices (triangles, quadrilaterals, pentagons, and hexagons). Identify shapes that do not belong to one of the given subcategories. | Grade 3 |
| New York | NY-3.G.2 | Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole. | Grade 3 |
| New York | NY-3.MD.1 | Tell and write time to the nearest minute and measure time intervals in minutes. Solve one-step word problems involving addition and subtraction of time intervals in minutes. | Grade 3 |
| New York | NY-3.MD.2a | Measure and estimate liquid volumes and masses of objects using grams (g), kilograms (kg), and liters (l). | Grade 3 |
| New York | NY-3.MD.2b | Add, subtract, multiply, or divide to solve one-step word problems involving masses or liquid volumes that are given in the same units. | Grade 3 |
| New York | NY-3.MD.3 | Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and two-step “how many more” and “how many less” problems using information presented in a scaled picture graph or a scaled bar graph. | Grade 3 |
| New York | NY-3.MD.4 | Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Show the data by making a line plot where the horizontal scale is marked off in appropriate units—whole numbers, halves, or quarters. | Grade 3 |
| New York | NY-3.MD.5 | Recognize area as an attribute of plane figures and understand concepts of area measurement. | Grade 3 |
| New York | NY-3.MD.6 | Measure areas by counting unit squares. | Grade 3 |
| New York | NY-3.MD.7 | Relate area to the operations of multiplication and addition. | Grade 3 |
| New York | NY-3.MD.8a | Solve real world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths or finding one unknown side length given the perimeter and other side lengths. | Grade 3 |
| New York | NY-3.MD.8b | Identify rectangles with the same perimeter and different areas or with the same area and different perimeters. | Grade 3 |
| New York | NY-3.NBT.1 | Use place value understanding to round whole numbers to the nearest 10 or 100. | Grade 3 |
| New York | NY-3.NBT.2 | Fluently add and subtract within 1,000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction. | Grade 3 |
| New York | NY-3.NBT.3 | Multiply one-digit whole numbers by multiples of 10 in the range 10–90 using strategies based on place value and properties of operations. | Grade 3 |
| New York | NY-3.NF.1 | Understand a unit fraction, 1/𝘣, is the quantity formed by 1 part when a whole is partitioned into 𝘣 equal parts. Understand a fraction 𝘢/𝑏 as the quantity formed by 𝘢 parts of size 1/𝘣. | Grade 3 |
| New York | NY-3.NF.2 | Understand a fraction as a number on the number line; represent fractions on a number line. | Grade 3 |
| New York | NY-3.NF.3 | Explain equivalence of fractions and compare fractions by reasoning about their size. | Grade 3 |
| New York | NY-3.OA.1 | Interpret products of whole numbers. | Grade 3 |
| New York | NY-3.OA.2 | Interpret whole-number quotients of whole numbers. | Grade 3 |
| New York | NY-3.OA.3 | Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities. | Grade 3 |
| New York | NY-3.OA.4 | Determine the unknown whole number in a multiplication or division equation relating three whole numbers. | Grade 3 |
| New York | NY-3.OA.5 | Apply properties of operations as strategies to multiply and divide. | Grade 3 |
| New York | NY-3.OA.6 | Understand division as an unknown-factor problem. | Grade 3 |
| New York | NY-3.OA.7a | Fluently solve single-digit multiplication and related divisions, using strategies such as the relationship between multiplication and division or properties of operations. | Grade 3 |
| New York | NY-3.OA.7b | Know from memory all products of two one-digit numbers. | Grade 3 |
| New York | NY-3.OA.8 | Solve two-step word problems posed with whole numbers and having whole-number answers using the four operations. | Grade 3 |
| New York | NY-3.OA.9 | Identify and extend arithmetic patterns (including patterns in the addition table or multiplication table). | Grade 3 |
| New York | NY-4.G.1 | Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures. | Grade 4 |
| New York | NY-4.G.2a | Identify and name triangles based on angle size (right, obtuse, acute). | Grade 4 |
| New York | NY-4.G.2b | Identify and name all quadrilaterals with 2 pairs of parallel sides as parallelograms. | Grade 4 |
| New York | NY-4.G.2c | Identify and name all quadrilaterals with four right angles as rectangles. | Grade 4 |
| New York | NY-4.G.3 | Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify line-symmetric figures and draw lines of symmetry. | Grade 4 |
| New York | NY-4.MD.1.i | Know relative sizes of measurement units: ft., in.; km, m, cm. | Grade 4 |
| New York | NY-4.MD.1.ii | Know the conversion factor and use it to convert measurements in a larger unit in terms of a smaller unit: ft., in.; km, m, cm; hr., min., sec. | Grade 4 |
| New York | NY-4.MD.1.iii | Given the conversion factor, convert all other measurements within a single system of measurement from a larger unit to a smaller unit. | Grade 4 |
| New York | NY-4.MD.1.iv | Record measurement equivalents in a two-column table. | Grade 4 |
| New York | NY-4.MD.2 | Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money. | Grade 4 |
| New York | NY-4.MD.3 | Apply the area and perimeter formulas for rectangles in real world and mathematical problems. | Grade 4 |
| New York | NY-4.MD.4 | Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots. | Grade 4 |
| New York | NY-4.MD.5 | Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement. | Grade 4 |
| New York | NY-4.MD.6 | Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure. | Grade 4 |
| New York | NY-4.MD.7 | Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems. | Grade 4 |
| New York | NY-4.NBT.1 | Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. | Grade 4 |
| New York | NY-4.NBT.2a | Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. | Grade 4 |
| New York | NY-4.NBT.2b | Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. | Grade 4 |
| New York | NY-4.NBT.3 | Use place value understanding to round multi-digit whole numbers to any place. | Grade 4 |
| New York | NY-4.NBT.4 | Fluently add and subtract multi-digit whole numbers using a standard algorithm. | Grade 4 |
| New York | NY-4.NBT.5 | Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. | Grade 4 |
| New York | NY-4.NBT.6 | Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. | Grade 4 |
| New York | NY-4.NF.1 | Explain why a fraction 𝘢/𝘣 is equivalent to a fraction (𝘢 × 𝘯)/(𝘣 × 𝘯) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. | Grade 4 |
| New York | NY-4.NF.2 | Compare two fractions with different numerators and different denominators. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions. | Grade 4 |
| New York | NY-4.NF.3 | Understand a fraction 𝘢/𝘣 with 𝘢 > 1 as a sum of fractions 1/𝘣. | Grade 4 |
| New York | NY-4.NF.4 | Apply and extend previous understandings of multiplication to multiply a whole number by a fraction. | Grade 4 |
| New York | NY-4.NF.5 | Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100. | Grade 4 |
| New York | NY-4.NF.6 | Use decimal notation for fractions with denominators 10 or 100. | Grade 4 |
| New York | NY-4.NF.7 | Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when two decimals refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions. | Grade 4 |
| New York | NY-4.OA.1 | Interpret a multiplication equation as a comparison. Represent verbal statements of multiplicative comparisons as multiplication equations. | Grade 4 |
| New York | NY-4.OA.2 | Multiply or divide to solve word problems involving multiplicative comparison, distinguishing multiplicative comparison from additive comparison. Use drawings and equations with a symbol for the unknown number to represent the problem. | Grade 4 |
| New York | NY-4.OA.3 | Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. | Grade 4 |
| New York | NY-4.OA.4 | Find all factor pairs for a whole number in the range 1–100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1–100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1–100 is prime or composite. | Grade 4 |
| New York | NY-4.OA.5 | Generate a number or shape pattern that follows a given rule. Identify and informally explain apparent features of the pattern that were not explicit in the rule itself. | Grade 4 |
| New York | NY-5.G.1 | Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond. | Grade 5 |
| New York | NY-5.G.2 | Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. | Grade 5 |
| New York | NY-5.G.3 | Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. | Grade 5 |
| New York | NY-5.G.4 | Classify two-dimensional figures in a hierarchy based on properties. | Grade 5 |
| New York | NY-5.MD.1 | Convert among different-sized standard measurement units within a given measurement system when the conversion factor is given. Use these conversions in solving multi-step, real world problems. | Grade 5 |
| New York | NY-5.MD.2 | Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. | Grade 5 |
| New York | NY-5.MD.3 | Recognize volume as an attribute of solid figures and understand concepts of volume measurement. | Grade 5 |
| New York | NY-5.MD.4 | Measure volumes by counting unit cubes, using cubic cm, cubic in., cubic ft., and improvised units. | Grade 5 |
| New York | NY-5.MD.5 | Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume. | Grade 5 |
| New York | NY-5.NBT.1 | Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. | Grade 5 |
| New York | NY-5.NBT.2 | Use whole-number exponents to denote powers of 10. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. | Grade 5 |
| New York | NY-5.NBT.3 | Read, write, and compare decimals to thousandths. | Grade 5 |
| New York | NY-5.NBT.4 | Use place value understanding to round decimals to any place. | Grade 5 |
| New York | NY-5.NBT.5 | Fluently multiply multi-digit whole numbers using a standard algorithm. | Grade 5 |
| New York | NY-5.NBT.6 | Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. | Grade 5 |
| New York | NY-5.NBT.7 | Using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between operations: add and subtract decimals to hundredths; multiply and divide decimals to hundredths. Relate the strategy to a written method and explain the reasoning used. | Grade 5 |
| New York | NY-5.NF.1 | Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. | Grade 5 |
| New York | NY-5.NF.2 | Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. | Grade 5 |
| New York | NY-5.NF.3 | Interpret a fraction as division of the numerator by the denominator (𝘢/𝘣 = 𝘢 ÷ 𝘣). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers. | Grade 5 |
| New York | NY-5.NF.4 | Apply and extend previous understandings of multiplication to multiply a fraction by a whole number or a fraction. | Grade 5 |
| New York | NY-5.NF.5 | Interpret multiplication as scaling (resizing). | Grade 5 |
| New York | NY-5.NF.6 | Solve real world problems involving multiplication of fractions and mixed numbers. | Grade 5 |
| New York | NY-5.NF.7 | Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. | Grade 5 |
| New York | NY-5.OA.1 | Apply the order of operations to evaluate numerical expressions. | Grade 5 |
| New York | NY-5.OA.2 | Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. | Grade 5 |
| New York | NY-5.OA.3 | Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. | Grade 5 |
| New York | NY-6.EE.1 | Write and evaluate numerical expressions involving whole-number exponents. | Grade 6 |
| New York | NY-6.EE.2 | Write, read, and evaluate expressions in which letters stand for numbers. | Grade 6 |
| New York | NY-6.EE.3 | Apply the properties of operations to generate equivalent expressions. | Grade 6 |
| New York | NY-6.EE.4 | Identify when two expressions are equivalent. | Grade 6 |
| New York | NY-6.EE.5 | Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true. | Grade 6 |
| New York | NY-6.EE.6 | Use variables to represent numbers and write expressions when solving a real-world or mathematical problem. Understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set. | Grade 6 |
| New York | NY-6.EE.7 | Solve real-world and mathematical problems by writing and solving equations of the form 𝘹 + 𝘱 = 𝘲; 𝘹 – 𝘱 = 𝘲; 𝘱𝘹 = 𝘲; and 𝘹/𝘱 = 𝘲 for cases in which 𝘱, 𝘲, and 𝘹 are all nonnegative rational numbers. | Grade 6 |
| New York | NY-6.EE.8 | Write an inequality of the form 𝘹 > 𝘤, 𝘹 ≥ 𝘤, 𝘹 ≤ 𝘤, or 𝘹 < 𝘤 to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of these forms have infinitely many solutions; represent solutions of such inequalities on a number line. | Grade 6 |
| New York | NY-6.EE.9 | Use variables to represent two quantities in a real-world problem that change in relationship to one another. Given a verbal context and an equation, identify the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. | Grade 6 |
| New York | NY-6.G.1 | Find area of triangles, trapezoids, and other polygons by composing into rectangles or decomposing into triangles and quadrilaterals. Apply these techniques in the context of solving real-world and mathematical problems. | Grade 6 |
| New York | NY-6.G.2 | Find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems. | Grade 6 |
| New York | NY-6.G.3 | Draw polygons in the coordinate plane given coordinates for the vertices. Use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems. | Grade 6 |
| New York | NY-6.G.4 | Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems. | Grade 6 |
| New York | NY-6.RP.1 | Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. | Grade 6 |
| New York | NY-6.RP.2 | Understand the concept of a unit rate 𝘢/𝘣 associated with a ratio 𝘢:𝘣 with 𝘣 ≠ 0 (𝘣 not equal to zero), and use rate language in the context of a ratio relationship. | Grade 6 |
| New York | NY-6.RP.3 | Use ratio and rate reasoning to solve real-world and mathematical problems. | Grade 6 |
| New York | NY-6.SP.5 | Summarize quantitative data sets in relation to their context. | Grade 6 |
| New York | NY-6.NS.1 | Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions. | Grade 6 |
| New York | NY-6.NS.2 | Fluently divide multi-digit numbers using a standard algorithm. | Grade 6 |
| New York | NY-6.NS.3 | Fluently add, subtract, multiply, and divide multi-digit decimals using a standard algorithm for each operation. | Grade 6 |
| New York | NY-6.NS.5 | Understand that positive and negative numbers are used together to describe quantities having opposite directions or values. Use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation. | Grade 6 |
| New York | NY-6.NS.6 | Understand a rational number as a point on the number line. Use number lines and coordinate axes to represent points on a number line and in the coordinate plane with negative number coordinates. | Grade 6 |
| New York | NY-6.NS.7 | Understand ordering and absolute value of rational numbers. | Grade 6 |
| New York | NY-6.NS.8 | Solve real-world and mathematical problems by graphing points on a coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. | Grade 6 |
| New York | NY-7.EE.1 | Add, subtract, factor, and expand linear expressions with rational coefficients by applying the properties of operations. | Grade 7 |
| New York | NY-7.EE.2 | Understand that rewriting an expression in different forms in real-world and mathematical problems can reveal and explain how the quantities are related. | Grade 7 |
| New York | NY-7.EE.3 | Solve multi-step real-world and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate. Assess the reasonableness of answers using mental computation and estimation strategies. | Grade 7 |
| New York | NY-7.EE.4 | Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. | Grade 7 |
| New York | NY-7.G.1 | Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale. | Grade 7 |
| New York | NY-7.G.2 | Draw triangles when given measures of angles and/or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle. | Grade 7 |
| New York | NY-7.G.3 | Describe the two-dimensional shapes that result from slicing three-dimensional solids parallel or perpendicular to the base. | Grade 7 |
| New York | NY-7.G.4 | Apply the formulas for the area and circumference of a circle to solve problems. | Grade 7 |
| New York | NY-7.G.5 | Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure. | Grade 7 |
| New York | NY-7.G.6 | Solve real-world and mathematical problems involving area of two-dimensional objects composed of triangles and trapezoids. Solve surface area problems involving right prisms and right pyramids composed of triangles and trapezoids. Find the volume of right triangular prisms, and solve volume problems involving three-dimensional objects composed of right rectangular prisms. | Grade 7 |
| New York | NY-7.RP.1 | Compute unit rates associated with ratios of fractions. | Grade 7 |
| New York | NY-7.RP.2 | Recognize and represent proportional relationships between quantities. | Grade 7 |
| New York | NY-7.RP.3 | Use proportional relationships to solve multistep ratio and percent problems. | Grade 7 |
| New York | NY-7.NS.1 | Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers. Represent addition and subtraction on a horizontal or vertical number line. | Grade 7 |
| New York | NY-7.NS.2 | Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers. | Grade 7 |
| New York | NY-7.NS.3 | Solve real-world and mathematical problems involving the four operations with rational numbers. | Grade 7 |
| New York | NY-8.EE.1 | Know and apply the properties of integer exponents to generate equivalent numerical expressions. | Grade 8 |
| New York | NY-8.EE.2 | Use square root and cube root symbols to represent solutions to equations of the form 𝘹² = 𝘱 and 𝘹³ = 𝘱, where 𝘱 is a positive rational number. Know square roots of perfect squares up to 225 and cube roots of perfect cubes up to 125. Know that the square root of a non-perfect square is irrational. | Grade 8 |
| New York | NY-8.EE.3 | Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other. | Grade 8 |
| New York | NY-8.EE.4 | Perform multiplication and division with numbers expressed in scientific notation, including problems where both standard decimal form and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities. Interpret scientific notation that has been generated by technology. | Grade 8 |
| New York | NY-8.EE.5 | Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. | Grade 8 |
| New York | NY-8.EE.6 | Use similar triangles to explain why the slope 𝘮 is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation 𝘺 = 𝘮𝘹 for a line through the origin and the equation 𝘺 = 𝘮𝘹 + 𝘣 for a line intercepting the vertical axis at 𝘣. | Grade 8 |
| New York | NY-8.EE.7 | Solve linear equations in one variable. | Grade 8 |
| New York | NY-8.EE.8 | Analyze and solve pairs of simultaneous linear equations. | Grade 8 |
| New York | NY-8.F.1 | Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output. | Grade 8 |
| New York | NY-8.F.2 | Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). | Grade 8 |
| New York | NY-8.F.3 | Interpret the equation 𝘺 = 𝘮𝘹 + 𝘣 as defining a linear function, whose graph is a straight line. Recognize examples of functions that are linear and non-linear. | Grade 8 |
| New York | NY-8.F.4 | Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (𝘹, 𝘺) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values. | Grade 8 |
| New York | NY-8.F.5 | Describe qualitatively the functional relationship between two quantities by analyzing a graph. Sketch a graph that exhibits the qualitative features of a function that has been described in a real-world context. | Grade 8 |
| New York | NY-8.G.1 | Verify experimentally the properties of rotations, reflections, and translations. | Grade 8 |
| New York | NY-8.G.2 | Know that a two-dimensional figure is congruent to another if the corresponding angles are congruent and the corresponding sides are congruent. Equivalently, two two-dimensional figures are congruent if one is the image of the other after a sequence of rotations, reflections, and translations. Given two congruent figures, describe a sequence that maps the congruence between them on the coordinate plane. | Grade 8 |
| New York | NY-8.G.3 | Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates. | Grade 8 |
| New York | NY-8.G.4 | Know that a two-dimensional figure is similar to another if the corresponding angles are congruent and the corresponding sides are in proportion. Equivalently, two two-dimensional figures are similar if one is the image of the other after a sequence of rotations, reflections, translations, and dilations. Given two similar two-dimensional figures, describe a sequence that maps the similarity between them on the coordinate plane. | Grade 8 |
| New York | NY-8.G.5 | Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. | Grade 8 |
| New York | NY-8.G.7 | Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions. | Grade 8 |
| New York | NY-8.G.8 | Apply the Pythagorean Theorem to find the distance between two points in a coordinate system. | Grade 8 |
| New York | NY-8.G.9 | Given the formulas for the volume of cones, cylinders, and spheres, solve mathematical and real-world problems. | Grade 8 |
| New York | NY-8.SP.1 | Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association. | Grade 8 |
| New York | NY-8.SP.2 | Understand that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line. | Grade 8 |
| New York | NY-8.NS.2 | Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line, and estimate the value of expressions. | Grade 8 |
| New York | AI-A.SSE.2 | Recognize and use the structure of an expression to identify ways to rewrite it. | Algebra I |
| New York | AI-A.SSE.3 | Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression. | Algebra I |
| New York | AI-A.APR.3 | Identify zeros of polynomial functions when suitable factorizations are available. | Algebra I |
| New York | AI-A.CED.2 | Create equations and linear inequalities in two variables to represent a real-world context. | Algebra I |
| New York | AI-A.CED.3 | Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context. | Algebra I |
| New York | AI-A.REI.3 | Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. | Algebra I |
| New York | AI-F.IF.2 | Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. | Algebra I |
| New York | AI-F.IF.4 | For a function that models a relationship between two quantities: | Algebra I |
| New York | AI-F.IF.7 | Graph functions and show key features of the graph by hand and by using technology where appropriate. | Algebra I |
| New York | AI-F.BF.1 | Write a function that describes a relationship between two quantities. | Algebra I |
| New York | AI-S.ID.6 | Represent bivariate data on a scatter plot, and describe how the variables’ values are related. | Algebra I |
| North Carolina | NC.K.CC.1 | Know number names and recognize patterns in the counting sequence by: | Kindergarten |
| North Carolina | NC.K.CC.2 | Count forward beginning from a given number within the known sequence, instead of having to begin at 1. | Kindergarten |
| North Carolina | NC.K.CC.3 | Write numbers from 0 to 20. Represent a number of objects with a written numeral 0-20, with 0 representing a count of no objects. | Kindergarten |
| North Carolina | NC.K.CC.4 | Understand the relationship between numbers and quantities. | Kindergarten |
| North Carolina | NC.K.CC.5 | Count to answer “How many?” in the following situations: | Kindergarten |
| North Carolina | NC.K.CC.6 | Identify whether the number of objects, within 10, in one group is greater than, less than, or equal to the number of objects in another group, by using matching and counting strategies. | Kindergarten |
| North Carolina | NC.K.CC.7 | Compare two numbers, within 10, presented as written numerals. | Kindergarten |
| North Carolina | NC.K.G.1 | Describe objects in the environment using names of shapes, and describe the relative positions of objects using positional terms. | Kindergarten |
| North Carolina | NC.K.G.2 | Correctly name squares, circles, triangles, rectangles, hexagons, cubes, cones, cylinders, and spheres regardless of their orientations or overall size. | Kindergarten |
| North Carolina | NC.K.G.3 | Identify squares, circles, triangles, rectangles, hexagons, cubes, cones, cylinders, and spheres as two-dimensional or three-dimensional. | Kindergarten |
| North Carolina | NC.K.G.4 | Analyze and compare two- and three-dimensional shapes, in different sizes and orientations, using informal language to describe their similarities, differences, attributes and other properties. | Kindergarten |
| North Carolina | NC.K.G.6 | Compose larger shapes from simple shapes. | Kindergarten |
| North Carolina | NC.K.MD.1 | Describe measurable attributes of objects; and describe several different measurable attributes of a single object. | Kindergarten |
| North Carolina | NC.K.MD.2 | Directly compare two objects with a measurable attribute in common, to see which object has “more of”/“less of” the attribute, and describe the difference. | Kindergarten |
| North Carolina | NC.K.MD.3 | Classify objects into given categories; count the numbers of objects in each category and sort the categories by count. | Kindergarten |
| North Carolina | NC.K.NBT.1 | Compose and decompose numbers from 11 to 19 into ten ones and some further ones by: | Kindergarten |
| North Carolina | NC.K.OA.1 | Represent addition and subtraction, within 10: | Kindergarten |
| North Carolina | NC.K.OA.2 | Solve addition and subtraction word problems, within 10, using objects or drawings to represent the problem, when solving: | Kindergarten |
| North Carolina | NC.K.OA.3 | Decompose numbers less than or equal to 10 into pairs in more than one way using objects or drawings, and record each decomposition by a drawing or expression. | Kindergarten |
| North Carolina | NC.K.OA.4 | For any number from 0 to 10, find the number that makes 10 when added to the given number using objects or drawings, and record the answer with a drawing or expression. | Kindergarten |
| North Carolina | NC.K.OA.6 | Recognize and combine groups with totals up to 5 (conceptual subitizing). | Kindergarten |
| North Carolina | NC.K.OA.5 | Demonstrate fluency with addition and subtraction within 5. | Kindergarten |
| North Carolina | NC.1.G.1 | Distinguish between defining and non-defining attributes and create shapes with defining attributes by: | Grade 1 |
| North Carolina | NC.1.G.2 | Create composite shapes by: | Grade 1 |
| North Carolina | NC.1.G.3 | Partition circles and rectangles into two and four equal shares. | Grade 1 |
| North Carolina | NC.1.MD.1 | Order three objects by length; compare the lengths of two objects indirectly by using a third object. | Grade 1 |
| North Carolina | NC.1.MD.2 | Measure lengths with non-standard units. | Grade 1 |
| North Carolina | NC.1.MD.3 | Tell and write time in hours and half-hours using analog and digital clocks. | Grade 1 |
| North Carolina | NC.1.MD.5 | Identify quarters, dimes, and nickels and relate their values to pennies. | Grade 1 |
| North Carolina | NC.1.MD.4 | Organize, represent, and interpret data with up to three categories. | Grade 1 |
| North Carolina | NC.1.NBT.1 | Count to 150, starting at any number less than 150. | Grade 1 |
| North Carolina | NC.1.NBT.7 | Read and write numerals, and represent a number of objects with a written numeral, to 100. | Grade 1 |
| North Carolina | NC.1.NBT.2 | Understand that the two digits of a two-digit number represent amounts of tens and ones. | Grade 1 |
| North Carolina | NC.1.NBT.3 | Compare two two-digit numbers based on the value of the tens and ones digits, recording the results of comparisons with the symbols >, =, and <. | Grade 1 |
| North Carolina | NC.1.NBT.4 | Using concrete models or drawings, strategies based on place value, properties of operations, and explaining the reasoning used, add, within 100, in the following situations: | Grade 1 |
| North Carolina | NC.1.NBT.5 | Given a two-digit number, mentally find 10 more or 10 less than the number, without having to count; explain the reasoning used. | Grade 1 |
| North Carolina | NC.1.NBT.6 | Subtract multiples of 10 in the range 10-90 from multiples of 10 in the range 10-90, explaining the reasoning, using: | Grade 1 |
| North Carolina | NC.1.OA.3 | Apply the commutative and associative properties as strategies for solving addition problems. | Grade 1 |
| North Carolina | NC.1.OA.4 | Solve an unknown-addend problem, within 20, by using addition strategies and/or changing it to a subtraction problem. | Grade 1 |
| North Carolina | NC.1.OA.9 | Demonstrate fluency with addition and subtraction within 10. | Grade 1 |
| North Carolina | NC.1.OA.6 | Add and subtract, within 20, using strategies such as: | Grade 1 |
| North Carolina | NC.1.OA.7 | Apply understanding of the equal sign to determine if equations involving addition and subtraction are true. | Grade 1 |
| North Carolina | NC.1.OA.8 | Determine the unknown whole number in an addition or subtraction equation involving three whole numbers. | Grade 1 |
| North Carolina | NC.2.G.1 | Recognize and draw triangles, quadrilaterals, pentagons, and hexagons, having specified attributes; recognize and describe attributes of rectangular prisms and cubes. | Grade 2 |
| North Carolina | NC.2.G.3 | Partition circles and rectangles into two, three, or four equal shares. | Grade 2 |
| North Carolina | NC.2.MD.1 | Measure the length of an object in standard units by selecting and using appropriate tools such as rulers, yardsticks, meter sticks, and measuring tapes. | Grade 2 |
| North Carolina | NC.2.MD.2 | Measure the length of an object twice, using length units of different lengths for the two measurements; describe how the two measurements relate to the size of the unit chosen. | Grade 2 |
| North Carolina | NC.2.MD.4 | Measure to determine how much longer one object is than another, expressing the length difference in terms of a standard length unit. | Grade 2 |
| North Carolina | NC.2.MD.5 | Use addition and subtraction, within 100, to solve word problems involving lengths that are given in the same units, using equations with a symbol for the unknown number to represent the problem. | Grade 2 |
| North Carolina | NC.2.MD.7 | Tell and write time from analog and digital clocks to the nearest five minutes, using a.m. and p.m. | Grade 2 |
| North Carolina | NC.2.MD.8 | Solve word problems involving: | Grade 2 |
| North Carolina | NC.2.MD.10 | Organize, represent, and interpret data with up to four categories. | Grade 2 |
| North Carolina | NC.2.NBT.1 | Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones. | Grade 2 |
| North Carolina | NC.2.NBT.2 | Count within 1000; skip-count by 5s, 10s, and 100s. | Grade 2 |
| North Carolina | NC.2.NBT.3 | Read and write numbers, within 1000, using base-ten numerals, number names, and expanded form. | Grade 2 |
| North Carolina | NC.2.NBT.4 | Compare two three-digit numbers based on the value of the hundreds, tens, and ones digits, using >, =, and < symbols to record the results of comparisons. | Grade 2 |
| North Carolina | NC.2.NBT.5 | Demonstrate fluency with addition and subtraction, within 100, by: | Grade 2 |
| North Carolina | NC.2.NBT.6 | Add up to three two-digit numbers using strategies based on place value and properties of operations. | Grade 2 |
| North Carolina | NC.2.NBT.7 | Add and subtract, within 1000, relating the strategy to a written method, using: | Grade 2 |
| North Carolina | NC.2.NBT.8 | Mentally add 10 or 100 to a given number 100–900, and mentally subtract 10 or 100 from a given number 100–900. | Grade 2 |
| North Carolina | NC.2.OA.1 | Represent and solve addition and subtraction word problems, within 100, with unknowns in all positions, by using representations and equations with a symbol for the unknown number to represent the problem, when solving: | Grade 2 |
| North Carolina | NC.2.OA.2 | Demonstrate fluency with addition and subtraction, within 20, using mental strategies. | Grade 2 |
| North Carolina | NC.2.OA.3 | Determine whether a group of objects, within 20, has an odd or even number of members by: | Grade 2 |
| North Carolina | NC.2.OA.4 | Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends. | Grade 2 |
| North Carolina | NC.3.G.1 | Reason with two-dimensional shapes and their attributes. | Grade 3 |
| North Carolina | NC.3.MD.1 | Tell and write time to the nearest minute. Solve word problems involving addition and subtraction of time intervals within the same hour. | Grade 3 |
| North Carolina | NC.3.MD.2 | Solve problems involving customary measurement. | Grade 3 |
| North Carolina | NC.3.MD.3 | Represent and interpret scaled picture and bar graphs: | Grade 3 |
| North Carolina | NC.3.MD.5 | Find the area of a rectangle with whole-number side lengths by tiling without gaps or overlaps and counting unit squares. | Grade 3 |
| North Carolina | NC.3.MD.7 | Relate area to the operations of multiplication and addition. | Grade 3 |
| North Carolina | NC.3.MD.8 | Solve problems involving perimeters of polygons, including finding the perimeter given the side lengths, and finding an unknown side length. | Grade 3 |
| North Carolina | NC.3.NBT.2 | Add and subtract whole numbers up to and including 1,000. | Grade 3 |
| North Carolina | NC.3.NBT.3 | Use concrete and pictorial models, based on place value and the properties of operations, to find the product of a one-digit whole number by a multiple of 10 in the range 10–90. | Grade 3 |
| North Carolina | NC.3.NF.1 | Interpret unit fractions with denominators of 2, 3, 4, 6, and 8 as quantities formed when a whole is partitioned into equal parts. | Grade 3 |
| North Carolina | NC.3.NF.2 | Interpret fractions with denominators of 2, 3, 4, 6, and 8 using area and length models. | Grade 3 |
| North Carolina | NC.3.NF.3 | Represent equivalent fractions with area and length models by: | Grade 3 |
| North Carolina | NC.3.NF.4 | Compare two fractions with the same numerator or the same denominator by reasoning about their size, using area and length models, and using the >, <, and = symbols. Recognize that comparisons are valid only when the two fractions refer to the same whole with denominators: halves, fourths and eighths; thirds and sixths. | Grade 3 |
| North Carolina | NC.3.OA.1 | For products of whole numbers with two factors up to and including 10: | Grade 3 |
| North Carolina | NC.3.OA.2 | For whole-number quotients of whole numbers with a one-digit divisor and a one-digit quotient: | Grade 3 |
| North Carolina | NC.3.OA.3 | Represent, interpret, and solve one-step problems involving multiplication and division. | Grade 3 |
| North Carolina | NC.3.OA.6 | Solve an unknown-factor problem, by using division strategies and/or changing it to a multiplication problem. | Grade 3 |
| North Carolina | NC.3.OA.7 | Demonstrate fluency with multiplication and division with factors, quotients and divisors up to and including 10. | Grade 3 |
| North Carolina | NC.3.OA.8 | Solve two-step word problems using addition, subtraction, and multiplication, representing problems using equations with a symbol for the unknown number. | Grade 3 |
| North Carolina | NC.3.OA.9 | Interpret patterns of multiplication on a hundreds board and/or multiplication table. | Grade 3 |
| North Carolina | NC.4.G.1 | Draw and identify points, lines, line segments, rays, angles, and perpendicular and parallel lines. | Grade 4 |
| North Carolina | NC.4.G.2 | Classify quadrilaterals and triangles based on angle measure, side lengths, and the presence or absence of parallel or perpendicular lines. | Grade 4 |
| North Carolina | NC.4.G.3 | Recognize symmetry in a two-dimensional figure, and identify and draw lines of symmetry. | Grade 4 |
| North Carolina | NC.4.MD.1 | Know relative sizes of measurement units. Solve problems involving metric measurement. | Grade 4 |
| North Carolina | NC.4.MD.2 | Use multiplicative reasoning to convert metric measurements from a larger unit to a smaller unit using place value understanding, two-column tables, and length models. | Grade 4 |
| North Carolina | NC.4.MD.8 | Solve word problems involving addition and subtraction of time intervals that cross the hour. | Grade 4 |
| North Carolina | NC.4.MD.3 | Solve problems with area and perimeter. | Grade 4 |
| North Carolina | NC.4.MD.4 | Represent and interpret data using whole numbers. | Grade 4 |
| North Carolina | NC.4.MD.6 | Develop an understanding of angles and angle measurement. | Grade 4 |
| North Carolina | NC.4.NBT.1 | Explain that in a multi-digit whole number, a digit in one place represents 10 times as much as it represents in the place to its right, up to 100,000. | Grade 4 |
| North Carolina | NC.4.NBT.2 | Read and write multi-digit whole numbers up to and including 100,000 using numerals, number names, and expanded form. | Grade 4 |
| North Carolina | NC.4.NBT.7 | Compare two multi-digit numbers up to and including 100,000 based on the values of the digits in each place, using >, =, and < symbols to record the results of comparisons. | Grade 4 |
| North Carolina | NC.4.NBT.4 | Add and subtract multi-digit whole numbers up to and including 100,000 using the standard algorithm with place value understanding. | Grade 4 |
| North Carolina | NC.4.NBT.5 | Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm. | Grade 4 |
| North Carolina | NC.4.NBT.6 | Find whole-number quotients and remainders with up to three-digit dividends and one-digit divisors with place value understanding using rectangular arrays, area models, repeated subtraction, partial quotients, properties of operations, and/or the relationship between multiplication and division. | Grade 4 |
| North Carolina | NC.4.NF.1 | Explain why a fraction is equivalent to another fraction by using area and length fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. | Grade 4 |
| North Carolina | NC.4.NF.2 | Compare two fractions with different numerators and different denominators, using the denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions by: | Grade 4 |
| North Carolina | NC.4.NF.3 | Understand and justify decompositions of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100. | Grade 4 |
| North Carolina | NC.4.NF.4 | Apply and extend previous understandings of multiplication to: | Grade 4 |
| North Carolina | NC.4.NF.6 | Use decimal notation to represent fractions. | Grade 4 |
| North Carolina | NC.4.NF.7 | Compare two decimals to hundredths by reasoning about their size using area and length models, and recording the results of comparisons with the symbols >, =, or <. Recognize that comparisons are valid only when the two decimals refer to the same whole. | Grade 4 |
| North Carolina | NC.4.OA.1 | Interpret a multiplication equation as a comparison. Multiply or divide to solve word problems involving multiplicative comparisons using models and equations with a symbol for the unknown number. Distinguish multiplicative comparison from additive comparison. | Grade 4 |
| North Carolina | NC.4.OA.3 | Solve two-step word problems involving the four operations with whole numbers. | Grade 4 |
| North Carolina | NC.4.OA.4 | Find all factor pairs for whole numbers up to and including 50 to: | Grade 4 |
| North Carolina | NC.4.OA.5 | Generate and analyze a number or shape pattern that follows a given rule. | Grade 4 |
| North Carolina | NC.5.G.1 | Graph points in the first quadrant of a coordinate plane, and identify and interpret the x and y coordinates to solve problems. | Grade 5 |
| North Carolina | NC.5.G.3 | Classify quadrilaterals into categories based on their properties. | Grade 5 |
| North Carolina | NC.5.MD.1 | Given a conversion chart, use multiplicative reasoning to solve one-step conversion problems within a given measurement system. | Grade 5 |
| North Carolina | NC.5.MD.2 | Represent and interpret data. | Grade 5 |
| North Carolina | NC.5.MD.4 | Recognize volume as an attribute of solid figures and measure volume by counting unit cubes, using cubic centimeters, cubic inches, cubic feet, and improvised units. | Grade 5 |
| North Carolina | NC.5.MD.5 | Relate volume to the operations of multiplication and addition. | Grade 5 |
| North Carolina | NC.5.NBT.1 | Explain the patterns in the place value system from one million to the thousandths place. | Grade 5 |
| North Carolina | NC.5.NBT.3 | Read, write, and compare decimals to thousandths. | Grade 5 |
| North Carolina | NC.5.NBT.5 | Demonstrate fluency with the multiplication of two whole numbers up to a three-digit number by a two-digit number using the standard algorithm. | Grade 5 |
| North Carolina | NC.5.NBT.6 | Find quotients with remainders when dividing whole numbers with up to four-digit dividends and two-digit divisors using rectangular arrays, area models, repeated subtraction, partial quotients, and/or the relationship between multiplication and division. Use models to make connections and develop the algorithm. | Grade 5 |
| North Carolina | NC.5.NBT.7 | Compute and solve real-world problems with multi-digit whole numbers and decimal numbers. | Grade 5 |
| North Carolina | NC.5.NF.1 | Add and subtract fractions, including mixed numbers, with unlike denominators using related fractions: halves, fourths and eighths; thirds, sixths, and twelfths; fifths, tenths, and hundredths. | Grade 5 |
| North Carolina | NC.5.NF.3 | Use fractions to model and solve division problems. | Grade 5 |
| North Carolina | NC.5.NF.4 | Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction, including mixed numbers. | Grade 5 |
| North Carolina | NC.5.NF.7 | Solve one-step word problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions using area and length models, and equations to represent the problem. | Grade 5 |
| North Carolina | NC.5.OA.2 | Write, explain, and evaluate numerical expressions involving the four operations to solve up to two-step problems. Include expressions involving: | Grade 5 |
| North Carolina | NC.5.OA.3 | Generate two numerical patterns using two given rules. | Grade 5 |
| North Carolina | NC.6.EE.1 | Write and evaluate numerical expressions, with and without grouping symbols, involving whole-number exponents. | Grade 6 |
| North Carolina | NC.6.EE.2 | Write, read, and evaluate algebraic expressions. | Grade 6 |
| North Carolina | NC.6.EE.3 | Apply the properties of operations to generate equivalent expressions without exponents. | Grade 6 |
| North Carolina | NC.6.EE.4 | Identify when two expressions are equivalent and justify with mathematical reasoning. | Grade 6 |
| North Carolina | NC.6.EE.5 | Use substitution to determine whether a given number in a specified set makes an equation true. | Grade 6 |
| North Carolina | NC.6.EE.6 | Use variables to represent numbers and write expressions when solving a real-world or mathematical problem. | Grade 6 |
| North Carolina | NC.6.EE.7 | Solve real-world and mathematical problems by writing and solving equations of the form: | Grade 6 |
| North Carolina | NC.6.EE.8 | Reason about inequalities by: | Grade 6 |
| North Carolina | NC.6.EE.9 | Represent and analyze quantitative relationships by: | Grade 6 |
| North Carolina | NC.6.G.2 | Apply and extend previous understandings of the volume of a right rectangular prism to find the volume of right rectangular prisms with fractional edge lengths. Apply this understanding to the context of solving real-world and mathematical problems. | Grade 6 |
| North Carolina | NC.6.G.3 | Use the coordinate plane to solve real-world and mathematical problems by: | Grade 6 |
| North Carolina | NC.6.G.4 | Represent right prisms and right pyramids using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems. | Grade 6 |
| North Carolina | NC.6.RP.1 | Understand the concept of a ratio and use ratio language to: | Grade 6 |
| North Carolina | NC.6.RP.2 | Understand that ratios can be expressed as equivalent unit ratios by finding and interpreting both unit ratios in context. | Grade 6 |
| North Carolina | NC.6.NS.1 | Use visual models and common denominators to: | Grade 6 |
| North Carolina | NC.6.NS.2 | Fluently divide using long division with a minimum of a four-digit dividend and interpret the quotient and remainder in context. | Grade 6 |
| North Carolina | NC.6.NS.3 | Apply and extend previous understandings of decimals to develop and fluently use the standard algorithms for addition, subtraction, multiplication and division of decimals. | Grade 6 |
| North Carolina | NC.6.NS.5 | Understand and use rational numbers to: | Grade 6 |
| North Carolina | NC.6.NS.6 | Understand rational numbers as points on the number line and as ordered pairs on a coordinate plane. | Grade 6 |
| North Carolina | NC.6.NS.7 | Understand ordering of rational numbers. | Grade 6 |
| North Carolina | NC.6.NS.8 | Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. | Grade 6 |
| North Carolina | NC.7.EE.1 | Apply properties of operations as strategies to: | Grade 7 |
| North Carolina | NC.7.EE.2 | Understand that equivalent expressions can reveal real-world and mathematical relationships. Interpret the meaning of the parts of each expression in context. | Grade 7 |
| North Carolina | NC.7.EE.3 | Solve multi-step real-world and mathematical problems posed with rational numbers in algebraic expressions. | Grade 7 |
| North Carolina | NC.7.EE.4 | Use variables to represent quantities to solve real-world or mathematical problems. | Grade 7 |
| North Carolina | NC.7.G.1 | Solve problems involving scale drawings of geometric figures by: | Grade 7 |
| North Carolina | NC.7.G.2 | Understand the characteristics of angles and side lengths that create a unique triangle, more than one triangle or no triangle. Build triangles from three measures of angles and/or sides. | Grade 7 |
| North Carolina | NC.7.G.4 | Understand area and circumference of a circle. | Grade 7 |
| North Carolina | NC.7.G.5 | Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve equations for an unknown angle in a figure. | Grade 7 |
| North Carolina | NC.7.RP.1 | Compute unit rates associated with ratios of fractions to solve real-world and mathematical problems. | Grade 7 |
| North Carolina | NC.7.RP.2 | Recognize and represent proportional relationships between quantities. | Grade 7 |
| North Carolina | NC.7.RP.3 | Use scale factors and unit rates in proportional relationships to solve ratio and percent problems. | Grade 7 |
| North Carolina | NC.7.NS.1 | Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers, using the properties of operations, and describing real-world contexts using sums and differences. | Grade 7 |
| North Carolina | NC.7.NS.2 | Apply and extend previous understandings of multiplication and division. | Grade 7 |
| North Carolina | NC.7.NS.3 | Solve real-world and mathematical problems involving numerical expressions with rational numbers using the four operations. | Grade 7 |
| North Carolina | NC.8.EE.1 | Develop and apply the properties of integer exponents to generate equivalent numerical expressions. | Grade 8 |
| North Carolina | NC.8.EE.2 | Use square root and cube root symbols to represent solutions to equations of the form 𝘹² = 𝘱 and 𝘹³ = 𝘱, where 𝘱 is a positive rational number. Evaluate square roots of perfect squares and cube roots of perfect cubes for positive numbers less than or equal to 400. | Grade 8 |
| North Carolina | NC.8.EE.3 | Use numbers expressed in scientific notation to estimate very large or very small quantities and to express how many times as much one is than the other. | Grade 8 |
| North Carolina | NC.8.EE.4 | Perform multiplication and division with numbers expressed in scientific notation to solve real-world problems, including problems where both decimal and scientific notation are used. | Grade 8 |
| North Carolina | NC.8.EE.7 | Solve real-world and mathematical problems by writing and solving equations and inequalities in one variable. | Grade 8 |
| North Carolina | NC.8.EE.8 | Analyze and solve a system of two linear equations in two variables in slope-intercept form. | Grade 8 |
| North Carolina | NC.8.F.1 | Understand that a function is a rule that assigns to each input exactly one output. | Grade 8 |
| North Carolina | NC.8.F.2 | Compare properties of two linear functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). | Grade 8 |
| North Carolina | NC.8.F.3 | Identify linear functions from tables, equations, and graphs. | Grade 8 |
| North Carolina | NC.8.F.4 | Analyze functions that model linear relationships. | Grade 8 |
| North Carolina | NC.8.F.5 | Qualitatively analyze the functional relationship between two quantities. | Grade 8 |
| North Carolina | NC.8.G.2 | Use transformations to define congruence. | Grade 8 |
| North Carolina | NC.8.G.3 | Describe the effect of dilations about the origin, translations, rotations about the origin in 90 degree increments, and reflections across the x-axis and y-axis on two-dimensional figures using coordinates. | Grade 8 |
| North Carolina | NC.8.G.5 | Use informal arguments to analyze angle relationships. | Grade 8 |
| North Carolina | NC.8.G.7 | Apply the Pythagorean Theorem and its converse to solve real-world and mathematical problems. | Grade 8 |
| North Carolina | NC.8.G.8 | Apply the Pythagorean Theorem to find the distance between two points in a coordinate system. | Grade 8 |
| North Carolina | NC.8.G.9 | Understand how the formulas for the volumes of cones, cylinders, and spheres are related and use the relationship to solve real-world and mathematical problems. | Grade 8 |
| North Carolina | NC.8.SP.1 | Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Investigate and describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association. | Grade 8 |
| North Carolina | NC.8.SP.2 | Model the relationship between bivariate quantitative data to: | Grade 8 |
| North Carolina | NC.8.SP.3 | Use the equation of a linear model to solve problems in the context of bivariate quantitative data, interpreting the slope and y-intercept. | Grade 8 |
| North Carolina | NC.8.NS.2 | Use rational approximations of irrational numbers to compare the size of irrational numbers and locate them approximately on a number line. Estimate the value of expressions involving: | Grade 8 |
| North Carolina | NC.M1.A-CED.3 | Create systems of linear equations and inequalities to model situations in context. | Math 1 |
| North Carolina | NC.M1.A-REI.3 | Solve linear equations and inequalities in one variable. | Math 1 |
| North Dakota | K.CC.1.i | Count to 100 by ones and by tens. | Kindergarten |
| North Dakota | K.CC.2.i | Count forward beginning from a given number within 100. | Kindergarten |
| North Dakota | K.CC.3.i | Write numbers sequentially from 0 to 20. | Kindergarten |
| North Dakota | K.CC.3.ii | Write a given number from 0 to 20. | Kindergarten |
| North Dakota | K.CC.4 | Understand the relationship between numbers and quantities up to 20; connect counting to cardinality. | Kindergarten |
| North Dakota | K.CC.5 | Count to answer “how many?” questions. | Kindergarten |
| North Dakota | K.CC.6 | Identify whether the number of objects in one group is greater than, less than, or equal to the number of objects in another group, using groups of up to 10 objects. | Kindergarten |
| North Dakota | K.CC.7 | Compare two numbers between 1 and 10 presented as written numerals. | Kindergarten |
| North Dakota | K.G.1 | Describe objects in the environment using names of shapes and solids (squares, circles, triangles, rectangles, cubes, and spheres). | Kindergarten |
| North Dakota | K.G.2 | Correctly name shapes and solids (squares, circles, triangles, rectangles, cubes, and spheres) regardless of their orientations or overall size. | Kindergarten |
| North Dakota | K.G.3 | Identify shapes and solids (squares, circles, triangles, rectangles, cubes, and spheres) as two-dimensional or three-dimensional. | Kindergarten |
| North Dakota | K.G.4 | Compare and classify two-dimensional shapes (squares, circles, triangles, rectangles) of different sizes and orientations, using informal language to describe their similarities, differences, and attributes. | Kindergarten |
| North Dakota | K.G.6 | Compose a new shape by combining two or more simple shapes. | Kindergarten |
| North Dakota | K.MD.1.i | Describe measurable attributes of objects, such as length or weight. | Kindergarten |
| North Dakota | K.MD.1.ii | Describe several measurable attributes of a single object. | Kindergarten |
| North Dakota | K.MD.2 | Compare two objects with a common measurable attribute and describe the difference. | Kindergarten |
| North Dakota | K.MD.3.i | Classify objects into given categories limiting the number in each category to 10 or less. | Kindergarten |
| North Dakota | K.MD.3.ii | Count the numbers of objects in each category and sort the categories by count. | Kindergarten |
| North Dakota | K.NBT.1.i | Compose and decompose numbers from 11 to 19 using a group of ten ones and additional ones. | Kindergarten |
| North Dakota | K.NBT.1.ii | Record each composition or decomposition with a drawing or equation. | Kindergarten |
| North Dakota | K.OA.1 | Represent addition and subtraction in a variety of ways. | Kindergarten |
| North Dakota | K.OA.2 | Use an appropriate strategy to solve word problems that involve adding and subtracting within 10. | Kindergarten |
| North Dakota | K.OA.3.i | Decompose numbers less than or equal to 10 into multiple combinations of two parts. | Kindergarten |
| North Dakota | K.OA.3.ii | Record each decomposition with a drawing or equation. | Kindergarten |
| North Dakota | K.OA.4.i | Find the number that makes 10 when added to a given number from 1 to 9. | Kindergarten |
| North Dakota | K.OA.4.ii | Record with a drawing or equation. | Kindergarten |
| North Dakota | K.OA.5 | Fluently add and subtract within 5. | Kindergarten |
| North Dakota | 1.G.1.i | Distinguish between defining attributes versus non-defining attributes. | Grade 1 |
| North Dakota | 1.G.1.ii | Use defining attributes to build and draw two-dimensional shapes (squares, circles, triangles, rectangles, trapezoids, rhombuses, pentagons, hexagons, octagons). | Grade 1 |
| North Dakota | 1.G.2 | Compose a new shape or solid from two-dimensional shapes and/or three-dimensional solids (squares, circles, triangles, rectangles, trapezoids, rhombuses, pentagons, hexagons, octagons, cubes, spheres, cylinders, cones, triangular prisms, and rectangular prisms). | Grade 1 |
| North Dakota | 1.G.3.i | Partition circles and rectangles into two equal shares. | Grade 1 |
| North Dakota | 1.G.3.ii | Describe the shares using the word halves, and use the phrase half of. | Grade 1 |
| North Dakota | 1.G.3.iii | Describe the whole as two of the shares. | Grade 1 |
| North Dakota | 1.MD.1.i | Order three objects by length. | Grade 1 |
| North Dakota | 1.MD.1.ii | Compare the lengths of two objects indirectly by using a third object. | Grade 1 |
| North Dakota | 1.MD.2.i | Demonstrate understanding that the length measurement of an object is the number of same-size length units that span the object with no gaps or overlaps. | Grade 1 |
| North Dakota | 1.MD.2.ii | Measure and express the length of an object using whole non-standards units. | Grade 1 |
| North Dakota | 1.MD.3 | Tell and write time to the hour and half-hour (including o’clock and half past) using analog and digital clocks. | Grade 1 |
| North Dakota | 1.MD.4.i | Organize, represent, and interpret data with up to three categories. | Grade 1 |
| North Dakota | 1.MD.4.ii | Ask and answer questions about the total number of data points, how many in each category, and how many more or less are in one category than in another. | Grade 1 |
| North Dakota | 1.MD.5 | Identify and tell the value of a dollar bill, quarter, dime, nickel, and penny. | Grade 1 |
| North Dakota | 1.MD.6 | Count and tell the value of combinations of dimes and pennies up to one dollar. | Grade 1 |
| North Dakota | 1.NBT.1.i | Count forward and backward within 120, starting at any given number. | Grade 1 |
| North Dakota | 1.NBT.1.ii | Read and write numerals within 120. | Grade 1 |
| North Dakota | 1.NBT.1.iii | Represent a number of objects up to 120 with a written numeral. | Grade 1 |
| North Dakota | 1.NBT.2 | Demonstrate understanding that the two digits of a two-digit number represent amounts of tens and ones. | Grade 1 |
| North Dakota | 1.NBT.3 | Compare two two-digit numbers based on meanings of the tens and ones digits, recording the results of comparisons with the symbols >, =, and <. | Grade 1 |
| North Dakota | 1.NBT.4.i | Demonstrate understanding of place value when adding two-digit numbers within 100. | Grade 1 |
| North Dakota | 1.NBT.4.ii | Use concrete models or drawing strategies based on place value, properties of operations, and/or the relationship between addition and subtraction to add and subtract within 100. | Grade 1 |
| North Dakota | 1.NBT.4.iii | Relate the strategy to a written method and explain the reasoning used. | Grade 1 |
| North Dakota | 1.NBT.5 | Mentally add or subtract 10 to or from a given two-digit number. Explain the reasoning used. | Grade 1 |
| North Dakota | 1.NBT.6.i | Use concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction to subtract multiples of 10 in the range of 10-90 from multiples of 10 in the same range resulting in a positive or zero difference. | Grade 1 |
| North Dakota | 1.NBT.6.ii | Use a written method to explain the strategy. | Grade 1 |
| North Dakota | 1.OA.1 | Use strategies to add and subtract within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions. | Grade 1 |
| North Dakota | 1.OA.3 | Apply properties of operations as strategies to add and subtract. | Grade 1 |
| North Dakota | 1.OA.4 | Demonstrate understanding of subtraction as an unknown-addend problem. | Grade 1 |
| North Dakota | 1.OA.5 | Relate counting to addition and subtraction. | Grade 1 |
| North Dakota | 1.OA.6.i | Use strategies to add and subtract within 20. | Grade 1 |
| North Dakota | 1.OA.6.ii | Fluently add and subtract within 10. | Grade 1 |
| North Dakota | 1.OA.7 | Demonstrate understanding of the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false. | Grade 1 |
| North Dakota | 1.OA.8 | Determine the unknown whole number in an addition or subtraction equation that uses three whole numbers. | Grade 1 |
| North Dakota | 2.G.1.i | Identify trapezoids, rhombuses, pentagons, hexagons, octagons, parallelograms, quadrilaterals, cubes, spheres, cylinders, cones, triangular prisms, rectangular prisms. | Grade 2 |
| North Dakota | 2.G.1.ii | Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces. | Grade 2 |
| North Dakota | 2.G.2 | Partition a rectangle into rows and columns of same-size squares and count to find the total number. | Grade 2 |
| North Dakota | 2.G.3.i | Partition circles and rectangles into two, three, or four equal shares. | Grade 2 |
| North Dakota | 2.G.3.ii | Describe the shares using the words halves, thirds, half of, a third of, etc., and describe the whole as two halves, three thirds, four fourths. Recognize that identical wholes can be equally divided in different ways. | Grade 2 |
| North Dakota | 2.MD.1 | Select and use appropriate tools to measure the length of an object. | Grade 2 |
| North Dakota | 2.MD.2.i | Measure the length of an object using two different standard units of measurement. | Grade 2 |
| North Dakota | 2.MD.2.ii | Describe how the two measurements relate to the size of the units chosen. | Grade 2 |
| North Dakota | 2.MD.4 | Measure to determine how much longer one object is than another, expressing the difference with a standard unit of measurement. | Grade 2 |
| North Dakota | 2.MD.7 | Tell and write time to the nearest five minutes (including quarter after and quarter to) with a.m. and p.m. using analog and digital clocks. | Grade 2 |
| North Dakota | 2.MD.8 | Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies, using $ and ¢ symbols appropriately. | Grade 2 |
| North Dakota | 2.MD.9.i | Generate data by measuring lengths of objects to the nearest whole standard unit. | Grade 2 |
| North Dakota | 2.MD.9.ii | Show the measurements by making a line plot, using a horizontal scale marked off in whole-number units. | Grade 2 |
| North Dakota | 2.MD.10.i | Draw picture graphs and bar graphs with single-unit scales to represent data sets with up to four categories. | Grade 2 |
| North Dakota | 2.MD.10.ii | Solve simple put-together, take-apart, and compare problems using information presented in a bar graph. | Grade 2 |
| North Dakota | 2.NBT.1 | Demonstrate understanding that the three digits of a three-digit number represent amounts of hundreds, tens, and ones. | Grade 2 |
| North Dakota | 2.NBT.2.i | Count forward and backward from any given number within 1000. | Grade 2 |
| North Dakota | 2.NBT.2.ii | Skip-count by 5s, 10s, and 100s. | Grade 2 |
| North Dakota | 2.NBT.3 | Read and write numbers to 1000 using base-ten numerals, number names, and expanded form. | Grade 2 |
| North Dakota | 2.NBT.4 | Compare two three-digit numbers based on meanings of the hundreds, tens, and ones digits, recording the results of comparisons with the symbols >, =, and <. | Grade 2 |
| North Dakota | 2.NBT.5 | Use strategies based on place value, properties of operations, and/or the relationship between addition and subtraction to fluently add and subtract within 100. | Grade 2 |
| North Dakota | 2.NBT.6 | Use strategies based on place value and properties of operations to add up to four two-digit numbers. | Grade 2 |
| North Dakota | 2.NBT.7.i | Demonstrate understanding of place value within 1000 when adding and subtracting three-digit numbers. | Grade 2 |
| North Dakota | 2.NBT.7.ii | Use concrete models or drawings and strategies based on place value, properties of operation, and/or the relationship between addition and subtraction to add and subtract within 1000. | Grade 2 |
| North Dakota | 2.NBT.7.iii | Use a written method to explain the strategy. | Grade 2 |
| North Dakota | 2.NBT.8 | Mentally add or subtract 10 or 100 to or from a given number between 100 and 900. | Grade 2 |
| North Dakota | 2.OA.1 | Use strategies to add and subtract within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions. | Grade 2 |
| North Dakota | 2.OA.2 | Use mental strategies to fluently add and subtract within 20. | Grade 2 |
| North Dakota | 2.OA.3.i | Determine whether a given number of objects up to 20 is odd or even. | Grade 2 |
| North Dakota | 2.OA.3.ii | Write an equation to represent an even number using two equal addends or groups of 2. | Grade 2 |
| North Dakota | 2.OA.4.i | Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns. | Grade 2 |
| North Dakota | 2.OA.4.ii | Write an equation to express the total as a sum of equal addends. | Grade 2 |
| North Dakota | 3.G.1.i | Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals). | Grade 3 |
| North Dakota | 3.G.1.ii | Recognize rhombuses, rectangles, and squares as examples of quadrilaterals. | Grade 3 |
| North Dakota | 3.G.1.iii | Draw examples of quadrilaterals that do not belong to any of these subcategories. | Grade 3 |
| North Dakota | 3.G.2.i | Partition shapes into parts with equal areas. | Grade 3 |
| North Dakota | 3.G.2.ii | Express the area of each part as a unit fraction of the whole. | Grade 3 |
| North Dakota | 3.MD.1.i | Tell and write time to the nearest minute and measure time intervals in minutes. | Grade 3 |
| North Dakota | 3.MD.1.ii | Solve elapsed time word problems on the hour and the half hour, using a variety of strategies. | Grade 3 |
| North Dakota | 3.MD.2.i | Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l). | Grade 3 |
| North Dakota | 3.MD.2.ii | Add, subtract, multiply, or divide to solve one-step word problems involving masses or volumes that are given in the same units. | Grade 3 |
| North Dakota | 3.MD.3.i | Draw scaled picture graphs and scaled bar graphs to represent data sets with several categories. | Grade 3 |
| North Dakota | 3.MD.3.ii | Solve one- and two-step “how many more” and “how many less” problems using information presented in scaled bar graphs. | Grade 3 |
| North Dakota | 3.MD.4.i | Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. | Grade 3 |
| North Dakota | 3.MD.4.ii | Show the data by making a line plot, where the horizontal scale is marked in appropriate units—whole numbers, halves, or quarters. | Grade 3 |
| North Dakota | 3.MD.5 | Recognize area as an attribute of plane figures and understand concepts of area measurement. | Grade 3 |
| North Dakota | 3.MD.6 | Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units). | Grade 3 |
| North Dakota | 3.MD.7 | Relate area to the operations of multiplication and addition. | Grade 3 |
| North Dakota | 3.MD.8.i | Solve real world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths. | Grade 3 |
| North Dakota | 3.MD.8.ii | Find an unknown side length. | Grade 3 |
| North Dakota | 3.MD.8.iii | Exhibit rectangles with the same perimeter and different area or with the same area and different perimeters. | Grade 3 |
| North Dakota | 3.NF.1.i | Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts. | Grade 3 |
| North Dakota | 3.NF.1.ii | Understand a fraction a/b as the quantity formed by “a” parts of size 1/b. | Grade 3 |
| North Dakota | 3.NF.2 | Understand a fraction as a number on the number line; represent fractions on a number line diagram. | Grade 3 |
| North Dakota | 3.NF.3.i | Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size. | Grade 3 |
| North Dakota | 3.NF.3.ii | Recognize and generate simple equivalent fractions. | Grade 3 |
| North Dakota | 3.NBT.1 | Use place value understanding to round whole numbers to the nearest 10 or 100. | Grade 3 |
| North Dakota | 3.NBT.2 | Using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction, fluently add and subtract within 1000. | Grade 3 |
| North Dakota | 3.NBT.3 | Using strategies based on place value and properties of operations, multiply one-digit whole numbers by multiples of 10 in the range 10-90. | Grade 3 |
| North Dakota | 3.OA.1 | Interpret and model products of whole numbers. | Grade 3 |
| North Dakota | 3.OA.2 | Interpret and model whole-number quotients of whole numbers, as the number in a group or the number of groups. | Grade 3 |
| North Dakota | 3.OA.3 | Using drawings and equations with a symbol for an unknown number, solve multiplication and division word problems within 100 in situations involving equal groups, arrays, and measurement quantities. | Grade 3 |
| North Dakota | 3.OA.4 | Determine the unknown whole number in a multiplication or division equation relating three whole numbers. | Grade 3 |
| North Dakota | 3.OA.5 | Apply properties of operations as strategies to multiply and divide (without the use of formal terms). | Grade 3 |
| North Dakota | 3.OA.6 | Understand division as an unknown-factor problem. | Grade 3 |
| North Dakota | 3.OA.7 | Using mental strategies, fluently multiply and divide within 100. | Grade 3 |
| North Dakota | 3.OA.8.i | Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. | Grade 3 |
| North Dakota | 3.OA.8.ii | Assess the reasonableness of answers using mental computation and estimation strategies. | Grade 3 |
| North Dakota | 3.OA.9 | Identify arithmetic patterns, and explain them using properties of operations. | Grade 3 |
| North Dakota | 4.G.1.i | Draw and label points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. | Grade 4 |
| North Dakota | 4.G.1.ii | Identify these in two-dimensional figures. | Grade 4 |
| North Dakota | 4.G.2.i | Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of specified size. | Grade 4 |
| North Dakota | 4.G.2.ii | Recognize right triangles as a category, and identify right triangles. | Grade 4 |
| North Dakota | 4.G.3.i | Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. | Grade 4 |
| North Dakota | 4.G.3.ii | Identify line-symmetric figures. | Grade 4 |
| North Dakota | 4.G.3.iii | Draw lines of symmetry. | Grade 4 |
| North Dakota | 4.MD.1.i | Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb., oz.; l, ml; hr., min., sec. | Grade 4 |
| North Dakota | 4.MD.1.ii | Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. | Grade 4 |
| North Dakota | 4.MD.1.iii | Record measurement equivalents in a two-column table. | Grade 4 |
| North Dakota | 4.MD.2.i | Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. | Grade 4 |
| North Dakota | 4.MD.2.ii | Using diagrams such as number line diagrams that feature a measurement scale, to represent measurement quantities. | Grade 4 |
| North Dakota | 4.MD.3 | Apply the area and perimeter formulas for rectangles in real world and mathematical problems. | Grade 4 |
| North Dakota | 4.MD.4.i | Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). | Grade 4 |
| North Dakota | 4.MD.4.ii | Solve problems involving addition and subtraction of fractions by using information presented in line plots. | Grade 4 |
| North Dakota | 4.MD.5.i | Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint. | Grade 4 |
| North Dakota | 4.MD.5.ii | Understand concepts of angle measurement. | Grade 4 |
| North Dakota | 4.MD.6.i | Measure angles in whole-number degrees using a protractor. | Grade 4 |
| North Dakota | 4.MD.6.ii | Using a protractor and ruler, draw angles of a specified measure. | Grade 4 |
| North Dakota | 4.MD.7.i | Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. | Grade 4 |
| North Dakota | 4.MD.7.ii | Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems. | Grade 4 |
| North Dakota | 4.NBT.1 | Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. | Grade 4 |
| North Dakota | 4.NBT.2.i | Read and write multi-digit whole numbers to the one millions place using base-ten numerals, word form, and expanded form. | Grade 4 |
| North Dakota | 4.NBT.2.ii | Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. | Grade 4 |
| North Dakota | 4.NBT.3 | Use place value and/or understanding of numbers to round multi-digit whole numbers to any place. | Grade 4 |
| North Dakota | 4.NBT.4 | Fluently add and subtract multi-digit whole numbers to the one millions place using strategies flexibly, including the standard algorithm. | Grade 4 |
| North Dakota | 4.NBT.5.i | Using strategies based on place value and the properties of operations, multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers. | Grade 4 |
| North Dakota | 4.NBT.5.ii | Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. | Grade 4 |
| North Dakota | 4.NBT.6.i | Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. | Grade 4 |
| North Dakota | 4.NBT.6.ii | Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. | Grade 4 |
| North Dakota | 4.NF.1.i | Using visual fraction models, explain why a fraction 𝘢/𝘣 is equivalent to a fraction (𝘯 × 𝘢)/(𝘯 × 𝘣). Use this principle to recognize and generate equivalent fractions. | Grade 4 |
| North Dakota | 4.NF.1.ii | Attention should focus on how the number and size of the parts differ even though the two fractions themselves are the same size. | Grade 4 |
| North Dakota | 4.NF.2.i | By creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2, compare two fractions with different numerators and different denominators. | Grade 4 |
| North Dakota | 4.NF.2.ii | Recognize that comparisons are valid only when the two fractions refer to the same whole. | Grade 4 |
| North Dakota | 4.NF.2.iii | Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model. | Grade 4 |
| North Dakota | 4.NF.3 | Understand a fraction 𝑎/𝑏 with 𝑎 > 1 as a sum of unit fractions 1/𝑏. | Grade 4 |
| North Dakota | 4.NF.4 | Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. | Grade 4 |
| North Dakota | 4.NF.5.i | Express a fraction with denominator 10 as an equivalent fraction with denominator 100. | Grade 4 |
| North Dakota | 4.NF.5.ii | Use this technique to add two fractions with respective denominators 10 and 100. | Grade 4 |
| North Dakota | 4.NF.6 | Use decimal notation for fractions with denominators 10 or 100. | Grade 4 |
| North Dakota | 4.NF.7.i | Compare two decimals to hundredths by reasoning about their size. | Grade 4 |
| North Dakota | 4.NF.7.ii | Recognize that comparisons are valid only when the two decimals refer to the same whole. | Grade 4 |
| North Dakota | 4.NF.7.iii | Record the results of comparisons with the symbols >, =, or <, and justify the conclusions. | Grade 4 |
| North Dakota | 4.OA.1.i | Interpret a multiplication equation as a comparison. | Grade 4 |
| North Dakota | 4.OA.1.ii | Represent verbal statements of multiplicative comparisons as multiplication equations. | Grade 4 |
| North Dakota | 4.OA.2.i | Use drawings and equations with a symbol for the unknown number (variable) to represent the problem. | Grade 4 |
| North Dakota | 4.OA.2.ii | Multiply or divide to solve word problems involving multiplicative comparison, distinguishing multiplicative comparison from additive comparison. | Grade 4 |
| North Dakota | 4.OA.3.i | Solve multistep word problems posed with whole numbers and having whole number answers using the four operations, including problems in which remainders must be interpreted. | Grade 4 |
| North Dakota | 4.OA.3.ii | Represent these problems using equations with a letter standing for the unknown quantity (variable). | Grade 4 |
| North Dakota | 4.OA.3.iii | Assess the reasonableness of answers using mental computation and estimation strategies including rounding. | Grade 4 |
| North Dakota | 4.OA.4.i | Find all factor pairs for a whole number in the range 1-36. | Grade 4 |
| North Dakota | 4.OA.4.ii | Recognize that a whole number is a multiple of each of its factors. | Grade 4 |
| North Dakota | 4.OA.4.iii | Determine whether a given whole number in the range 1-36 is a multiple of a given one-digit number. | Grade 4 |
| North Dakota | 4.OA.4.iv | Determine whether a given whole number in the range 1-36 is prime or composite. | Grade 4 |
| North Dakota | 4.OA.5.i | Generate a number or shape pattern that follows a given rule. | Grade 4 |
| North Dakota | 4.OA.5.ii | Identify apparent features of the pattern that were not explicit in the rule itself. | Grade 4 |
| North Dakota | 5.G.1.i | Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. | Grade 5 |
| North Dakota | 5.G.1.ii | Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (x-coordinate and x-axis, y-coordinate and y-axis). | Grade 5 |
| North Dakota | 5.G.2.i | Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane. | Grade 5 |
| North Dakota | 5.G.2.ii | Interpret coordinate values of points in the context of the situation. | Grade 5 |
| North Dakota | 5.G.3 | Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. | Grade 5 |
| North Dakota | 5.G.4 | Classify two-dimensional figures in a hierarchy based on properties. | Grade 5 |
| North Dakota | 5.MD.1.i | Convert among different-sized standard measurement units within a given measurement system. | Grade 5 |
| North Dakota | 5.MD.1.ii | Use these conversions in solving multi-step, real world problems. | Grade 5 |
| North Dakota | 5.MD.2.i | Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). | Grade 5 |
| North Dakota | 5.MD.2.ii | Use operations on fractions for this grade to solve problems involving information presented in line plots. | Grade 5 |
| North Dakota | 5.MD.3 | Recognize volume as an attribute of solid figures and understand concepts of volume measurement. | Grade 5 |
| North Dakota | 5.MD.4 | Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft., and improvised units. | Grade 5 |
| North Dakota | 5.MD.5 | Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume. | Grade 5 |
| North Dakota | 5.NF.1 | Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. | Grade 5 |
| North Dakota | 5.NF.2.i | Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, by using visual fraction models and equations to represent the problem. | Grade 5 |
| North Dakota | 5.NF.2.ii | Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. | Grade 5 |
| North Dakota | 5.NF.3.i | Interpret a fraction as division of the numerator by the denominator (𝑎/𝑏 = 𝑎 ÷ 𝑏). | Grade 5 |
| North Dakota | 5.NF.3.ii | Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers by using visual fraction models and equations to represent the problem. | Grade 5 |
| North Dakota | 5.NF.4 | Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. | Grade 5 |
| North Dakota | 5.NF.5 | Interpret multiplication as scaling (resizing). | Grade 5 |
| North Dakota | 5.NF.6 | Solve real world problems involving multiplication of fractions and mixed numbers using visual fraction models and equations to represent the problem. | Grade 5 |
| North Dakota | 5.NF.7 | Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. | Grade 5 |
| North Dakota | 5.NBT.1 | Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. | Grade 5 |
| North Dakota | 5.NBT.2.i | Explain patterns in the number of zeros of the product when multiplying a number by powers of 10. | Grade 5 |
| North Dakota | 5.NBT.2.ii | Explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. | Grade 5 |
| North Dakota | 5.NBT.2.iii | Use whole-number exponents to denote powers of 10. | Grade 5 |
| North Dakota | 5.NBT.3 | Read, write, and compare decimals to thousandths. | Grade 5 |
| North Dakota | 5.NBT.4 | Use place value understanding to round decimals to any place. | Grade 5 |
| North Dakota | 5.NBT.5 | Fluently multiply multi-digit whole numbers using strategies flexibly, including the standard algorithm. | Grade 5 |
| North Dakota | 5.NBT.6.i | Using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division, find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors. | Grade 5 |
| North Dakota | 5.NBT.6.ii | Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. | Grade 5 |
| North Dakota | 5.NBT.7.i | Using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction, add, subtract, multiply, and divide decimals to hundredths. | Grade 5 |
| North Dakota | 5.NBT.7.ii | Relate the strategy to a written method and explain the reasoning used. | Grade 5 |
| North Dakota | 5.OA.1 | Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. | Grade 5 |
| North Dakota | 5.OA.2.i | Write simple expressions that record calculations with numbers. | Grade 5 |
| North Dakota | 5.OA.2.ii | Interpret numerical expressions without evaluating them. | Grade 5 |
| North Dakota | 5.OA.3.i | Generate two numerical patterns using two given rules. | Grade 5 |
| North Dakota | 5.OA.3.ii | Identify apparent relationships between corresponding terms. | Grade 5 |
| North Dakota | 5.OA.3.iii | Form ordered pairs consisting of corresponding terms from the two patterns. | Grade 5 |
| North Dakota | 5.OA.3.iv | Graph the ordered pairs on a coordinate plane. | Grade 5 |
| North Dakota | 5.OA.4.i | Find all factor pairs for a whole number in the range 1-100. | Grade 5 |
| North Dakota | 5.OA.4.iii | Determine whether a given whole number in the range 1-100 is a multiple of a given one-digit number. | Grade 5 |
| North Dakota | 5.OA.4.iv | Determine whether a given whole number in the range 1-100 is prime or composite. | Grade 5 |
| North Dakota | 6.EE.1 | Write and evaluate numerical expressions involving whole-number exponents. | Grade 6 |
| North Dakota | 6.EE.2 | Write, read, and evaluate expressions in which letters stand for numbers. | Grade 6 |
| North Dakota | 6.EE.3 | Apply the properties of operations to generate equivalent expressions. | Grade 6 |
| North Dakota | 6.EE.4 | Identify when two expressions are equivalent. | Grade 6 |
| North Dakota | 6.EE.5.i | Understand solving an equation or inequality as a process of answering a question: Which values from a specified set, if any, make the equation or inequality true? | Grade 6 |
| North Dakota | 6.EE.5.ii | Use substitution to determine whether a given number in a specified set makes an equation or inequality true. | Grade 6 |
| North Dakota | 6.EE.6.i | Use variables to represent numbers and write expressions when solving a real world or mathematical problem. | Grade 6 |
| North Dakota | 6.EE.6.ii | Understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set. | Grade 6 |
| North Dakota | 6.EE.7 | Solve real world and mathematical problems by writing and solving equations of the form 𝑥 + 𝑝 = 𝑞 and 𝑝𝑥 = 𝑞 for cases in which 𝑝, 𝑞 and 𝑥 are all nonnegative rational numbers. | Grade 6 |
| North Dakota | 6.EE.8.i | Write a statement of inequality of the form 𝑥 > 𝑐 or the form 𝑥 < 𝑐 to represent a constraint or condition in a real world or mathematical problem. | Grade 6 |
| North Dakota | 6.EE.8.ii | Recognize that inequalities of the form 𝑥 > 𝑐 or the form 𝑥 < 𝑐 have infinitely many solutions; represent solutions of such inequalities on number line diagrams. | Grade 6 |
| North Dakota | 6.EE.9.i | Use variables to represent two quantities in a real world problem that change in relationship to one another. | Grade 6 |
| North Dakota | 6.EE.9.ii | Write an equation to express one quantity (dependent variable) in terms of the other quantity (independent variable). | Grade 6 |
| North Dakota | 6.EE.9.iii | Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. | Grade 6 |
| North Dakota | 6.G.1.i | Based on prior knowledge of area of rectangles, decompose or compose triangles to find the area of a triangle. | Grade 6 |
| North Dakota | 6.G.1.ii | Using knowledge of area of triangles and rectangles, compose and/or decompose triangles, special quadrilaterals, and polygons to find their areas. | Grade 6 |
| North Dakota | 6.G.1.iii | Apply these techniques in the context of solving real world mathematical problems. | Grade 6 |
| North Dakota | 6.G.2.i | Using cubes of an appropriate size, pack a right rectangular prism having fractional edge lengths to find its volume. Then show that the volume is the same as would be found by multiplying the edge lengths of the prism. | Grade 6 |
| North Dakota | 6.G.2.ii | Apply the formulas 𝑉 = 𝑙𝑤ℎ and 𝑉= 𝐵ℎ to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real world and mathematical problems. | Grade 6 |
| North Dakota | 6.G.3.i | Draw polygons in the coordinate plane given coordinates for the vertices. | Grade 6 |
| North Dakota | 6.G.3.ii | Use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. | Grade 6 |
| North Dakota | 6.G.3.iii | Apply these techniques in the context of solving real world and mathematical problems. | Grade 6 |
| North Dakota | 6.G.4.i | Represent three-dimensional figures using nets made up of rectangles and triangles (right prisms and pyramids whose bases are triangles and rectangles). | Grade 6 |
| North Dakota | 6.G.4.ii | Use the nets to find the surface area of these figures. | Grade 6 |
| North Dakota | 6.G.4.iii | Apply these techniques in the context of solving real world and mathematical problems. | Grade 6 |
| North Dakota | 6.RP.1 | Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. | Grade 6 |
| North Dakota | 6.RP.2 | Understand the concept of a unit rate 𝑎/𝑏 associated with a ratio 𝑎:𝑏 with 𝑏 ≠ 0, and use rate language in the context of a ratio relationship. | Grade 6 |
| North Dakota | 6.RP.3 | Use tables of equivalent ratios, tape diagrams, double number line diagrams, and equations to reason about ratios and rates in real world and mathematical problems. | Grade 6 |
| North Dakota | 6.SP.5 | Summarize numerical data sets in relation to their context by: | Grade 6 |
| North Dakota | 6.NS.1.i | Use visual fraction models and equations to interpret and compute quotients of fractions. | Grade 6 |
| North Dakota | 6.NS.1.ii | Use models and equations to solve word problems involving division of fractions by fractions. | Grade 6 |
| North Dakota | 6.NS.2 | Fluently divide multi-digit numbers using strategies flexibly, including the standard algorithm. | Grade 6 |
| North Dakota | 6.NS.3 | Fluently add, subtract, multiply, and divide multi-digit decimals using strategies flexibly, including the standard algorithm for each operation. | Grade 6 |
| North Dakota | 6.NS.5.i | Understand that rational numbers are used together to describe quantities having opposite directions or values (may include temperature above/below zero, elevation above/below sea level, debits/credits, positive/negative electric charge, etc.). | Grade 6 |
| North Dakota | 6.NS.5.ii | Use rational numbers to represent quantities in real world contexts, explaining the meaning of 0 in each situation. | Grade 6 |
| North Dakota | 6.NS.6.i | Understand a rational number as a point on the number line. | Grade 6 |
| North Dakota | 6.NS.6.ii | Extend number line diagrams and coordinate axes from previous grades to represent points on the line and in the plane with negative number coordinates. | Grade 6 |
| North Dakota | 6.NS.7 | Understand ordering and absolute value of rational numbers. | Grade 6 |
| North Dakota | 6.NS.8 | Solve real world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. | Grade 6 |
| North Dakota | 7.EE.1 | Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients with an emphasis on writing equivalent expressions. | Grade 7 |
| North Dakota | 7.EE.2 | Understand that rewriting an expression in different forms in a problem context can clarify the problem and how the quantities in it are related. | Grade 7 |
| North Dakota | 7.EE.3.i | Solve multi-step real-life and mathematical problems posed with rational numbers in any form (positive and negative, fractions, decimals, and integers), using tools strategically. | Grade 7 |
| North Dakota | 7.EE.3.ii | Apply properties of operations to calculate with numbers in any form. | Grade 7 |
| North Dakota | 7.EE.3.iii | Convert between forms as appropriate. | Grade 7 |
| North Dakota | 7.EE.3.iv | Assess the reasonableness of answers using mental computation and estimation strategies. | Grade 7 |
| North Dakota | 7.EE.4 | Use variables to represent quantities in a real world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. | Grade 7 |
| North Dakota | 7.G.1 | Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale. | Grade 7 |
| North Dakota | 7.G.2 | Draw geometric shapes from given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle. Use a variety of methods such as freehand, with ruler and protractor, and with technology. | Grade 7 |
| North Dakota | 7.G.3 | Describe the cross-sections (two-dimensional figures that result from slicing three-dimensional figures, as in plane sections) of right rectangular prisms and right rectangular pyramids. | Grade 7 |
| North Dakota | 7.G.4.i | Know the formulas for the area and circumference of a circle and use them to solve problems. | Grade 7 |
| North Dakota | 7.G.4.ii | Informally derive the relationship between the circumference and area of a circle. | Grade 7 |
| North Dakota | 7.G.5 | Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve equations for an unknown angle in a figure. | Grade 7 |
| North Dakota | 7.G.6.i | Solve real world and mathematical problems involving area of two-dimensional figures composed of polygons and/or circles, including composite figures. | Grade 7 |
| North Dakota | 7.G.6.ii | Use nets to solve real world and mathematical problems involving surface area of prisms and cylinders, including composite solids. | Grade 7 |
| North Dakota | 7.G.6.iii | Solve real world and mathematical problems involving volumes of right prisms, including composite solids. | Grade 7 |
| North Dakota | 7.RP.1 | Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. | Grade 7 |
| North Dakota | 7.RP.2 | Recognize and represent proportional relationships between quantities. | Grade 7 |
| North Dakota | 7.RP.3 | Use proportional relationships to solve multi-step ratio and percent problems. | Grade 7 |
| North Dakota | 7.NS.1 | Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram. | Grade 7 |
| North Dakota | 7.NS.2 | Apply and extend previous understandings of multiplication, division, and fractions to multiply and divide rational numbers. | Grade 7 |
| North Dakota | 7.NS.3 | Solve real world and mathematical problems involving the four operations with rational numbers. | Grade 7 |
| North Dakota | 8.EE.1 | Develop, know and apply the properties of integer exponents to generate equivalent numeric and algebraic expressions. | Grade 8 |
| North Dakota | 8.EE.2.i | Use square root and cube root symbols to represent solutions to equations of the form 𝑥² = 𝑝 and 𝑥³ = 𝑝, where 𝑝 is a positive rational number. | Grade 8 |
| North Dakota | 8.EE.2.ii | Evaluate square roots of small perfect squares and cube roots of small perfect cubes. | Grade 8 |
| North Dakota | 8.EE.3 | Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other. | Grade 8 |
| North Dakota | 8.EE.4.i | Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. | Grade 8 |
| North Dakota | 8.EE.4.ii | Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities (such as use millimeters per year for seafloor spreading). | Grade 8 |
| North Dakota | 8.EE.4.iii | Interpret scientific notation that has been generated by technology. | Grade 8 |
| North Dakota | 8.EE.5.i | Graph proportional relationships, interpreting the unit rate as the slope of the graph. | Grade 8 |
| North Dakota | 8.EE.5.ii | Compare two different proportional relationships represented in different ways. | Grade 8 |
| North Dakota | 8.EE.6.i | Use similar triangles to explain why the slope 𝑚 is the same between any two distinct points on a non-vertical line in the coordinate plane. | Grade 8 |
| North Dakota | 8.EE.6.ii | Derive the equation 𝑦 = 𝑚𝑥 for a line through the origin and the equation 𝑦 = 𝑚𝑥 + 𝑏 for a line intercepting the vertical axis at 𝑏. | Grade 8 |
| North Dakota | 8.EE.7 | Solve linear equations in one variable. | Grade 8 |
| North Dakota | 8.EE.8 | Analyze and solve pairs of simultaneous linear equations. | Grade 8 |
| North Dakota | 8.F.1.i | Understand that a function is a rule that assigns to each input exactly one output. | Grade 8 |
| North Dakota | 8.F.1.ii | Understand that the graph of a function is the set of ordered pairs consisting of an input and the corresponding output. | Grade 8 |
| North Dakota | 8.F.2 | Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, and/or by verbal descriptions). | Grade 8 |
| North Dakota | 8.F.3.i | Interpret the equation 𝑦 = 𝑚𝑥 + 𝑏 as defining a linear function, whose graph is a straight line. | Grade 8 |
| North Dakota | 8.F.3.ii | Give examples of functions that are not linear. | Grade 8 |
| North Dakota | 8.F.4.i | Construct a function to model a linear relationship between two quantities. | Grade 8 |
| North Dakota | 8.F.4.ii | Determine the rate of change and initial value of the function from a description of a relationship or from two (𝑥, 𝑦) values, including reading these from a table or from a graph. | Grade 8 |
| North Dakota | 8.F.4.iii | Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values. | Grade 8 |
| North Dakota | 8.F.5.i | Describe qualitatively the functional relationship between two quantities by analyzing a graph (may include where the function is increasing or decreasing, linear or nonlinear, etc.). | Grade 8 |
| North Dakota | 8.F.5.ii | Sketch a graph that exhibits the qualitative features of a function that has been described verbally. | Grade 8 |
| North Dakota | 8.G.1 | Understand the properties of rotations, reflections, and translations by experimentation. | Grade 8 |
| North Dakota | 8.G.2.i | Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations. | Grade 8 |
| North Dakota | 8.G.2.ii | Given two congruent figures, describe a sequence of transformations that exhibits the congruence between them. | Grade 8 |
| North Dakota | 8.G.3 | Describe the effect of dilations, translations, rotations and reflections on two-dimensional figures using coordinates. | Grade 8 |
| North Dakota | 8.G.4.i | Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations. | Grade 8 |
| North Dakota | 8.G.4.ii | Given two similar two-dimensional figures, describe a sequence of transformations that exhibits the similarity between them. | Grade 8 |
| North Dakota | 8.G.5 | Use informal arguments to establish facts about: | Grade 8 |
| North Dakota | 8.G.7 | Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real world and mathematical problems in two and three dimensions. | Grade 8 |
| North Dakota | 8.G.8 | Apply the Pythagorean Theorem to find the distance between two points in a coordinate system. | Grade 8 |
| North Dakota | 8.G.9.i | Know the formulas for the volume of cones, cylinders and spheres. | Grade 8 |
| North Dakota | 8.G.9.ii | Use the formulas to solve real world and mathematical problems. | Grade 8 |
| North Dakota | 8.SP.1.i | Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. | Grade 8 |
| North Dakota | 8.SP.1.ii | Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association. | Grade 8 |
| North Dakota | 8.SP.2.i | Know that straight lines are widely used to model relationships between two quantitative variables. | Grade 8 |
| North Dakota | 8.SP.2.ii | For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line. | Grade 8 |
| North Dakota | 8.NS.2 | Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (such as 𝜋²). | Grade 8 |
| North Dakota | HS.A-APR.3.i | Identify zeros of polynomials when suitable factorizations are available. | High School |
| North Dakota | HS.A-APR.3.ii | Use the zeros to construct a rough graph of the function defined by the polynomial. | High School |
| North Dakota | HS.A-CED.2.i | Create equations in two or more variables to represent relationships between quantities. | High School |
| North Dakota | HS.A-CED.2.ii | Graph equations on coordinate axes with appropriate labels and scales. | High School |
| North Dakota | HS.A-CED.3 | Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context. | High School |
| North Dakota | HS.A-REI.3 | Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. | High School |
| North Dakota | HS.A-SSE.2 | Use the structure of an expression to identify ways to rewrite it. | High School |
| North Dakota | HA.A.SSE.3 | Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression. | High School |
| North Dakota | HS.F-BF.1 | Write a function that describes a relationship between two quantities. | High School |
| North Dakota | HS.F-IF.2 | Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. | High School |
| North Dakota | HS.F-IF.4 | Use tables, graphs, verbal descriptions, and equations to interpret and sketch the key features of a function modeling the relationship between two quantities. | High School |
| North Dakota | HS.F-IF.7 | Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. | High School |
| North Dakota | HS.S-ID.6 | Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. | High School |
| Ohio | K.CC.1 | Count to 100 by ones and by tens. | Kindergarten |
| Ohio | K.CC.2 | Count forward within 100 beginning from any given number other than 1. | Kindergarten |
| Ohio | K.CC.3 | Write numerals from 0 to 20. Represent a number of objects with a written numeral 0-20 (with 0 representing a count of no objects). | Kindergarten |
| Ohio | K.CC.4 | Understand the relationship between numbers and quantities; connect counting to cardinality using a variety of objects including pennies. | Kindergarten |
| Ohio | K.CC.5 | Count to answer “how many?” questions about as many as 20 things arranged in a line, a rectangular array, or a circle, or as many as 10 things in a scattered configuration; given a number from 1-20, count out that many objects. | Kindergarten |
| Ohio | K.CC.6 | Orally identify (without using inequality symbols) whether the number of objects in one group is greater/more than, less/fewer than, or the same as the number of objects in another group, not to exceed 10 objects in each group. | Kindergarten |
| Ohio | K.CC.7 | Compare (without using inequality symbols) two numbers between 0 and 10 when presented as written numerals. | Kindergarten |
| Ohio | K.G.1 | Describe objects in the environment using names of shapes, and describe the relative positions of these objects using terms such as above, below, beside, in front of, behind, and next to. | Kindergarten |
| Ohio | K.G.2 | Correctly name shapes regardless of their orientations or overall size. | Kindergarten |
| Ohio | K.G.3 | Identify shapes as two-dimensional (lying in a plane, “flat”) or three-dimensional (“solid”). | Kindergarten |
| Ohio | K.G.4 | Describe and compare two- or three-dimensional shapes, in different sizes and orientations, using informal language to describe their commonalities, differences, parts, and other attributes. | Kindergarten |
| Ohio | K.G.6 | Combine simple shapes to form larger shapes. | Kindergarten |
| Ohio | K.MD.1 | Identify and describe measurable attributes (length, weight, and height) of a single object using vocabulary terms such as long/short, heavy/light, or tall/short. | Kindergarten |
| Ohio | K.MD.2 | Directly compare two objects with a measurable attribute in common to see which object has “more of” or “less of” the attribute, and describe the difference. | Kindergarten |
| Ohio | K.MD.3 | Classify objects into given categories; count the numbers of objects in each category and sort the categories by count. The number of objects in each category should be less than or equal to ten. Counting and sorting coins should be limited to pennies. | Kindergarten |
| Ohio | K.NBT.1 | Compose and decompose numbers from 11 to 19 into a group of ten ones and some further ones by using objects and, when appropriate, drawings or equations; understand that these numbers are composed of a group of ten ones and one, two, three, four, five, six, seven, eight, or nine ones. | Kindergarten |
| Ohio | K.OA.1 | Represent addition and subtraction with objects, fingers, mental images, drawings, sounds such as claps, acting out situations, verbal explanations, expressions, or equations. | Kindergarten |
| Ohio | K.OA.2 | Solve addition and subtraction problems (written or oral), and add and subtract within 10 by using objects or drawings to represent the problem. | Kindergarten |
| Ohio | K.OA.3 | Decompose numbers and record compositions for numbers less than or equal to 10 into pairs in more than one way by using objects and, when appropriate, drawings or equations. | Kindergarten |
| Ohio | K.OA.4 | For any number from 1 to 9, find the number that makes 10 when added to the given number, e.g., by using objects or drawings, and record the answer with a drawing or, when appropriate, an equation. | Kindergarten |
| Ohio | K.OA.5 | Fluently add and subtract within 5. | Kindergarten |
| Ohio | 1.G.1 | Distinguish between defining attributes, e.g., triangles are closed and three-sided, versus non-defining attributes, e.g., color, orientation, overall size; build and draw shapes that possess defining attributes. | Grade 1 |
| Ohio | 1.G.2 | Compose two-dimensional shapes (rectangles, squares, trapezoids, triangles, half-circles, and quarter-circles) or three-dimensional shapes (cubes, right rectangular prisms, right circular cones, and right circular cylinders) to create a composite shape, and compose new shapes from the composite shape. Students do not need to learn formal names such as "right rectangular prism. | Grade 1 |
| Ohio | 1.G.3 | Partition circles and rectangles into two and four equal shares, describe the shares using the words halves, fourths, and quarters, and use the phrases half of, fourth of, and quarter of. Describe the whole as two of or four of the shares in real-world contexts. Understand for these examples that decomposing into more equal shares creates smaller shares. | Grade 1 |
| Ohio | 1.MD.1 | Order three objects by length; compare the lengths of two objects indirectly by using a third object. | Grade 1 |
| Ohio | 1.MD.2 | Express the length of an object as a whole number of length units by laying multiple copies of a shorter object (the length unit) end to end; understand that the length measurement of an object is the number of same-size length units that span it with no gaps or overlaps. | Grade 1 |
| Ohio | 1.MD.3 | Work with time and money. | Grade 1 |
| Ohio | 1.MD.4 | Organize, represent, and interpret data with up to three categories; ask and answer questions about the total number of data points, how many in each category, and how many more or less are in one category than in another. | Grade 1 |
| Ohio | 1.NBT.1 | Count to 120, starting at any number less than 120. In this range, read and write numerals and represent a number of objects with a written numeral. | Grade 1 |
| Ohio | 1.NBT.2 | Understand that the two digits of a two-digit number represent amounts of tens and ones. Understand the following as special cases: 10 can be thought of as a bundle of ten ones—called a “ten;” the numbers from 11 to 19 are composed of a ten and one, two, three, four, five, six, seven, eight, or nine ones; and the numbers 10, 20, 30, 40, 50, 60, 70, 80, 90 refer to one, two, three, four, five, six, seven, eight, or nine tens (and 0 ones). | Grade 1 |
| Ohio | 1.NBT.3 | Compare two two-digit numbers based on meanings of the tens and ones digits, recording the results of comparisons with the symbols >, =, and <. | Grade 1 |
| Ohio | 1.NBT.4 | Add within 100, including adding a two-digit number and a one-digit number and adding a two-digit number and a multiple of 10, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; record the strategy with a written numerical method (drawings and, when appropriate, equations) and explain the reasoning used. Understand that when adding two-digit numbers, tens are added to tens; ones are added to ones; and sometimes it is necessary to compose a ten. | Grade 1 |
| Ohio | 1.NBT.5 | Given a two-digit number, mentally find 10 more or 10 less than the number, without having to count; explain the reasoning used. | Grade 1 |
| Ohio | 1.NBT.6 | Subtract multiples of 10 in the range 10-90 from multiples of 10 in the range 10-90 (positive or zero differences), using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. | Grade 1 |
| Ohio | 1.OA.1 | Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart and comparing, with unknowns in all positions, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem. | Grade 1 |
| Ohio | 1.OA.3 | Apply properties of operations as strategies to add and subtract. | Grade 1 |
| Ohio | 1.OA.4 | Understand subtraction as an unknown-addend problem. | Grade 1 |
| Ohio | 1.OA.5 | Relate counting to addition and subtraction, e.g., by counting on 2 to add 2. | Grade 1 |
| Ohio | 1.OA.6 | Add and subtract within 20, demonstrating fluency with various strategies for addition and subtraction within 10. Strategies may include counting on; making ten, e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14; decomposing a number leading to a ten, e.g., 13 − 4 = 13 − 3 − 1 = 10 − 1 = 9; using the relationship between addition and subtraction, e.g., knowing that 8 + 4 = 12, one knows 12 − 8 = 4; and creating equivalent but easier or known sums, e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13. | Grade 1 |
| Ohio | 1.OA.7 | Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false. | Grade 1 |
| Ohio | 1.OA.8 | Determine the unknown whole number in an addition or subtraction equation relating three whole numbers. | Grade 1 |
| Ohio | 2.G.1 | Recognize and identify triangles, quadrilaterals, pentagons, and hexagons based on the number of sides or vertices. Recognize and identify cubes, rectangular prisms, cones, and cylinders. | Grade 2 |
| Ohio | 2.G.2 | Partition a rectangle into rows and columns of same-size squares and count to find the total number of them. | Grade 2 |
| Ohio | 2.G.3 | Partition circles and rectangles into two, three, or four equal shares; describe the shares using the words halves, thirds, or fourths and quarters, and use the phrases half of, third of, or fourth of and quarter of. Describe the whole as two halves, three thirds, or four fourths in real-world contexts. Recognize that equal shares of identical wholes need not have the same shape. | Grade 2 |
| Ohio | 2.MD.1 | Measure the length of an object by selecting and using appropriate tools such as rulers, yardsticks, meter sticks, and measuring tapes. | Grade 2 |
| Ohio | 2.MD.2 | Measure the length of an object twice, using length units of different lengths for the two measurements; describe how the two measurements relate to the size of the unit chosen. | Grade 2 |
| Ohio | 2.MD.4 | Measure to determine how much longer one object is than another, expressing the length difference in terms of a standard length unit. | Grade 2 |
| Ohio | 2.MD.5 | Use addition and subtraction within 100 to solve word problems involving lengths that are given in the same whole number units, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem. | Grade 2 |
| Ohio | 2.MD.7 | Tell and write time from analog and digital clocks to the nearest five minutes, using a.m. and p.m. | Grade 2 |
| Ohio | 2.MD.8 | Solve problems with money. | Grade 2 |
| Ohio | 2.MD.9 | Generate measurement data by measuring lengths of several objects to the nearest whole unit or by making repeated measurements of the same object. Show the measurements by creating a line plot, where the horizontal scale is marked off in whole-number units. | Grade 2 |
| Ohio | 2.MD.10 | Organize, represent, and interpret data with up to four categories; complete picture graphs when single-unit scales are provided; complete bar graphs when single-unit scales are provided; solve simple put-together, take-apart, and compare problems in a graph. | Grade 2 |
| Ohio | 2.NBT.1 | Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones. Understand the following as special cases: | Grade 2 |
| Ohio | 2.NBT.2 | Count forward and backward within 1,000 by ones, tens, and hundreds starting at any number; skip-count by 5s starting at any multiple of 5. | Grade 2 |
| Ohio | 2.NBT.3 | Read and write numbers to 1,000 using base-ten numerals, number names, expanded form, and equivalent representations, e.g., 716 is 700 + 10 + 6, or 6 + 700 + 10, or 6 ones and 71 tens, etc. | Grade 2 |
| Ohio | 2.NBT.4 | Compare two three-digit numbers based on meanings of the hundreds, tens, and ones digits, using >, =, and < symbols to record the results of comparisons. | Grade 2 |
| Ohio | 2.NBT.5 | Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction. | Grade 2 |
| Ohio | 2.NBT.6 | Add up to four two-digit numbers using strategies based on place value and properties of operations. | Grade 2 |
| Ohio | 2.NBT.7 | Add and subtract within 1,000, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; record the strategy with a written numerical method (drawings and, when appropriate, equations) and explain the reasoning used. Understand that in adding or subtracting three-digit numbers, hundreds are added or subtracted from hundreds, tens are added or subtracted from tens, ones are added or subtracted from ones; and sometimes it is necessary to compose or decompose tens or hundreds. | Grade 2 |
| Ohio | 2.NBT.8 | Mentally add 10 or 100 to a given number 100-900, and mentally subtract 10 or 100 from a given number 100-900. | Grade 2 |
| Ohio | 2.OA.1 | Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem. | Grade 2 |
| Ohio | 2.OA.2 | Fluently add and subtract within 20 using mental strategies. By end of Grade 2, know from memory all sums of two one-digit numbers. | Grade 2 |
| Ohio | 2.OA.3 | Determine whether a group of objects (up to 20) has an odd or even number of members, e.g., by pairing objects or counting them by 2s; write an equation to express an even number as a sum of two equal addends. | Grade 2 |
| Ohio | 2.OA.4 | Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends. | Grade 2 |
| Ohio | 3.G.1 | Draw and describe triangles, quadrilaterals (rhombuses, rectangles, and squares), and polygons (up to 8 sides) based on the number of sides and the presence or absence of square corners (right angles). | Grade 3 |
| Ohio | 3.G.2 | Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole. | Grade 3 |
| Ohio | 3.MD.2 | Measure and estimate liquid volumes and masses of objects using standard units of grams, kilograms, and liters. Add, subtract, multiply, or divide whole numbers to solve one-step word problems involving masses or volumes that are given in the same units, e.g., by using drawings (such as a beaker with a measurement scale) to represent the problem. | Grade 3 |
| Ohio | 3.MD.3 | Create scaled picture graphs to represent a data set with several categories. Create scaled bar graphs to represent a data set with several categories. Solve two-step “how many more” and “how many less” problems using information presented in the scaled graphs. | Grade 3 |
| Ohio | 3.MD.4 | Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Show the data by creating a line plot, where the horizontal scale is marked off in appropriate units—whole numbers, halves, or quarters. | Grade 3 |
| Ohio | 3.MD.5 | Recognize area as an attribute of plane figures and understand concepts of area measurement. | Grade 3 |
| Ohio | 3.MD.6 | Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units). | Grade 3 |
| Ohio | 3.MD.7 | Relate area to the operations of multiplication and addition. | Grade 3 |
| Ohio | 3.MD.8 | Solve real-world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters. | Grade 3 |
| Ohio | 3.NBT.1 | Use place value understanding to round whole numbers to the nearest 10 or 100. | Grade 3 |
| Ohio | 3.NBT.2 | Fluently add and subtract within 1,000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction. | Grade 3 |
| Ohio | 3.NBT.3 | Multiply one-digit whole numbers by multiples of 10 in the range 10-90, e.g., 9 × 80, 5 × 60 using strategies based on place value and properties of operations. | Grade 3 |
| Ohio | 3.NF.1 | Understand a fraction 1/𝑏 as the quantity formed by 1 part when a whole is partitioned into 𝑏 equal parts; understand a fraction 𝑎/𝑏 as the quantity formed by 𝑎 parts of size 1/𝑏. | Grade 3 |
| Ohio | 3.NF.2 | Understand a fraction as a number on the number line; represent fractions on a number line diagram. | Grade 3 |
| Ohio | 3.NF.3 | Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size. | Grade 3 |
| Ohio | 3.OA.1 | Interpret products of whole numbers, e.g., interpret 5 x 7 as the total number of objects in 5 groups of 7 objects each. | Grade 3 |
| Ohio | 3.OA.2 | Interpret whole-number quotients of whole numbers, e.g., interpret 56 ÷ 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each. | Grade 3 |
| Ohio | 3.OA.3 | Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem. | Grade 3 |
| Ohio | 3.OA.4 | Determine the unknown whole number in a multiplication or division equation relating three whole numbers. | Grade 3 |
| Ohio | 3.OA.5 | Apply properties of operations as strategies to multiply and divide. | Grade 3 |
| Ohio | 3.OA.6 | Understand division as an unknown-factor problem. | Grade 3 |
| Ohio | 3.OA.7 | Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division, e.g., knowing that 8 × 5 = 40, one knows 40 ÷ 5 = 8, or properties of operations. | Grade 3 |
| Ohio | 3.OA.8 | Solve two-step word problems using the four operations. Represent these problems using equations with a letter or a symbol, which stands for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. | Grade 3 |
| Ohio | 3.OA.9 | Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations. | Grade 3 |
| Ohio | 4.G.1 | Draw points, lines, line segments, rays, angles (right, acute, and obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures. | Grade 4 |
| Ohio | 4.G.2 | Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines or the presence or absence of angles of a specified size. | Grade 4 |
| Ohio | 4.MD.1 | Know relative sizes of the metric measurement units within one system of units. Metric units include kilometer, meter, centimeter, and millimeter; kilogram and gram; and liter and milliliter. Express a larger measurement unit in terms of a smaller unit. Record measurement conversions in a two-column table. | Grade 4 |
| Ohio | 4.MD.3 | Develop efficient strategies to determine the area and perimeter of rectangles in real-world situations and mathematical problems. | Grade 4 |
| Ohio | 4.MD.4 | Display and interpret data in graphs (picture graphs, bar graphs, and line plots) to solve problems using numbers and operations for this grade. | Grade 4 |
| Ohio | 4.MD.5 | Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement. | Grade 4 |
| Ohio | 4.MD.6 | Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure. | Grade 4 |
| Ohio | 4.MD.7 | Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real-world and mathematical problems, e.g., by using an equation with a symbol for the unknown angle measure. | Grade 4 |
| Ohio | 4.NBT.1 | Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right by applying concepts of place value, multiplication, or division. | Grade 4 |
| Ohio | 4.NBT.2 | Read and write multi-digit whole numbers using standard form, word form, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. | Grade 4 |
| Ohio | 4.NBT.3 | Use place value understanding to round multi-digit whole numbers to any place through 1,000,000. | Grade 4 |
| Ohio | 4.NBT.4 | Fluently add and subtract multi-digit whole numbers using a standard algorithm. | Grade 4 |
| Ohio | 4.NBT.5 | Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. | Grade 4 |
| Ohio | 4.NBT.6 | Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. | Grade 4 |
| Ohio | 4.NF.1 | Explain why a fraction 𝑎/𝑏 is equivalent to a fraction (𝑛 × 𝑎)/(𝑛 × 𝑏) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. | Grade 4 |
| Ohio | 4.NF.2 | Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as ½. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model. | Grade 4 |
| Ohio | 4.NF.3 | Understand a fraction 𝑎/𝑏 with 𝑎 > 1 as a sum of fractions 1/𝑏. | Grade 4 |
| Ohio | 4.NF.4 | Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. | Grade 4 |
| Ohio | 4.NF.5 | Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100. | Grade 4 |
| Ohio | 4.NF.6 | Use decimal notation for fractions with denominators 10 or 100. | Grade 4 |
| Ohio | 4.NF.7 | Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual model. | Grade 4 |
| Ohio | 4.OA.1 | Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 × 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations. | Grade 4 |
| Ohio | 4.OA.2 | Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison. | Grade 4 |
| Ohio | 4.OA.3 | Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. | Grade 4 |
| Ohio | 4.OA.4 | Find all factor pairs for a whole number in the range 1-100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1-100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1-100 is prime or composite. | Grade 4 |
| Ohio | 4.OA.5 | Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. | Grade 4 |
| Ohio | 5.G.1 | Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond, e.g., 𝑥-axis and 𝑥-coordinate, 𝑦-axis and 𝑦-coordinate. | Grade 5 |
| Ohio | 5.G.2 | Represent real-world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. | Grade 5 |
| Ohio | 5.G.3 | Identify and describe commonalities and differences between types of triangles based on angle measures (equiangular, right, acute, and obtuse triangles) and side lengths (isosceles, equilateral, and scalene triangles). | Grade 5 |
| Ohio | 5.G.4 | Identify and describe commonalities and differences between types of quadrilaterals based on angle measures, side lengths, and the presence or absence of parallel and perpendicular lines, e.g., squares, rectangles, parallelograms, trapezoids, and rhombuses. | Grade 5 |
| Ohio | 5.MD.1 | Know relative sizes of these U.S. customary measurement units: pounds, ounces, miles, yards, feet, inches, gallons, quarts, pints, cups, fluid ounces, hours, minutes, and seconds. Convert between pounds and ounces; miles and feet; yards, feet, and inches; gallons, quarts, pints, cups, and fluid ounces; hours, minutes, and seconds in solving multi-step, real-world problems. | Grade 5 |
| Ohio | 5.MD.2 | Display and interpret data in graphs (picture graphs, bar graphs, and line plots) to solve problems using numbers and operations for this grade, e.g., including U.S. customary units in fractions ½, ¼, ⅛, or decimals. | Grade 5 |
| Ohio | 5.MD.3 | Recognize volume as an attribute of solid figures and understand concepts of volume measurement. | Grade 5 |
| Ohio | 5.MD.4 | Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. | Grade 5 |
| Ohio | 5.MD.5 | Relate volume to the operations of multiplication and addition and solve real-world and mathematical problems involving volume. | Grade 5 |
| Ohio | 5.NBT.1 | Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. | Grade 5 |
| Ohio | 5.NBT.2 | Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. | Grade 5 |
| Ohio | 5.NBT.3 | Read, write, and compare decimals to thousandths. | Grade 5 |
| Ohio | 5.NBT.4 | Use place value understanding to round decimals to any place, millions through hundredths. | Grade 5 |
| Ohio | 5.NBT.5 | Fluently multiply multi-digit whole numbers using a standard algorithm. | Grade 5 |
| Ohio | 5.NBT.6 | Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. | Grade 5 |
| Ohio | 5.NBT.7 | Solve real-world problems by adding, subtracting, multiplying, and dividing decimals using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction, or multiplication and division; relate the strategy to a written method and explain the reasoning used. | Grade 5 |
| Ohio | 5.NF.1 | Add and subtract fractions with unlike denominators (including mixed numbers and fractions greater than 1) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. | Grade 5 |
| Ohio | 5.NF.2 | Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. | Grade 5 |
| Ohio | 5.NF.3 | Interpret a fraction as division of the numerator by the denominator (𝑎/𝑏 = 𝑎 ÷ 𝑏). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. | Grade 5 |
| Ohio | 5.NF.4 | Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. | Grade 5 |
| Ohio | 5.NF.5 | Interpret multiplication as scaling (resizing). | Grade 5 |
| Ohio | 5.NF.6 | Solve real-world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. | Grade 5 |
| Ohio | 5.NF.7 | Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. | Grade 5 |
| Ohio | 5.OA.1 | Use parentheses in numerical expressions, and evaluate expressions with this symbol. Formal use of algebraic order of operations is not necessary. | Grade 5 |
| Ohio | 5.OA.2 | Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. | Grade 5 |
| Ohio | 5.OA.3 | Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. | Grade 5 |
| Ohio | 6.EE.1 | Write and evaluate numerical expressions involving whole-number exponents. | Grade 6 |
| Ohio | 6.EE.2 | Write, read, and evaluate expressions in which letters stand for numbers. | Grade 6 |
| Ohio | 6.EE.3 | Apply the properties of operations to generate equivalent expressions. | Grade 6 |
| Ohio | 6.EE.4 | Identify when two expressions are equivalent, i.e., when the two expressions name the same number regardless of which value is substituted into them. | Grade 6 |
| Ohio | 6.EE.5 | Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true. | Grade 6 |
| Ohio | 6.EE.6 | Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set. | Grade 6 |
| Ohio | 6.EE.7 | Solve real-world and mathematical problems by writing and solving equations of the form 𝑥 + 𝑝 = 𝑞 and 𝑝𝑥 = 𝑞 for cases in which 𝑝, 𝑞, and 𝑥 are all nonnegative rational numbers. | Grade 6 |
| Ohio | 6.EE.8 | Write an inequality of the form 𝑥 > 𝑐 or 𝑥 𝑐 or 𝑥 < 𝑐 have infinitely many solutions; represent solutions of such inequalities on number line diagrams. | Grade 6 |
| Ohio | 6.EE.9 | Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. | Grade 6 |
| Ohio | 6.G.1 | Through composition into rectangles or decomposition into triangles, find the area of right triangles, other triangles, special quadrilaterals, and polygons; apply these techniques in the context of solving real-world and mathematical problems. | Grade 6 |
| Ohio | 6.G.2 | Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas 𝑉 = 𝑙 ⋅ 𝑤 ⋅ ℎ and 𝑉 = 𝐵 ⋅ ℎ to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems. | Grade 6 |
| Ohio | 6.G.3 | Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems. | Grade 6 |
| Ohio | 6.G.4 | Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems. | Grade 6 |
| Ohio | 6.RP.1 | Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. | Grade 6 |
| Ohio | 6.RP.2 | Understand the concept of a unit rate 𝑎/𝑏 associated with a ratio 𝑎:𝑏 with 𝑏 ≠ 0, and use rate language in the context of a ratio relationship. | Grade 6 |
| Ohio | 6.RP.3 | Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. | Grade 6 |
| Ohio | 6.SP.5 | Summarize numerical data sets in relation to their context. | Grade 6 |
| Ohio | 6.NS.1 | Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. | Grade 6 |
| Ohio | 6.NS.2 | Fluently divide multi-digit numbers using a standard algorithm. | Grade 6 |
| Ohio | 6.NS.3 | Fluently add, subtract, multiply, and divide multi-digit decimals using a standard algorithm for each operation. | Grade 6 |
| Ohio | 6.NS.5 | Understand that positive and negative numbers are used together to describe quantities having opposite directions or values, e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge; use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation. | Grade 6 |
| Ohio | 6.NS.6 | Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates. | Grade 6 |
| Ohio | 6.NS.7 | Understand ordering and absolute value of rational numbers. | Grade 6 |
| Ohio | 6.NS.8 | Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. | Grade 6 |
| Ohio | 7.EE.1 | Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients. | Grade 7 |
| Ohio | 7.EE.2 | In a problem context, understand that rewriting an expression in an equivalent form can reveal and explain properties of the quantities represented by the expression and can reveal how those quantities are related. | Grade 7 |
| Ohio | 7.EE.3 | Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. | Grade 7 |
| Ohio | 7.EE.4 | Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. | Grade 7 |
| Ohio | 7.G.2 | Draw (freehand, with ruler and protractor, and with technology) geometric figures with given conditions. | Grade 7 |
| Ohio | 7.G.3 | Describe the two-dimensional figures that result from slicing three-dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids. | Grade 7 |
| Ohio | 7.G.5 | Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure. | Grade 7 |
| Ohio | 7.G.6 | Solve real-world and mathematical problems involving area, volume, and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. | Grade 7 |
| Ohio | 7.RP.1 | Compute unit rates associated with ratios of fractions, including ratios of lengths, areas, and other quantities measured in like or different units. | Grade 7 |
| Ohio | 7.RP.2 | Recognize and represent proportional relationships between quantities. | Grade 7 |
| Ohio | 7.RP.3 | Use proportional relationships to solve multistep ratio and percent problems. | Grade 7 |
| Ohio | 7.NS.1 | Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram. | Grade 7 |
| Ohio | 7.NS.2 | Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers. | Grade 7 |
| Ohio | 7.NS.3 | Solve real-world and mathematical problems involving the four operations with rational numbers. Computations with rational numbers extend the rules for manipulating fractions to complex fractions. | Grade 7 |
| Ohio | 8.EE.1 | Understand, explain, and apply the properties of integer exponents to generate equivalent numerical expressions. | Grade 8 |
| Ohio | 8.EE.2 | Use square root and cube root symbols to represent solutions to equations of the form 𝑥² = 𝑝 and 𝑥³ = 𝑝, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that √2 is irrational. | Grade 8 |
| Ohio | 8.EE.3 | Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities and to express how many times as much one is than the other. | Grade 8 |
| Ohio | 8.EE.4 | Perform operations with numbers expressed in scientific notation, including problems where both decimal notation and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities, e.g., use millimeters per year for seafloor spreading. Interpret scientific notation that has been generated by technology. | Grade 8 |
| Ohio | 8.EE.5 | Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. | Grade 8 |
| Ohio | 8.EE.6 | Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation 𝑦 = 𝑚𝑥 for a line through the origin and the equation 𝑦 = 𝑚𝑥 + 𝑏 for a line intercepting the vertical axis at 𝑏. | Grade 8 |
| Ohio | 8.EE.7 | Solve linear equations in one variable. | Grade 8 |
| Ohio | 8.EE.8 | Analyze and solve pairs of simultaneous linear equations graphically. | Grade 8 |
| Ohio | 8.F.1 | Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output. | Grade 8 |
| Ohio | 8.F.2 | Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). | Grade 8 |
| Ohio | 8.F.3 | Interpret the equation 𝑦 = 𝑚𝑥 + 𝑏 as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. | Grade 8 |
| Ohio | 8.F.4 | Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (𝑥, 𝑦) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values. | Grade 8 |
| Ohio | 8.F.5 | Describe qualitatively the functional relationship between two quantities by analyzing a graph, e.g., where the function is increasing or decreasing, linear or nonlinear. Sketch a graph that exhibits the qualitative features of a function that has been described verbally. | Grade 8 |
| Ohio | 8.G.1 | Verify experimentally the properties of rotations, reflections, and translations (include examples both with and without coordinates). | Grade 8 |
| Ohio | 8.G.2 | Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them. | Grade 8 |
| Ohio | 8.G.3 | Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates. | Grade 8 |
| Ohio | 8.G.4 | Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two-dimensional figures, describe a sequence that exhibits the similarity between them. | Grade 8 |
| Ohio | 8.G.5 | Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. | Grade 8 |
| Ohio | 8.G.7 | Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions. | Grade 8 |
| Ohio | 8.G.8 | Apply the Pythagorean Theorem to find the distance between two points in a coordinate system. | Grade 8 |
| Ohio | 8.G.9 | Solve real-world and mathematical problems involving volumes of cones, cylinders, and spheres. | Grade 8 |
| Ohio | 8.SP.1 | Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering; outliers; positive, negative, or no association; and linear association and nonlinear association. | Grade 8 |
| Ohio | 8.SP.2 | Understand that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line. | Grade 8 |
| Ohio | 8.NS.2 | Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions, e.g., π². | Grade 8 |
| Ohio | HSA.APR.3 | Identify zeros of polynomials, when factoring is reasonable, and use the zeros to construct a rough graph of the function defined by the polynomial. | High School - Algebra |
| Ohio | HSA.CED.2 | Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. | High School - Algebra |
| Ohio | HSA.CED.3 | Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context. | High School - Algebra |
| Ohio | HSA.REI.3 | Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. | High School - Algebra |
| Ohio | HSA.SSE.2 | Use the structure of an expression to identify ways to rewrite it. | High School - Algebra |
| Ohio | HSA.SSE.3 | Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression. | High School - Algebra |
| Ohio | HSF.BF.1 | Write a function that describes a relationship between two quantities. | High School - Functions |
| Ohio | HSF.IF.2 | Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. | High School - Functions |
| Ohio | HSF.IF.4 | For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. | High School - Functions |
| Ohio | HSF.IF.7 | Graph functions expressed symbolically and indicate key features of the graph, by hand in simple cases and using technology for more complicated cases. Include applications and how key features relate to characteristics of a situation, making selection of a particular type of function model appropriate. | High School - Functions |
| Ohio | HSG.CO.14 | Classify two-dimensional figures in a hierarchy based on properties. | High School - Geometry |
| Ohio | HSS.ID.6 | Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. | High School - Statistics and Probability |
| Oklahoma | K.N.1.1 | Count aloud forward in sequence to 100 by 1s and 10s. | Kindergarten |
| Oklahoma | K.N.1.3 | Use ordinal numbers to represent the position of an object in a sequence up to 10. | Kindergarten |
| Oklahoma | K.N.1.5 | Count forward, with and without objects, from any given number up to 20. | Kindergarten |
| Oklahoma | K.N.1.6 | Read, write, discuss, and represent whole numbers from 0 to at least 20. Representations may include numerals, pictures, real-object and pictographs, spoken words, and manipulatives. | Kindergarten |
| Oklahoma | K.N.1.7 | Find a number that is 1 more or 1 less than a given number up to 10. | Kindergarten |
| Oklahoma | K.N.1.8 | Compare and order whole numbers from 0 to 10 with and without objects, using the vocabulary "more than,” “less than,” or “equal to.” | Kindergarten |
| Oklahoma | K.N.2.1 | Compose and decompose numbers up to 10 using objects and pictures. | Kindergarten |
| Oklahoma | K.N.4.1 | Identify pennies, nickels, dimes, and quarters by name. | Kindergarten |
| Oklahoma | K.A.1.1 | Sort and group up to 10 objects into a set based upon characteristics such as color, size, and shape. Explain verbally what the objects have in common. | Kindergarten |
| Oklahoma | K.GM.1.1 | Recognize squares, circles, triangles, and rectangles. | Kindergarten |
| Oklahoma | K.GM.1.2 | Sort two-dimensional objects using characteristics such as shape and size. | Kindergarten |
| Oklahoma | K.GM.1.3 | Identify attributes of two-dimensional shapes using informal and formal geometric language interchangeably, such as the number of corners/vertices and the number of sides/edges. | Kindergarten |
| Oklahoma | K.GM.1.4 | Use smaller two-dimensional shapes to fill in the outline of a larger two-dimensional shape. | Kindergarten |
| Oklahoma | K.GM.2.1 | Use words to compare objects according to length, size, weight, position, and location. | Kindergarten |
| Oklahoma | K.GM.2.2 | Order up to 6 objects using measurable attributes, such as length and weight. | Kindergarten |
| Oklahoma | K.GM.2.3 | Identify more than one shared attribute between objects, and sort objects into sets. | Kindergarten |
| Oklahoma | K.GM.2.4 | Compare the number of objects needed to fill two different containers. | Kindergarten |
| Oklahoma | K.D.1.1 | Collect and organize information about objects and events in the environment. | Kindergarten |
| Oklahoma | K.D.1.3 | Draw conclusions from real-object graphs and pictographs. | Kindergarten |
| Oklahoma | 1.N.1.2 | Use concrete representations to describe whole numbers between 10 and 100 in terms of tens and ones. Know that 10 is equivalent to 10 ones and 100 is equivalent to 10 tens. | Grade 1 |
| Oklahoma | 1.N.1.3 | Read, write, discuss, and represent whole numbers up to 100. Representations may include numerals, words, addition and subtraction, pictures, tally marks, number lines, and manipulatives. | Grade 1 |
| Oklahoma | 1.N.1.4 | Count forward, with objects, from any given number up to 100 by 1s, 2s, 5s and 10s. | Grade 1 |
| Oklahoma | 1.N.1.5 | Count forward, without objects, by multiples of 1s, 2s, 5s, and 10s, up to 100. | Grade 1 |
| Oklahoma | 1.N.1.6 | Find a number that is 10 more or 10 less than a given number up to 100. | Grade 1 |
| Oklahoma | 1.N.1.7 | Compare and order whole numbers from 0 to 100. | Grade 1 |
| Oklahoma | 1.N.1.9 | Use words such as “more than,” “less than,” and “equal to” to describe the relative value of numbers. | Grade 1 |
| Oklahoma | 1.N.2.1 | Represent and solve problems using addition and subtraction with sums and minuends of up to 10. | Grade 1 |
| Oklahoma | 1.N.2.2 | Determine if equations involving addition and subtraction are true. | Grade 1 |
| Oklahoma | 1.N.2.3 | Demonstrate fluency with basic facts of addition and subtraction with sums and minuends of up to 10. | Grade 1 |
| Oklahoma | 1.N.3.1 | Partition a regular polygon using physical models and recognize when those parts are equal. | Grade 1 |
| Oklahoma | 1.N.3.2 | Partition (fair share) sets of objects into two and three equal groups. | Grade 1 |
| Oklahoma | 1.N.4.1 | Identify pennies, nickels, dimes, and quarters by name and value. | Grade 1 |
| Oklahoma | 1.GM.1.1 | Identify regular and irregular trapezoids and hexagons by pointing to the shape when given the name. | Grade 1 |
| Oklahoma | 1.GM.1.2 | Compose larger, defined shapes using smaller two-dimensional shapes. | Grade 1 |
| Oklahoma | 1.GM.1.3 | Compose structures with three-dimensional shapes. | Grade 1 |
| Oklahoma | 1.GM.1.4 | Recognize three-dimensional shapes such as cubes, cones, cylinders, pyramids, and spheres. | Grade 1 |
| Oklahoma | 1.GM.2.1 | Use nonstandard and standard measuring tools to measure the length of objects. | Grade 1 |
| Oklahoma | 1.GM.2.2 | Illustrate that the length of an object is the number of same-size units of length that, when laid end-to-end with no gaps or overlaps, reach from one end of the object to the other. | Grade 1 |
| Oklahoma | 1.GM.2.3 | Measure the same object/distance with units of two different lengths, and describe how and why the measurements differ. | Grade 1 |
| Oklahoma | 1.GM.2.4 | Describe a length to the nearest whole unit using a number with standard and nonstandard units. | Grade 1 |
| Oklahoma | 1.GM.2.5 | Use standard and nonstandard tools to identify volume/capacity. Compare and sort containers that hold more, less, or the same amount. | Grade 1 |
| Oklahoma | 1.GM.3.1 | Tell time to the hour and half-hour (analog and digital). | Grade 1 |
| Oklahoma | 1.D.1.1 | Collect, sort, and organize data in up to three categories using representations (e.g., tally marks, tables, Venn diagrams). | Grade 1 |
| Oklahoma | 1.D.1.2 | Use data to create pictographs and bar graphs that demonstrate one-to-one correspondence. | Grade 1 |
| Oklahoma | 1.D.1.3 | Draw conclusions from pictographs and bar graphs. | Grade 1 |
| Oklahoma | 2.N.1.1 | Read, write, discuss, and represent whole numbers up to 1,000. Representations should include, but are not limited to, numerals, words, pictures, tally marks, number lines, and manipulatives. | Grade 2 |
| Oklahoma | 2.N.1.3 | Use place value to describe whole numbers between 10 and 1,000 in terms of hundreds, tens, and ones, including written, standard, and expanded forms. Know that 10 is equivalent to 10 ones and 100 is equivalent to 10 tens. | Grade 2 |
| Oklahoma | 2.N.1.4 | Find 10 more or 10 less than a given three-digit number. Find 100 more or 100 less than a given three-digit number. | Grade 2 |
| Oklahoma | 2.N.1.6 | Use place value understanding to round numbers to the nearest ten and nearest hundred (up to 1,000). Recognize when to round in real-world situations. | Grade 2 |
| Oklahoma | 2.N.1.7 | Use place value to compare and order whole numbers up to 1,000 using comparative language, numbers, and symbols (e.g., 425 > 276, 73 < 107, page 351 comes after page 350, 753 is between 700 and 800). | Grade 2 |
| Oklahoma | 2.N.2.1 | Use the relationship between addition and subtraction to generate basic facts with sums and minuends of up to 20. | Grade 2 |
| Oklahoma | 2.N.2.2 | Demonstrate fluency with basic facts of addition and subtraction with sums and minuends of up to 20. | Grade 2 |
| Oklahoma | 2.N.2.4 | Use strategies and algorithms based on knowledge of place value and equality to add and subtract two-digit numbers. | Grade 2 |
| Oklahoma | 2.N.2.5 | Solve addition and subtraction problems involving whole numbers up to two digits. | Grade 2 |
| Oklahoma | 2.N.2.6 | Use concrete models and structured arrangements, such as repeated addition, arrays, and ten frames to develop an understanding of multiplication. | Grade 2 |
| Oklahoma | 2.N.3.1 | Identify the parts of a set and area that represent fractions for halves, thirds, and fourths. | Grade 2 |
| Oklahoma | 2.N.3.2 | Construct equal-sized portions through fair sharing (length, set, and area models for halves, thirds, and fourths). | Grade 2 |
| Oklahoma | 2.N.4.1 | Determine the value of a collection of coins up to one dollar using the cent symbol. | Grade 2 |
| Oklahoma | 2.N.4.2 | Use a combination of coins to represent a given amount of money up to one dollar. | Grade 2 |
| Oklahoma | 2.A.2.1 | Use objects and number lines to represent number sentences. | Grade 2 |
| Oklahoma | 2.A.2.2 | Generate models and situations to represent number sentences and vice versa. | Grade 2 |
| Oklahoma | 2.A.2.3 | Apply the commutative property, identity property, and number sense to find values for unknowns that make addition and subtraction number sentences true or false. | Grade 2 |
| Oklahoma | 2.GM.1.1 | Recognize regular and irregular trapezoids and hexagons. | Grade 2 |
| Oklahoma | 2.GM.1.2 | Describe, compare, and classify two-dimensional figures according to their geometric attributes. | Grade 2 |
| Oklahoma | 2.GM.1.3 | Compose and decompose two-dimensional shapes using triangles, squares, hexagons, trapezoids, and rhombi. | Grade 2 |
| Oklahoma | 2.GM.1.5 | Recognize right angles and classify angles as smaller or larger than a right angle. | Grade 2 |
| Oklahoma | 2.GM.2.1 | Explain the relationship between the size of the unit of measurement and the number of units needed to measure the length of an object. | Grade 2 |
| Oklahoma | 2.GM.2.2 | Explain the relationship between length and the numbers on a ruler by using a ruler to measure lengths to the nearest whole unit. | Grade 2 |
| Oklahoma | 2.GM.3.1 | Distinguish between a.m. and p.m. | Grade 2 |
| Oklahoma | 2.GM.3.2 | Read and write time to the quarter hour on an analog and digital clock. | Grade 2 |
| Oklahoma | 2.D.1.2 | Organize a collection of data with up to four categories using pictographs and bar graphs in intervals of 1s, 2s, 5s or 10s. | Grade 2 |
| Oklahoma | 2.D.1.3 | Write and solve one-step word problems involving addition or subtraction using data represented within pictographs and bar graphs with intervals of one. | Grade 2 |
| Oklahoma | 2.D.1.4 | Draw conclusions and make predictions from information in a pictograph and bar graph. | Grade 2 |
| Oklahoma | 3.N.1.1 | Read, write, discuss, and represent whole numbers up to 100,000. Representations should include but are not limited to numerals, words, pictures, number lines, and manipulatives (e.g., 350 = 3 hundreds, 5 tens = 35 tens = 3 hundreds, 4 tens, 10 ones). | Grade 3 |
| Oklahoma | 3.N.1.2 | Use place value to describe whole numbers between 1,000 and 100,000 in terms of ten thousands, thousands, hundreds, tens and ones, including written, standard, and expanded forms. | Grade 3 |
| Oklahoma | 3.N.1.3 | Applying knowledge of place values, use mental strategies (no written computations) to find 100 more or 100 less than a given number, 1,000 more or 1,000 less than a given number, and 10,000 more or 10,000 less than a given number, up to a five-digit number. | Grade 3 |
| Oklahoma | 3.N.1.4 | Use place value to compare and order whole numbers, up to 100,000, using comparative language, numbers, and symbols. | Grade 3 |
| Oklahoma | 3.N.2.1 | Represent multiplication facts by modeling a variety of approaches (e.g., manipulatives, repeated addition, equal-sized groups, arrays, area models, equal jumps on a number line, skip counting). | Grade 3 |
| Oklahoma | 3.N.2.2 | Demonstrate fluency with multiplication facts using factors up to 10. | Grade 3 |
| Oklahoma | 3.N.2.3 | Use strategies and algorithms based on knowledge of place value and equality to fluently add and subtract up to five-digit numbers (answer not to exceed 100,000). | Grade 3 |
| Oklahoma | 3.N.2.4 | Recognize when to round numbers and apply understanding to estimate sums and differences to the nearest ten thousand, thousand, hundred, and ten. | Grade 3 |
| Oklahoma | 3.N.2.5 | Use addition and subtraction to solve problems involving whole numbers. Use various strategies, including the relationship between addition and subtraction and the context of the problem to assess the reasonableness of results. | Grade 3 |
| Oklahoma | 3.N.2.6 | Represent division facts and divisibility by modeling a variety of approaches (e.g., repeated subtraction, equal sharing, forming equal groups) to show the relationship between multiplication and division. | Grade 3 |
| Oklahoma | 3.N.2.7 | Apply the relationship between multiplication and division to represent and solve problems. | Grade 3 |
| Oklahoma | 3.N.2.8 | Use various strategies (e.g., base ten blocks, area models, arrays, repeated addition, algorithms) based on knowledge of place value, equality, and properties of addition and multiplication to multiply a two-digit factor by a one-digit factor. | Grade 3 |
| Oklahoma | 3.N.3.1 | Read and write fractions with words and symbols using appropriate terminology (i.e., numerator and denominator). | Grade 3 |
| Oklahoma | 3.N.3.2 | Model fractions using length, set, and area for halves, thirds, fourths, sixths, and eighths. | Grade 3 |
| Oklahoma | 3.N.3.3 | Apply understanding of unit fractions and use this understanding to compose and decompose fractions related to the same whole. | Grade 3 |
| Oklahoma | 3.N.3.4 | Use models and number lines to order and compare fractions that are related to the same whole. | Grade 3 |
| Oklahoma | 3.A.1.1 | Create, describe, and extend patterns involving addition, subtraction, or multiplication to solve problems in a variety of contexts. | Grade 3 |
| Oklahoma | 3.A.1.3 | Explore and develop visual representations of increasing and decreasing geometric patterns and construct the next steps. | Grade 3 |
| Oklahoma | 3.A.2.1 | Use number sense with the properties of addition, subtraction, and multiplication, to find unknowns (represented by symbols) in one-step equations. Generate real-world situations to represent number sentences. | Grade 3 |
| Oklahoma | 3.A.2.2 | Identify, represent, and apply the number properties (commutative, identity, and associative properties of addition and multiplication) using models and manipulatives to solve problems. | Grade 3 |
| Oklahoma | 3.GM.1.1 | Sort three-dimensional shapes based on attributes. | Grade 3 |
| Oklahoma | 3.GM.1.2 | Build a three-dimensional figure using unit cubes when shown a picture of a three-dimensional shape. | Grade 3 |
| Oklahoma | 3.GM.1.3 | Classify angles within a polygon as acute, right, obtuse, and straight. | Grade 3 |
| Oklahoma | 3.GM.2.1 | Find the perimeter of a polygon, given whole number lengths of the sides, using a variety of models. | Grade 3 |
| Oklahoma | 3.GM.2.2 | Analyze why length and width are multiplied to find the area of a rectangle by decomposing the rectangle into one unit by one unit squares and viewing these as rows and columns to determine the area. | Grade 3 |
| Oklahoma | 3.GM.2.3 | Count cubes systematically to identify the number of cubes needed to pack the whole or half of a three-dimensional structure. | Grade 3 |
| Oklahoma | 3.GM.2.4 | Find the area of two-dimensional figures by counting the total number of same-size unit squares that fill the shape without gaps or overlaps. | Grade 3 |
| Oklahoma | 3.GM.2.5 | Choose an appropriate measurement instrument and measure the length of objects to the nearest whole centimeter or whole meter. | Grade 3 |
| Oklahoma | 3.GM.2.6 | Choose an appropriate measurement instrument and measure the length of objects to the nearest whole yard, whole foot, or half inch. | Grade 3 |
| Oklahoma | 3.GM.3.1 | Read and write time to the nearest five-minute interval (analog and digital). | Grade 3 |
| Oklahoma | 3.GM.3.2 | Determine the solutions to problems involving addition and subtraction of time in intervals of five minutes, up to one hour, using pictorial models, number line diagrams, or other tools. | Grade 3 |
| Oklahoma | 3.D.1.1 | Collect and organize a data set with multiple categories using a frequency table, line plot, pictograph, or bar graph with scaled intervals. | Grade 3 |
| Oklahoma | 3.D.1.2 | Solve one- and two-step problems using categorical data represented with a frequency table, pictograph, or bar graph with scaled intervals. | Grade 3 |
| Oklahoma | 4.N.1.3 | Applying knowledge of place value, use mental strategies (no written computations) to multiply or divide a number by 10, 100 and 1,000. | Grade 4 |
| Oklahoma | 4.N.2.1 | Demonstrate fluency with multiplication and division facts with factors up to 12. | Grade 4 |
| Oklahoma | 4.N.2.2 | Multiply 3-digit by 1-digit and 2-digit by 2-digit whole numbers, using various strategies, including but not limited to standard algorithms. | Grade 4 |
| Oklahoma | 4.N.2.3 | Estimate products of 3-digit by 1-digit and 2-digit by 2-digit whole number factors using a variety of strategies (e.g., rounding, front end estimation, adjusting, compatible numbers) to assess the reasonableness of results. Explore larger numbers using technology to investigate patterns. | Grade 4 |
| Oklahoma | 4.N.2.4 | Apply and analyze models to solve multi-step problems requiring the use of addition, subtraction, and multiplication of multi- digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. | Grade 4 |
| Oklahoma | 4.N.2.5 | Use strategies and algorithms (e.g., mental strategies, standard algorithms, partial quotients, repeated subtraction, the commutative, associative, and distributive properties) based on knowledge of place value, equality, and properties of operations to divide a 3-digit dividend by a 1-digit whole number divisor, with and without remainders. | Grade 4 |
| Oklahoma | 4.N.3.1 | Represent and rename equivalent fractions using fraction models (e.g., parts of a set, area models, fraction strips, number lines). | Grade 4 |
| Oklahoma | 4.N.3.2 | Use benchmark fractions (0, 1/4, 1/3, 1/2, 2/3, 3/4, 1) to locate additional fractions with denominators up to twelfths on a number line. | Grade 4 |
| Oklahoma | 4.N.3.3 | Use models to order and compare whole numbers and fractions less than and greater than one, using comparative language and symbols. | Grade 4 |
| Oklahoma | 4.N.3.4 | Decompose a fraction into a sum of fractions with the same denominator in more than one way, using concrete and pictorial models and recording results with numerical representations (e.g., 3/4 = 1/4 + 1/4 + 1/4 𝑎𝑛𝑑 3/4 = 2/4 + 1/4). | Grade 4 |
| Oklahoma | 4.N.3.5 | Use models to add and subtract fractions with like denominators. | Grade 4 |
| Oklahoma | 4.N.3.6 | Represent tenths and hundredths with concrete and pictorial models, making connections between fractions and decimals. | Grade 4 |
| Oklahoma | 4.N.3.7 | Read and write decimals in standard, word, and expanded form up to at least the hundredths place in a variety of contexts, including money. | Grade 4 |
| Oklahoma | 4.N.3.8 | Compare and order decimals and whole numbers using place value and various models including but not limited to grids, number lines, and base 10 blocks. | Grade 4 |
| Oklahoma | 4.N.3.9 | Compare and order benchmark fractions (0, 1/4, 1/3, 1/2, 2/3, 3/4, 1) and decimals (0, 0.25, 0.50, 0.75, 1.00) in a variety of representations. | Grade 4 |
| Oklahoma | 4.N.4.2 | Given a total cost (dollars and coins up to twenty dollars) and amount paid (dollars and coins up to twenty dollars), find the change required in a variety of ways. | Grade 4 |
| Oklahoma | 4.A.1.1 | Create an input/output chart or table to represent or extend a numerical pattern. | Grade 4 |
| Oklahoma | 4.A.1.2 | Describe the single operation rule for a pattern from an input/output table or function machine involving any operation of a whole number. | Grade 4 |
| Oklahoma | 4.A.1.3 | Construct models to show growth patterns involving geometric shapes and define the single operation rule of the pattern. | Grade 4 |
| Oklahoma | 4.A.2.1 | Use the relationships between multiplication and division with the properties of multiplication to solve problems and find values for variables that make number sentences true. | Grade 4 |
| Oklahoma | 4.A.2.2 | Solve for a variable in an equation involving addition, subtraction, multiplication, or division with whole numbers. Analyze models to represent number sentences and vice versa. | Grade 4 |
| Oklahoma | 4.A.2.3 | Determine the unknown addend or factor in equivalent and non-equivalent expressions (e.g., 5 + 6 = 4 + [], 3 ∙ 8 < 3 ∙ []). | Grade 4 |
| Oklahoma | 4.GM.1.1 | Identify points, lines, line segments, rays, angles, endpoints, and parallel and perpendicular lines in various models. | Grade 4 |
| Oklahoma | 4.GM.1.2 | Describe, classify, and construct quadrilaterals, including squares, rectangles, trapezoids, rhombuses, parallelograms, and kites. Recognize quadrilaterals in various models. | Grade 4 |
| Oklahoma | 4.GM.1.3 | Given two three-dimensional shapes, identify each shape. Compare and contrast their similarities and differences based on their attributes. | Grade 4 |
| Oklahoma | 4.GM.2.1 | Measure angles in geometric figures and real-world objects with a protractor or angle ruler. | Grade 4 |
| Oklahoma | 4.GM.2.2 | Find the area of polygons by determining if they can be decomposed into rectangles. | Grade 4 |
| Oklahoma | 4.GM.2.3 | Develop the concept that the volume of rectangular prisms with whole-number edge lengths can be found by counting the total number of same-sized unit cubes that fill a shape without gaps or overlaps. Use a variety of tools and create models to determine the volume using appropriate measurements (e.g., cm³). | Grade 4 |
| Oklahoma | 4.GM.2.4 | Choose an appropriate instrument to measure the length of an object to the nearest whole centimeter or quarter inch. | Grade 4 |
| Oklahoma | 4.GM.2.7 | Determine and justify the best use of customary and metric measurements in a variety of situations (liquid volumes, mass vs. weight, temperatures above 0 (zero) degrees, and length). | Grade 4 |
| Oklahoma | 4.GM.3.1 | Determine elapsed time. | Grade 4 |
| Oklahoma | 4.GM.3.2 | Convert one measure of time to another including seconds to minutes, minutes to hours, hours to days, and vice versa, using various models. | Grade 4 |
| Oklahoma | 4.D.1.1 | Create and organize data on a frequency table or line plot marked with whole numbers and fractions using appropriate titles, labels, and units. | Grade 4 |
| Oklahoma | 5.N.1.1 | Represent decimal fractions using a variety of models (e.g., 10 by 10 grids, base-ten blocks, meter stick) and show the rational number relationships among fractions, decimals and whole numbers. | Grade 5 |
| Oklahoma | 5.N.1.2 | Read, write, and represent decimals using place value to describe decimal numbers including fractional numbers as small as thousandths and whole numbers up to seven digits. | Grade 5 |
| Oklahoma | 5.N.1.3 | Compare and order decimals and fractions, including mixed numbers and fractions less than one, and locate on a number line. | Grade 5 |
| Oklahoma | 5.N.1.4 | Recognize and generate equivalent terminating decimals, fractions, mixed numbers, and fractions in various models. | Grade 5 |
| Oklahoma | 5.N.2.1 | Estimate solutions to division problems to assess the reasonableness of results. | Grade 5 |
| Oklahoma | 5.N.2.2 | Divide multi-digit numbers, by one- and two-digit divisors, based on knowledge of place value, including but not limited to standard algorithms. | Grade 5 |
| Oklahoma | 5.N.2.3 | Recognize that remainders can be represented in a variety of ways, including a whole number, fraction, or decimal. Determine the most meaningful form of a remainder based on the context of the problem. | Grade 5 |
| Oklahoma | 5.N.2.4 | Construct models to solve multi-digit whole number problems requiring addition, subtraction, multiplication, and division using various representations, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results. | Grade 5 |
| Oklahoma | 5.N.3.1 | Estimate sums and differences of fractions with like and unlike denominators, mixed numbers, and decimals to assess the reasonableness of the results. | Grade 5 |
| Oklahoma | 5.N.3.2 | Illustrate addition and subtraction of fractions with like and unlike denominators, mixed numbers, and decimals using a variety of mathematical models (e.g., fraction strips, area models, number lines, fraction rods). | Grade 5 |
| Oklahoma | 5.N.3.3 | Add and subtract fractions with like and unlike denominators, mixed numbers, and decimals, involving money, measurement, geometry, and data. Use various models and efficient strategies, including but not limited to standard algorithms. | Grade 5 |
| Oklahoma | 5.N.3.4 | Apply mental math and knowledge of place value (no written computations) to find 0.1 more or 0.1 less than a number, 0.01 more or 0.01 less than a number, and 0.001 more or 0.001 less than a number. | Grade 5 |
| Oklahoma | 5.A.1.1 | Use tables and rules with up to two operations to describe patterns of change and make predictions and generalizations about various mathematical situations. | Grade 5 |
| Oklahoma | 5.A.1.2 | Use a rule or table to represent ordered pairs of whole numbers and graph these ordered pairs on a coordinate plane, identifying the origin and axes in relation to the coordinates. | Grade 5 |
| Oklahoma | 5.A.2.1 | Generate equivalent numerical expressions and solve problems using number sense involving whole numbers by applying the commutative property, associative property, distributive property, and order of operations (excluding exponents). | Grade 5 |
| Oklahoma | 5.A.2.2 | Determine whether an equation or inequality involving a variable is true or false for a given value of the variable. | Grade 5 |
| Oklahoma | 5.A.2.3 | Evaluate expressions involving variables when values for the variables are given. | Grade 5 |
| Oklahoma | 5.GM.1.1 | Describe, identify, classify, and construct triangles (equilateral, right, scalene, isosceles) by their attributes using various mathematical models. | Grade 5 |
| Oklahoma | 5.GM.1.2 | Describe, identify, and classify three-dimensional figures (cubes, rectangular prisms, and pyramids) and their attributes (number of edges, faces, vertices, shapes of faces), given various mathematical models. | Grade 5 |
| Oklahoma | 5.GM.1.3 | Recognize and draw a net for a three-dimensional figure (cube, rectangular prism, pyramid). | Grade 5 |
| Oklahoma | 5.GM.2.1 | Determine the volume of rectangular prisms by the number of unit cubes (n) used to construct the shape and by the product of the dimensions of the prism 𝑎 ⋅ 𝑏 ⋅ 𝑐 = 𝑛. Understand rectangular prisms of different dimensions (p, q, and r) can have the same volume if 𝑎 ⋅ 𝑏 ⋅ 𝑐 = 𝑝 ⋅ 𝑞 ⋅ 𝑟 = 𝑛. | Grade 5 |
| Oklahoma | 5.GM.3.1 | Measure and compare angles according to size using various tools. | Grade 5 |
| Oklahoma | 5.GM.3.3 | Apply the relationship between inches, feet, and yards to measure, convert, and compare objects to solve problems. | Grade 5 |
| Oklahoma | 5.GM.3.4 | Apply the relationship between millimeters, centimeters, and meters to measure, convert, and compare objects to solve problems. | Grade 5 |
| Oklahoma | 5.D.1.1 | Find the measures of central tendency (i.e., mean, median, mode) and range of a set of data. Understand that the mean is a “leveling out” or central balance point of the data. | Grade 5 |
| Oklahoma | 5.D.1.2 | Create and analyze line and double-bar graphs with increments of whole numbers, fractions, and decimals. | Grade 5 |
| Oklahoma | 6.N.1.1 | Use manipulatives and models (e.g., number lines) to determine positive and negative numbers and their contexts, identify opposites, and explain the meaning of 0 (zero) in a variety of situations. | Grade 6 |
| Oklahoma | 6.N.1.2 | Compare and order positive rational numbers, represented in various forms, or integers using the symbols , and =. | Grade 6 |
| Oklahoma | 6.N.1.3 | Explain that a percent represents parts “out of 100” and ratios “to 100.” | Grade 6 |
| Oklahoma | 6.N.1.4 | Determine equivalencies among fractions, mixed numbers, decimals, and percents. | Grade 6 |
| Oklahoma | 6.N.2.1 | Estimate solutions for integer addition and subtraction of problems in order to assess the reasonableness of results. | Grade 6 |
| Oklahoma | 6.N.2.2 | Illustrate addition and subtraction of integers using a variety of representations. | Grade 6 |
| Oklahoma | 6.N.2.3 | Add and subtract integers in a variety of situations; use efficient and generalizable procedures including but not limited to standard algorithms. | Grade 6 |
| Oklahoma | 6.N.2.5 | Factor whole numbers and express prime and composite numbers as a product of prime factors with exponents. | Grade 6 |
| Oklahoma | 6.N.3.1 | Identify and use ratios to compare and relate quantities in multiple ways. Recognize that multiplicative comparison and additive comparison are different. | Grade 6 |
| Oklahoma | 6.N.3.2 | Determine the unit rate for ratios. | Grade 6 |
| Oklahoma | 6.N.3.3 | Apply the relationship between ratios, equivalent fractions, unit rates, and percents to solve problems in various contexts. | Grade 6 |
| Oklahoma | 6.N.4.1 | Estimate solutions to problems with whole numbers, decimals, fractions, and mixed numbers, and use the estimates to assess the reasonableness of results in the context of the problem. | Grade 6 |
| Oklahoma | 6.N.4.2 | Illustrate multiplication and division of fractions and decimals to show connections to fractions, whole number multiplication, and inverse relationships. | Grade 6 |
| Oklahoma | 6.N.4.3 | Multiply and divide fractions and decimals using efficient and generalizable procedures. | Grade 6 |
| Oklahoma | 6.N.4.4 | Use mathematical modeling to solve and interpret problems including money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers. | Grade 6 |
| Oklahoma | 6.A.1.1 | Plot integer- and rational-valued (limited to halves and fourths) ordered-pairs as coordinates in all four quadrants and recognize the reflective relationships among coordinates that differ only by their signs. | Grade 6 |
| Oklahoma | 6.A.1.2 | Represent relationships between two varying positive quantities involving no more than two operations with rules, graphs, and tables; translate between any two of these representations. | Grade 6 |
| Oklahoma | 6.A.1.3 | Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false. | Grade 6 |
| Oklahoma | 6.A.2.1 | Generate equivalent expressions and evaluate expressions involving positive rational numbers by applying the commutative, associative, and distributive properties and order of operations to model and solve mathematical problems. | Grade 6 |
| Oklahoma | 6.A.3.1 | Model mathematical situations using expressions, equations and inequalities involving variables and rational numbers. | Grade 6 |
| Oklahoma | 6.A.3.2 | Use number sense and properties of operations and equality to model and solve mathematical problems involving equations in the form 𝑥 + 𝑝 = 𝑞 and 𝑝𝑥 = 𝑞, where p and q are nonnegative rational numbers. Graph the solution on a number line, interpret the solution in the original context, and assess the reasonableness of the solution. | Grade 6 |
| Oklahoma | 6.GM.1.1 | Predict, describe, and apply translations (slides), reflections (flips), and rotations (turns) to a two-dimensional figure. | Grade 6 |
| Oklahoma | 6.GM.1.2 | Recognize that translations, reflections, and rotations preserve congruence and use them to show that two figures are congruent. | Grade 6 |
| Oklahoma | 6.GM.1.3 | Identify and describe the line(s) of symmetry in two-dimensional shapes. | Grade 6 |
| Oklahoma | 6.GM.2.1 | Develop and use formulas for the area of squares and parallelograms using a variety of methods including but not limited to the standard algorithms and finding unknown measures. | Grade 6 |
| Oklahoma | 6.GM.2.2 | Develop and use formulas to determine the area of triangles and find unknown measures. | Grade 6 |
| Oklahoma | 6.GM.2.3 | Find the area of right triangles, other triangles, special quadrilaterals, and polygons that can be decomposed into triangles and other shapes. | Grade 6 |
| Oklahoma | 6.GM.3.1 | Solve problems using the relationships between the angles (vertical, complementary, and supplementary) formed by intersecting lines. | Grade 6 |
| Oklahoma | 6.GM.3.2 | Develop and use the fact that the sum of the interior angles of a triangle is 180 ̊ to determine missing angle measures in a triangle. | Grade 6 |
| Oklahoma | 6.GM.4.1 | Estimate weights and capacities using benchmarks in customary and metric measurement systems with appropriate units. | Grade 6 |
| Oklahoma | 6.GM.4.2 | Solve problems that require the conversion of lengths within the same measurement systems using appropriate units. | Grade 6 |
| Oklahoma | 6.D.1.1 | Interpret the mean, median, and mode for a set of data. | Grade 6 |
| Oklahoma | 6.D.1.2 | Explain and justify which measure of center (mean, median, or mode) would provide the most descriptive information for a given set of data. | Grade 6 |
| Oklahoma | 7.N.1.2 | Recognize and generate equivalent representations of rational numbers, including equivalent fractions. | Grade 7 |
| Oklahoma | 7.N.2.1 | Estimate solutions to multiplication and division of integers in order to assess the reasonableness of results. | Grade 7 |
| Oklahoma | 7.N.2.2 | Illustrate multiplication and division of integers using a variety of representations. | Grade 7 |
| Oklahoma | 7.N.2.4 | Raise rational numbers (integers, fractions, and decimals) to positive integer exponents. | Grade 7 |
| Oklahoma | 7.N.2.5 | Model and solve problems using rational numbers involving addition, subtraction, multiplication, division, and positive integer exponents. | Grade 7 |
| Oklahoma | 7.A.1.1 | Identify a relationship between two varying quantities, x and y, as proportional if it can be expressed in the form y/x = 𝑘 or y=kx; distinguish proportional relationships from non-proportional relationships. | Grade 7 |
| Oklahoma | 7.A.1.2 | Recognize that the graph of a proportional relationship is a line through the origin and the coordinate (1, r), where r is the slope and the unit rate (constant of proportionality, k). | Grade 7 |
| Oklahoma | 7.A.2.1 | Represent proportional relationships with tables, verbal descriptions, symbols, and graphs; translate from one representation to another. Determine and compare the unit rate (constant of proportionality, slope, or rate of change) given any of these representations. | Grade 7 |
| Oklahoma | 7.A.2.2 | Solve multi-step problems with proportional relationships (e.g., distance-time, percent increase or decrease, discounts, tips, unit pricing, mixtures and concentrations, similar figures, other mathematical situations). | Grade 7 |
| Oklahoma | 7.A.2.3 | Use proportional reasoning to solve problems involving ratios. | Grade 7 |
| Oklahoma | 7.A.3.1 | Write and solve problems leading to linear equations with one variable in the form px + q = r and p(x + q) = r, where p, q, and r are rational numbers. | Grade 7 |
| Oklahoma | 7.A.3.2 | Represent, write, solve, and graph problems leading to linear inequalities with one variable in the form 𝑥 + 𝑝 > 𝑞 and 𝑥 + 𝑝 < 𝑞, where 𝑝, and 𝑞 are nonnegative rational numbers. | Grade 7 |
| Oklahoma | 7.A.4.1 | Use properties of operations (associative, commutative, and distributive) to generate equivalent numerical and algebraic expressions containing rational numbers, grouping symbols and whole number exponents. | Grade 7 |
| Oklahoma | 7.A.4.2 | Evaluate numerical expressions using calculators and other technologies and justify solutions using order of operations and grouping symbols. | Grade 7 |
| Oklahoma | 7.GM.1.1 | Recognize that the surface area of a rectangular prism can be found by finding the area of each component of the net of that figure. Know that rectangular prisms of different dimensions can have the same surface area. | Grade 7 |
| Oklahoma | 7.GM.1.2 | Using a variety of tools and strategies, develop the concept that surface area of a rectangular prism can be found by wrapping the figure with same-sized square units without gaps or overlap. Use appropriate measurements (e.g., cm²). | Grade 7 |
| Oklahoma | 7.GM.1.3 | Using a variety of tools and strategies, develop the concept that the volume of rectangular prisms can be found by counting the total number of same-sized unit cubes that fill a shape without gaps or overlaps. Use appropriate measurements (e.g., cm³). | Grade 7 |
| Oklahoma | 7.GM.2.1 | Develop and use the formula to determine the area of a trapezoid. | Grade 7 |
| Oklahoma | 7.GM.3.2 | Demonstrate an understanding of the proportional relationship between the diameter and circumference of a circle and that the unit rate (constant of proportionality) is pi (𝜋) and can be approximated by rational numbers such as 22/7 and 3.14. | Grade 7 |
| Oklahoma | 7.GM.3.3 | Calculate the circumference and area of circles to solve problems in various contexts, in terms of pi (𝜋) and using approximations for pi (𝜋). | Grade 7 |
| Oklahoma | 7.GM.4.1 | Describe the properties of similarity, compare geometric figures for similarity, and determine scale factors resulting from dilations. | Grade 7 |
| Oklahoma | 7.GM.4.2 | Apply proportions, ratios, and scale factors to solve problems involving scale drawings and to determine side lengths and areas of similar triangles and rectangles. | Grade 7 |
| Oklahoma | 7.GM.4.3 | Graph and describe translations (with directional and algebraic instructions), reflections across the x- and y-axes, and rotations in 90º increments about the origin of figures on a coordinate plane, and determine the coordinates of the vertices of a figure after a transformation. | Grade 7 |
| Oklahoma | PA.N.1.2 | Express and compare approximations of very large and very small numbers using scientific notation. | Pre-Algebra |
| Oklahoma | PA.N.1.3 | Multiply and divide numbers expressed in scientific notation and express the answer in scientific notation. | Pre-Algebra |
| Oklahoma | PA.N.1.4 | Compare and order real numbers; locate real numbers on a number line. Identify the square roots of perfect squares to 400 or, if it is not a perfect square root, locate it as an irrational number between two consecutive positive integers. | Pre-Algebra |
| Oklahoma | PA.A.1.1 | Recognize that a function is a relationship between an independent variable and a dependent variable in which the value of the independent variable determines the value of the dependent variable. | Pre-Algebra |
| Oklahoma | PA.A.1.2 | Use linear functions to represent and model mathematical situations. | Pre-Algebra |
| Oklahoma | PA.A.1.3 | Identify a function as linear if it can be expressed in the form y=mx + b or if its graph is a non-vertical straight line. | Pre-Algebra |
| Oklahoma | PA.A.2.1 | Represent linear functions with tables, verbal descriptions, symbols, and graphs; translate from one representation to another. | Pre-Algebra |
| Oklahoma | PA.A.2.2 | Identify, describe, and analyze linear relationships between two variables. | Pre-Algebra |
| Oklahoma | PA.A.2.3 | Identify graphical properties of linear functions, including slope and intercepts. Know that the slope equals the rate of change, and that the y-intercept is zero when the function represents a proportional relationship. | Pre-Algebra |
| Oklahoma | PA.A.2.5 | Solve problems involving linear functions and interpret results in the original context. | Pre-Algebra |
| Oklahoma | PA.A.3.1 | Use substitution to simplify and evaluate algebraic expressions. | Pre-Algebra |
| Oklahoma | PA.A.3.2 | Justify steps in generating equivalent expressions by combining like terms and using order of operations (to include grouping symbols). Identify the properties used, including the properties of operations (associative, commutative, and distributive). | Pre-Algebra |
| Oklahoma | PA.A.4.1 | Solve mathematical problems using linear equations with one variable where there could be one, infinitely many, or no solutions. Represent situations using linear equations and interpret solutions in the original context. | Pre-Algebra |
| Oklahoma | PA.A.4.2 | Represent, write, solve, and graph problems leading to linear inequalities with one variable in the form 𝑝𝑥 + 𝑞 > 𝑟 and 𝑝𝑥 + 𝑞 < 𝑟, where p, q, and r are rational numbers. | Pre-Algebra |
| Oklahoma | PA.A.4.3 | Represent real-world situations using equations and inequalities involving one variable. | Pre-Algebra |
| Oklahoma | PA.GM.1.1 | Justify the Pythagorean theorem using measurements, diagrams, or dynamic software to solve problems in two dimensions involving right triangles. | Pre-Algebra |
| Oklahoma | PA.GM.1.2 | Use the Pythagorean theorem to find the distance between any two points in a coordinate plane. | Pre-Algebra |
| Oklahoma | PA.GM.2.1 | Calculate the surface area of a rectangular prism using decomposition or nets. Use appropriate units (e.g., cm²). | Pre-Algebra |
| Oklahoma | PA.GM.2.2 | Calculate the surface area of a cylinder, in terms of pi (Π) and using approximations for pi (Π), using decomposition or nets. Use appropriate units (e.g., cm²). | Pre-Algebra |
| Oklahoma | PA.GM.2.3 | Justify why base area (B) and height (h) in the formula V=Bh are multiplied to find the volume of a rectangular prism. Use appropriate units (e.g., cm³). | Pre-Algebra |
| Oklahoma | PA.GM.2.4 | Develop and use the formulas 𝑉 = (𝜋𝑟)$ℎ and 𝑉 = 𝐵ℎ to determine the volume of right cylinders, in terms of π and using approximations for pi (Τ). Justify why base area (B) and height (h) are multiplied to find the volume of a right cylinder. Use appropriate units (e.g., cm³). | Pre-Algebra |
| Oklahoma | PA.D.1.3 | Collect, display, and interpret data using scatter plots. Use the shape of the scatter plot to find the informal line of best fit, make statements about the average rate of change, and make predictions about values not in the original data set. Use appropriate titles, labels, and units. | Pre-Algebra |
| Oklahoma | A1.N.1.1 | Write square roots and cube roots of constants and monomial algebraic expressions in simplest radical form. | Algebra 1 |
| Oklahoma | A1.A.1.1 | Use knowledge of solving equations with rational values to represent, use and apply mathematical models (e.g., angle measures, geometric formulas, dimensional analysis, Pythagorean theorem, science, statistics) and interpret the solutions in the original context. | Algebra 1 |
| Oklahoma | A1.A.1.3 | Analyze, use and apply mathematical models to solve problems involving systems of linear equations with a maximum of two variables by graphing, substitution, and elimination. Graphing calculators or other appropriate technology may be utilized. Interpret the solutions in the original context. | Algebra 1 |
| Oklahoma | A1.A.2.1 | Represent relationships using mathematical models with linear inequalities; solve the resulting inequalities, graph on a coordinate plane, and interpret the solutions. | Algebra 1 |
| Oklahoma | A1.A.3.3 | Factor common monomial factors from polynomial expressions and factor quadratic expressions with a leading coefficient of 1. | Algebra 1 |
| Oklahoma | A1.A.3.4 | Evaluate linear, absolute value, rational, and radical expressions. Include applying a nonstandard operation such as x ⨀ y=2x+y | Algebra 1 |
| Oklahoma | A1.A.4.4 | Express linear equations in slope-intercept, point-slope, and standard forms. Convert between these forms. | Algebra 1 |
| Oklahoma | A1.F.1.1 | Distinguish between relations and functions. | Algebra 1 |
| Oklahoma | A1.F.1.2 | Identify the dependent variable, independent variable, domain and range given a function, equation, or graph. Identify restrictions on the domain and range in mathematical models. | Algebra 1 |
| Oklahoma | A1.F.3.2 | Use function notation; evaluate a function, including nonlinear, at a given point in its domain algebraically and graphically. Interpret the results in terms of the original context. | Algebra 1 |
| Oklahoma | G.2D.1.1 | Use properties of parallel lines cut by a transversal to determine angle relationships and solve problems. | Geometry |
| Oklahoma | G.2D.1.2 | Use the angle relationships formed by lines cut by a transversal to determine if the lines are parallel and verify, using algebraic and deductive proofs. | Geometry |
| Oklahoma | G.2D.1.3 | Apply the properties of angles (corresponding, exterior, interior, vertical, complementary, supplementary) to solve problems using mathematical models, algebraic reasoning, and proofs. | Geometry |
| Oklahoma | G.2D.1.7 | Apply the properties of polygons, and use them to represent and apply mathematical models involving perimeter and area (e.g., triangles, special quadrilaterals, regular polygons up to 12 sides, composite figures). | Geometry |
| Oklahoma | G.2D.1.11 | Use numeric, graphic, and algebraic representations of transformations in two dimensions (e.g., reflections, translations, dilations, rotations about the origin by multiples of 90º) to solve problems involving figures on a coordinate plane and identify types of symmetry. | Geometry |
| Oklahoma | G.3D.1.1 | Represent, use, and apply mathematical models and other tools (e.g., nets, measuring devices, formulas) to solve problems involving surface area and volume of three-dimensional figures (prisms, cylinders, pyramids, cones, spheres, composites of these figures). | Geometry |
| Oklahoma | G.C.1.1 | Apply the properties of circles to solve problems involving circumference and area, using approximate values and in terms of pi, using algebraic and logical reasoning. | Geometry |
| Oklahoma | A2.N.1.3 | Understand and apply the relationship between rational exponents to integer exponents and radicals to solve problems. | Algebra 2 |
| Oklahoma | A2.A.1.1 | Use mathematical models to represent quadratic relationships and solve using factoring, completing the square, the quadratic formula, and various methods (including graphing calculator or other appropriate technology). Find non-real roots when they exist. | Algebra 2 |
| Oklahoma | A2.A.1.2 | Use mathematical models to represent exponential relationships, such as compound interest, depreciation, and population growth. Solve these equations algebraically or graphically (including graphing calculator or other appropriate technology). | Algebra 2 |
| Oklahoma | A2.A.1.4 | Solve polynomial equations with real roots using various methods (e.g., polynomial division, synthetic division, using graphing calculators or other appropriate technology). | Algebra 2 |
| Oklahoma | A2.A.2.1 | Factor polynomial expressions including, but not limited to, trinomials, differences of squares, sum and difference of cubes, and factoring by grouping, using a variety of tools and strategies. | Algebra 2 |
| Oklahoma | A2.A.2.4 | Recognize that a quadratic function has different equivalent representations [𝑓(𝑥) = 𝑎𝑥² + 𝑏𝑥 + 𝑐, 𝑓(𝑥) = 𝑎(𝑥 − ℎ)² + 𝑘, 𝑎𝑛𝑑 𝑓(𝑥) = 𝑎(𝑥 − 𝑝)(𝑥 − 𝑞)]. Identify and use the mathematical model that is most appropriate to solve problems. | Algebra 2 |
| Oklahoma | A2.D.1.2 | Collect data and use scatter plots to analyze patterns and describe linear, exponential, or quadratic relationships between two variables. | Algebra 2 |
| Oklahoma | PC.F.1.3 | Interpret characteristics of graphs and tables for a function that models a relationship between two quantities in terms of the quantities. | Precalculus |
| Ontario | K.1 | Investigate the idea that quantity is greater when counting forwards and less when counting backwards. | Kindergarten |
| Ontario | K.2 | Investigate some concepts of quantity through identifying and comparing sets with more, fewer, or the same number of objects. | Kindergarten |
| Ontario | K.3 | Recognize some quantities without having to count, using a variety of tools or strategies. | Kindergarten |
| Ontario | K.4 | Demonstrate an understanding of the counting concepts of stable order and of order irrelevance. | Kindergarten |
| Ontario | K.5 | Use, read, and represent whole numbers to 10 in a variety of meaningful contexts. | Kindergarten |
| Ontario | K.6 | Demonstrate awareness of addition and subtraction in everyday activities. | Kindergarten |
| Ontario | K.7 | Demonstrate an understanding of number relationships for numbers from 0 to 10, through investigation. | Kindergarten |
| Ontario | K.8 | Investigate and develop strategies for composing and decomposing quantities to 10. | Kindergarten |
| Ontario | K.9 | Compose and decompose quantities to 10. | Kindergarten |
| Ontario | K.10 | Investigate addition and subtraction in everyday experiences and routines through the use of modelling strategies, manipulatives, and counting strategies. | Kindergarten |
| Ontario | K.11 | Begin to make use of one-to-one correspondence in counting objects and matching groups of objects. | Kindergarten |
| Ontario | K.12 | Investigate addition and subtraction in everyday activities through the use of manipulatives, visual models, or oral exploration. | Kindergarten |
| Ontario | 1.B.1.1 | Whole Numbers: read and represent whole numbers up to and including 50, and describe various ways they are used in everyday life. | Grade 1 |
| Ontario | 1.B.1.2 | Whole Numbers: compose and decompose whole numbers up to and including 50, using a variety of tools and strategies, in various contexts. | Grade 1 |
| Ontario | 1.B.1.3 | Whole Numbers: compare and order whole numbers up to and including 50, in various contexts. | Grade 1 |
| Ontario | 1.B.1.4 | Whole Numbers: estimate the number of objects in collections of up to 50, and verify their estimates by counting. | Grade 1 |
| Ontario | 1.B.1.5 | Whole Numbers: count to 50 by 1s, 2s, 5s, and 10s, using a variety of tools and strategies. | Grade 1 |
| Ontario | 1.B.1.6 | Fractions: use drawings to represent and solve fair-share problems that involve 2 and 4 sharers, respectively, and have remainders of 1 or 2. | Grade 1 |
| Ontario | 1.B.1.7 | Fractions: recognize that one half and two fourths of the same whole are equal, in fair-sharing contexts. | Grade 1 |
| Ontario | 1.B.1.8 | Fractions: use drawings to compare and order unit fractions representing the individual portions that result when a whole is shared by different numbers of sharers, up to a maximum of 10. | Grade 1 |
| Ontario | 1.B.2.1 | Properties and Relationships: use the properties of addition and subtraction, and the relationship between addition and subtraction, to solve problems and check calculations. | Grade 1 |
| Ontario | 1.B.2.2 | Math Facts: recall and demonstrate addition facts for numbers up to 10, and related subtraction facts. | Grade 1 |
| Ontario | 1.B.2.3 | Mental Math: use mental math strategies, including estimation, to add and subtract whole numbers that add up to no more than 20, and explain the strategies used. | Grade 1 |
| Ontario | 1.B.2.4 | Addition and Subtraction: use objects, diagrams, and equations to represent, describe, and solve situations involving addition and subtraction of whole numbers that add up to no more than 50. | Grade 1 |
| Ontario | 1.B.2.5 | Multiplication and Division: represent and solve equal-group problems where the total number of items is no more than 10, including problems in which each group is a half, using tools and drawings. | Grade 1 |
| Ontario | 1.C.1.1 | Patterns: identify and describe the regularities in a variety of patterns, including patterns found in real-life contexts. | Grade 1 |
| Ontario | 1.C.1.2 | Patterns: create and translate patterns using movements, sounds, objects, shapes, letters, and numbers. | Grade 1 |
| Ontario | 1.C.1.3 | Patterns: determine pattern rules and use them to extend patterns, make and justify predictions, and identify missing elements in patterns. | Grade 1 |
| Ontario | 1.C.1.4 | Patterns: create and describe patterns to illustrate relationships among whole numbers up to 50. | Grade 1 |
| Ontario | 1.C.2.2 | Equalities and Inequalities: determine whether given pairs of addition and subtraction expressions are equivalent or not. | Grade 1 |
| Ontario | 1.C.2.3 | Equalities and Inequalities: identify and use equivalent relationships for whole numbers up to 50, in various contexts. | Grade 1 |
| Ontario | 1.D.1.1 | Data Collection and Organization: sort sets of data about people or things according to one attribute, and describe rules used for sorting. | Grade 1 |
| Ontario | 1.D.1.2 | Data Collection and Organization: collect data through observations, experiments, and interviews to answer questions of interest that focus on a single piece of information; record the data using methods of their choice; and organize the data in tally tables. | Grade 1 |
| Ontario | 1.D.1.3 | Data Visualization: display sets of data, using one-to-one correspondence, in concrete graphs and pictographs with proper sources, titles, and labels. | Grade 1 |
| Ontario | 1.D.1.4 | Data Analysis: order categories of data from greatest to least frequency for various data sets displayed in tally tables, concrete graphs, and pictographs. | Grade 1 |
| Ontario | 1.D.1.5 | Data Analysis: analyse different sets of data presented in various ways, including in tally tables, concrete graphs, and pictographs, by asking and answering questions about the data and drawing conclusions, then make convincing arguments and informed decisions. | Grade 1 |
| Ontario | 1.E.1.1 | Geometric Reasoning: sort threedimensional objects and two-dimensional shapes according to one attribute at a time, and identify the sorting rule being used. | Grade 1 |
| Ontario | 1.E.1.2 | Geometric Reasoning: construct three-dimensional objects, and identify two-dimensional shapes contained within structures and objects. | Grade 1 |
| Ontario | 1.E.1.3 | Geometric Reasoning: construct and describe two-dimensional shapes and three-dimensional objects that have matching halves. | Grade 1 |
| Ontario | 1.E.1.4 | Location and Movement: describe the relative locations of objects or people, using positional language. | Grade 1 |
| Ontario | 1.E.1.5 | Location and Movement: give and follow directions for moving from one location to another. | Grade 1 |
| Ontario | 1.E.2.1 | Attributes: identify measurable attributes of two-dimensional shapes and threedimensional objects, including length, area, mass, capacity, and angle. | Grade 1 |
| Ontario | 1.E.2.2 | Attributes: compare several everyday objects and order them according to length, area, mass, and capacity. | Grade 1 |
| Ontario | 2.B.1.1 | Whole Numbers: read, represent, compose, and decompose whole numbers up to and including 200, using a variety of tools and strategies, and describe various ways they are used in everyday life. | Grade 2 |
| Ontario | 2.B.1.2 | Whole Numbers: compare and order whole numbers up to and including 200, in various contexts. | Grade 2 |
| Ontario | 2.B.1.3 | Whole Numbers: estimate the number of objects in collections of up to 200 and verify their estimates by counting. | Grade 2 |
| Ontario | 2.B.1.4 | Whole Numbers: count to 200, including by 20s, 25s, and 50s, using a variety of tools and strategies. | Grade 2 |
| Ontario | 2.B.1.5 | Whole Numbers: describe what makes a number even or odd. | Grade 2 |
| Ontario | 2.B.1.6 | Fractions: use drawings to represent, solve, and compare the results of fair-share problems that involve sharing up to 10 items among 2, 3, 4, and 6 sharers, including problems that result in whole numbers, mixed numbers, and fractional amounts. | Grade 2 |
| Ontario | 2.B.1.7 | Fractions: recognize that one third and two sixths of the same whole are equal, in fair-sharing contexts. | Grade 2 |
| Ontario | 2.B.2.1 | Properties and Relationships: use the properties of addition and subtraction, and the relationships between addition and multiplication and between subtraction and division, to solve problems and check calculations. | Grade 2 |
| Ontario | 2.B.2.2 | Properties and Relationships: recall and demonstrate addition facts for numbers up to 20, and related subtraction facts. | Grade 2 |
| Ontario | 2.B.2.3 | Mental Math: use mental math strategies, including estimation, to add and subtract whole numbers that add up to no more than 50, and explain the strategies used. | Grade 2 |
| Ontario | 2.B.2.4 | Addition and Subtraction: use objects, diagrams, and equations to represent, describe, and solve situations involving addition and subtraction of whole numbers that add up to no more than 100. | Grade 2 |
| Ontario | 2.B.2.5 | Multiplication and Division: represent multiplication as repeated equal groups, including groups of one half and one fourth, and solve related problems, using various tools and drawings. | Grade 2 |
| Ontario | 2.B.2.6 | Multiplication and Division: represent division of up to 12 items as the equal sharing of a quantity, and solve related problems, using various tools and drawings. | Grade 2 |
| Ontario | 2.C.1.1 | Patterns: identify and describe a variety of patterns involving geometric designs, including patterns found in real-life contexts. | Grade 2 |
| Ontario | 2.C.1.2 | Patterns: create and translate patterns using various representations, including shapes and numbers. | Grade 2 |
| Ontario | 2.C.1.3 | Patterns: determine pattern rules and use them to extend patterns, make and justify predictions, and identify missing elements in patterns represented with shapes and numbers. | Grade 2 |
| Ontario | 2.C.1.4 | Patterns: create and describe patterns to illustrate relationships among whole numbers up to 100. | Grade 2 |
| Ontario | 2.C.2.1 | Variables: identify when symbols are being used as variables, and describe how they are being used. | Grade 2 |
| Ontario | 2.C.2.2 | Equalities and Inequalities: determine what needs to be added to or subtracted from addition and subtraction expressions to make them equivalent. | Grade 2 |
| Ontario | 2.C.2.3 | Equalities and Inequalities: identify and use equivalent relationships for whole numbers up to 100, in various contexts. | Grade 2 |
| Ontario | 2.D.1.1 | Probability: sort sets of data about people or things according to two attributes, using tables and logic diagrams, including Venn and Carroll diagrams. | Grade 2 |
| Ontario | 2.D.1.3 | Probability: display sets of data, using one-to-one correspondence, in concrete graphs, pictographs, line plots, and bar graphs with proper sources, titles, and labels. | Grade 2 |
| Ontario | 2.D.1.4 | Probability: identify the mode(s), if any, for various data sets presented in concrete graphs, pictographs, line plots, bar graphs, and tables, and explain what this measure indicates about the data. | Grade 2 |
| Ontario | 2.E.1.1 | Geometric Reasoning: sort and identify twodimensional shapes by comparing number of sides, side lengths, angles, and number of lines of symmetry. | Grade 2 |
| Ontario | 2.E.1.2 | Geometric Reasoning: compose and decompose twodimensional shapes, and show that the area of a shape remains constant regardless of how its parts are rearranged. | Grade 2 |
| Ontario | 2.E.1.3 | Geometric Reasoning: identify congruent lengths and angles in twodimensional shapes by mentally and physically matching them, and determine if the shapes are congruent. | Grade 2 |
| Ontario | 2.E.1.5 | Location and Movement: describe the relative positions of several objects and the movements needed to get from one object to another. | Grade 2 |
| Ontario | 2.E.2.1 | Length: choose and use non-standard units appropriately to measure lengths, and describe the inverse relationship between the size of a unit and the number of units needed. | Grade 2 |
| Ontario | 2.E.2.3 | Length: measure and draw lengths in centimetres and metres, using a measuring tool, and recognize the impact of starting at points other than zero. | Grade 2 |
| Ontario | 2.E.2.4 | Time: use units of time, including seconds, minutes, hours, and nonstandard units, to describe the duration of various events. | Grade 2 |
| Ontario | 3.B.1.1 | Whole Numbers: read, represent, compose, and decompose whole numbers up to and including 1000, using a variety of tools and strategies, and describe various ways they are used in everyday life. | Grade 3 |
| Ontario | 3.B.1.2 | Whole Numbers: compare and order whole numbers up to and including 1000, in various contexts. | Grade 3 |
| Ontario | 3.B.1.3 | Whole Numbers: round whole numbers to the nearest ten or hundred, in various contexts. | Grade 3 |
| Ontario | 3.B.1.4 | Whole Numbers: count to 1000, including by 50s, 100s, and 200s, using a variety of tools and strategies. | Grade 3 |
| Ontario | 3.B.1.5 | Whole Numbers: use place value when describing and representing multi-digit numbers in a variety of ways, including with base ten materials. | Grade 3 |
| Ontario | 3.B.1.6 | Fractions: use drawings to represent, solve, and compare the results of fair-share problems that involve sharing up to 20 items among 2, 3, 4, 5, 6, 8, and 10 sharers, including problems that result in whole numbers, mixed numbers, and fractional amounts. | Grade 3 |
| Ontario | 3.B.1.7 | Fractions: represent and solve fair-share problems that focus on determining and using equivalent fractions, including problems that involve halves, fourths, and eighths; thirds and sixths; and fifths and tenths. | Grade 3 |
| Ontario | 3.B.2.1 | Properties and Relationships: use the properties of operations, and the relationships between multiplication and division, to solve problems and check calculations. | Grade 3 |
| Ontario | 3.B.2.2 | Properties and Relationships: recall and demonstrate multiplication facts of 2, 5, and 10, and related division facts. | Grade 3 |
| Ontario | 3.B.2.3 | Mental Math: use mental math strategies, including estimation, to add and subtract whole numbers that add up to no more than 1000, and explain the strategies used. | Grade 3 |
| Ontario | 3.B.2.4 | Addition and Subtraction: demonstrate an understanding of algorithms for adding and subtracting whole numbers by making connections to and describing the way other tools and strategies are used to add and subtract. | Grade 3 |
| Ontario | 3.B.2.5 | Addition and Subtraction: represent and solve problems involving the addition and subtraction of whole numbers that add up to no more than 1000, using various tools and algorithms. | Grade 3 |
| Ontario | 3.B.2.6 | Multiplication and Division: represent multiplication of numbers up to 10 × 10 and division up to 100 ÷ 10, using a variety of tools and drawings, including arrays. | Grade 3 |
| Ontario | 3.B.2.7 | Multiplication and Division: represent and solve problems involving multiplication and division, including problems that involve groups of one half, one fourth, and one third, using tools and drawings. | Grade 3 |
| Ontario | 3.B.2.8 | Multiplication and Division: represent the connection between the numerator of a fraction and the repeated addition of the unit fraction with the same denominator using various tools and drawings, and standard fractional notation. | Grade 3 |
| Ontario | 3.B.2.9 | Multiplication and Division: use the ratios of 1 to 2, 1 to 5, and 1 to 10 to scale up numbers and to solve problems. | Grade 3 |
| Ontario | 3.C.1.1 | Patterns: identify and describe repeating elements and operations in a variety of patterns, including patterns found in real-life contexts. | Grade 3 |
| Ontario | 3.C.1.2 | Patterns: create and translate patterns that have repeating elements, movements, or operations using various representations, including shapes, numbers, and tables of values. | Grade 3 |
| Ontario | 3.C.1.3 | Patterns: determine pattern rules and use them to extend patterns, make and justify predictions, and identify missing elements in patterns that have repeating elements, movements, or operations. | Grade 3 |
| Ontario | 3.C.1.4 | Patterns: create and describe patterns to illustrate relationships among whole numbers up to 1000. | Grade 3 |
| Ontario | 3.C.2.1 | Variables: describe how variables are used, and use them in various contexts as appropriate. | Grade 3 |
| Ontario | 3.C.2.2 | Equalities and Inequalities: determine whether given sets of addition, subtraction, multiplication, and division expressions are equivalent or not. | Grade 3 |
| Ontario | 3.C.2.3 | Equalities and Inequalities: identify and use equivalent relationships for whole numbers up to 1000, in various contexts. | Grade 3 |
| Ontario | 3.D.1.1 | Probability: sort sets of data about people or things according to two and three attributes, using tables and logic diagrams, including Venn, Carroll, and tree diagrams, as appropriate. | Grade 3 |
| Ontario | 3.D.1.2 | Probability: collect data through observations, experiments, and interviews to answer questions of interest that focus on qualitative and quantitative data, and organize the data using frequency tables. | Grade 3 |
| Ontario | 3.D.1.3 | Probability: display sets of data, using many-to-one correspondence, in pictographs and bar graphs with proper sources, titles, and labels, and appropriate scales. | Grade 3 |
| Ontario | 3.D.1.4 | Probability: determine the mean and identify the mode(s), if any, for various data sets involving whole numbers, and explain what each of these measures indicates about the data. | Grade 3 |
| Ontario | 3.D.1.5 | Probability: analyse different data sets presented in various ways, including in frequency tables and in graphs with different scales, by asking and answering questions about the data and drawing conclusions, then make convincing arguments and informed decisions. | Grade 3 |
| Ontario | 3.E.1.1 | Geometric Reasoning: sort, construct, and identify cubes, prisms, pyramids, cylinders, and cones by comparing their faces, edges, vertices, and angles. | Grade 3 |
| Ontario | 3.E.1.2 | Geometric Reasoning: compose and decompose various structures, and identify the two-dimensional shapes and three-dimensional objects that these structures contain. | Grade 3 |
| Ontario | 3.E.2.1 | Length, Mass, and Capacity: use appropriate units of length to estimate, measure, and compare the perimeters of polygons and curved shapes, and construct polygons with a given perimeter. | Grade 3 |
| Ontario | 3.E.2.2 | Length, Mass, and Capacity: explain the relationships between millimetres, centimetres, metres, and kilometres as metric units of length, and use benchmarks for these units to estimate lengths. | Grade 3 |
| Ontario | 3.E.2.3 | Length, Mass, and Capacity: use nonstandard units appropriately to estimate, measure, and compare capacity, and explain the effect that overfilling or underfilling, and gaps between units, have on accuracy. | Grade 3 |
| Ontario | 3.E.2.4 | Length, Mass, and Capacity: compare, estimate, and measure the mass of various objects, using a pan balance and non-standard units. | Grade 3 |
| Ontario | 3.E.2.5 | Length, Mass, and Capacity: use various units of different sizes to measure the same attribute of a given item, and demonstrate that even though using different-sized units produces a different count, the size of the attribute remains the same. | Grade 3 |
| Ontario | 3.E.2.6 | Time: use analog and digital clocks and timers to tell time in hours, minutes, and seconds. | Grade 3 |
| Ontario | 3.E.2.7 | Area: compare the areas of two-dimensional shapes by matching, covering, or decomposing and recomposing the shapes, and demonstrate that different shapes can have the same area. | Grade 3 |
| Ontario | 3.E.2.8 | Area: use appropriate non-standard units to measure area, and explain the effect that gaps and overlaps have on accuracy. | Grade 3 |
| Ontario | 3.E.2.9 | Area: use square centimetres (cm2) and square metres (m2) to estimate, measure, and compare the areas of various twodimensional shapes, including those with curved sides. | Grade 3 |
| Ontario | 3.F.1.1 | Money Concepts: estimate and calculate the change required for various simple cash transactions involving wholedollar amounts and amounts of less than one dollar. | Grade 3 |
| Ontario | 4.B.1.1 | Whole Numbers: read, represent, compose, and decompose whole numbers up to and including 10 000, using appropriate tools and strategies, and describe various ways they are used in everyday life. | Grade 4 |
| Ontario | 4.B.1.2 | Whole Numbers: compare and order whole numbers up to and including 10 000, in various contexts. | Grade 4 |
| Ontario | 4.B.1.3 | Whole Numbers: round whole numbers to the nearest ten, hundred, or thousand, in various contexts. | Grade 4 |
| Ontario | 4.B.1.4 | Fractions and Decimals: represent fractions from halves to tenths using drawings, tools, and standard fractional notation, and explain the meanings of the denominator and the numerator. | Grade 4 |
| Ontario | 4.B.1.5 | Fractions and Decimals: use drawings and models to represent, compare, and order fractions representing the individual portions that result from two different fair-share scenarios involving any combination of 2, 3, 4, 5, 6, 8, and 10 sharers. | Grade 4 |
| Ontario | 4.B.1.6 | Fractions and Decimals: count to 10 by halves, thirds, fourths, fifths, sixths, eighths, and tenths, with and without the use of tools. | Grade 4 |
| Ontario | 4.B.1.7 | Fractions and Decimals: read, represent, compare, and order decimal tenths, in various contexts. | Grade 4 |
| Ontario | 4.B.1.8 | Fractions and Decimals: round decimal numbers to the nearest whole number, in various contexts. | Grade 4 |
| Ontario | 4.B.1.9 | Fractions and Decimals: describe relationships and show equivalences among fractions and decimal tenths, in various contexts. | Grade 4 |
| Ontario | 4.B.2.1 | Properties and Relationships: use the properties of operations, and the relationships between addition, subtraction, multiplication, and division, to solve problems involving whole numbers, including those requiring more than one operation, and check calculations. | Grade 4 |
| Ontario | 4.B.2.2 | Properties and Relationships: recall and demonstrate multiplication facts for 1 × 1 to 10 × 10, and related division facts. | Grade 4 |
| Ontario | 4.B.2.3 | Mental Math: use mental math strategies to multiply whole numbers by 10, 100, and 1000, divide whole numbers by 10, and add and subtract decimal tenths, and explain the strategies used. | Grade 4 |
| Ontario | 4.B.2.4 | Addition and Subtraction: represent and solve problems involving the addition and subtraction of whole numbers that add up to no more than 10 000 and of decimal tenths, using appropriate tools and strategies, including algorithms. | Grade 4 |
| Ontario | 4.B.2.5 | Multiplication and Division: represent and solve problems involving the multiplication of two or three-digit whole numbers by one-digit whole numbers and by 10, 100, and 1000, using appropriate tools, including arrays. | Grade 4 |
| Ontario | 4.B.2.6 | Multiplication and Division: represent and solve problems involving the division of two or three-digit whole numbers by one-digit whole numbers, expressing any remainder as a fraction when appropriate, using appropriate tools, including arrays. | Grade 4 |
| Ontario | 4.B.2.7 | Multiplication and Division: represent the relationship between the repeated addition of a unit fraction and the multiplication of that unit fraction by a whole number, using tools, drawings, and standard fractional notation. | Grade 4 |
| Ontario | 4.B.2.8 | Multiplication and Division: show simple multiplicative relationships involving wholenumber rates, using various tools and drawings. | Grade 4 |
| Ontario | 4.C.1.1 | Patterns: identify and describe repeating and growing patterns, including patterns found in real-life contexts. | Grade 4 |
| Ontario | 4.C.1.2 | Patterns: create and translate repeating and growing patterns using various representations, including tables of values and graphs. | Grade 4 |
| Ontario | 4.C.1.3 | Patterns: determine pattern rules and use them to extend patterns, make and justify predictions, and identify missing elements in repeating and growing patterns. | Grade 4 |
| Ontario | 4.C.1.4 | Patterns: create and describe patterns to illustrate relationships among whole numbers and decimal tenths. | Grade 4 |
| Ontario | 4.C.2.1 | Variables: identify and use symbols as variables in expressions and equations. | Grade 4 |
| Ontario | 4.C.2.2 | Equalities and Inequalities: solve equations that involve whole numbers up to 50 in various contexts, and verify solutions. | Grade 4 |
| Ontario | 4.C.2.3 | Equalities and Inequalities: solve inequalities that involve addition and subtraction of whole numbers up to 20, and verify and graph the solutions. | Grade 4 |
| Ontario | 4.D.1.4 | Probability: create an infographic about a data set, representing the data in appropriate ways, including in frequency tables, stem-and-leaf plots, and multiple-bar graphs, and incorporating any other relevant information that helps to tell a story about the data. | Grade 4 |
| Ontario | 4.D.1.6 | Probability: analyse different sets of data presented in various ways, including in stem-and-leaf plots and multiple-bar graphs, by asking and answering questions about the data and drawing conclusions, then make convincing arguments and informed decisions. | Grade 4 |
| Ontario | 4.E.1.1 | Geometric Reasoning: identify geometric properties of rectangles, including the number of right angles, parallel and perpendicular sides, and lines of symmetry. | Grade 4 |
| Ontario | 4.E.1.2 | Location and Movement: plot and read coordinates in the first quadrant of a Cartesian plane, and describe the translations that move a point from one coordinate to another. | Grade 4 |
| Ontario | 4.E.1.3 | Location and Movement: describe and perform translations and reflections on a grid, and predict the results of these transformations. | Grade 4 |
| Ontario | 4.E.2.1 | The Metric System: explain the relationships between grams and kilograms as metric units of mass, and between litres and millilitres as metric units of capacity, and use benchmarks for these units to estimate mass and capacity. | Grade 4 |
| Ontario | 4.E.2.2 | The Metric System: use metric prefixes to describe the relative size of different metric units, and choose appropriate units and tools to measure length, mass, and capacity. | Grade 4 |
| Ontario | 4.E.2.3 | Time: solve problems involving elapsed time by applying the relationships between different units of time. | Grade 4 |
| Ontario | 4.E.2.4 | Angles: identify angles and classify them as right, straight, acute, or obtuse. | Grade 4 |
| Ontario | 4.E.2.5 | Area: use the row and column structure of an array to measure the areas of rectangles and to show that the area of any rectangle can be found by multiplying its side lengths. | Grade 4 |
| Ontario | 4.E.2.6 | Area: apply the formula for the area of a rectangle to find the unknown measurement when given two of the three. | Grade 4 |
| Ontario | 5.B.1.1 | Whole Numbers: read, represent, compose, and decompose whole numbers up to and including 100 000, using appropriate tools and strategies, and describe various ways they are used in everyday life. | Grade 5 |
| Ontario | 5.B.1.2 | Whole Numbers: compare and order whole numbers up to and including 100 000, in various contexts. | Grade 5 |
| Ontario | 5.B.1.3 | Fractions, Decimals, and Percents: represent equivalent fractions from halves to twelfths, including improper fractions and mixed numbers, using appropriate tools, in various contexts. | Grade 5 |
| Ontario | 5.B.1.4 | Fractions, Decimals, and Percents: compare and order fractions from halves to twelfths, including improper fractions and mixed numbers, in various contexts. | Grade 5 |
| Ontario | 5.B.1.5 | Fractions, Decimals, and Percents: read, represent, compare, and order decimal numbers up to hundredths, in various contexts. | Grade 5 |
| Ontario | 5.B.1.6 | Fractions, Decimals, and Percents: round decimal numbers to the nearest tenth, in various contexts. | Grade 5 |
| Ontario | 5.B.1.7 | Fractions, Decimals, and Percents: describe relationships and show equivalences among fractions, decimal numbers up to hundredths, and whole number percents, using appropriate tools and drawings, in various contexts. | Grade 5 |
| Ontario | 5.B.2.1 | Properties and Relationships: use the properties of operations, and the relationships between operations, to solve problems involving whole numbers and decimal numbers, including those requiring more than one operation, and check calculations. | Grade 5 |
| Ontario | 5.B.2.2 | Properties and Relationships: recall and demonstrate multiplication facts from 0 × 0 to 12 × 12, and related division facts. | Grade 5 |
| Ontario | 5.B.2.3 | Mental Math: use mental math strategies to multiply whole numbers by 0.1 and 0.01 and estimate sums and differences of decimal numbers up to hundredths, and explain the strategies used. | Grade 5 |
| Ontario | 5.B.2.4 | Addition and Subtraction: represent and solve problems involving the addition and subtraction of whole numbers that add up to no more than 100 000, and of decimal numbers up to hundredths, using appropriate tools, strategies, and algorithms. | Grade 5 |
| Ontario | 5.B.2.5 | Addition and Subtraction: add and subtract fractions with like denominators, in various contexts. | Grade 5 |
| Ontario | 5.B.2.6 | Multiplication and Division: represent and solve problems involving the multiplication of two-digit whole numbers by two-digit whole numbers using the area model and using algorithms, and make connections between the two methods. | Grade 5 |
| Ontario | 5.B.2.7 | Multiplication and Division: represent and solve problems involving the division of three-digit whole numbers by two-digit whole numbers using the area model and using algorithms, and make connections between the two methods, while expressing any remainder appropriately. | Grade 5 |
| Ontario | 5.B.2.8 | Multiplication and Division: multiply and divide one-digit whole numbers by unit fractions, using appropriate tools and drawings. | Grade 5 |
| Ontario | 5.B.2.9 | Multiplication and Division: represent and create equivalent ratios and rates, using a variety of tools and models, in various contexts. | Grade 5 |
| Ontario | 5.C.1.1 | Patterns: identify and describe repeating, growing, and shrinking patterns, including patterns found in real-life contexts. | Grade 5 |
| Ontario | 5.C.1.2 | Patterns: create and translate growing and shrinking patterns using various representations, including tables of values and graphs. | Grade 5 |
| Ontario | 5.C.1.3 | Patterns: determine pattern rules and use them to extend patterns, make and justify predictions, and identify missing elements in repeating, growing, and shrinking patterns. | Grade 5 |
| Ontario | 5.C.1.4 | Patterns: create and describe patterns to illustrate relationships among whole numbers and decimal tenths and hundredths. | Grade 5 |
| Ontario | 5.C.2.1 | Variables and Expressions: translate among words, algebraic expressions, and visual representations that describe equivalent relationships. | Grade 5 |
| Ontario | 5.C.2.2 | Variables and Expressions: evaluate algebraic expressions that involve whole numbers. | Grade 5 |
| Ontario | 5.C.2.3 | Equalities and Inequalities: solve equations that involve whole numbers up to 100 in various contexts, and verify solutions. | Grade 5 |
| Ontario | 5.C.2.4 | Equalities and Inequalities: solve inequalities that involve one operation and whole numbers up to 50, and verify and graph the solutions. | Grade 5 |
| Ontario | 5.D.1.4 | Probability: create an infographic about a data set, representing the data in appropriate ways, including in relative-frequency tables and stackedbar graphs, and incorporating any other relevant information that helps to tell a story about the data. | Grade 5 |
| Ontario | 5.D.1.6 | Probability: analyse different sets of data presented in various ways, including in stacked-bar graphs and in misleading graphs, by asking and answering questions about the data, challenging preconceived notions, and drawing conclusions, then make convincing arguments and informed decisions. | Grade 5 |
| Ontario | 5.E.1.1 | Geometric Reasoning: identify geometric properties of triangles, and construct different types of triangles when given side or angle measurements. | Grade 5 |
| Ontario | 5.E.1.2 | Geometric Reasoning: identify and construct congruent triangles, rectangles, and parallelograms. | Grade 5 |
| Ontario | 5.E.1.3 | Geometric Reasoning: draw top, front, and side views of objects, and match drawings with objects. | Grade 5 |
| Ontario | 5.E.1.4 | Location and Movement: plot and read coordinates in the first quadrant of a Cartesian plane using various scales, and describe the translations that move a point from one coordinate to another. | Grade 5 |
| Ontario | 5.E.1.5 | Location and Movement: describe and perform translations, reflections, and rotations up to 180° on a grid, and predict the results of these transformations. | Grade 5 |
| Ontario | 5.E.2.1 | The Metric System: use appropriate metric units to estimate and measure length, area, mass, and capacity. | Grade 5 |
| Ontario | 5.E.2.2 | The Metric System: solve problems that involve converting larger metric units into smaller ones, and describe the base ten relationships among metric units. | Grade 5 |
| Ontario | 5.E.2.3 | Angles: compare angles and determine their relative size by matching them and by measuring them using appropriate nonstandard units. | Grade 5 |
| Ontario | 5.E.2.4 | Angles: explain how protractors work, use them to measure and construct angles up to 180°, and use benchmark angles to estimate the size of other angles. | Grade 5 |
| Ontario | 5.E.2.5 | Area: use the area relationships among rectangles, parallelograms, and triangles to develop the formulas for the area of a parallelogram and the area of a triangle, and solve related problems. | Grade 5 |
| Ontario | 5.E.2.6 | Area: show that twodimensional shapes with the same area can have different perimeters, and solve related problems. | Grade 5 |
| Ontario | 5.F.1.5 | Financial Management: calculate unit rates for various goods and services, and identify which rates offer the best value. | Grade 5 |
| Ontario | 6.B.1.1 | Rational Numbers: read and represent whole numbers up to and including one million, using appropriate tools and strategies, and describe various ways they are used in everyday life. | Grade 6 |
| Ontario | 6.B.1.2 | Rational Numbers: read and represent integers, using a variety of tools and strategies, including horizontal and vertical number lines. | Grade 6 |
| Ontario | 6.B.1.3 | Rational Numbers: compare and order integers, decimal numbers, and fractions, separately and in combination, in various contexts. | Grade 6 |
| Ontario | 6.B.1.4 | Fractions, Decimals, and Percents: read, represent, compare, and order decimal numbers up to thousandths, in various contexts. | Grade 6 |
| Ontario | 6.B.1.5 | Fractions, Decimals, and Percents: round decimal numbers, both terminating and repeating, to the nearest tenth, hundredth, or whole number, as applicable, in various contexts. | Grade 6 |
| Ontario | 6.B.1.6 | Fractions, Decimals, and Percents: describe relationships and show equivalences among fractions and decimal numbers up to thousandths, using appropriate tools and drawings, in various contexts. | Grade 6 |
| Ontario | 6.B.2.1 | Properties and Relationships: use the properties of operations, and the relationships between operations, to solve problems involving whole numbers, decimal numbers, fractions, ratios, rates, and whole number percents, including those requiring multiple steps or multiple operations. | Grade 6 |
| Ontario | 6.B.2.10 | Multiplication and Division: divide whole numbers by proper fractions, using appropriate tools and strategies. | Grade 6 |
| Ontario | 6.B.2.11 | Multiplication and Division: represent and solve problems involving the division of decimal numbers up to thousandths by whole numbers up to 10, using appropriate tools and strategies. | Grade 6 |
| Ontario | 6.B.2.12 | Multiplication and Division: solve problems involving ratios, including percents and rates, using appropriate tools and strategies. | Grade 6 |
| Ontario | 6.B.2.3 | Mental Math: use mental math strategies to calculate percents of whole numbers, including 1%, 5%, 10%, 15%, 25%, and 50%, and explain the strategies used. | Grade 6 |
| Ontario | 6.B.2.4 | Addition and Subtraction: represent and solve problems involving the addition and subtraction of whole numbers and decimal numbers, using estimation and algorithms. | Grade 6 |
| Ontario | 6.B.2.5 | Addition and Subtraction: add and subtract fractions with like and unlike denominators, using appropriate tools, in various contexts. | Grade 6 |
| Ontario | 6.B.2.7 | Multiplication and Division: represent and solve problems involving the multiplication of three-digit whole numbers by decimal tenths, using algorithms. | Grade 6 |
| Ontario | 6.B.2.8 | Multiplication and Division: represent and solve problems involving the division of three-digit whole numbers by decimal tenths, using appropriate tools, strategies, and algorithms, and expressing remainders as appropriate. | Grade 6 |
| Ontario | 6.B.2.9 | Multiplication and Division: multiply whole numbers by proper fractions, using appropriate tools and strategies. | Grade 6 |
| Ontario | 6.C.2.1 | Variables and Expressions: add monomials with a degree of 1 that involve whole numbers, using tools. | Grade 6 |
| Ontario | 6.C.2.2 | Variables and Expressions: evaluate algebraic expressions that involve whole numbers and decimal tenths. | Grade 6 |
| Ontario | 6.C.2.3 | Equalities and Inequalities: solve equations that involve multiple terms and whole numbers in various contexts, and verify solutions. | Grade 6 |
| Ontario | 6.C.2.4 | Equalities and Inequalities: solve inequalities that involve two operations and whole numbers up to 100, and verify and graph the solutions. | Grade 6 |
| Ontario | 6.D.1.1 | Probability: describe the difference between discrete and continuous data, and provide examples of each. | Grade 6 |
| Ontario | 6.D.1.2 | Probability: collect qualitative data and discrete and continuous quantitative data to answer questions of interest about a population, and organize the sets of data as appropriate, including using intervals. | Grade 6 |
| Ontario | 6.D.1.5 | Probability: determine the range as a measure of spread and the measures of central tendency for various data sets, and use this information to compare two or more data sets. | Grade 6 |
| Ontario | 6.E.1.1 | Geometric Reasoning: create lists of geometric properties of various types of quadrilaterals, including the properties of the diagonals, rotational symmetry, and line symmetry. | Grade 6 |
| Ontario | 6.E.1.2 | Geometric Reasoning: construct three-dimensional objects when given their top, front, and side views. | Grade 6 |
| Ontario | 6.E.1.3 | Location and Movement: plot and read coordinates in all four quadrants of a Cartesian plane, and describe the translations that move a point from one coordinate to another. | Grade 6 |
| Ontario | 6.E.1.4 | Location and Movement: describe and perform combinations of translations, reflections, and rotations up to 360° on a grid, and predict the results of these transformations. | Grade 6 |
| Ontario | 6.E.2.1 | The Metric System: measure length, area, mass, and capacity using the appropriate metric units, and solve problems that require converting smaller units to larger ones and vice versa. | Grade 6 |
| Ontario | 6.E.2.2 | Angles: use a protractor to measure and construct angles up to 360°, and state the relationship between angles that are measured clockwise and those that are measured counterclockwise. | Grade 6 |
| Ontario | 6.E.2.3 | Angles: use the properties of supplementary angles, complementary angles, opposite angles, and interior and exterior angles to solve for unknown angle measures. | Grade 6 |
| Ontario | 6.E.2.4 | Area and Surface Area: determine the areas of trapezoids, rhombuses, kites, and composite polygons by decomposing them into shapes with known areas. | Grade 6 |
| Ontario | 6.E.2.5 | Area and Surface Area: create and use nets to demonstrate the relationship between the faces of prisms and pyramids and their surface areas. | Grade 6 |
| Ontario | 6.E.2.6 | Area and Surface Area: determine the surface areas of prisms and pyramids by calculating the areas of their twodimensional faces and adding them together. | Grade 6 |
| Ontario | 7.B.1.1 | Multiplication and Division: represent and compare whole numbers up to and including one billion, including in expanded form using powers of ten, and describe various ways they are used in everyday life. | Grade 7 |
| Ontario | 7.B.1.2 | Multiplication and Division: identify and represent perfect squares, and determine their square roots, in various contexts. | Grade 7 |
| Ontario | 7.B.1.3 | Multiplication and Division: read, represent, compare, and order rational numbers, including positive and negative fractions and decimal numbers to thousandths, in various contexts. | Grade 7 |
| Ontario | 7.B.1.4 | Fractions, Decimals, and Percents: use equivalent fractions to simplify fractions, when appropriate, in various contexts. | Grade 7 |
| Ontario | 7.B.1.5 | Fractions, Decimals, and Percents: generate fractions and decimal numbers between any two quantities. | Grade 7 |
| Ontario | 7.B.1.6 | Fractions, Decimals, and Percents: round decimal numbers to the nearest tenth, hundredth, or whole number, as applicable, in various contexts. | Grade 7 |
| Ontario | 7.B.1.7 | Fractions, Decimals, and Percents: convert between fractions, decimal numbers, and percents, in various contexts. | Grade 7 |
| Ontario | 7.B.2.1 | Properties and Relationships: use the properties and order of operations, and the relationships between operations, to solve problems involving whole numbers, decimal numbers, fractions, ratios, rates, and percents, including those requiring multiple steps or multiple operations. | Grade 7 |
| Ontario | 7.B.2.10 | Multiplication and Division: identify proportional and non-proportional situations and apply proportional reasoning to solve problems. | Grade 7 |
| Ontario | 7.B.2.2 | Properties and Relationships: understand and recall commonly used percents, fractions, and decimal equivalents. | Grade 7 |
| Ontario | 7.B.2.3 | Mental Math: use mental math strategies to increase and decrease a whole number by 1%, 5%, 10%, 25%, 50%, and 100%, and explain the strategies used. | Grade 7 |
| Ontario | 7.B.2.4 | Addition and Subtraction: use objects, diagrams, and equations to represent, describe, and solve situations involving addition and subtraction of integers. | Grade 7 |
| Ontario | 7.B.2.5 | Addition and Subtraction: add and subtract fractions, including by creating equivalent fractions, in various contexts. | Grade 7 |
| Ontario | 7.B.2.7 | Multiplication and Division: evaluate and express repeated multiplication of whole numbers using exponential notation, in various contexts. | Grade 7 |
| Ontario | 7.B.2.8 | Multiplication and Division: multiply and divide fractions by fractions, using tools in various contexts. | Grade 7 |
| Ontario | 7.B.2.9 | Multiplication and Division: multiply and divide decimal numbers by decimal numbers, in various contexts. | Grade 7 |
| Ontario | 7.C.2.1 | Variables and Expressions: add and subtract monomials with a degree of 1 that involve whole numbers, using tools. | Grade 7 |
| Ontario | 7.C.2.2 | Variables and Expressions: evaluate algebraic expressions that involve whole numbers and decimal numbers. | Grade 7 |
| Ontario | 7.C.2.3 | Equalities and Inequalities: solve equations that involve multiple terms, whole numbers, and decimal numbers in various contexts, and verify solutions. | Grade 7 |
| Ontario | 7.C.2.4 | Equalities and Inequalities: solve inequalities that involve multiple terms and whole numbers, and verify and graph the solutions. | Grade 7 |
| Ontario | 7.D.1.1 | Probability: explain why percentages are used to represent the distribution of a variable for a population or sample in large sets of data, and provide examples. | Grade 7 |
| Ontario | 7.D.1.2 | Probability: collect qualitative data and discrete and continuous quantitative data to answer questions of interest, and organize the sets of data as appropriate, including using percentages. | Grade 7 |
| Ontario | 7.D.1.5 | Probability: determine the impact of adding or removing data from a data set on a measure of central tendency, and describe how these changes alter the shape and distribution of the data. | Grade 7 |
| Ontario | 7.D.1.6 | Probability: analyse different sets of data presented in various ways, including in circle graphs and in misleading graphs, by asking and answering questions about the data, challenging preconceived notions, and drawing conclusions, then make convincing arguments and informed decisions. | Grade 7 |
| Ontario | 7.E.1.2 | Geometric Reasoning: draw top, front, and side views, as well as perspective views, of objects and physical spaces, using appropriate scales. | Grade 7 |
| Ontario | 7.E.1.4 | Location and Movement: describe and perform translations, reflections, and rotations on a Cartesian plane, and predict the results of these transformations. | Grade 7 |
| Ontario | 7.E.2.1 | The Metric System: describe the differences and similarities between volume and capacity, and apply the relationship between millilitres (mL) and cubic centimetres (cm3) to solve problems. | Grade 7 |
| Ontario | 7.E.2.2 | The Metric System: solve problems involving perimeter, area, and volume that require converting from one metric unit of measurement to another. | Grade 7 |
| Ontario | 7.E.2.3 | Circles: use the relationships between the radius, diameter, and circumference of a circle to explain the formula for finding the circumference and to solve related problems. | Grade 7 |
| Ontario | 7.E.2.4 | Circles: construct circles when given the radius, diameter, or circumference. | Grade 7 |
| Ontario | 7.E.2.5 | Circles: show the relationships between the radius, diameter, and area of a circle, and use these relationships to develop the formula for measuring the area of a circle and to solve related problems. | Grade 7 |
| Ontario | 7.E.2.6 | Volume and Surface Area: represent cylinders as nets and determine their surface area by adding the areas of their parts. | Grade 7 |
| Ontario | 7.E.2.7 | Volume and Surface Area: show that the volume of a prism or cylinder can be determined by multiplying the area of its base by its height, and apply this relationship to find the area of the base, volume, and height of prisms and cylinders when given two of the three measurements. | Grade 7 |
| Ontario | 8.B.1.1 | Rational and Irrational Numbers: represent and compare very large and very small numbers, including through the use of scientific notation, and describe various ways they are used in everyday life. | Grade 8 |
| Ontario | 8.B.1.2 | Rational and Irrational Numbers: describe, compare, and order numbers in the real number system (rational and irrational numbers), separately and in combination, in various contexts. | Grade 8 |
| Ontario | 8.B.1.3 | Rational and Irrational Numbers: estimate and calculate square roots, in various contexts. | Grade 8 |
| Ontario | 8.B.1.4 | Fractions, Decimals, and Percents: use fractions, decimal numbers, and percents, including percents of more than 100% or less than 1%, interchangeably and flexibly to solve a variety of problems. | Grade 8 |
| Ontario | 8.B.2.1 | Properties and Relationships: use the properties and order of operations, and the relationships between operations, to solve problems involving rational numbers, ratios, rates, and percents, including those requiring multiple steps or multiple operations. | Grade 8 |
| Ontario | 8.B.2.3 | Mental Math: use mental math strategies to multiply and divide whole numbers and decimal numbers up to thousandths by powers of ten, and explain the strategies used. | Grade 8 |
| Ontario | 8.B.2.4 | Addition and Subtraction: add and subtract integers, using appropriate strategies, in various contexts. | Grade 8 |
| Ontario | 8.B.2.5 | Addition and Subtraction: add and subtract fractions, using appropriate strategies, in various contexts. | Grade 8 |
| Ontario | 8.B.2.6 | Multiplication and Division: multiply and divide fractions by fractions, as well as by whole numbers and mixed numbers, in various contexts. | Grade 8 |
| Ontario | 8.B.2.7 | Multiplication and Division: multiply and divide integers, using appropriate strategies, in various contexts. | Grade 8 |
| Ontario | 8.B.2.8 | Multiplication and Division: compare proportional situations and determine unknown values in proportional situations, and apply proportional reasoning to solve problems in various contexts. | Grade 8 |
| Ontario | 8.C.2.1 | Variables and Expressions: add and subtract monomials with a degree of 1, and add binomials with a degree of 1 that involve integers, using tools. | Grade 8 |
| Ontario | 8.C.2.2 | Variables and Expressions: evaluate algebraic expressions that involve rational numbers. | Grade 8 |
| Ontario | 8.C.2.3 | Equalities and Inequalities: solve equations that involve multiple terms, integers, and decimal numbers in various contexts, and verify solutions. | Grade 8 |
| Ontario | 8.C.2.4 | Equalities and Inequalities: solve inequalities that involve integers, and verify and graph the solutions. | Grade 8 |
| Ontario | 8.D.1.3 | Probability: select from among a variety of graphs, including scatter plots, the type of graph best suited to represent various sets of data; display the data in the graphs with proper sources, titles, and labels, and appropriate scales; and justify their choice of graphs. | Grade 8 |
| Ontario | 8.D.1.4 | Probability: create an infographic about a data set, representing the data in appropriate ways, including in tables and scatter plots, and incorporating any other relevant information that helps to tell a story about the data. | Grade 8 |
| Ontario | 8.D.1.5 | Probability: use mathematical language, including the terms “strong”, “weak”, “none”, “positive”, and “negative”, to describe the relationship between two variables for various data sets with and without outliers. | Grade 8 |
| Ontario | 8.D.1.6 | Probability: analyse different sets of data presented in various ways, including in scatter plots and in misleading graphs, by asking and answering questions about the data, challenging preconceived notions, and drawing conclusions, then make convincing arguments and informed decisions. | Grade 8 |
| Ontario | 8.E.1.2 | Geometric Reasoning: make objects and models using appropriate scales, given their top, front, and side views or their perspective views. | Grade 8 |
| Ontario | 8.E.1.3 | Geometric Reasoning: use scale drawings to calculate actual lengths and areas, and reproduce scale drawings at different ratios. | Grade 8 |
| Ontario | 8.E.1.4 | Location and Movement: describe and perform translations, reflections, rotations, and dilations on a Cartesian plane, and predict the results of these transformations. | Grade 8 |
| Ontario | 8.E.2.2 | Lines and Angles: solve problems involving angle properties, including the properties of intersecting and parallel lines and of polygons. | Grade 8 |
| Ontario | 8.E.2.3 | Length, Area, and Volume: solve problems involving the perimeter, circumference, area, volume, and surface area of composite two- dimensional shapes and three- dimensional objects, using appropriate formulas. | Grade 8 |
| Ontario | 8.E.2.4 | Length, Area, and Volume: describe the Pythagorean relationship using various geometric models, and apply the theorem to solve problems involving an unknown side length for a given right triangle. | Grade 8 |
| Ontario | 9.MG.SPPAS9.2 | Solve problems using the Pythagorean theorem, as required in applications. | Grade 9 |
| Ontario | 9.MG.IAGR.1 | Determine, through investigation using a variety of tools, and describe the properties and relationships of the interior and exterior angles of triangles, quadrilaterals, and other polygons, and apply the results to problems involving the angles of polygons. | Grade 9 |
| Ontario | 9.NSA.OWE.1 | Substitute into and evaluate algebraic expressions involving exponents (i.e., evaluate expressions involving natural-number exponents with rational-number bases). | Grade 9 |
| Ontario | 9.NSA.OWE.4 | Extend the multiplication rule to derive and understand the power of a power rule, and apply it to simplify expressions involving one and two variables with positive exponents. | Grade 9 |
| Ontario | 9.NSA.SPIPR.1 | Illustrate equivalent ratios, using a variety of tools. | Grade 9 |
| Ontario | 9.NSA.SPIPR.2 | Represent, using equivalent ratios and proportions, directly proportional relationships arising from realistic situations. | Grade 9 |
| Ontario | 9.NSA.SPIPR.3 | Solve for the unknown value in a proportion, using a variety of methods. | Grade 9 |
| Ontario | 9.NSA.SPIPR.4 | Make comparisons using unit rates. | Grade 9 |
| Ontario | 9.NSA.SPIPR.5 | Solve problems involving ratios, rates, and directly proportional relationships in various contexts, using a variety of methods. | Grade 9 |
| Ontario | 9.NSA.SPIPR.6 | Solve problems requiring the expression of percents, fractions, and decimals in their equivalent forms. | Grade 9 |
| Ontario | 9.NSA.MESE.1 | Simplify numerical expressions involving integers and rational numbers, with and without the use of technology. | Grade 9 |
| Ontario | 9.NSA.MESE.2 | Solve problems requiring the manipulation of expressions arising from applications of percent, ratio, rate, and proportion. | Grade 9 |
| Ontario | 9.NSA.MESE.3 | Relate their understanding of inverse operations to squaring and taking the square root, and apply inverse operations to simplify expressions and solve equations. | Grade 9 |
| Ontario | 9.NSA.MESE.7 | Solve first-degree equations, including equations with fractional coefficients, using a variety of tools (e.g., computer algebra systems, paper and pencil) and strategies (e.g., the balance analogy, algebraic strategies). | Grade 9 |
| Ontario | 9.NSA.MESE.9 | Solve problems that can be modelled with first-degree equations, and compare algebraic methods to other solution methods. | Grade 9 |
| Ontario | 9.NSA.SESE.2 | Substitute into and evaluate algebraic expressions involving exponents (i.e., evaluate expressions involving natural-number exponents with rational-number bases). | Grade 9 |
| Ontario | 9.NSA.SESE.5 | Solve first-degree equations with nonfractional coefficients, using a variety of tools and strategies. | Grade 9 |
| Ontario | 9.NSA.SESE.6 | Substitute into algebraic equations and solve for one variable in the first degree. | Grade 9 |
| Ontario | 9.LR.UDMIR.1 | Interpret the meanings of points on scatter plots or graphs that represent linear relations, including scatter plots or graphs in more than one quadrant. | Grade 9 |
| Ontario | 9.LR.UDMIR.2 | Pose problems, identify variables, and formulate hypotheses associated with relationships between two variables. | Grade 9 |
| Ontario | 9.LR.UCLR.1 | Construct tables of values, graphs, and equations, using a variety of tools (e.g., graphing calculators, spreadsheets, graphing software, paper and pencil), to represent linear relations derived from descriptions of realistic situations. | Grade 9 |
| Ontario | 9.LR.UCLR.2 | Construct tables of values, scatter plots, and lines or curves of best fit as appropriate, using a variety of tools (e.g., spreadsheets, graphing software, graphing calculators, paper and pencil), for linearly related and non-linearly related data collected from a variety of sources. | Grade 9 |
| Ontario | 9.LR.UCLR.3 | Identify, through investigation, some properties of linear relations, and apply these properties to determine whether a relation is linear or non-linear. | Grade 9 |
| Ontario | 9.LR.UCRC.4 | Compare the properties of direct variation and partial variation in applications, and identify the initial value. | Grade 9 |
| Ontario | 9.LR.UCLR.5 | Determine the equation of a line of best fit for a scatter plot, using an informal process. | Grade 9 |
| Ontario | 9.LR.DCLR.3 | Identify, through investigation, some properties of linear relations, and apply these properties to determine whether a relation is linear or non-linear. | Grade 9 |
| Ontario | 9.LR.DCLR.4 | Determine, through investigation, that the rate of change of a linear relation can be found by choosing any two points on the line that represents the relation, finding the vertical change between the points and the horizontal change between the points, and writing the ratio rise/run. | Grade 9 |
| Ontario | 9.LR.DCLR.5 | Determine, through investigation, connections among the representations of a constant rate of change of a linear relation. | Grade 9 |
| Ontario | 9.LR.DCLR.7 | Express a linear relation as an equation in two variables, using the rate of change and the initial value. | Grade 9 |
| Ontario | 9.LR.DCLR.8 | Describe the meaning of the rate of change and the initial value for a linear relation arising from a realistic situation and describe a situation that could be modelled by a given linear equation. | Grade 9 |
| Ontario | 9.LR.CVRLR.1 | Determine values of a linear relation by using a table of values, by using the equation of the relation, and by interpolating or extrapolating from the graph of the relation. | Grade 9 |
| Ontario | 9.LR.CVRLR.2 | Describe a situation that would explain the events illustrated by a given graph of a relationship between two variables. | Grade 9 |
| Ontario | 9.LR.CVRLR.3 | Determine other representations of a linear relation, given one representation. | Grade 9 |
| Ontario | 9.LR.CVRLR.4 | Describe the effects on a linear graph and make the corresponding changes to the linear equation when the conditions of the situation they represent are varied. | Grade 9 |
| Ontario | 9.LR.CVRLR.5 | Determine other representations of a linear relation arising from a realistic situation, given one representation. | Grade 9 |
| Ontario | 9.LR.CVRLR.6 | Solve problems that can be modelled with first-degree equations, and compare algebraic methods to other solution methods. | Grade 9 |
| Ontario | 9.LR.CVRLR.7 | Determine graphically the point of intersection of two linear relations, and interpret the intersection point in the context of an application. | Grade 9 |
| Ontario | 9.AG.IPS.1 | Determine, through investigation, various formulas for the slope of a line segment or a line and use the formulas to determine the slope of a line segment or a line. | Grade 9 |
| Ontario | 9.AG.IPS.2 | Identify, through investigation with technology, the geometric significance of m and b in the equation y = mx + b. | Grade 9 |
| Ontario | 9.AG.IPS.3 | Determine, through investigation, connections among the representations of a constant rate of change of a linear relation. | Grade 9 |
| Ontario | 9.AG.IPS.4 | Identify, through investigation, properties of the slopes of lines and line segments, using graphing technology to facilitate investigations, where appropriate. | Grade 9 |
| Ontario | 9.AG.UPLRSP.1 | Graph lines by hand, using a variety of techniques. | Grade 9 |
| Ontario | 9.AG.UPLRSP.2 | Determine the equation of a line from information about the line (e.g., the slope and y-intercept; the slope and a point; two points). | Grade 9 |
| Ontario | 9.AG.UPLRSP.3 | Describe the meaning of the slope and y-intercept for a linear relation arising from a realistic situation. | Grade 9 |
| Ontario | 9.AG.UPLRSP.4 | Identify and explain any restrictions on the variables in a linear relation arising from a realistic situation. | Grade 9 |
| Ontario | 9.AG.UPLRSP.5 | Determine graphically the point of intersection of two linear relations, and interpret the intersection point in the context of an application. | Grade 9 |
| Ontario | 10.QR.ICQR.4 | Compare, through investigation using technology, the graphical representations of a quadratic relation in the form y = x² + bx + c and the same relation in the factored form y = (x – r)(x – s), and describe the connections between each algebraic representation and the graph. | Grade 10 |
| Ontario | 10.AG.ULSSP.1 | Solve systems of two linear equations involving two variables, using the algebraic method of substitution or elimination. | Grade 10 |
| Ontario | 10.AG.ULSSP.2 | Solve problems that arise from realistic situations described in words or represented by linear systems of two equations involving two variables, by choosing an appropriate algebraic or graphical method. | Grade 10 |
| Ontario | 10.AG.SPIPLS.2 | Develop the formula for the length of a line segment, and use this formula to solve problems. | Grade 10 |
| Ontario | 10.T.SSPST.2 | Describe and compare the concepts of similarity and congruence. | Grade 10 |
| Ontario | 10.T.SPTRT.2 | Determine the measures of the sides and angles in right triangles, using the primary trigonometric ratios and the Pythagorean theorem. | Grade 10 |
| Ontario | 10.T.SPTRT.3 | Solve problems involving the measures of sides and angles in right triangles in reallife applications, using the primary trigonometric ratios and the Pythagorean theorem. | Grade 10 |
| Ontario | 10.MT.SPTRT.2 | Determine the measures of the sides and angles in right triangles, using the primary trigonometric ratios and the Pythagorean theorem. | Grade 10 |
| Ontario | 10.MT.SPTRT.3 | Solve problems involving the measures of sides and angles in right triangles in real life applications, using the primary trigonometric ratios and the Pythagorean theorem. | Grade 10 |
| Ontario | 10.MT.SPSAV.4 | Solve problems involving the surface areas of prisms, pyramids, and cylinders, and the volumes of prisms, pyramids, cylinders, cones, and spheres, including problems involving combinations of these figures, using the metric system or the imperial system, as appropriate. | Grade 10 |
| Ontario | 10.MLR.MSAE.1 | Solve first-degree equations involving one variable, including equations with fractional coefficients. | Grade 10 |
| Ontario | 10.MLR.MSAE.2 | Determine the value of a variable in the first degree, using a formula. | Grade 10 |
| Ontario | 10.MLR.MSAE.3 | Express the equation of a line in the form y = mx + b, given the form Ax + By + C = 0. | Grade 10 |
| Ontario | 10.MLR.GWEL.2 | Identify, through investigation, y = mx + b as a common form for the equation of a straight line, and identify the special cases x = a, y = b. | Grade 10 |
| Ontario | 10.MLR.GWEL.3 | Identify, through investigation with technology, the geometric significance of m and b in the equation y = mx + b. | Grade 10 |
| Ontario | 10.MLR.GWEL.4 | Identify, through investigation, properties of the slopes of lines and line segments, using graphing technology to facilitate investigations, where appropriate. | Grade 10 |
| Ontario | 10.MLR.GWEL.5 | Graph lines by hand, using a variety of techniques. | Grade 10 |
| Ontario | 10.MLR.GWEL.6 | Determine the equation of a line, given its graph, the slope and y-intercept, the slope and a point on the line, or two points on the line. | Grade 10 |
| Ontario | 10.MLR.SISLE.1 | Determine graphically the point of intersection of two linear relations. | Grade 10 |
| Oregon | K.OA.A.1 | Represent addition as putting together and adding to and subtraction as taking apart and taking from using objects, drawings, physical expressions, numbers or equations. | Kindergarten |
| Oregon | K.OA.A.2 | Add and subtract within 10. Model authentic contexts and solve problems that use addition and subtraction within 10. | Kindergarten |
| Oregon | K.OA.A.3 | Using objects or drawings, and equations, decompose numbers less than or equal to 10 into pairs in more than one way. | Kindergarten |
| Oregon | K.OA.A.4 | By using objects, drawings, or equations, find the unknown number that makes 10 when added to a given number from 1 - 9. | Kindergarten |
| Oregon | K.OA.A.5 | Fluently add and subtract within 5 with accurate, efficient, and flexible strategies. | Kindergarten |
| Oregon | K.NCC.A.1 | Orally count to 100 by ones and by tens in sequential order. | Kindergarten |
| Oregon | K.NCC.A.2 | Count forward beginning from a given number within 100 of a known sequence. | Kindergarten |
| Oregon | K.NCC.A.3 | Identify number names, write numbers, and the count sequence from 0-20. Represent a number of objects with a written number 0-20. | Kindergarten |
| Oregon | K.NCC.B.4 | Understand the relationship between numbers and quantities; connect counting to cardinality. | Kindergarten |
| Oregon | K.NCC.B.5 | Count to answer how many? questions using up to 20 objects arranged in a variety of configurations or as 10 objects in a scattered configuration. Given a number from 1-20, count out that many objects. | Kindergarten |
| Oregon | K.NCC.C.7 | Compare two numbers between 1 and 10 presented as written numerals. | Kindergarten |
| Oregon | K.NBT.A.1 | Compose and decompose from 11 to 19 into groups of ten ones and some further ones using objects, drawings, or equations. | Kindergarten |
| Oregon | K.GM.A.1 | Describe objects in the environment using names of shapes and describe the relative positions of these objects in their environment. | Kindergarten |
| Oregon | K.GM.A.2 | Correctly name common two-dimensional and three-dimensional geometric shapes regardless of their orientations or overall size. | Kindergarten |
| Oregon | K.GM.A.3 | Identify shapes as two-dimensional or three-dimensional. | Kindergarten |
| Oregon | K.GM.B.4 | Analyze and compare two and three-dimensional shapes, in different sizes and orientations, using informal language to describe their similarities, differences, parts and attributes. | Kindergarten |
| Oregon | K.GM.B.6 | Compose common shapes to form larger shapes. | Kindergarten |
| Oregon | K.GM.C.7 | Describe several measurable attributes of a single object using measurable terms, such as length or weight. | Kindergarten |
| Oregon | K.GM.C.8 | Directly compare two objects with a measurable attribute in common, and describe which object has more or less of the attribute. | Kindergarten |
| Oregon | K.DR.B.2 | Analyze data sets by counting the number of objects in each category and interpret results by classifying and sorting objects by count. | Kindergarten |
| Oregon | 1.OA.A.1 | Use addition and subtraction within 20 to solve and represent problems in authentic contexts involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions. | Grade 1 |
| Oregon | 1.OA.B.3 | Apply properties of operations as strategies to add and subtract. | Grade 1 |
| Oregon | 1.OA.B.4 | Understand subtraction as an unknown-addend problem. | Grade 1 |
| Oregon | 1.OA.C.5 | Relate counting to addition and subtraction. | Grade 1 |
| Oregon | 1.OA.C.6 | Add and subtract within 20, demonstrating fluency for addition and subtraction within 10 with accurate, efficient, and flexible strategies. | Grade 1 |
| Oregon | 1.OA.D.7 | Use the meaning of the equal sign to determine whether equations involving addition and subtraction are true or false. | Grade 1 |
| Oregon | 1.OA.D.8 | Determine the unknown whole number in an addition or subtraction equation relating three whole numbers. | Grade 1 |
| Oregon | 1.NBT.A.1 | Count to 120, starting at any number less than 120. In this range, read and write numerals and represent a number of objects with a written numeral. | Grade 1 |
| Oregon | 1.NBT.B.2 | Understand 10 as a bundle of ten ones and that the two digits of a two-digit number represent amounts of tens and ones. | Grade 1 |
| Oregon | 1.NBT.B.3 | Compare two two-digit numbers based on meanings of the tens and ones digits, recording the results of comparisons with the symbols >, =, and <. | Grade 1 |
| Oregon | 1.NBT.C.4 | Add within 100 using concrete or visual representations and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction. Relate the strategy to a written method and explain why sometimes it is necessary to compose a ten. | Grade 1 |
| Oregon | 1.NBT.C.5 | Without having to count, mentally find 10 more or 10 less than a given two-digit number and explain the reasoning used. | Grade 1 |
| Oregon | 1.NBT.C.6 | Subtract multiples of 10 in the range 10-90 from multiples of 10 in the range 10-90 using concrete or visual representations and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction. Relate the strategy and model used to a written method and explain the reasoning used. | Grade 1 |
| Oregon | 1.GM.A.1 | Distinguish between defining attributes versus non-defining attributes for a wide variety of shapes. Build and draw shapes to possess defining attributes. | Grade 1 |
| Oregon | 1.GM.A.2 | Compose common two-dimensional shapes or three-dimensional shapes to create a composite shape, and create additional new shapes from composite shapes. | Grade 1 |
| Oregon | 1.GM.A.3 | Partition circles and rectangles into two and four equal shares. Describe the equal shares and understand that partitioning into more equal shares creates smaller shares. | Grade 1 |
| Oregon | 1.GM.B.4 | Order three objects by length; compare the lengths of two objects indirectly by using a third object. | Grade 1 |
| Oregon | 1.GM.B.5 | Express the length of an object as a whole number of non-standard length units, by laying multiple copies of a shorter object (the length unit) end to end. | Grade 1 |
| Oregon | 1.GM.C.6 | Tell and write time in hours and half-hours using analog and digital clocks. | Grade 1 |
| Oregon | 1.DR.B.2 | Analyze data sets with up to three categories by representing data visually, such as with graphs and charts, and interpret information presented to answer investigative questions. | Grade 1 |
| Oregon | 2.OA.A.1 | Use addition and subtraction within 100 to solve one- and two-step problems in authentic contexts by using drawings and equations with a symbol for the unknown. | Grade 2 |
| Oregon | 2.OA.B.2 | Fluently add and subtract within 20 using accurate, efficient, and flexible strategies and algorithms based on place value and properties of operations. | Grade 2 |
| Oregon | 2.OA.C.3 | Determine whether a group up to 20 objects has an odd or even number by pairing objects or counting them by 2s; record using drawings and equations including expressing an even number as a sum of two equal addends. | Grade 2 |
| Oregon | 2.OA.C.4 | Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends. | Grade 2 |
| Oregon | 2.NBT.A.1 | Understand 100 as a bundle of ten tens and that the three digits of a three-digit number represent amounts of hundreds, tens, and ones. | Grade 2 |
| Oregon | 2.NBT.A.2 | Count within 1000; skip-count by 5's, 10's, and 100's. | Grade 2 |
| Oregon | 2.NBT.A.3 | Read and write numbers to 1000 using base-ten numerals, number names, and expanded form. | Grade 2 |
| Oregon | 2.NBT.A.4 | Compare two three-digit numbers based on meanings of the hundreds, tens, and ones digits, using >, =, and < symbols to record the results of comparisons. | Grade 2 |
| Oregon | 2.NBT.B.5 | Fluently add & subtract within 100 using accurate, efficient, & flexible strategies based on place value, properties of operations, and/or the relationship between addition and subtraction. | Grade 2 |
| Oregon | 2.NBT.B.6 | Add up to four two-digit numbers using strategies based on place value and properties of operations and describe how two different strategies result in the same sum. | Grade 2 |
| Oregon | 2.NBT.B.7 | Add and subtract within 1000 using concrete or visual representations and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction. Relate the strategy to a written method and explain why sometimes it is necessary to compose or decompose tens or hundreds. | Grade 2 |
| Oregon | 2.NBT.B.8 | Without having to count, mentally find 10 more or 10 less and 100 more or 100 less than a given three-digit number. | Grade 2 |
| Oregon | 2.GM.A.1 | Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces. | Grade 2 |
| Oregon | 2.GM.A.2 | Partition a rectangle into rows and columns of same-size squares and count to find the total number of them. | Grade 2 |
| Oregon | 2.GM.A.3 | Partition circles and rectangles into two, three, or four equal parts. Recognize that equal parts of identical wholes need not have the same shape. | Grade 2 |
| Oregon | 2.GM.B.4 | Measure the length of an object by selecting and using appropriate measurement tools. | Grade 2 |
| Oregon | 2.GM.B.5 | Measure the length of an object using two different length units and describe how the measurements relate to the size of the unit chosen. | Grade 2 |
| Oregon | 2.GM.B.7 | Measure two objects and determine the difference in their lengths in terms of a standard length unit. | Grade 2 |
| Oregon | 2.GM.C.8 | Use addition and subtraction within 100 to solve problems in authentic contexts involving lengths that are given in the same units. | Grade 2 |
| Oregon | 2.GM.D.10 | Tell and write time from analog and digital clocks to the nearest five minutes, using a.m. and p.m. | Grade 2 |
| Oregon | 2.GM.D.11 | Solve problems in authentic contexts involving dollar bills, quarters, dimes, nickels, and pennies, using $ (dollars) and c (cents) symbols appropriately. | Grade 2 |
| Oregon | 2.DR.A.1 | Generate questions to investigate situations within the classroom. Collect or consider data that can naturally answer questions by using measurements with whole-number units. | Grade 2 |
| Oregon | 2.DR.B.2 | Analyze data with a single-unit scale and interpret information presented to answer investigative questions. | Grade 2 |
| Oregon | 3.OA.A.1 | Represent and interpret multiplication of two factors as repeated addition of equal groups. | Grade 3 |
| Oregon | 3.OA.A.2 | Represent and interpret whole-number quotients as dividing an amount into equal sized groups. | Grade 3 |
| Oregon | 3.OA.A.3 | Use multiplication and division within 100 to solve problems in authentic contexts involving equal groups, arrays, and/or measurement quantities. | Grade 3 |
| Oregon | 3.OA.A.4 | Determine the unknown number in a multiplication or division equation relating three whole numbers by applying the understanding of the inverse relationship of multiplication and division. | Grade 3 |
| Oregon | 3.OA.B.5 | Apply properties of operations as strategies to multiply and divide. | Grade 3 |
| Oregon | 3.OA.B.6 | Understand division as an unknown-factor in a multiplication problem. | Grade 3 |
| Oregon | 3.OA.C.7 | Fluently multiply and divide within 100 using accurate, efficient, and flexible strategies and algorithms based on place value and properties of operations. | Grade 3 |
| Oregon | 3.OA.D.8 | Solve two-step problems in authentic contexts that use addition, subtraction, multiplication, and division in equations with a letter standing for the unknown quantity. | Grade 3 |
| Oregon | 3.OA.D.9 | Identify and explain arithmetic patterns using properties of operations, including patterns in the addition table or multiplication table. | Grade 3 |
| Oregon | 3.NBT.A.1 | Use place value understanding to round whole numbers within 1000 to the nearest 10 or 100. | Grade 3 |
| Oregon | 3.NBT.A.2 | Fluently add and subtract within 1000 using accurate, efficient, and flexible strategies and algorithms based on place value and properties of operations. | Grade 3 |
| Oregon | 3.NBT.A.3 | Find the product of one-digit whole numbers by multiples of 10 in the range 10-90, such as 9 x 80. Students use a range of strategies and algorithms based on place value and properties of operations. | Grade 3 |
| Oregon | 3.NF.A.1 | Understand the concept of a unit fraction and explain how multiple copies of a unit fraction form a non-unit fraction. | Grade 3 |
| Oregon | 3.NF.A.2 | Understand a fraction as a number on the number line; Represent fractions on a number line diagram. | Grade 3 |
| Oregon | 3.NF.A.3 | Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size. | Grade 3 |
| Oregon | 3.GM.A.1 | Understand that shapes in different categories may share attributes and that shared attributes can define a larger category. | Grade 3 |
| Oregon | 3.GM.A.2 | Partition shapes into parts with equal areas and express the area of each part as a unit fraction of the whole. | Grade 3 |
| Oregon | 3.GM.B.3 | Tell, write, and measure time to the nearest minute. Solve problems in authentic contexts that involve addition and subtraction of time intervals in minutes. | Grade 3 |
| Oregon | 3.GM.B.4 | Measure, estimate and solve problems in authentic contexts that involve liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l). | Grade 3 |
| Oregon | 3.GM.C.5 | Recognize area as an attribute of plane figures and understand concepts of area measurement presented in authentic contexts by tiling and counting unit squares. | Grade 3 |
| Oregon | 3.GM.C.6 | Measure areas by counting standard and non-standard unit squares. | Grade 3 |
| Oregon | 3.GM.C.7 | Relate area to multiplication and addition. Use relevant representations to solve problems in authentic contexts. | Grade 3 |
| Oregon | 3.GM.D.8 | Solve problems involving authentic contexts for perimeters of polygons. | Grade 3 |
| Oregon | 3.DR.A.1 | Generate questions to investigate situations within the classroom, school or community. Collect or consider measurement data that can naturally answer questions by using information presented in a scaled picture and/or bar graph. | Grade 3 |
| Oregon | 3.DR.B.2 | Analyze measurement data with a scaled picture graph or a scaled bar graph to represent a data set with several categories. Interpret information presented to answer investigative questions. | Grade 3 |
| Oregon | 4.OA.A.1 | Interpret a multiplication equation as comparing quantities. Represent verbal statements of multiplicative comparisons as equations. | Grade 4 |
| Oregon | 4.OA.A.2 | Multiply or divide to solve problems in authentic contexts involving multiplicative comparison, distinguishing multiplicative comparison from additive comparison. | Grade 4 |
| Oregon | 4.OA.A.3 | Solve multistep problems in authentic contexts using whole numbers and having whole- number answers using the four operations, including problems in which remainders must be interpreted. | Grade 4 |
| Oregon | 4.OA.B.4 | Find all factor pairs for a whole number in the range 1-100. Determine whether a given whole number in the range of 1-100 is a multiple of a given one-digit number, and whether it is prime or composite. | Grade 4 |
| Oregon | 4.OA.C.1 | Analyze a number, visual, or contextual pattern that follows a given rule. | Grade 4 |
| Oregon | 4.NBT.A.1 | Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. | Grade 4 |
| Oregon | 4.NBT.A.2 | Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Use understandings of place value within these forms to compare two multi- digit numbers using >, =, and < symbols. | Grade 4 |
| Oregon | 4.NBT.A.3 | Use place value understanding to round multi-digit whole numbers to any place. | Grade 4 |
| Oregon | 4.NBT.B.4 | Fluently add and subtract multi-digit whole numbers using accurate, efficient, and flexible strategies and algorithms based on place value and properties of operations. | Grade 4 |
| Oregon | 4.NBT.B.5 | Use representations and strategies to multiply a whole number of up to four digits by a one- digit number, and a two-digit number by a two-digit number using strategies based on place value and the properties of operations. | Grade 4 |
| Oregon | 4.NBT.B.6 | Use representations and strategies to find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. | Grade 4 |
| Oregon | 4.NF.A.1 | Use visual fraction representations to recognize, generate, and explain relationships between equivalent fractions. | Grade 4 |
| Oregon | 4.NF.A.2 | Compare two fractions with different numerators and/or different denominators, record the results with the symbols >, =, or <, and justify the conclusions. | Grade 4 |
| Oregon | 4.NF.B.3 | Understand a fraction (a/b) as the sum (a) of fractions of the same denominator (1/b). Solve problems in authentic contexts involving addition and subtraction of fractions referring to the same whole and having like denominators. | Grade 4 |
| Oregon | 4.NF.B.4 | Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Represent and solve problems in authentic contexts involving multiplication of a fraction by a whole number. | Grade 4 |
| Oregon | 4.NF.C.5 | Demonstrate and explain the concept of equivalent fractions with denominators of 10 and 100, using concrete materials and visual models. Add two fractions with denominators of 10 and 100. | Grade 4 |
| Oregon | 4.NF.C.6 | Use and interpret decimal notation for fractions with denominators 10 or 100. | Grade 4 |
| Oregon | 4.NF.C.7 | Use decimal notation for fractions with denominators 10 or 100. Compare two decimals to hundredths place by reasoning about their size, and record the comparison using the symbols >, =, or <. | Grade 4 |
| Oregon | 4.GM.A.1 | Explore, investigate, and draw points, lines, line segments, rays, angles, and perpendicular and parallel lines. Identify these in two-dimensional figures. | Grade 4 |
| Oregon | 4.GM.A.2 | Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. | Grade 4 |
| Oregon | 4.GM.A.3 | Recognize and draw a line of symmetry for a two dimensional figure. | Grade 4 |
| Oregon | 4.GM.B.4 | Know relative sizes of measurement units and express measurements in a larger unit in terms of a smaller unit. | Grade 4 |
| Oregon | 4.GM.B.5 | Apply knowledge of the four operations and relative size of measurement units to solve problems in authentic contexts that include familiar fractions or decimals. | Grade 4 |
| Oregon | 4.GM.B.6 | Apply the area and perimeter formulas for rectangles in authentic contexts and mathematical problems. | Grade 4 |
| Oregon | 4.GM.C.7 | Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint. Understand and apply concepts of angle measurement. | Grade 4 |
| Oregon | 4.GM.C.8 | Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure. | Grade 4 |
| Oregon | 4.GM.C.9 | Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. | Grade 4 |
| Oregon | 4.DR.B.2 | Analyze line plots to display a distribution of numerical measurement data, which include displays of data sets of fractional measurements with the same denominator. Interpret information presented to answer investigative questions. | Grade 4 |
| Oregon | 5.OA.A.1 | Write and evaluate numerical expressions that include parentheses. | Grade 5 |
| Oregon | 5.OA.A.2 | Write expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. | Grade 5 |
| Oregon | 5.OA.B.3 | Generate two numerical patterns using two given rules. Identify and analyze relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns and graph them on a coordinate plane. | Grade 5 |
| Oregon | 5.NBT.A.1 | Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. | Grade 5 |
| Oregon | 5.NBT.A.2 | Use whole number exponents to denote powers of 10 and explain the patterns in placement of digits that occur when multiplying and/or dividing whole numbers and decimals by powers of 10. | Grade 5 |
| Oregon | 5.NBT.A.3 | Read, write, and compare decimals to thousandths. | Grade 5 |
| Oregon | 5.NBT.A.4 | Use place value understanding to round decimals to any place. | Grade 5 |
| Oregon | 5.NBT.B.5 | Fluently multiply multi-digit whole numbers using accurate, efficient, and flexible strategies and algorithms based on place value and properties of operations. | Grade 5 |
| Oregon | 5.NBT.B.6 | Use a variety of representations and strategies to find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors. | Grade 5 |
| Oregon | 5.NBT.B.7 | Use a variety of representations and strategies to add, subtract, multiply, and divide decimals to hundredths. Relate the strategy to a written method and explain the reasoning used. | Grade 5 |
| Oregon | 5.NF.A.1 | Add and subtract fractions with unlike denominators, including common fractions larger than one and mixed numbers. | Grade 5 |
| Oregon | 5.NF.A.2 | Solve problems in authentic contexts involving addition and subtraction of fractions with unlike denominators, including common fractions larger than one and mixed numbers. | Grade 5 |
| Oregon | 5.NF.B.3 | Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve problems in authentic contexts involving division of whole numbers that result in answers that are common fractions or mixed numbers. | Grade 5 |
| Oregon | 5.NF.B.4 | Apply and extend previous understanding and strategies of multiplication to multiply a fraction or whole number by a fraction. Multiply fractional side lengths to find areas of rectangles, and represent fractional products as rectangular areas. | Grade 5 |
| Oregon | 5.NF.B.5 | Apply and extend previous understandings of multiplication and division to represent and calculate multiplication and division of fractions. Interpret multiplication as scaling (resizing) by comparing the size of products of two factors. | Grade 5 |
| Oregon | 5.NF.B.6 | Solve problems in authentic contexts involving multiplication of common fractions and mixed numbers. | Grade 5 |
| Oregon | 5.NF.B.7 | Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions, including solving problems in authentic contexts. | Grade 5 |
| Oregon | 5.GM.A.1 | Graph and name coordinate points in the first quadrant using the standard (x, y) notation. Understand the coordinate points values represent the distance traveled along the horizontal x-axis and vertical y-axis. | Grade 5 |
| Oregon | 5.GM.A.2 | Represent authentic contexts and mathematical problems by graphing points in the first quadrant of the coordinate plane. Interpret the meaning of the coordinate values based on the context of a given situation. | Grade 5 |
| Oregon | 5.GM.B.3 | Classify two-dimensional figures within a hierarchy based on their geometrical properties, and explain the relationship across and within different categories of these figures. | Grade 5 |
| Oregon | 5.GM.C.4 | Convert between different-sized standard measurement units within a given measurement system. Use these conversions in solving multi-step problems in authentic contexts. | Grade 5 |
| Oregon | 5.GM.D.5 | Recognize that volume is a measurable attribute of solid figures. | Grade 5 |
| Oregon | 5.GM.D.6 | Measure the volume of a rectangular prism by counting unit cubes using standard and nonstandard units. | Grade 5 |
| Oregon | 5.GM.D.7 | Relate volume of rectangular prisms to the operations of multiplication and addition. Solve problems in authentic contexts involving volume using a variety of strategies. | Grade 5 |
| Oregon | 5.DR.B.2 | Analyze graphical representations and describe the distribution of the numerical data through line plots or categorical data through bar graphs. Interpret information presented to answer investigative questions. | Grade 5 |
| Oregon | 6.AEE.A.1 | Write and evaluate numerical expressions involving whole-number bases and exponents. | Grade 6 |
| Oregon | 6.AEE.A.2 | Write, read, and evaluate expressions in which letters stand for numbers. Apply knowledge of common mathematical terms to move between the verbal and mathematical forms of an expression including expressions that arise from authentic contexts. | Grade 6 |
| Oregon | 6.AEE.A.3 | Apply the properties of operations to generate equivalent expressions and to determine when two expressions are equivalent. | Grade 6 |
| Oregon | 6.AEE.B.4 | Understand solving an equation or inequality as a process of answering which values from a specified set, if any, make the equation or inequality true. Use substitution to determine which number(s) in a given set make an equation or inequality true. | Grade 6 |
| Oregon | 6.AEE.B.5 | Use variables to represent numbers and write expressions when solving problems in authentic contexts. | Grade 6 |
| Oregon | 6.AEE.B.6 | Write and solve equations of the form x + p = q and px = q in problems that arise from authentic contexts for cases in which p, q and x are all nonnegative rational numbers. | Grade 6 |
| Oregon | 6.AEE.B.7 | Write inequalities of the form x > c and x c and x < c. | Grade 6 |
| Oregon | 6.AEE.C.8 | Use variables to represent and analyze two quantities to solve problems in authentic contexts. Including those that change in relationship to one another; write an equation to express one quantity in terms of the other quantity. | Grade 6 |
| Oregon | 6.RP.A.1 | Understand the concept of a ratio in authentic contexts, and use ratio language to describe a ratio relationship between two quantities. | Grade 6 |
| Oregon | 6.RP.A.2 | Understand the concept of a unit rate in authentic contexts and use rate language in the context of a ratio relationship. | Grade 6 |
| Oregon | 6.RP.A.3 | Use ratio and rate reasoning to solve problems in authentic contexts that use equivalent ratios, unit rates, percents, and/or measurement units. | Grade 6 |
| Oregon | 6.NS.A.1 | Represent, interpret, and compute quotients of fractions to solve problems in authentic contexts involving division of fractions by fractions. | Grade 6 |
| Oregon | 6.NS.B.2 | Fluently divide multi-digit numbers using accurate, efficient, and flexible strategies and algorithms based on place value and properties of operations. | Grade 6 |
| Oregon | 6.NS.B.3 | Fluently add, subtract, multiply, and divide positive rational numbers using accurate, efficient, and flexible strategies and algorithms. | Grade 6 |
| Oregon | 6.NS.C.5 | Understand that positive and negative numbers are used together to describe quantities having opposite directions or values. Use positive and negative numbers to represent quantities in authentic contexts, explaining the meaning of zero in each situation. | Grade 6 |
| Oregon | 6.NS.C.6 | Represent a rational number as a point on the number line. Extend number line diagrams and coordinate axes to represent points on the line and in the coordinate plane with negative number coordinates. | Grade 6 |
| Oregon | 6.NS.C.7 | Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram. Write, interpret, and explain statements of order for rational numbers and absolute value in authentic applications. | Grade 6 |
| Oregon | 6.NS.C.8 | Graph points in all four quadrants of the coordinate plane to solve problems in authentic contexts. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. | Grade 6 |
| Oregon | 6.GM.A.1 | Find the area of triangles, quadrilaterals, and other polygons by composing into rectangles or decomposing into triangles and other shapes. Apply these techniques to solve problems in authentic contexts. | Grade 6 |
| Oregon | 6.GM.A.2 | Find the volume of a right rectangular prism with fractional edge lengths by filling it with unit cubes of appropriate unit fraction edge lengths. Connect and apply to the formulas V = l w h and V = b h to find volumes of right rectangular prisms with fractional edge lengths to solve problems in authentic contexts. | Grade 6 |
| Oregon | 6.GM.A.3 | Draw polygons in the four quadrant coordinate plane given coordinates for the vertices and find the length of a side. Apply these techniques to solve problems in authentic contexts. | Grade 6 |
| Oregon | 6.GM.A.4 | Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures, including those from authentic contexts. | Grade 6 |
| Oregon | 6.DR.D.4 | Interpret quantitative measures of center to describe differences between groups from data collected to answer investigative questions. | Grade 6 |
| Oregon | 7.AEE.A.1 | Identify and write equivalent expressions with rational numbers by applying associative, commutative, and distributive properties. | Grade 7 |
| Oregon | 7.AEE.A.2 | Understand that rewriting an expression in different forms in a contextual problem can show how quantities are related. | Grade 7 |
| Oregon | 7.AEE.B.3 | Write and solve problems in authentic contexts using expressions and equations with positive and negative rational numbers in any form. Contexts can be limited to those that can be solved with one or two-step linear equations. | Grade 7 |
| Oregon | 7.AEE.B.4 | Use variables to represent quantities and construct one- and two-step linear inequalities with positive rational numbers to solve authentic problems by reasoning about the quantities. | Grade 7 |
| Oregon | 7.RP.A.1 | Solve problems in authentic contexts involving unit rates associated with ratios of fractions. | Grade 7 |
| Oregon | 7.RP.A.2 | Recognize and represent proportional relationships between quantities in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships. Identify the constant of proportionality (unit rate) within various representations. | Grade 7 |
| Oregon | 7.RP.A.3 | Use proportional relationships to solve ratio and percent problems in authentic contexts. | Grade 7 |
| Oregon | 7.NS.A.1 | Apply and extend previous understandings of addition, subtraction and absolute value to add and subtract rational numbers in authentic contexts. Understand subtraction as adding the additive inverse, p - q = p + (-q). | Grade 7 |
| Oregon | 7.NS.A.2 | Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers. Interpret operations of rational numbers solving problems in authentic contexts. | Grade 7 |
| Oregon | 7.NS.A.3 | Understand that equivalent rational numbers can be written as fractions, decimals and percents. | Grade 7 |
| Oregon | 7.GM.A.1 | Solve problems involving scale drawings of geometric figures. Reproduce a scale drawing at a different scale and compute actual lengths and areas from a scale drawing. | Grade 7 |
| Oregon | 7.GM.A.2 | Draw triangles from three measures of angles or sides. Understand the possible side lengths and angle measures that determine a unique triangle, more than one triangle, or no triangle. | Grade 7 |
| Oregon | 7.GM.B.3 | Understand the relationship between area and circumference of circles. Choose and use the appropriate formula to solve problems with radius, diameter, circumference and area of circles. | Grade 7 |
| Oregon | 7.GM.B.4 | Apply facts about supplementary, complementary, vertical, and adjacent angles in a multi- step problem to determine an unknown angle in a figure. | Grade 7 |
| Oregon | 7.GM.B.5 | Solve problems in authentic contexts involving two- and three-dimensional figures. Given formulas, calculate area, volume and surface area. | Grade 7 |
| Oregon | 8.AEE.A.1 | Apply the properties of integer exponents using powers of 10 to generate equivalent numerical expressions. | Grade 8 |
| Oregon | 8.AEE.A.2 | Represent solutions to equations using square root and cube root symbols. | Grade 8 |
| Oregon | 8.AEE.A.3 | Estimate very large or very small quantities using scientific notation with a single digit times an integer power of ten. | Grade 8 |
| Oregon | 8.AEE.A.4 | Perform operations with numbers expressed in scientific notation. | Grade 8 |
| Oregon | 8.AEE.B.5 | Graph proportional relationships in authentic contexts. Interpret the unit rate as the slope of the graph, and compare two different proportional relationships represented in different ways. | Grade 8 |
| Oregon | 8.AEE.B.6 | Write the equation for a line in slope intercept form y = mx + b, where m and b are rational numbers, and explain in context why the slope m is the same between any two distinct points. | Grade 8 |
| Oregon | 8.AEE.C.7 | Solve linear equations with one variable including equations with rational number coefficients, with the variable on both sides, or whose solutions require using the distributive property and/or combining like terms. | Grade 8 |
| Oregon | 8.AEE.C.8 | Find, analyze, and interpret solutions to pairs of simultaneous linear equations using graphs or tables. | Grade 8 |
| Oregon | 8.AFN.A.1 | Understand in authentic contexts, that the graph of a function is the set of ordered pairs consisting of an input and a corresponding output. | Grade 8 |
| Oregon | 8.AFN.A.2 | Compare the properties of two functions represented algebraically, graphically, numerically in tables, or verbally by description. | Grade 8 |
| Oregon | 8.AFN.A.3 | Understand and identify linear functions, whose graph is a straight line, and identify examples of functions that are not linear. | Grade 8 |
| Oregon | 8.AFN.B.4 | Construct a function to model a linear relationship in authentic contexts between two quantities. | Grade 8 |
| Oregon | 8.AFN.B.5 | Describe qualitatively the functional relationship between two quantities in authentic contexts by analyzing a graph. | Grade 8 |
| Oregon | 8.NS.A.2 | Use rational approximations of irrational numbers to compare size and locate on a number line. | Grade 8 |
| Oregon | 8.GM.A.1 | Verify experimentally the properties of rotations, reflections, and translations. | Grade 8 |
| Oregon | 8.GM.A.2 | Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations. | Grade 8 |
| Oregon | 8.GM.A.3 | Describe the effect of dilations, translations, rotations and reflections on two-dimensional figures using coordinates. | Grade 8 |
| Oregon | 8.GM.A.4 | Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and/or dilations. | Grade 8 |
| Oregon | 8.GM.A.5 | Use informal arguments to establish facts about interior and exterior angles of triangles and angles formed by parallel lines cut with a transversal. | Grade 8 |
| Oregon | 8.GM.B.7 | Apply the Pythagorean Theorem in authentic contexts to determine unknown side lengths in right triangles. | Grade 8 |
| Oregon | 8.GM.B.8 | Apply the Pythagorean Theorem to find the distance between two points in a coordinate system. | Grade 8 |
| Oregon | 8.GM.C.9 | Choose and use the appropriate formula for the volume of cones, cylinders, and spheres to solve problems in authentic contexts. | Grade 8 |
| Oregon | 8.DR.B.2 | Collect or consider data using surveys and measurements to capture patterns of association, and critically analyze data collection methods. | Grade 8 |
| Oregon | 8.DR.C.3 | Analyze patterns of association between two quantitative or categorical variables and reason about distributions to compare groups. | Grade 8 |
| Oregon | HS.AEE.A.2 | Create and recognize an equivalent form of an expression to understand the quantity represented in an authentic context. | High School |
| Oregon | HS.AEE.B.4 | Define variables and create equations with two or more variables to represent relationships between quantities in order to solve problems in authentic contexts. | High School |
| Oregon | HS.AEE.C.7 | Represent constraints by equations or inequalities, and by systems of equations and/or inequalities; interpret solutions as viable or nonviable options in authentic contexts. | High School |
| Oregon | HS.AEE.D.11 | Graph and explain why the points in a half plane are solutions to a linear inequality and the solutions to a system of inequalities are the points in the intersection of corresponding half planes. Interpret the meaning of the coordinates of these points in authentic contexts. | High School |
| Oregon | HS.AFN.A.2 | Use function notation and interpret statements that use function notation in terms of the context and the relationship it describes. | High School |
| Oregon | HS.AFN.C.6 | Interpret key features of functions, from multiple representations, and conversely predict features of functions from knowledge of context. | High School |
| Oregon | HS.AFN.C.7 | Graph functions using technology to show key features. | High School |
| Oregon | HS.DR.C.8 | Identify appropriate ways to summarize and then represent the distribution of univariate and bivariate data multiple ways with graphs and/or tables. Use technology to present data that supports interpretation of tabular and graphical representations. | High School |
| Pennsylvania | CC.2.2.K.A.1 | Students acquire the knowledge and skills needed to: Extend the concepts of putting together and taking apart to add and subtract within 10. | Kindergarten |
| Pennsylvania | CC.2.3.K.A.1 | Students acquire the knowledge and skills needed to: Identify and describe two- and three-dimensional shapes. | Kindergarten |
| Pennsylvania | CC.2.3.K.A.2 | Students acquire the knowledge and skills needed to: Analyze, compare, create, and compose two- and three-dimensional shapes. | Kindergarten |
| Pennsylvania | CC.2.4.K.A.1 | Students acquire the knowledge and skills needed to: Describe and compare attributes of length, area, weight, and capacity of everyday objects. | Kindergarten |
| Pennsylvania | CC.2.4.K.A.4 | Students acquire the knowledge and skills needed to: Classify objects and count the number of objects in each category. | Kindergarten |
| Pennsylvania | CC.2.1.K.A.1 | Students acquire the knowledge and skills needed to: Know number names and write and recite the count sequence. | Kindergarten |
| Pennsylvania | CC.2.1.K.A.2 | Students acquire the knowledge and skills needed to: Apply one-to-one correspondence to count the number of objects. | Kindergarten |
| Pennsylvania | CC.2.1.K.A.3 | Students acquire the knowledge and skills needed to: Apply the concept of magnitude to compare numbers and quantities. | Kindergarten |
| Pennsylvania | CC.2.2.1.A.1 | Students acquire the knowledge and skills needed to: Represent and solve problems involving addition and subtraction within 20. | Grade 1 |
| Pennsylvania | CC.2.2.1.A.2 | Students acquire the knowledge and skills needed to: Understand and apply properties of operations and the relationship between addition and subtraction. | Grade 1 |
| Pennsylvania | CC.2.3.1.A.1 | Students acquire the knowledge and skills needed to: Compose and distinguish between two- and three-dimensional shapes based on their attributes. | Grade 1 |
| Pennsylvania | CC.2.3.1.A.2 | Students acquire the knowledge and skills needed to: Use the understanding of fractions to partition shapes into halves and quarters. | Grade 1 |
| Pennsylvania | CC.2.4.1.A.1 | Students acquire the knowledge and skills needed to: Order lengths and measure them both indirectly and by repeating length units. | Grade 1 |
| Pennsylvania | CC.2.4.1.A.2 | Students acquire the knowledge and skills needed to: Tell and write time to the nearest half hour using both analog and digital clocks. | Grade 1 |
| Pennsylvania | CC.2.4.1.A.4 | Students acquire the knowledge and skills needed to: Represent and interpret data using tables/charts. | Grade 1 |
| Pennsylvania | CC.2.1.1.B.1 | Students acquire the knowledge and skills needed to: Extend the counting sequence to read and write numerals to represent objects. | Grade 1 |
| Pennsylvania | CC.2.1.1.B.2 | Students acquire the knowledge and skills needed to: Use place-value concepts to represent amounts of tens and ones and to compare two digit numbers. | Grade 1 |
| Pennsylvania | CC.2.1.1.B.3 | Students acquire the knowledge and skills needed to: Use place-value concepts and properties of operations to add and subtract within 100. | Grade 1 |
| Pennsylvania | CC.2.2.2.A.1 | Students acquire the knowledge and skills needed to: Represent and solve problems involving addition and subtraction within 100. | Grade 2 |
| Pennsylvania | CC.2.2.2.A.2 | Students acquire the knowledge and skills needed to: Use mental strategies to add and subtract within 20. | Grade 2 |
| Pennsylvania | CC.2.2.2.A.3 | Students acquire the knowledge and skills needed to: Work with equal groups of objects to gain foundations for multiplication. | Grade 2 |
| Pennsylvania | CC.2.3.2.A.1 | Students acquire the knowledge and skills needed to: Analyze and draw two- and three-dimensional shapes having specified attributes. | Grade 2 |
| Pennsylvania | CC.2.3.2.A.2 | Students acquire the knowledge and skills needed to: Use the understanding of fractions to partition shapes into halves, quarters, and thirds. | Grade 2 |
| Pennsylvania | CC.2.4.2.A.1 | Students acquire the knowledge and skills needed to: Measure and estimate lengths in standard units using appropriate tools. | Grade 2 |
| Pennsylvania | CC.2.4.2.A.2 | Students acquire the knowledge and skills needed to: Tell and write time to the nearest five minutes using both analog and digital clocks. | Grade 2 |
| Pennsylvania | CC.2.4.2.A.3 | Students acquire the knowledge and skills needed to: Solve problems and make change using coins and paper currency with appropriate symbols. | Grade 2 |
| Pennsylvania | CC.2.4.2.A.4 | Students acquire the knowledge and skills needed to: Represent and interpret data using line plots, picture graphs, and bar graphs. | Grade 2 |
| Pennsylvania | CC.2.4.2.A.6 | Students acquire the knowledge and skills needed to: Extend the concepts of addition and subtraction to problems involving length. | Grade 2 |
| Pennsylvania | CC.2.1.2.B.1 | Students acquire the knowledge and skills needed to: Use place-value concepts to represent amounts of tens and ones and to compare three digit numbers. | Grade 2 |
| Pennsylvania | CC.2.1.2.B.2 | Students acquire the knowledge and skills needed to: Use place-value concepts to read, write and skip count to 1000. | Grade 2 |
| Pennsylvania | CC.2.1.2.B.3 | Students acquire the knowledge and skills needed to: Use place-value understanding and properties of operations to add and subtract within 1000. | Grade 2 |
| Pennsylvania | CC.2.2.3.A.1 | Students acquire the knowledge and skills needed to: Represent and solve problems involving multiplication and division. | Grade 3 |
| Pennsylvania | CC.2.2.3.A.2 | Students acquire the knowledge and skills needed to: Understand properties of multiplication and the relationship between multiplication and division. | Grade 3 |
| Pennsylvania | CC.2.2.3.A.3 | Students acquire the knowledge and skills needed to: Demonstrate multiplication and division fluency. | Grade 3 |
| Pennsylvania | CC.2.2.3.A.4 | Students acquire the knowledge and skills needed to: Solve problems involving the four operations, and identify and explain patterns in arithmetic. | Grade 3 |
| Pennsylvania | CC.2.3.3.A.1 | Students acquire the knowledge and skills needed to: Identify, compare, and classify shapes and their attributes. | Grade 3 |
| Pennsylvania | CC.2.3.3.A.2 | Students acquire the knowledge and skills needed to: Use the understanding of fractions to partition shapes into parts with equal areas and express the area of each part as a unit fraction of the whole. | Grade 3 |
| Pennsylvania | CC.2.4.3.A.1 | Students acquire the knowledge and skills needed to: Solve problems involving measurement and estimation of temperature, liquid volume, mass, and length. | Grade 3 |
| Pennsylvania | CC.2.4.3.A.2 | Students acquire the knowledge and skills needed to: Tell and write time to the nearest minute and solve problems by calculating time intervals. | Grade 3 |
| Pennsylvania | CC.2.4.3.A.4 | Students acquire the knowledge and skills needed to: Represent and interpret data using tally charts, tables, pictographs, line plots, and bar graphs. | Grade 3 |
| Pennsylvania | CC.2.4.3.A.5 | Students acquire the knowledge and skills needed to: Determine the area of a rectangle and apply the concept to multiplication and to addition. | Grade 3 |
| Pennsylvania | CC.2.4.3.A.6 | Students acquire the knowledge and skills needed to: Solve problems involving perimeters of polygons and distinguish between linear and area measures. | Grade 3 |
| Pennsylvania | CC.2.1.3.C.1 | Students acquire the knowledge and skills needed to: Explore and develop an understanding of fractions as numbers. | Grade 3 |
| Pennsylvania | CC.2.1.3.B.1 | Students acquire the knowledge and skills needed to: Apply place-value understanding and properties of operations to perform multi-digit arithmetic. | Grade 3 |
| Pennsylvania | CC.2.2.4.A.1 | Students acquire the knowledge and skills needed to: Represent and solve problems involving the four operations. | Grade 4 |
| Pennsylvania | CC.2.2.4.A.2 | Students acquire the knowledge and skills needed to: Develop and/or apply number theory concepts to find factors and multiples. | Grade 4 |
| Pennsylvania | CC.2.2.4.A.4 | Students acquire the knowledge and skills needed to: Generate and analyze patterns using one rule. | Grade 4 |
| Pennsylvania | CC.2.3.4.A.1 | Students acquire the knowledge and skills needed to: Draw lines and angles and identify these in two-dimensional figures. | Grade 4 |
| Pennsylvania | CC.2.3.4.A.2 | Students acquire the knowledge and skills needed to: Classify two-dimensional figures by properties of their lines and angles. | Grade 4 |
| Pennsylvania | CC.2.3.4.A.3 | Students acquire the knowledge and skills needed to: Recognize symmetric shapes and draw lines of symmetry. | Grade 4 |
| Pennsylvania | CC.2.4.4.A.1 | Students acquire the knowledge and skills needed to: Solve problems involving measurement and conversions from a larger unit to a smaller unit. | Grade 4 |
| Pennsylvania | CC.2.4.4.A.4 | Students acquire the knowledge and skills needed to: Represent and interpret data involving fractions using information provided in a line plot. | Grade 4 |
| Pennsylvania | CC.2.4.4.A.6 | Students acquire the knowledge and skills needed to: Measure angles and use properties of adjacent angles to solve problems. | Grade 4 |
| Pennsylvania | CC.2.1.4.C.1 | Students acquire the knowledge and skills needed to: Extend the understanding of fractions to show equivalence and ordering. | Grade 4 |
| Pennsylvania | CC.2.1.4.C.2 | Students acquire the knowledge and skills needed to: Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers. | Grade 4 |
| Pennsylvania | CC.2.1.4.C.3 | Students acquire the knowledge and skills needed to: Connect decimal notation to fractions, and compare decimal fractions (base 10 denominator, e.g., 19/100). | Grade 4 |
| Pennsylvania | CC.2.1.4.B.1 | Students acquire the knowledge and skills needed to: Apply place-value concepts to show an understanding of multi-digit whole numbers. | Grade 4 |
| Pennsylvania | CC.2.1.4.B.2 | Students acquire the knowledge and skills needed to: Use place-value understanding and properties of operations to perform multi-digit arithmetic. | Grade 4 |
| Pennsylvania | CC.2.2.5.A.1 | Students acquire the knowledge and skills needed to: Interpret and evaluate numerical expressions using order of operations. | Grade 5 |
| Pennsylvania | CC.2.2.5.A.4 | Students acquire the knowledge and skills needed to: Analyze patterns and relationships using two rules. | Grade 5 |
| Pennsylvania | CC.2.3.5.A.1 | Students acquire the knowledge and skills needed to: Graph points in the first quadrant on the coordinate plane and interpret these points when solving real world and mathematical problems. | Grade 5 |
| Pennsylvania | CC.2.3.5.A.2 | Students acquire the knowledge and skills needed to: Classify two-dimensional figures into categories based on an understanding of their properties. | Grade 5 |
| Pennsylvania | CC.2.4.5.A.1 | Students acquire the knowledge and skills needed to: Solve problems using conversions within a given measurement system. | Grade 5 |
| Pennsylvania | CC.2.4.5.A.2 | Students acquire the knowledge and skills needed to: Represent and interpret data using appropriate scale. | Grade 5 |
| Pennsylvania | CC.2.4.5.A.4 | Students acquire the knowledge and skills needed to: Solve problems involving computation of fractions using information provided in a line plot. | Grade 5 |
| Pennsylvania | CC.2.4.5.A.5 | Students acquire the knowledge and skills needed to: Apply concepts of volume to solve problems and relate volume to multiplication and to addition. | Grade 5 |
| Pennsylvania | CC.2.1.5.C.1 | Students acquire the knowledge and skills needed to: Use the understanding of equivalency to add and subtract fractions. | Grade 5 |
| Pennsylvania | CC.2.1.5.C.2 | Students acquire the knowledge and skills needed to: Apply and extend previous understandings of multiplication and division to multiply and divide fractions. | Grade 5 |
| Pennsylvania | CC.2.1.5.B.1 | Students acquire the knowledge and skills needed to: Apply place-value concepts to show an understanding of operations and rounding as they pertain to whole numbers and decimals. | Grade 5 |
| Pennsylvania | CC.2.1.5.B.2 | Students acquire the knowledge and skills needed to: Extend an understanding of operations with whole numbers to perform operations including decimals. | Grade 5 |
| Pennsylvania | CC.2.2.6.B.1 | Students acquire the knowledge and skills needed to: Apply and extend previous understandings of arithmetic to algebraic expressions. | Grade 6 |
| Pennsylvania | CC.2.2.6.B.2 | Students acquire the knowledge and skills needed to: Understand the process of solving a one-variable equation or inequality and apply to real-world and mathematical problems. | Grade 6 |
| Pennsylvania | CC.2.2.6.B.3 | Students acquire the knowledge and skills needed to: Represent and analyze quantitative relationships between dependent and independent variables. | Grade 6 |
| Pennsylvania | CC.2.3.6.A.1 | Students acquire the knowledge and skills needed to: Apply appropriate tools to solve real-world and mathematical problems involving area, surface area, and volume. | Grade 6 |
| Pennsylvania | CC.2.4.6.B.1 | Students acquire the knowledge and skills needed to: Demonstrate an understanding of statistical variability by displaying, analyzing, and summarizing distributions. | Grade 6 |
| Pennsylvania | CC.2.1.6.D.1 | Students acquire the knowledge and skills needed to: Understand ratio concepts and use ratio reasoning to solve problems. | Grade 6 |
| Pennsylvania | CC.2.1.6.E.1 | Students acquire the knowledge and skills needed to: Apply and extend previous understandings of multiplication and division to divide fractions by fractions. | Grade 6 |
| Pennsylvania | CC.2.1.6.E.2 | Students acquire the knowledge and skills needed to: Identify and choose appropriate processes to compute fluently with multi-digit numbers. | Grade 6 |
| Pennsylvania | CC.2.1.6.E.4 | Students acquire the knowledge and skills needed to: Apply and extend previous understandings of numbers to the system of rational numbers. | Grade 6 |
| Pennsylvania | CC.2.2.7.B.1 | Students acquire the knowledge and skills needed to: Apply properties of operations to generate equivalent expressions. | Grade 7 |
| Pennsylvania | CC.2.2.7.B.3 | Students acquire the knowledge and skills needed to: Model and solve real-world and mathematical problems by using and connecting numerical, algebraic, and/or graphical representations. | Grade 7 |
| Pennsylvania | CC.2.3.7.A.1 | Students acquire the knowledge and skills needed to: Solve real-world and mathematical problems involving angle measure, area, surface area, circumference, and volume. | Grade 7 |
| Pennsylvania | CC.2.3.7.A.2 | Students acquire the knowledge and skills needed to: Visualize and represent geometric figures and describe the relationships between them. | Grade 7 |
| Pennsylvania | CC.2.1.7.D.1 | Students acquire the knowledge and skills needed to: Analyze proportional relationships and use them to model and solve real-world and mathematical problems. | Grade 7 |
| Pennsylvania | CC.2.1.7.E.1 | Students acquire the knowledge and skills needed to: Apply and extend previous understandings of operations with fractions to operations with rational numbers. | Grade 7 |
| Pennsylvania | CC.2.2.8.B.1 | Students acquire the knowledge and skills needed to: Apply concepts of radicals and integer exponents to generate equivalent expressions. | Grade 8 |
| Pennsylvania | CC.2.2.8.B.2 | Students acquire the knowledge and skills needed to: Understand the connections between proportional relationships, lines, and linear equations. | Grade 8 |
| Pennsylvania | CC.2.2.8.B.3 | Students acquire the knowledge and skills needed to: Analyze and solve linear equations and pairs of simultaneous linear equations. | Grade 8 |
| Pennsylvania | CC.2.2.8.C.1 | Students acquire the knowledge and skills needed to: Define, evaluate, and compare functions. | Grade 8 |
| Pennsylvania | CC.2.2.8.C.2 | Students acquire the knowledge and skills needed to: Use concepts of functions to model relationships between quantities. | Grade 8 |
| Pennsylvania | CC.2.3.8.A.1 | Students acquire the knowledge and skills needed to: Apply the concepts of volume of cylinders, cones, and spheres to solve real-world and mathematical problems. | Grade 8 |
| Pennsylvania | CC.2.3.8.A.2 | Students acquire the knowledge and skills needed to: Understand and apply congruence, similarity, and geometric transformations using various tools. | Grade 8 |
| Pennsylvania | CC.2.3.8.A.3 | Students acquire the knowledge and skills needed to: Understand and apply the Pythagorean Theorem to solve problems. | Grade 8 |
| Pennsylvania | CC.2.4.8.B.1 | Students acquire the knowledge and skills needed to: Analyze and/or interpret bivariate data displayed in multiple representations. | Grade 8 |
| Pennsylvania | CC.2.1.8.E.4 | Students acquire the knowledge and skills needed to: Estimate irrational numbers by comparing them to rational numbers. | Grade 8 |
| Pennsylvania | CC.2.2.HS.D.1 | Students acquire the knowledge and skills needed to: Interpret the structure of expressions to represent a quantity in terms of its context. | High School |
| Pennsylvania | CC.2.2.HS.D.2 | Students acquire the knowledge and skills needed to: Write expressions in equivalent forms to solve problems. | High School |
| Pennsylvania | CC.2.2.HS.D.4 | Students acquire the knowledge and skills needed to: Understand the relationship between zeros and factors of polynomials to make generalizations about functions and their graphs. | High School |
| Pennsylvania | CC.2.2.HS.D.7 | Students acquire the knowledge and skills needed to: Create and graph equations or inequalities to describe numbers or relationships. | High School |
| Pennsylvania | CC.2.2.HS.D.10 | Students acquire the knowledge and skills needed to: Represent, solve, and interpret equations/inequalities and systems of equations/inequalities algebraically and graphically. | High School |
| Pennsylvania | CC.2.2.HS.C.1 | Students acquire the knowledge and skills needed to: Use the concept and notation of functions to interpret and apply them in terms of their context. | High School |
| Pennsylvania | CC.2.2.HS.C.2 | Students acquire the knowledge and skills needed to: Graph and analyze functions and use their properties to make connections between the different representations. | High School |
| Pennsylvania | CC.2.2.HS.C.3 | Students acquire the knowledge and skills needed to: Write functions or sequences that model relationships between two quantities. | High School |
| Pennsylvania | CC.2.4.HS.B.2 | Students acquire the knowledge and skills needed to: Summarize, represent, and interpret data on two categorical and quantitative variables. | High School |
| Quebec | E1.A.MON.A.1 | Determines the operation(s) to perform in a given situation | Grade 1 |
| Quebec | E1.A.MON.A.2 | Uses objects, diagrams or equations to represent a situation and conversely, describes a situation represented by objects, diagrams or equations (use of different meanings of addition and subtraction): transformation (adding, taking away), uniting, comparing | Grade 1 |
| Quebec | E1.A.MON.A.3a | Uses objects, diagrams or equations to represent a situation and conversely, describes a situation represented by objects, diagrams or equations (use of different meanings of multiplication and division): rectangular arrays, repeated addition, Cartesian product, sharing, and number of times x goes into y (using objects and diagrams) | Grade 1 |
| Quebec | E1.A.MON.A.5a | Determines numerical equivalencies using relationships between operations (addition and subtraction) and the commutative property of addition | Grade 1 |
| Quebec | E1.A.MON.A.4 | Establishes equality relations between numerical expressions (e.g. 3 + 2 = 6 - 1) | Grade 1 |
| Quebec | E1.A.ON.A.2a | Builds a repertoire of memorized addition and subtraction facts: Builds a memory of addition facts (0 + 0 to 10 + 10) and the corresponding subtraction facts, using objects, drawings, charts or tables | Grade 1 |
| Quebec | E1.A.ON.A.2b | Builds a repertoire of memorized addition and subtraction facts: Develops various strategies that promote mastery of number facts and relates them to the properties of addition | Grade 1 |
| Quebec | E1.A.ON.A.2c | Builds a repertoire of memorized addition and subtraction facts: Masters all addition facts (0 + 0 to 10 + 10) and the corresponding subtraction facts | Grade 1 |
| Quebec | E1.A.ON.A.3a | Develops processes for mental computation: Uses his/her own processes to determine the sum or difference of two natural numbers | Grade 1 |
| Quebec | E1.A.ON.A.4a | Develops processes for written computation (addition and subtraction): Uses his/her own processes as well as objects and drawings to determine the sum or difference of two natural numbers less than 1000 | Grade 1 |
| Quebec | E1.A.ON.A.5 | Determines the missing term in an equation (relationships between operations): a + b = ?, a + ? = c, ? + b = c, a - b = ?, a - ? = c, ? - b = c | Grade 1 |
| Quebec | E1.A.ON.A.13 | Using his/her own words and mathematical language that is at an appropriate level for the cycle, describes numerical patterns (e.g. number rhymes, tables and charts) | Grade 1 |
| Quebec | E1.A.UWN.A.1a | Counts or recites counting rhymes involving natural numbers: counts forward from a given number | Grade 1 |
| Quebec | E1.A.UWN.A.1b | Counts or recites counting rhymes involving natural numbers: counts forward or backward | Grade 1 |
| Quebec | E1.A.UWN.A.1c | Counts or recites counting rhymes involving natural numbers: skip counts (e.g. by twos) | Grade 1 |
| Quebec | E1.A.UWN.A.2a | Counts collections (using objects or drawings): matches the gesture to the corresponding number word; recognizes the cardinal aspect of a number and the conservation of number in various combinations | Grade 1 |
| Quebec | E1.A.UWN.A.2b | Counts collections (using objects or drawings): counts from a given number | Grade 1 |
| Quebec | E1.A.UWN.A.2c | Counts collections (using objects or drawings): counts a collection by grouping or regrouping | Grade 1 |
| Quebec | E1.A.UWN.A.5 | Composes and decomposes a natural number in a variety of ways | Grade 1 |
| Quebec | E1.A.UWN.A.6 | Identifies equivalent expressions | Grade 1 |
| Quebec | E1.A.UWN.A.7 | Compares natural numbers | Grade 1 |
| Quebec | E1.A.UWN.A.8 | Arranges natural numbers in increasing or decreasing order | Grade 1 |
| Quebec | E1.A.UWN.A.10 | Locates natural numbers using different visual aids (e.g. hundreds chart, number strip, number line) | Grade 1 |
| Quebec | E1.M.G.1 | Estimates and measures time using conventional units | Grade 1 |
| Quebec | E1.M.G.2 | Establishes relationships between units of measure | Grade 1 |
| Quebec | E1.A.UWN.A.13 | Approximates a collection, using objects or drawings (e.g. estimate, round up/down to a given value) | Grade 1 |
| Quebec | E1.A.UWN.B.2 | Represents a fraction in a variety of ways, based on a whole or a collection of objects | Grade 1 |
| Quebec | E1.A.UWN.A.4a | Represents natural numbers in different ways or associates a number with a set of objects or drawings: emphasis on apparent, accessible groupings using objects, drawings or unstructured materials | Grade 1 |
| Quebec | E2.A.MON.A.1 | Determines the operation(s) to perform in a given situation | Grade 2 |
| Quebec | E2.A.MON.A.2 | Uses objects, diagrams or equations to represent a situation and conversely, describes a situation represented by objects, diagrams or equations (use of different meanings of addition and subtraction): transformation (adding, taking away), uniting, comparing | Grade 2 |
| Quebec | E2.A.MON.A.3a | Uses objects, diagrams or equations to represent a situation and conversely, describes a situation represented by objects, diagrams or equations (use of different meanings of multiplication and division): rectangular arrays, repeated addition, Cartesian product, sharing, and number of times x goes into y (using objects and diagrams) | Grade 2 |
| Quebec | E2.A.MON.A.5a | Determines numerical equivalencies using relationships between operations (addition and subtraction) and the commutative property of addition | Grade 2 |
| Quebec | E2.A.MON.A.4 | Establishes equality relations between numerical expressions (e.g. 3 + 2 = 6 - 1) | Grade 2 |
| Quebec | E2.A.ON.A.2a | Builds a repertoire of memorized addition and subtraction facts: Builds a memory of addition facts (0 + 0 to 10 + 10) and the corresponding subtraction facts, using objects, drawings, charts or tables | Grade 2 |
| Quebec | E2.A.ON.A.2b | Builds a repertoire of memorized addition and subtraction facts: Develops various strategies that promote mastery of number facts and relates them to the properties of addition | Grade 2 |
| Quebec | E2.A.ON.A.2c | Builds a repertoire of memorized addition and subtraction facts: Masters all addition facts (0 + 0 to 10 + 10) and the corresponding subtraction facts | Grade 2 |
| Quebec | E2.A.ON.A.3a | Develops processes for mental computation: Uses his/her own processes to determine the sum or difference of two natural numbers | Grade 2 |
| Quebec | E2.A.ON.A.4a | Develops processes for written computation (addition and subtraction): Uses his/her own processes as well as objects and drawings to determine the sum or difference of two natural numbers less than 1000 | Grade 2 |
| Quebec | E2.A.ON.A.5 | Determines the missing term in an equation (relationships between operations): a + b = ?, a + ? = c, ? + b = c, a - b = ?, a - ? = c, ? - b = c | Grade 2 |
| Quebec | E2.A.ON.A.13 | Using his/her own words and mathematical language that is at an appropriate level for the cycle, describes numerical patterns (e.g. number rhymes, tables and charts) | Grade 2 |
| Quebec | E2.A.UWN.A.1a | Counts or recites counting rhymes involving natural numbers: counts forward from a given number | Grade 2 |
| Quebec | E2.A.UWN.A.1b | Counts or recites counting rhymes involving natural numbers: counts forward or backward | Grade 2 |
| Quebec | E2.A.UWN.A.1c | Counts or recites counting rhymes involving natural numbers: skip counts (e.g. by twos) | Grade 2 |
| Quebec | E2.A.UWN.A.2b | Counts collections (using objects or drawings): counts from a given number | Grade 2 |
| Quebec | E2.A.UWN.A.2c | Counts collections (using objects or drawings): counts a collection by grouping or regrouping | Grade 2 |
| Quebec | E2.A.UWN.A.4b | Represents natural numbers in different ways or associates a number with a set of objects or drawings: emphasis on exchanging apparent, non-accessible groupings, using structured materials (e.g. base ten blocks, number tables) | Grade 2 |
| Quebec | E2.A.UWN.A.5 | Composes and decomposes a natural number in a variety of ways | Grade 2 |
| Quebec | E2.A.UWN.A.6 | Identifies equivalent expressions | Grade 2 |
| Quebec | E2.A.UWN.A.7 | Compares natural numbers | Grade 2 |
| Quebec | E2.A.UWN.A.8 | Arranges natural numbers in increasing or decreasing order | Grade 2 |
| Quebec | E2.A.UWN.A.10 | Locates natural numbers using different visual aids (e.g. hundreds chart, number strip, number line) | Grade 2 |
| Quebec | E2.M.G.1 | Estimates and measures time using conventional units | Grade 2 |
| Quebec | E2.M.G.2 | Establishes relationships between units of measure | Grade 2 |
| Quebec | E2.A.UWN.A.13 | Approximates a collection, using objects or drawings (e.g. estimate, round up/down to a given value) | Grade 2 |
| Quebec | E2.A.UWN.B.2 | Represents a fraction in a variety of ways, based on a whole or a collection of objects | Grade 2 |
| Quebec | E2.A.UWN.A.4a | Represents natural numbers in different ways or associates a number with a set of objects or drawings: emphasis on apparent, accessible groupings using objects, drawings or unstructured materials | Grade 2 |
| Quebec | E3.S.3b | Interprets data using a table, a bar graph, a pictograph and a broken-line graph | Grade 3 |
| Quebec | E3.S.4b | Displays data using table, a bar graph, a pictograph and a broken-line graph | Grade 3 |
| Quebec | E3.M.A.6 | Calculates the perimeter of plane figures | Grade 3 |
| Quebec | E3.A.MON.B.3a | Determines numerical equivalencies using the relationship between operations (addition and subtraction), the commutative property of addition and the associative property | Grade 3 |
| Quebec | E3.A.MON.A.4 | Establishes equality relations between numerical expressions (e.g. 3 + 2 = 6 - 1) | Grade 3 |
| Quebec | E3.A.ON.C.2a | Develops processes for mental computation: adds and subtracts decimals | Grade 3 |
| Quebec | E3.A.ON.C.3a | Develops processes for written computation: adds and subtracts decimals whose result does not go beyond the second decimal place | Grade 3 |
| Quebec | E3.A.ON.B.1 | Generates a set of equivalent fractions | Grade 3 |
| Quebec | E3.A.ON.A.2b | Builds a repertoire of memorized addition and subtraction facts: Develops various strategies that promote mastery of number facts and relates them to the properties of addition | Grade 3 |
| Quebec | E3.A.ON.A.2c | Builds a repertoire of memorized addition and subtraction facts: Masters all addition facts (0 + 0 to 10 + 10) and the corresponding subtraction facts | Grade 3 |
| Quebec | E3.A.ON.A.3b | Develops processes for mental computation: Uses his/her own processes to determine the product or quotient of two natural numbers | Grade 3 |
| Quebec | E3.A.ON.A.4b | Develops processes for written computation (addition and subtraction): Uses conventional processes to determine the sum of two natural numbers of up to four digits | Grade 3 |
| Quebec | E3.A.ON.A.4c | Develops processes for written computation (addition and subtraction): Uses conventional processes to determine the difference between two natural numbers of up to four digits whose result is greater than 0 | Grade 3 |
| Quebec | E3.A.ON.A.6a | Builds a repertoire of memorized multiplication and division facts: Builds a memory of multiplication facts and the corresponding division facts using objects drawings charts or tables | Grade 3 |
| Quebec | E3.A.ON.A.6b | Builds a repertoire of memorized multiplication and division facts: Develops various strategies that promote mastery of number facts and relate them to the properties of multiplication | Grade 3 |
| Quebec | E3.A.ON.A.6c | Builds a repertoire of memorized multiplication and division facts: Masters all multiplication facts and the corresponding division facts | Grade 3 |
| Quebec | E3.A.ON.A.7a | Develops processes for written computation (multiplication and division): Uses his/her own processes as well as materials and drawings to determine the product or quotient of a three-digit natural number and a one-digit natural number, expresses the remainder of a division as a fraction, depending on the context | Grade 3 |
| Quebec | E3.G.C.6 | Describes quadrilaterals (e.g. parallel segments, perpendicular segments, right angles, acute angles, obtuse angles) | Grade 3 |
| Quebec | E3.G.C.7 | Classifies quadrilaterals | Grade 3 |
| Quebec | E3.G.B.5 | Describes prisms and pyramids in terms of faces, vertices and edges | Grade 3 |
| Quebec | E3.G.B.6 | Classifies prisms and pyramids | Grade 3 |
| Quebec | E3.G.A.3 | Locates objects on an axis (based on the types of numbers studied) | Grade 3 |
| Quebec | E3.G.A.4a | Locates points in a Cartesian plane in the first quadrant | Grade 3 |
| Quebec | E3.M.G.2 | Establishes relationships between units of measure | Grade 3 |
| Quebec | E3.A.UWN.C.1 | Represents decimals in a variety of ways (using objects or drawings) | Grade 3 |
| Quebec | E3.A.UWN.C.2 | Identifies equivalent representations (using objects or drawings) | Grade 3 |
| Quebec | E3.A.UWN.C.4 | Understands the role of the decimal point | Grade 3 |
| Quebec | E3.A.UWN.C.5 | Composes and decomposes a decimal written in decimal notation | Grade 3 |
| Quebec | E3.A.UWN.C.6 | Recognizes equivalent expressions | Grade 3 |
| Quebec | E3.A.UWN.C.7a | Locates decimals on a number line between two consecutive natural numbers | Grade 3 |
| Quebec | E3.A.UWN.C.8 | Compares two decimals | Grade 3 |
| Quebec | E3.A.UWN.C.9 | Approximates (e.g. estimates, rounds to a given value, truncates decimal places) | Grade 3 |
| Quebec | E3.A.MON.B.1a | Uses objects, diagrams or equations to represent a situation and conversely, describes a situation represented by objects, diagrams or equations (use of different meanings of addition and subtraction): transformation (adding, taking away), uniting, comparing | Grade 3 |
| Quebec | E3.A.MON.B.2 | Uses objects, diagrams or equations to represent a situation and conversely, describes a situation represented by objects, diagrams or equations (use of different meanings of multiplication and division: rectangular arrays, Cartesian product, area, volume, sharing, number of times x goes into y, and comparisons) | Grade 3 |
| Quebec | E3.A.UWN.B.2 | Represents a fraction in a variety of ways, based on a whole or a collection of objects | Grade 3 |
| Quebec | E3.A.UWN.B.3 | Matches a fraction to part of a whole (congruent or equivalent parts) or part of a group of objects, and vice versa | Grade 3 |
| Quebec | E3.A.UWN.B.4 | Identifies the different meanings of fractions (sharing, division, ratio) | Grade 3 |
| Quebec | E3.A.UWN.B.5 | Distinguishes a numerator from a denominator | Grade 3 |
| Quebec | E3.A.UWN.B.8 | Verifies whether two fractions are equivalent | Grade 3 |
| Quebec | E3.A.UWN.A.2c | Counts collections (using objects or drawings): counts a collection by grouping or regrouping | Grade 3 |
| Quebec | E3.A.UWN.A.2d | Counts collections (using objects or drawings): counts a pre-grouped collection | Grade 3 |
| Quebec | E3.A.UWN.A.4b | Represents natural numbers in different ways or associates a number with a set of objects or drawings: emphasis on exchanging apparent, non-accessible groupings, using structured materials (e.g. base ten blocks, number tables) | Grade 3 |
| Quebec | E3.A.UWN.A.5 | Composes and decomposes a natural number in a variety of ways | Grade 3 |
| Quebec | E3.A.MON.A.3b | Uses objects, diagrams or equations to represent a situation and conversely, describes a situation represented by objects, diagrams or equations (use of different meanings of multiplication and division): rectangular arrays, repeated addition, Cartesian product, area, volume, repeated subtraction, sharing, number of times x goes into y, and comparisons (using objects, diagrams or equations) | Grade 3 |
| Quebec | E3.A.MON.A.5b | Determines numerical equivalencies using relationships between operations (the four operations), the commutative property of addition and multiplication and the associative property | Grade 3 |
| Quebec | E3.M.B.1a | Estimates and measures surface area using unconventional units | Grade 3 |
| Quebec | E3.A.UWN.A.4c | Represents natural numbers in different ways or associates a number with a set of objects or drawings: emphasis on place value in non-apparent, non-accessible groupings, using materials for which groupings are symbolic (e.g. abacus, money) | Grade 3 |
| Quebec | E3.A.UWN.A.6 | Identifies equivalent expressions (e.g. 52 = 40 + 12, 25 + 27 = 40 + 12) | Grade 3 |
| Quebec | E3.A.UWN.A.7 | Compares natural numbers | Grade 3 |
| Quebec | E4.S.3b | Interprets data using a table, a bar graph, a pictograph and a broken-line graph | Grade 4 |
| Quebec | E4.S.4b | Displays data using table, a bar graph, a pictograph and a broken-line graph | Grade 4 |
| Quebec | E4.A.MON.B.3a | Determines numerical equivalencies using the relationship between operations (addition and subtraction), the commutative property of addition and the associative property | Grade 4 |
| Quebec | E4.A.ON.C.2a | Develops processes for mental computation: adds and subtracts decimals | Grade 4 |
| Quebec | E4.A.ON.C.3a | Develops processes for written computation: adds and subtracts decimals whose result does not go beyond the second decimal place | Grade 4 |
| Quebec | E4.A.ON.B.1 | Generates a set of equivalent fractions | Grade 4 |
| Quebec | E4.A.ON.A.3b | Develops processes for mental computation: Uses his/her own processes to determine the product or quotient of two natural numbers | Grade 4 |
| Quebec | E4.A.ON.A.4b | Develops processes for written computation (addition and subtraction): Uses conventional processes to determine the sum of two natural numbers of up to four digits | Grade 4 |
| Quebec | E4.A.ON.A.4c | Develops processes for written computation (addition and subtraction): Uses conventional processes to determine the difference between two natural numbers of up to four digits whose result is greater than 0 | Grade 4 |
| Quebec | E4.A.ON.A.6a | Builds a repertoire of memorized multiplication and division facts: Builds a memory of multiplication facts (0 x 0 to 10 x 10) and the corresponding division facts using objects drawings charts or tables | Grade 4 |
| Quebec | E4.A.ON.A.6b | Builds a repertoire of memorized multiplication and division facts: Develops various strategies that promote mastery of number facts and relate them to the properties of multiplication | Grade 4 |
| Quebec | E4.A.ON.A.6c | Builds a repertoire of memorized multiplication and division facts: Masters all multiplication facts (0 x 0 to 10 x 10) and the corresponding division facts | Grade 4 |
| Quebec | E4.A.ON.A.7a | Develops processes for written computation (multiplication and division): Uses his/her own processes as well as materials and drawings to determine the product or quotient of a three-digit natural number and a one-digit natural number, expresses the remainder of a division as a fraction, depending on the context | Grade 4 |
| Quebec | E4.A.ON.A.9 | Decomposes a number into prime factors | Grade 4 |
| Quebec | E4.A.ON.A.8 | Determines the missing term in an equation (relationships between operations): a + b = ?, a + ? = c, ? + b = c, a - b = ?, a - ? = c, ? - b = c | Grade 4 |
| Quebec | E4.G.C.6 | Describes quadrilaterals (e.g. parallel segments, perpendicular segments, right angles, acute angles, obtuse angles) | Grade 4 |
| Quebec | E4.G.C.7 | Classifies quadrilaterals | Grade 4 |
| Quebec | E4.G.B.5 | Describes prisms and pyramids in terms of faces, vertices and edges | Grade 4 |
| Quebec | E4.G.B.6 | Classifies prisms and pyramids | Grade 4 |
| Quebec | E4.G.A.3 | Locates objects on an axis (based on the types of numbers studied) | Grade 4 |
| Quebec | E4.G.A.4a | Locates points in a Cartesian plane in the first quadrant | Grade 4 |
| Quebec | E4.M.G.2 | Establishes relationships between units of measure | Grade 4 |
| Quebec | E4.A.UWN.C.1 | Represents decimals in a variety of ways (using objects or drawings) | Grade 4 |
| Quebec | E4.A.UWN.C.2 | Identifies equivalent representations (using objects or drawings) | Grade 4 |
| Quebec | E4.A.UWN.C.4 | Understands the role of the decimal point | Grade 4 |
| Quebec | E4.A.UWN.C.5 | Composes and decomposes a decimal written in decimal notation | Grade 4 |
| Quebec | E4.A.UWN.C.6 | Recognizes equivalent expressions | Grade 4 |
| Quebec | E4.A.UWN.C.7a | Locates decimals on a number line between two consecutive natural numbers | Grade 4 |
| Quebec | E4.A.UWN.C.7b | Locates decimals on a number line between two decimals | Grade 4 |
| Quebec | E4.A.UWN.C.8 | Compares two decimals | Grade 4 |
| Quebec | E4.A.UWN.C.9 | Approximates (e.g. estimates, rounds to a given value, truncates decimal places) | Grade 4 |
| Quebec | E4.A.MON.B.1a | Uses objects, diagrams or equations to represent a situation and conversely, describes a situation represented by objects, diagrams or equations (use of different meanings of addition and subtraction): transformation (adding, taking away), uniting, comparing | Grade 4 |
| Quebec | E4.A.MON.B.2 | Uses objects, diagrams or equations to represent a situation and conversely, describes a situation represented by objects, diagrams or equations (use of different meanings of multiplication and division: rectangular arrays, Cartesian product, area, volume, sharing, number of times x goes into y, and comparisons) | Grade 4 |
| Quebec | E4.A.UWN.B.2 | Represents a fraction in a variety of ways, based on a whole or a collection of objects | Grade 4 |
| Quebec | E4.A.UWN.B.3 | Matches a fraction to part of a whole (congruent or equivalent parts) or part of a group of objects, and vice versa | Grade 4 |
| Quebec | E4.A.UWN.B.4 | Identifies the different meanings of fractions (sharing, division, ratio) | Grade 4 |
| Quebec | E4.A.UWN.B.5 | Distinguishes a numerator from a denominator | Grade 4 |
| Quebec | E4.A.UWN.B.8 | Verifies whether two fractions are equivalent | Grade 4 |
| Quebec | E4.A.UWN.B.10 | Orders fractions with the same denominator | Grade 4 |
| Quebec | E4.A.UWN.A.2c | Counts collections (using objects or drawings): counts a collection by grouping or regrouping | Grade 4 |
| Quebec | E4.A.UWN.A.2d | Counts collections (using objects or drawings): counts a pre-grouped collection | Grade 4 |
| Quebec | E4.A.UWN.A.4b | Represents natural numbers in different ways or associates a number with a set of objects or drawings: emphasis on exchanging apparent, non-accessible groupings, using structured materials (e.g. base ten blocks, number tables) | Grade 4 |
| Quebec | E4.A.UWN.A.5 | Composes and decomposes a natural number in a variety of ways | Grade 4 |
| Quebec | E4.A.MON.A.3b | Uses objects, diagrams or equations to represent a situation and conversely, describes a situation represented by objects, diagrams or equations (use of different meanings of multiplication and division): rectangular arrays, repeated addition, Cartesian product, area, volume, repeated subtraction, sharing, number of times x goes into y, and comparisons (using objects, diagrams or equations) | Grade 4 |
| Quebec | E4.G.D.3a | Observes and produces frieze patterns and tessellations using reflections | Grade 4 |
| Quebec | E4.M.B.1a | Estimates and measures surface area using unconventional units | Grade 4 |
| Quebec | E4.A.MON.A.5b | Determines numerical equivalencies using relationships between operations (the four operations), the commutative property of addition and multiplication and the associative property | Grade 4 |
| Quebec | E4.A.UWN.A.6 | Identifies equivalent expressions (e.g. 52 = 40 + 12, 25 + 27 = 40 + 12) | Grade 4 |
| Quebec | E4.A.UWN.A.7 | Compares natural numbers | Grade 4 |
| Quebec | E5.M.D.2 | Estimates and determines the degree measurement of angles | Grade 5 |
| Quebec | E5.S.3c | Interprets data using a table, a bar graph, a pictograph, a broken-line graph and a circle graph | Grade 5 |
| Quebec | E5.A.ON.C.1b | Approximates the result of a multiplication or division | Grade 5 |
| Quebec | E5.A.ON.C.2b | Develops processes for mental computation: performs operations involving decimals (multiplication, division by a natural number) | Grade 5 |
| Quebec | E5.A.ON.C.3b | Develops processes for written computation: multiplies decimals whose product does not go beyond the second decimal place | Grade 5 |
| Quebec | E5.A.ON.C.3c | Develops processes for written computation: divides a decimal by a natural number less than 11 | Grade 5 |
| Quebec | E5.A.ON.B.1 | Generates a set of equivalent fractions | Grade 5 |
| Quebec | E5.A.ON.B.3 | Adds and subtracts fractions when the denominator of one fraction is a multiple of the other fraction(s) | Grade 5 |
| Quebec | E5.A.ON.B.4 | Multiplies a natural number by a fraction | Grade 5 |
| Quebec | E5.A.ON.A.3b | Develops processes for mental computation: Uses his/her own processes to determine the product or quotient of two natural numbers | Grade 5 |
| Quebec | E5.A.ON.A.6b | Builds a repertoire of memorized multiplication and division facts: Develops various strategies that promote mastery of number facts and relate them to the properties of multiplication | Grade 5 |
| Quebec | E5.A.ON.A.6c | Builds a repertoire of memorized multiplication and division facts: Masters all multiplication facts (0 x 0 to 10 x 10) and the corresponding division facts | Grade 5 |
| Quebec | E5.A.ON.A.7b | Develops processes for written computation (multiplication and division): Uses conventional processes to determine the product of a three-digit natural number and a two-digit natural number | Grade 5 |
| Quebec | E5.A.ON.A.7c | Develops processes for written computation (multiplication and division): Uses conventional processes to determine the quotient of a four-digit natural number and a two-digit natural number, expresses the remainder of a division as a decimal that does not go beyond the second decimal place | Grade 5 |
| Quebec | E5.A.ON.A.9 | Decomposes a number into prime factors | Grade 5 |
| Quebec | E5.A.ON.A.10 | Calculates the power of a number | Grade 5 |
| Quebec | E5.A.ON.A.12 | Performs a series of operations in accordance with the order of operations | Grade 5 |
| Quebec | E5.A.ON.A.8 | Determines the missing term in an equation (relationships between operations): a + b = ?, a + ? = c, ? + b = c, a - b = ?, a - ? = c, ? - b = c | Grade 5 |
| Quebec | E5.G.C.8 | Describes triangles: scalene triangles, right triangles, isosceles triangles, equilateral triangles | Grade 5 |
| Quebec | E5.G.C.9 | Classifies triangles | Grade 5 |
| Quebec | E5.G.A.4b | Locates points in a Cartesian plane in all four quadrants | Grade 5 |
| Quebec | E5.G.A.3 | Locates objects on an axis (based on the types of numbers studied) | Grade 5 |
| Quebec | E5.M.G.2 | Establishes relationships between units of measure | Grade 5 |
| Quebec | E5.A.UWN.C.1 | Represents decimals in a variety of ways (using objects or drawings) | Grade 5 |
| Quebec | E5.A.UWN.C.2 | Identifies equivalent representations (using objects or drawings) | Grade 5 |
| Quebec | E5.A.UWN.C.5 | Composes and decomposes a decimal written in decimal notation | Grade 5 |
| Quebec | E5.A.UWN.C.6 | Recognizes equivalent expressions | Grade 5 |
| Quebec | E5.A.UWN.C.7a | Locates decimals on a number line between two consecutive natural numbers | Grade 5 |
| Quebec | E5.A.UWN.C.7b | Locates decimals on a number line between two decimals | Grade 5 |
| Quebec | E5.A.MON.B.1a | Uses objects, diagrams or equations to represent a situation and conversely, describes a situation represented by objects, diagrams or equations (use of different meanings of addition and subtraction): transformation (adding, taking away), uniting, comparing | Grade 5 |
| Quebec | E5.A.MON.B.2 | Uses objects, diagrams or equations to represent a situation and conversely, describes a situation represented by objects, diagrams or equations (use of different meanings of multiplication and division: rectangular arrays, Cartesian product, area, volume, sharing, number of times x goes into y, and comparisons) | Grade 5 |
| Quebec | E5.A.UWN.B.2 | Represents a fraction in a variety of ways, based on a whole or a collection of objects | Grade 5 |
| Quebec | E5.A.UWN.B.8 | Verifies whether two fractions are equivalent | Grade 5 |
| Quebec | E5.A.UWN.B.10 | Orders fractions with the same denominator | Grade 5 |
| Quebec | E5.A.UWN.B.12 | Orders fractions with the same numerator | Grade 5 |
| Quebec | E5.A.UWN.B.13 | Locates fractions on a number line | Grade 5 |
| Quebec | E5.A.UWN.D.3 | Locates integers on a number line or Cartesian plane | Grade 5 |
| Quebec | E5.A.UWN.D.4 | Compares integers | Grade 5 |
| Quebec | E5.A.UWN.D.5 | Arranges integers in increasing or decreasing order | Grade 5 |
| Quebec | E5.A.UWN.A.14 | Represents the power of a natural number | Grade 5 |
| Quebec | E5.A.MON.A.5c | Determines numerical equivalencies using relationships between operations (the four operations), the commutative property of addition and multiplication, the associative property and the distributive property of multiplication over addition or subtraction | Grade 5 |
| Quebec | E5.A.MON.A.6 | Translates a situation using a series of operations in accordance with the order of operations | Grade 5 |
| Quebec | E6.M.D.2 | Estimates and determines the degree measurement of angles | Grade 6 |
| Quebec | E6.S.1 | Formulates questions for a survey (based on age-appropriate topics, students' language level, etc.) | Grade 6 |
| Quebec | E6.A.ON.C.1b | Approximates the result of a multiplication or division | Grade 6 |
| Quebec | E6.A.ON.C.2b | Develops processes for mental computation: performs operations involving decimals (multiplication, division by a natural number) | Grade 6 |
| Quebec | E6.A.ON.C.3b | Develops processes for written computation: multiplies decimals whose product does not go beyond the second decimal place | Grade 6 |
| Quebec | E6.A.ON.C.3c | Develops processes for written computation: divides a decimal by a natural number less than 11 | Grade 6 |
| Quebec | E6.A.ON.B.1 | Generates a set of equivalent fractions | Grade 6 |
| Quebec | E6.A.ON.B.3 | Adds and subtracts fractions when the denominator of one fraction is a multiple of the other fraction(s) | Grade 6 |
| Quebec | E6.A.ON.B.4 | Multiplies a natural number by a fraction | Grade 6 |
| Quebec | E6.A.ON.A.3b | Develops processes for mental computation: Uses his/her own processes to determine the product or quotient of two natural numbers | Grade 6 |
| Quebec | E6.A.ON.A.7b | Develops processes for written computation (multiplication and division): Uses conventional processes to determine the product of a three-digit natural number and a two-digit natural number | Grade 6 |
| Quebec | E6.A.ON.A.7c | Develops processes for written computation (multiplication and division): Uses conventional processes to determine the quotient of a four-digit natural number and a two-digit natural number, expresses the remainder of a division as a decimal that does not go beyond the second decimal place | Grade 6 |
| Quebec | E6.A.ON.A.9 | Decomposes a number into prime factors | Grade 6 |
| Quebec | E6.A.ON.A.10 | Calculates the power of a number | Grade 6 |
| Quebec | E6.A.ON.A.12 | Performs a series of operations in accordance with the order of operations | Grade 6 |
| Quebec | E6.G.C.8 | Describes triangles: scalene triangles, right triangles, isosceles triangles, equilateral triangles | Grade 6 |
| Quebec | E6.G.C.9 | Classifies triangles | Grade 6 |
| Quebec | E6.G.A.4b | Locates points in a Cartesian plane in all four quadrants | Grade 6 |
| Quebec | E6.G.A.3 | Locates objects on an axis (based on the types of numbers studied) | Grade 6 |
| Quebec | E6.M.G.2 | Establishes relationships between units of measure | Grade 6 |
| Quebec | E6.A.UWN.C.1 | Represents decimals in a variety of ways (using objects or drawings) | Grade 6 |
| Quebec | E6.A.UWN.C.2 | Identifies equivalent representations (using objects or drawings) | Grade 6 |
| Quebec | E6.A.UWN.C.5 | Composes and decomposes a decimal written in decimal notation | Grade 6 |
| Quebec | E6.A.UWN.C.6 | Recognizes equivalent expressions | Grade 6 |
| Quebec | E6.A.UWN.C.7a | Locates decimals on a number line between two consecutive natural numbers | Grade 6 |
| Quebec | E6.A.UWN.C.7b | Locates decimals on a number line between two decimals | Grade 6 |
| Quebec | E6.A.MON.B.1a | Uses objects, diagrams or equations to represent a situation and conversely, describes a situation represented by objects, diagrams or equations (use of different meanings of addition and subtraction): transformation (adding, taking away), uniting, comparing | Grade 6 |
| Quebec | E6.A.MON.B.2 | Uses objects, diagrams or equations to represent a situation and conversely, describes a situation represented by objects, diagrams or equations (use of different meanings of multiplication and division: rectangular arrays, Cartesian product, area, volume, sharing, number of times x goes into y, and comparisons) | Grade 6 |
| Quebec | E6.A.UWN.B.2 | Represents a fraction in a variety of ways, based on a whole or a collection of objects | Grade 6 |
| Quebec | E6.A.UWN.B.8 | Verifies whether two fractions are equivalent | Grade 6 |
| Quebec | E6.A.UWN.B.12 | Orders fractions with the same numerator | Grade 6 |
| Quebec | E6.A.UWN.B.13 | Locates fractions on a number line | Grade 6 |
| Quebec | E6.A.UWN.D.3 | Locates integers on a number line or Cartesian plane | Grade 6 |
| Quebec | E6.A.UWN.D.4 | Compares integers | Grade 6 |
| Quebec | E6.A.UWN.D.5 | Arranges integers in increasing or decreasing order | Grade 6 |
| Quebec | E6.A.UWN.A.14 | Represents the power of a natural number | Grade 6 |
| Quebec | E6.A.MON.A.5c | Determines numerical equivalencies using relationships between operations (the four operations), the commutative property of addition and multiplication, the associative property and the distributive property of multiplication over addition or subtraction | Grade 6 |
| Quebec | E6.A.MON.A.6 | Translates a situation using a series of operations in accordance with the order of operations | Grade 6 |
| Quebec | S1.AG.ASAG.A.2 | Locates points in a Cartesian plane, based on the types of numbers studied (x- and y-coordinates of a point) | Grade 7 |
| Quebec | S1.A.ORN.7a | Computes, in writing, the four operations with numbers that are easy to work with (including large numbers), using equivalent ways of writing numbers and the properties of operations: numbers written in decimal notation, using rules of signs | Grade 7 |
| Quebec | S1.A.ORN.6 | Mentally computes the four operations, especially with numbers written in decimal notation, using equivalent ways of writing numbers and the properties of operations | Grade 7 |
| Quebec | S1.A.ORN.7b | Computes, in writing, the four operations with numbers that are easy to work with (including large numbers), using equivalent ways of writing numbers and the properties of operations: positive numbers written in fractional notation, with or without the use of objects or diagrams | Grade 7 |
| Quebec | S2.A.ORN.5 | Mentally computes the four operations, especially with numbers written in decimal notation, using equivalent ways of writing numbers and the properties of operations | Grade 7 |
| Quebec | S2.A.ORN.7b | Computes, in writing, the four operations with numbers that are easy to work with (including large numbers), using equivalent ways of writing numbers and the properties of operations: positive numbers written in fractional notation, with or without the use of objects or diagrams | Grade 7 |
| Quebec | S1.A.ORN.8 | Computes, in writing, sequences of operations (numbers written in decimal notation) in accordance with the order of operations, using equivalent ways of writing numbers and the properties of operations (with no more than two levels of parentheses) | Grade 7 |
| Quebec | S1.G.SSAS.A.5 | Recognizes and names regular convex polygons | Grade 7 |
| Quebec | S1.G.SSAS.D.3 | Recognizes the geometric transformation(s) linking a figure and its image | Grade 7 |
| Quebec | S1.G.SSAS.C.3 | Identifies congruence (translation, rotation and reflection) between two figures | Grade 7 |
| Quebec | S1.G.SSAS.C.4 | Constructs the image of a figure under a translation, rotation and reflection | Grade 7 |
| Quebec | S1.G.SSAS.C.5 | Recognizes dilatation with a positive scale factor | Grade 7 |
| Quebec | S1.G.SSAS.C.6 | Constructs the image of a figure under a dilatation with a positive scale factor | Grade 7 |
| Quebec | S1.A.UAPS.1a | Calculates a certain percentage of a number | Grade 7 |
| Quebec | S1.A.UAPS.1b | Calculates the value corresponding to 100 per cent | Grade 7 |
| Quebec | S1.A.UAPS.2 | Recognizes ratios and rates | Grade 7 |
| Quebec | S1.A.UAPS.3 | Interprets ratios and rates | Grade 7 |
| Quebec | S1.A.UAPS.4 | Describes the effect of changing a term in a ratio or rate | Grade 7 |
| Quebec | S1.A.UAPS.8 | Represents or interprets a proportional situation using a graph, a table of values or a proportion | Grade 7 |
| Quebec | S1.A.UAPS.9 | Solves proportional situations (direct or inverse variation) by using different strategies (e.g. unit-rate method, factor of change, proportionality ratio, additive procedure, constant product [inverse variation]) | Grade 7 |
| Quebec | S1.AL.UMAE.B.1 | Calculates the numeric value of an algebraic expression | Grade 7 |
| Quebec | S1.AL.UMAE.B.2 | Performs the following operations on algebraic expressions, with or without objects or diagrams: addition and subtraction, multiplication and division by a constant, multiplication of first-degree monomials | Grade 7 |
| Quebec | S1.AL.UMAE.B.3 | Factors out the common factor in numerical expressions (distributive property of multiplication over addition or subtraction) | Grade 7 |
| Quebec | S1.AL.UMAE.C.9 | Uses different methods to solve first-degree equations with one unknown of the form ax + b = cx + d : trial and error, drawings, arithmetic methods (inverse or equivalent operations), algebraic methods (balancing equations or hidden terms) | Grade 7 |
| Quebec | S1.A.UORN.6 | Translates (mathematizes) a situation using a sequence of operations (no more than two levels of parentheses) | Grade 7 |
| Quebec | S1.A.URN.10 | Defines the concept absolute value in context (e.g. difference between two numbers, distance between two points) | Grade 7 |
| Quebec | S1.A.URN.11c | Represents and writes numbers in exponential notation (integral exponent) | Grade 7 |
| Quebec | S1.A.URN.15a | Compares and arranges in order numbers written in fractional or decimal notation | Grade 7 |
| Quebec | S1.A.URN.15b | Compares and arranges in order numbers expressed in different ways (fractional, decimal, exponential [integral exponent], percentage, square root, scientific notation) | Grade 7 |
| Quebec | S2.A.ORN.7a | Computes, in writing, the four operations with numbers that are easy to work with (including large numbers), using equivalent ways of writing numbers and the properties of operations: numbers written in decimal notation, using rules of signs | Grade 8 |
| Quebec | S2.A.ORN.6 | Mentally computes the four operations, especially with numbers written in decimal notation, using equivalent ways of writing numbers and the properties of operations | Grade 8 |
| Quebec | S2.G.SSAS.C.4 | Constructs the image of a figure under a translation, rotation and reflection | Grade 8 |
| Quebec | S2.A.UAPS.1b | Calculates the value corresponding to 100 per cent | Grade 8 |
| Quebec | S2.AL.UMAE.C.9 | Uses different methods to solve first-degree equations with one unknown of the form ax + b = cx + d : trial and error, drawings, arithmetic methods (inverse or equivalent operations), algebraic methods (balancing equations or hidden terms) | Grade 8 |
| Quebec | S2.AL.UMAE.D.4b | Solves a system involving various functional models (mostly graphical solutions) | Grade 8 |
| Quebec | S2.AL.UMAE.D.2a | Translates a situation algebraically or graphically using a system of equations | Grade 8 |
| Quebec | S2.AL.UMAE.B.1 | Calculates the numeric value of an algebraic expression | Grade 8 |
| Quebec | S2.AL.UMAE.B.2 | Performs the following operations on algebraic expressions, with or without objects or diagrams: addition and subtraction, multiplication and division by a constant, multiplication of first-degree monomials | Grade 8 |
| Quebec | S2.AL.UMAE.B.6b | Factors polynomials by factoring by grouping (polynomials including decomposable second-degree trinomials) | Grade 8 |
| Quebec | S2.AL.UMAE.B.6c | Factors polynomials by completing the square (factoring and switching from one type of notation to another) | Grade 8 |
| Quebec | S2.A.URN.10 | Defines the concept absolute value in context (e.g. difference between two numbers, distance between two points) | Grade 8 |
| Quebec | S2.G.SSAS.C.3 | Identifies congruence (translation, rotation and reflection) between two figures | Grade 8 |
| Quebec | S2.G.SSAS.C.5 | Recognizes dilatation with a positive scale factor | Grade 8 |
| Quebec | S2.G.SSAS.C.6 | Constructs the image of a figure under a dilatation with a positive scale factor | Grade 8 |
| Quebec | S2.G.SSAS.D.3 | Recognizes the geometric transformation(s) linking a figure and its image | Grade 8 |
| Rhode Island | K.CC.A.1 | Count to 100 by ones and by tens. | Kindergarten |
| Rhode Island | K.CC.A.2 | Count forward beginning from a given number within the known sequence (instead of having to begin at 1). | Kindergarten |
| Rhode Island | K.CC.A.3 | Write numbers from 0 to 20. Represent a number of objects with a written numeral 0-20 (with 0 representing a count of no objects). | Kindergarten |
| Rhode Island | K.CC.B.4 | Understand the relationship between numbers and quantities; connect counting to cardinality. | Kindergarten |
| Rhode Island | K.CC.B.5 | Count to answer “how many?” questions about as many as 20 things arranged in a line, a rectangular array, or a circle, or as many as 10 things in a scattered configuration; given a number from 1-20, count out that many objects. | Kindergarten |
| Rhode Island | K.CC.C.6 | Identify whether the number of objects in one group is greater than, less than, or equal to the number of objects in another group, e.g., by using matching and counting strategies. | Kindergarten |
| Rhode Island | K.CC.C.7 | Compare two numbers between 1 and 10 presented as written numerals. | Kindergarten |
| Rhode Island | K.G.A.1 | Describe objects in the environment using names of shapes, and describe the relative positions of these objects using terms such as above, below, beside, in front of, behind, and next to. | Kindergarten |
| Rhode Island | K.G.A.2 | Correctly name shapes regardless of their orientations or overall size. | Kindergarten |
| Rhode Island | K.G.A.3 | Identify shapes as two-dimensional (lying in a plane, “flat”) or three-dimensional (“solid”). | Kindergarten |
| Rhode Island | K.G.B.4 | Analyze and compare two- and three-dimensional shapes, in different sizes and orientations, using informal language to describe their similarities, differences, parts (e.g., number of sides and vertices/“corners”) and other attributes (e.g., having sides of equal length). | Kindergarten |
| Rhode Island | K.G.B.6 | Compose simple shapes to form larger shapes. | Kindergarten |
| Rhode Island | K.MD.A.1 | Describe measurable attributes of objects, such as length or weight. Describe several measurable attributes of a single object. | Kindergarten |
| Rhode Island | K.MD.A.2 | Directly compare two objects with a measurable attribute in common, to see which object has “more of”/“less of” the attribute, and describe the difference. | Kindergarten |
| Rhode Island | K.MD.B.3 | Classify objects into given categories; count the numbers of objects in each category and sort the categories by count. | Kindergarten |
| Rhode Island | K.NBT.A.1 | Compose and decompose numbers from 11 to 19 into ten ones and some further ones, e.g., by using objects or drawings, and record each composition or decomposition by a drawing or equation (e.g., 18 = 10 + 8); understand that these numbers are composed of ten ones and one, two, three, four, five, six, seven, eight, or nine ones. | Kindergarten |
| Rhode Island | K.OA.A.1 | Represent addition and subtraction with objects, fingers, mental images, drawings, sounds (e.g., claps), acting out situations, verbal explanations, expressions, or equations. | Kindergarten |
| Rhode Island | K.OA.A.2 | Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem. | Kindergarten |
| Rhode Island | K.OA.A.3 | Decompose numbers less than or equal to 10 into pairs in more than one way, e.g., by using objects or drawings, and record each decomposition by a drawing or equation (e.g., 5 = 2 + 3 and 5 = 4 + 1). | Kindergarten |
| Rhode Island | K.OA.A.4 | For any number from 1 to 9, find the number that makes 10 when added to the given number, e.g., by using objects or drawings, and record the answer with a drawing or equation. | Kindergarten |
| Rhode Island | K.OA.A.5 | Fluently add and subtract within 5. | Kindergarten |
| Rhode Island | 1.G.A.1 | Distinguish between defining attributes (e.g., triangles are closed and three-sided) versus non-defining attributes (e.g., color, orientation, overall size); build and draw shapes to possess defining attributes. | Grade 1 |
| Rhode Island | 1.G.A.2 | Compose two-dimensional shapes (rectangles, squares, trapezoids, triangles, half-circles, and quarter-circles) or three-dimensional shapes (cubes, right rectangular prisms, right circular cones, and right circular cylinders) to create a composite shape, and compose new shapes from the composite shape. | Grade 1 |
| Rhode Island | 1.G.A.3 | Partition circles and rectangles into two and four equal shares, describe the shares using the words halves, fourths, and quarters, and use the phrases half of, fourth of, and quarter of. Describe the whole as two of, or four of the shares. Understand for these examples that decomposing into more equal shares creates smaller shares. | Grade 1 |
| Rhode Island | 1.MD.A.1 | Order three objects by length; compare the lengths of two objects indirectly by using a third object. | Grade 1 |
| Rhode Island | 1.MD.A.2 | Express the length of an object as a whole number of length units, by laying multiple copies of a shorter object (the length unit) end to end; understand that the length measurement of an object is the number of same-size length units that span it with no gaps or overlaps. | Grade 1 |
| Rhode Island | 1.MD.B.3 | Tell and write time in hours and half-hours using analog and digital clocks. | Grade 1 |
| Rhode Island | 1.MD.C.4 | Organize, represent, and interpret data with up to three categories; ask and answer questions about the total number of data points, how many in each category, and how many more or less are in one category than in another. | Grade 1 |
| Rhode Island | 1.NBT.A.1 | Count to 120, starting at any number less than 120. In this range, read and write numerals and represent a number of objects with a written numeral. | Grade 1 |
| Rhode Island | 1.NBT.B.2 | Understand that the two digits of a two-digit number represent amounts of tens and ones. | Grade 1 |
| Rhode Island | 1.NBT.B.3 | Compare two two-digit numbers based on meanings of the tens and ones digits, recording the results of comparisons with the symbols >, =, and <. | Grade 1 |
| Rhode Island | 1.NBT.C.4 | Add within 100, including adding a two-digit number and a one-digit number, and adding a two-digit number and a multiple of 10, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Understand that in adding two-digit numbers, one adds tens and tens, ones and ones; and sometimes it is necessary to compose a ten. | Grade 1 |
| Rhode Island | 1.NBT.C.5 | Given a two-digit number, mentally find 10 more or 10 less than the number, without having to count; explain the reasoning used. | Grade 1 |
| Rhode Island | 1.NBT.C.6 | Subtract multiples of 10 in the range 10-90 from multiples of 10 in the range 10-90 (positive or zero differences), using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. | Grade 1 |
| Rhode Island | 1.OA.A.1 | Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem. | Grade 1 |
| Rhode Island | 1.OA.B.3 | Apply properties of operations as strategies to add and subtract. | Grade 1 |
| Rhode Island | 1.OA.B.4 | Understand subtraction as an unknown-addend problem. | Grade 1 |
| Rhode Island | 1.OA.C.5 | Relate counting to addition and subtraction (e.g., by counting on 2 to add 2). | Grade 1 |
| Rhode Island | 1.OA.C.6 | Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to a ten (e.g., 13 - 4 = 13 - 3 - 1 = 10 - 1 = 9); using the relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 - 8 = 4); and creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13). | Grade 1 |
| Rhode Island | 1.OA.D.7 | Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false. | Grade 1 |
| Rhode Island | 1.OA.D.8 | Determine the unknown whole number in an addition or subtraction equation relating three whole numbers. | Grade 1 |
| Rhode Island | 2.G.A.1 | Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces. Identify triangles, quadrilaterals, pentagons, hexagons, and cubes. | Grade 2 |
| Rhode Island | 2.G.A.2 | Partition a rectangle into rows and columns of same-size squares and count to find the total number of them. | Grade 2 |
| Rhode Island | 2.G.A.3 | Partition circles and rectangles into two, three, or four equal shares, describe the shares using the words halves, thirds, half of, a third of, etc., and describe the whole as two halves, three thirds, four fourths. Recognize that equal shares of identical wholes need not have the same shape. | Grade 2 |
| Rhode Island | 2.MD.A.1 | Measure the length of an object by selecting and using appropriate tools such as rulers, yardsticks, meter sticks, and measuring tapes. | Grade 2 |
| Rhode Island | 2.MD.A.2 | Measure the length of an object twice, using length units of different lengths for the two measurements; describe how the two measurements relate to the size of the unit chosen. | Grade 2 |
| Rhode Island | 2.MD.A.4 | Measure to determine how much longer one object is than another, expressing the length difference in terms of a standard length unit. | Grade 2 |
| Rhode Island | 2.MD.B.5 | Use addition and subtraction within 100 to solve word problems involving lengths that are given in the same units, e.g., by using drawings (such as drawings of rulers) and equations with a symbol for the unknown number to represent the problem. | Grade 2 |
| Rhode Island | 2.MD.C.7 | Tell and write time from analog and digital clocks to the nearest five minutes, using a.m. and p.m. | Grade 2 |
| Rhode Island | 2.MD.C.8 | Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies, using $ and ¢ symbols appropriately. | Grade 2 |
| Rhode Island | 2.MD.D.9 | Generate measurement data by measuring lengths of several objects to the nearest whole unit, or by making repeated measurements of the same object. Show the measurements by making a line plot, where the horizontal scale is marked off in whole-number units. | Grade 2 |
| Rhode Island | 2.MD.D.10 | Draw a picture graph and a bar graph (with single-unit scale) to represent a data set with up to four categories. Solve simple put-together, take-apart, and compare problems using information presented in a bar graph. | Grade 2 |
| Rhode Island | 2.NBT.A.1 | Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones. | Grade 2 |
| Rhode Island | 2.NBT.A.2 | Count within 1000; skip-count by 5s, 10s, and 100s. | Grade 2 |
| Rhode Island | 2.NBT.A.3 | Read and write numbers to 1000 using base-ten numerals, number names, and expanded form. | Grade 2 |
| Rhode Island | 2.NBT.A.4 | Compare two three-digit numbers based on meanings of the hundreds, tens, and ones digits, using >, =, and < symbols to record the results of comparisons. | Grade 2 |
| Rhode Island | 2.NBT.B.5 | Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction. | Grade 2 |
| Rhode Island | 2.NBT.B.6 | Add up to four two-digit numbers using strategies based on place value and properties of operations. | Grade 2 |
| Rhode Island | 2.NBT.B.7 | Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method. Understand that in adding or subtracting three-digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds. | Grade 2 |
| Rhode Island | 2.NBT.B.8 | Mentally add 10 or 100 to a given number 100–900, and mentally subtract 10 or 100 from a given number 100–900. | Grade 2 |
| Rhode Island | 2.OA.A.1 | Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem. | Grade 2 |
| Rhode Island | 2.OA.B.2 | Fluently add and subtract within 20 using mental strategies. By end of Grade 2, know from memory all sums of two one-digit numbers. | Grade 2 |
| Rhode Island | 2.OA.C.3 | Determine whether a group of objects (up to 20) has an odd or even number of members, e.g., by pairing objects or counting them by 2s; write an equation to express an even number as a sum of two equal addends. | Grade 2 |
| Rhode Island | 2.OA.C.4 | Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends. | Grade 2 |
| Rhode Island | 3.G.A.1 | Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories. | Grade 3 |
| Rhode Island | 3.G.A.2 | Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole. | Grade 3 |
| Rhode Island | 3.MD.A.1 | Tell and write time to the nearest minute and measure time intervals in minutes. Solve word problems involving addition and subtraction of time intervals in minutes, e.g., by representing the problem on a number line diagram. | Grade 3 |
| Rhode Island | 3.MD.A.2 | Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l). Add, subtract, multiply, or divide to solve one-step word problems involving masses or volumes that are given in the same units, e.g., by using drawings (such as a beaker with a measurement scale) to represent the problem. | Grade 3 |
| Rhode Island | 3.MD.B.3 | Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and two-step “how many more” and “how many less” problems using information presented in scaled bar graphs. | Grade 3 |
| Rhode Island | 3.MD.B.4 | Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Show the data by making a line plot, where the horizontal scale is marked off in appropriate units-whole numbers, halves, or quarters. | Grade 3 |
| Rhode Island | 3.MD.C.5 | Recognize area as an attribute of plane figures and understand concepts of area measurement. | Grade 3 |
| Rhode Island | 3.MD.C.6 | Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units). | Grade 3 |
| Rhode Island | 3.MD.C.7 | Relate area to the operations of multiplication and addition. | Grade 3 |
| Rhode Island | 3.MD.D.8 | Solve real world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters. | Grade 3 |
| Rhode Island | 3.NBT.A.1 | Use place value understanding to round whole numbers to the nearest 10 or 100. | Grade 3 |
| Rhode Island | 3.NBT.A.2 | Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction. | Grade 3 |
| Rhode Island | 3.NBT.A.3 | Multiply one-digit whole numbers by multiples of 10 in the range 10–90 (e.g., 9 × 80, 5 × 60) using strategies based on place value and properties of operations. | Grade 3 |
| Rhode Island | 3.NF.A.1 | Understand a fraction 1/𝘣 as the quantity formed by 1 part when a whole is partitioned into 𝘣 equal parts; understand a fraction 𝘢/𝑏 as the quantity formed by 𝘢 parts of size 1/𝘣. | Grade 3 |
| Rhode Island | 3.NF.A.2 | Understand a fraction as a number on the number line; represent fractions on a number line diagram. | Grade 3 |
| Rhode Island | 3.NF.A.3 | Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size. | Grade 3 |
| Rhode Island | 3.OA.A.1 | Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each. | Grade 3 |
| Rhode Island | 3.OA.A.2 | Interpret whole-number quotients of whole numbers, e.g., interpret 56 ÷ 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each. | Grade 3 |
| Rhode Island | 3.OA.A.3 | Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem. | Grade 3 |
| Rhode Island | 3.OA.A.4 | Determine the unknown whole number in a multiplication or division equation relating three whole numbers. | Grade 3 |
| Rhode Island | 3.OA.B.5 | Apply properties of operations as strategies to multiply and divide. | Grade 3 |
| Rhode Island | 3.OA.B.6 | Understand division as an unknown-factor problem. | Grade 3 |
| Rhode Island | 3.OA.C.7 | Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 × 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers. | Grade 3 |
| Rhode Island | 3.OA.D.8 | Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. | Grade 3 |
| Rhode Island | 3.OA.D.9 | Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations. | Grade 3 |
| Rhode Island | 4.G.A.1 | Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures. | Grade 4 |
| Rhode Island | 4.G.A.2 | Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles. | Grade 4 |
| Rhode Island | 4.G.A.3 | Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify line-symmetric figures and draw lines of symmetry. | Grade 4 |
| Rhode Island | 4.MD.A.1 | Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table. | Grade 4 |
| Rhode Island | 4.MD.A.2 | Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. | Grade 4 |
| Rhode Island | 4.MD.A.3 | Apply the area and perimeter formulas for rectangles in real world and mathematical problems. | Grade 4 |
| Rhode Island | 4.MD.B.4 | Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots. | Grade 4 |
| Rhode Island | 4.MD.C.5 | Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement. | Grade 4 |
| Rhode Island | 4.MD.C.6 | Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure. | Grade 4 |
| Rhode Island | 4.MD.C.7 | Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems, e.g., by using an equation with a symbol for the unknown angle measure. | Grade 4 |
| Rhode Island | 4.NBT.A.1 | Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. | Grade 4 |
| Rhode Island | 4.NBT.A.2 | Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. | Grade 4 |
| Rhode Island | 4.NBT.A.3 | Use place value understanding to round multi-digit whole numbers to any place. | Grade 4 |
| Rhode Island | 4.NBT.B.4 | Fluently add and subtract multi-digit whole numbers using the standard algorithm. | Grade 4 |
| Rhode Island | 4.NBT.B.5 | Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. | Grade 4 |
| Rhode Island | 4.NBT.B.6 | Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. | Grade 4 |
| Rhode Island | 4.NF.A.1 | Explain why a fraction 𝘢/𝘣 is equivalent to a fraction (𝘯 × 𝘢)/(𝘯 × 𝘣) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. | Grade 4 |
| Rhode Island | 4.NF.A.2 | Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model. | Grade 4 |
| Rhode Island | 4.NF.B.3 | Understand a fraction 𝘢/𝘣 with 𝘢 > 1 as a sum of fractions 1/𝘣. | Grade 4 |
| Rhode Island | 4.NF.B.4 | Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. | Grade 4 |
| Rhode Island | 4.NF.C.5 | Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100. | Grade 4 |
| Rhode Island | 4.NF.C.6 | Use decimal notation for fractions with denominators 10 or 100. | Grade 4 |
| Rhode Island | 4.NF.C.7 | Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual model. | Grade 4 |
| Rhode Island | 4.OA.A.1 | Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 × 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations. | Grade 4 |
| Rhode Island | 4.OA.A.2 | Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison. | Grade 4 |
| Rhode Island | 4.OA.A.3 | Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. | Grade 4 |
| Rhode Island | 4.OA.B.4 | Find all factor pairs for a whole number in the range 1-100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1-100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1-100 is prime or composite. | Grade 4 |
| Rhode Island | 4.OA.C.5 | Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. | Grade 4 |
| Rhode Island | 5.G.A.1 | Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., 𝘹-axis and 𝘹-coordinate, 𝘺-axis and 𝘺-coordinate). | Grade 5 |
| Rhode Island | 5.G.A.2 | Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. | Grade 5 |
| Rhode Island | 5.G.B.3 | Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. | Grade 5 |
| Rhode Island | 5.G.B.4 | Classify two-dimensional figures in a hierarchy based on properties. | Grade 5 |
| Rhode Island | 5.MD.A.1 | Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. | Grade 5 |
| Rhode Island | 5.MD.B.2 | Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. | Grade 5 |
| Rhode Island | 5.MD.C.3 | Recognize volume as an attribute of solid figures and understand concepts of volume measurement. | Grade 5 |
| Rhode Island | 5.MD.C.4 | Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. | Grade 5 |
| Rhode Island | 5.MD.C.5 | Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume. | Grade 5 |
| Rhode Island | 5.NBT.A.1 | Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. | Grade 5 |
| Rhode Island | 5.NBT.A.2 | Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. | Grade 5 |
| Rhode Island | 5.NBT.A.3 | Read, write, and compare decimals to thousandths. | Grade 5 |
| Rhode Island | 5.NBT.A.4 | Use place value understanding to round decimals to any place. | Grade 5 |
| Rhode Island | 5.NBT.B.5 | Fluently multiply multi-digit whole numbers using the standard algorithm. | Grade 5 |
| Rhode Island | 5.NBT.B.6 | Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. | Grade 5 |
| Rhode Island | 5.NBT.B.7 | Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. | Grade 5 |
| Rhode Island | 5.NF.A.1 | Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. | Grade 5 |
| Rhode Island | 5.NF.A.2 | Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. | Grade 5 |
| Rhode Island | 5.NF.B.3 | Interpret a fraction as division of the numerator by the denominator (𝘢/𝘣 = 𝘢 ÷ 𝘣). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. | Grade 5 |
| Rhode Island | 5.NF.B.4 | Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. | Grade 5 |
| Rhode Island | 5.NF.B.5 | Interpret multiplication as scaling (resizing). | Grade 5 |
| Rhode Island | 5.NF.B.6 | Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. | Grade 5 |
| Rhode Island | 5.NF.B.7 | Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. | Grade 5 |
| Rhode Island | 5.OA.A.1 | Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. | Grade 5 |
| Rhode Island | 5.OA.A.2 | Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. | Grade 5 |
| Rhode Island | 5.OA.B.3 | Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. | Grade 5 |
| Rhode Island | 6.EE.A.1 | Write and evaluate numerical expressions involving whole-number exponents. | Grade 6 |
| Rhode Island | 6.EE.A.2 | Write, read, and evaluate expressions in which letters stand for numbers. | Grade 6 |
| Rhode Island | 6.EE.A.3 | Apply the properties of operations to generate equivalent expressions. | Grade 6 |
| Rhode Island | 6.EE.A.4 | Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). | Grade 6 |
| Rhode Island | 6.EE.B.5 | Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true. | Grade 6 |
| Rhode Island | 6.EE.B.6 | Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set. | Grade 6 |
| Rhode Island | 6.EE.B.7 | Solve real-world and mathematical problems by writing and solving equations of the form 𝘹 + 𝘱 = 𝘲 and 𝘱𝘹 = 𝘲 for cases in which 𝘱, 𝘲 and 𝘹 are all nonnegative rational numbers. | Grade 6 |
| Rhode Island | 6.EE.B.8 | Write an inequality of the form 𝘹 > 𝘤 or 𝘹 𝘤 or 𝘹 < 𝘤 have infinitely many solutions; represent solutions of such inequalities on number line diagrams. | Grade 6 |
| Rhode Island | 6.EE.C.9 | Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. | Grade 6 |
| Rhode Island | 6.G.A.1 | Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems. | Grade 6 |
| Rhode Island | 6.G.A.2 | Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas 𝘝 = 𝘭 𝘸 𝘩 and 𝘝 = 𝘣 𝘩 to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems. | Grade 6 |
| Rhode Island | 6.G.A.3 | Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems. | Grade 6 |
| Rhode Island | 6.G.A.4 | Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems. | Grade 6 |
| Rhode Island | 6.RP.A.1 | Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. | Grade 6 |
| Rhode Island | 6.RP.A.2 | Understand the concept of a unit rate 𝘢/𝘣 associated with a ratio 𝘢:𝘣 with 𝘣 ≠ 0, and use rate language in the context of a ratio relationship. | Grade 6 |
| Rhode Island | 6.RP.A.3 | Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. | Grade 6 |
| Rhode Island | 6.SP.B.5 | Summarize numerical data sets in relation to their context, such as by: | Grade 6 |
| Rhode Island | 6.NS.A.1 | Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. | Grade 6 |
| Rhode Island | 6.NS.B.2 | Fluently divide multi-digit numbers using the standard algorithm. | Grade 6 |
| Rhode Island | 6.NS.B.3 | Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation. | Grade 6 |
| Rhode Island | 6.NS.C.5 | Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation. | Grade 6 |
| Rhode Island | 6.NS.C.6 | Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates. | Grade 6 |
| Rhode Island | 6.NS.C.7 | Understand ordering and absolute value of rational numbers. | Grade 6 |
| Rhode Island | 6.NS.C.8 | Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. | Grade 6 |
| Rhode Island | 7.EE.A.1 | Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients. | Grade 7 |
| Rhode Island | 7.EE.A.2 | Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. | Grade 7 |
| Rhode Island | 7.EE.B.3 | Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. | Grade 7 |
| Rhode Island | 7.EE.B.4 | Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. | Grade 7 |
| Rhode Island | 7.G.A.1 | Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale. | Grade 7 |
| Rhode Island | 7.G.A.2 | Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle. | Grade 7 |
| Rhode Island | 7.G.A.3 | Describe the two-dimensional figures that result from slicing three-dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids. | Grade 7 |
| Rhode Island | 7.G.B.4 | Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle. | Grade 7 |
| Rhode Island | 7.G.B.5 | Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure. | Grade 7 |
| Rhode Island | 7.G.B.6 | Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. | Grade 7 |
| Rhode Island | 7.RP.A.1 | Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. | Grade 7 |
| Rhode Island | 7.RP.A.2 | Recognize and represent proportional relationships between quantities. | Grade 7 |
| Rhode Island | 7.RP.A.3 | Use proportional relationships to solve multistep ratio and percent problems. | Grade 7 |
| Rhode Island | 7.NS.A.1 | Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram. | Grade 7 |
| Rhode Island | 7.NS.A.2 | Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers. | Grade 7 |
| Rhode Island | 7.NS.A.3 | Solve real-world and mathematical problems involving the four operations with rational numbers. | Grade 7 |
| Rhode Island | 8.EE.A.1 | Know and apply the properties of integer exponents to generate equivalent numerical expressions. | Grade 8 |
| Rhode Island | 8.EE.A.2 | Use square root and cube root symbols to represent solutions to equations of the form 𝘹² = 𝘱 and 𝘹³ = 𝘱, where 𝘱 is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that √2 is irrational. | Grade 8 |
| Rhode Island | 8.EE.A.3 | Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other. | Grade 8 |
| Rhode Island | 8.EE.A.4 | Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology. | Grade 8 |
| Rhode Island | 8.EE.B.5 | Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. | Grade 8 |
| Rhode Island | 8.EE.B.6 | Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation 𝘺 = 𝘮𝘹 for a line through the origin and the equation 𝘺 = 𝘮𝘹 + 𝘣 for a line intercepting the vertical axis at 𝘣. | Grade 8 |
| Rhode Island | 8.EE.C.7 | Solve linear equations in one variable. | Grade 8 |
| Rhode Island | 8.EE.C.8 | Analyze and solve pairs of simultaneous linear equations. | Grade 8 |
| Rhode Island | 8.F.A.1 | Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output. | Grade 8 |
| Rhode Island | 8.F.A.2 | Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). | Grade 8 |
| Rhode Island | 8.F.A.3 | Interpret the equation 𝘺 = 𝘮𝘹 + 𝘣 as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. | Grade 8 |
| Rhode Island | 8.F.B.4 | Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (𝘹, 𝘺) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values. | Grade 8 |
| Rhode Island | 8.F.B.5 | Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally. | Grade 8 |
| Rhode Island | 8.G.A.1 | Verify experimentally the properties of rotations, reflections, and translations. | Grade 8 |
| Rhode Island | 8.G.A.2 | Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them. | Grade 8 |
| Rhode Island | 8.G.A.3 | Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates. | Grade 8 |
| Rhode Island | 8.G.A.4 | Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two-dimensional figures, describe a sequence that exhibits the similarity between them. | Grade 8 |
| Rhode Island | 8.G.A.5 | Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. | Grade 8 |
| Rhode Island | 8.G.B.7 | Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions. | Grade 8 |
| Rhode Island | 8.G.B.8 | Apply the Pythagorean Theorem to find the distance between two points in a coordinate system. | Grade 8 |
| Rhode Island | 8.G.C.9 | Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems. | Grade 8 |
| Rhode Island | 8.SP.A.1 | Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association. | Grade 8 |
| Rhode Island | 8.SP.A.2 | Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line. | Grade 8 |
| Rhode Island | 8.NS.A.2 | Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g., π²). | Grade 8 |
| Rhode Island | A-APR.B.3 | Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial. | High School |
| Rhode Island | A-CED.A.2 | Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. | High School |
| Rhode Island | A-CED.A.3 | Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context. | High School |
| Rhode Island | A-REI.B.3 | Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. | High School |
| Rhode Island | A-SSE.A.2 | Use the structure of an expression to identify ways to rewrite it. | High School |
| Rhode Island | A-SSE.B.3 | Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression. | High School |
| Rhode Island | F-BF.A.1 | Write a function that describes a relationship between two quantities. | High School |
| Rhode Island | F-IF.A.2 | Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. | High School |
| Rhode Island | F-IF.B.4 | For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. | High School |
| Rhode Island | F-IF.C.7 | Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. | High School |
| Rhode Island | S-ID.B.6 | Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. | High School |
| South Carolina | K.ATO.1 | Model situations that involve addition and subtraction within 10 using objects, fingers, mental images, drawings, acting out situations, verbal explanations, expressions, and equations. | Kindergarten |
| South Carolina | K.ATO.2 | Solve real-world/story problems using objects and drawings to find sums up to 10 and differences within 10. | Kindergarten |
| South Carolina | K.ATO.3 | Compose and decompose numbers up to 10 using objects, drawings, and equations. | Kindergarten |
| South Carolina | K.ATO.4 | Create a sum of 10 using objects and drawings when given one of two addends 1 - 9. | Kindergarten |
| South Carolina | K.ATO.5 | Add and subtract fluently within 5. | Kindergarten |
| South Carolina | K.ATO.6 | Describe simple repeating patterns using AB, AAB, ABB, and ABC type patterns. | Kindergarten |
| South Carolina | K.G.1 | Describe positions of objects by appropriately using terms, including below, above, beside, between, inside, outside, in front of, or behind. | Kindergarten |
| South Carolina | K.G.2 | Identify and describe a given shape and shapes of objects in everyday situations to include two-dimensional shapes (i.e., triangle, square, rectangle, hexagon, and circle) and three-dimensional shapes (i.e., cone, cube, cylinder, and sphere). | Kindergarten |
| South Carolina | K.G.3 | Classify shapes as two-dimensional/flat or three-dimensional/solid and explain the reasoning used. | Kindergarten |
| South Carolina | K.G.4 | Analyze and compare two- and three-dimensional shapes of different sizes and orientations using informal language. | Kindergarten |
| South Carolina | K.G.5 | Draw two-dimensional shapes (i.e., square, rectangle, triangle, hexagon, and circle) and create models of three-dimensional shapes (i.e., cone, cube, cylinder, and sphere). | Kindergarten |
| South Carolina | K.MDA.1 | Identify measureable attributes (length, weight) of an object. | Kindergarten |
| South Carolina | K.MDA.2 | Compare objects using words such as shorter/longer, shorter/taller, and lighter/heavier. | Kindergarten |
| South Carolina | K.MDA.3 | Sort and classify data into 2 or 3 categories with data not to exceed 20 items in each category. | Kindergarten |
| South Carolina | K.MDA.4 | Represent data using object and picture graphs and draw conclusions from the graphs. | Kindergarten |
| South Carolina | K.NS.1 | Count forward by ones and tens to 100. | Kindergarten |
| South Carolina | K.NS.2 | Count forward by ones beginning from any number less than 100. | Kindergarten |
| South Carolina | K.NS.3 | Read numbers from 0 - 20 and represent a number of objects 0 - 20 with a written numeral. | Kindergarten |
| South Carolina | K.NS.4 | Understand the relationship between number and quantity. Connect counting to cardinality. | Kindergarten |
| South Carolina | K.NS.5 | Count a given number of objects from 1 - 20 and connect this sequence in a one-to-one manner. | Kindergarten |
| South Carolina | K.NS.6 | Recognize a quantity of up to ten objects in an organized arrangement (subitizing). | Kindergarten |
| South Carolina | K.NS.7 | Determine whether the number of up to ten objects in one group is more than, less than, or equal to the number of up to ten objects in another group using matching and counting strategies. | Kindergarten |
| South Carolina | K.NS.8 | Compare two written numerals up to 10 using more than, less than or equal to. | Kindergarten |
| South Carolina | K.NS.9 | Identify first through fifth and last positions in a line of objects. | Kindergarten |
| South Carolina | K.NSBT.1 | Compose and decompose numbers from 11 - 19 separating ten ones from the remaining ones using objects and drawings. | Kindergarten |
| South Carolina | 1.ATO.1 | Solve real-world/story problems using addition (as a joining action and as a part-part-whole action) and subtraction (as a separation action, finding parts of the whole, and as a comparison) through 20 with unknowns in all positions. | Grade 1 |
| South Carolina | 1.ATO.3 | Apply Commutative and Associative Properties of Addition to find the sum (through 20) of two or three addends. | Grade 1 |
| South Carolina | 1.ATO.4 | Understand subtraction as an unknown addend problem. | Grade 1 |
| South Carolina | 1.ATO.5 | Recognize how counting relates to addition and subtraction. | Grade 1 |
| South Carolina | 1.ATO.6 | Demonstrate addition and subtraction through 20 and fluency with addition and related subtraction facts through 10. | Grade 1 |
| South Carolina | 1.ATO.7 | Understand the meaning of the equal sign as a relationship between two quantities (sameness) and determine if equations involving addition and subtraction are true. | Grade 1 |
| South Carolina | 1.ATO.8 | Determine the missing number in addition and subtraction equations within 20. | Grade 1 |
| South Carolina | 1.ATO.9 | Create, extend and explain using pictures and words for repeating patterns (e.g., AB, AAB, ABB, and AC type patterns) and growing patterns (between 2 and 4 terms/figures). | Grade 1 |
| South Carolina | 1.G.1 | Distinguish between a two-dimensional shape's defining (e.g., number of sides) and non-defining attributes (e.g., color). | Grade 1 |
| South Carolina | 1.G.2 | Combine two-dimensional shapes (i.e., square, rectangle, triangle, hexagon, rhombus, and trapezoid) or three-dimensional shapes (i.e., cube, rectangular prism, cone, and cylinder) in more than one way to form a composite shape. | Grade 1 |
| South Carolina | 1.G.3 | Partition two-dimensional shapes (i.e., square, rectangle, circle) into two or four equal parts. | Grade 1 |
| South Carolina | 1.G.4 | Identify and name two-dimensional shapes (i.e., square, rectangle, triangle, hexagon, rhombus, trapezoid, and circle). | Grade 1 |
| South Carolina | 1.MDA.1 | Order three objects by length using indirect comparison. | Grade 1 |
| South Carolina | 1.MDA.2 | Use nonstandard physical models to show the length of an object as the number of same size units of length with no gaps or overlaps. | Grade 1 |
| South Carolina | 1.MDA.3 | Use analog and digital clocks to tell and record time to the hour and half hour. | Grade 1 |
| South Carolina | 1.MDA.4 | Collect, organize, and represent data with up to 3 categories using object graphs, picture graphs, t-charts and tallies. | Grade 1 |
| South Carolina | 1.MDA.5 | Draw conclusions from given object graphs, picture graphs, t-charts, tallies, and bar graphs. | Grade 1 |
| South Carolina | 1.MDA.6 | Identify a penny, nickel, dime and quarter and write the coin values using a ¢ symbol. | Grade 1 |
| South Carolina | 1.NSBT.1 | Extend the number sequence to count forward by ones to 120; count by fives and tens to 100; read, write and represent numbers to 100 using concrete models, standard form, and equations in expanded form; read and write in word form numbers zero through nineteen, and multiples of ten through ninety. | Grade 1 |
| South Carolina | 1.NSBT.2 | Understand place value through 99. | Grade 1 |
| South Carolina | 1.NSBT.3 | Compare two two-digit numbers based on the meanings of the tens and ones digits, using the words greater than, equal to, or less than. | Grade 1 |
| South Carolina | 1.NSBT.4 | Add through 99 using concrete models, drawings, and strategies based on place value. | Grade 1 |
| South Carolina | 1.NSBT.5 | Determine the number that is 10 more or 10 less than a given number through 99 and explain the reasoning verbally and with multiple representations, including concrete models. | Grade 1 |
| South Carolina | 1.NSBT.6 | Subtract a multiple of 10 from a larger multiple of 10, both in the range 10 to 90, using concrete models, drawings, and strategies based on place value. | Grade 1 |
| South Carolina | 2.ATO.1 | Solve one- and two-step real-world/story problems using addition (as a joining action and as a part-part-whole action) and subtraction (as a separation action, finding parts of the whole, and as a comparison) through 99 with unknowns in all positions. | Grade 2 |
| South Carolina | 2.ATO.2 | Demonstrate fluency with addition and related subtraction facts through 20. | Grade 2 |
| South Carolina | 2.ATO.3 | Determine whether a number through 20 is odd or even using pairings of objects, counting by twos, or finding two equal addends to represent the number (e.g., 3 + 3 = 6). | Grade 2 |
| South Carolina | 2.ATO.4 | Use repeated addition to find the total number of objects arranged in a rectangular array with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends. | Grade 2 |
| South Carolina | 2.G.1 | Identify triangles, quadrilaterals, hexagons, and cubes. Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces. | Grade 2 |
| South Carolina | 2.G.2 | Partition a rectangle into rows and columns of same-size squares to form an array and count to find the total number of parts. | Grade 2 |
| South Carolina | 2.G.3 | Partition squares, rectangles and circles into two or four equal parts, and describe the parts using the words halves, fourths, a half of, and a fourth of. Understand that when partitioning a square, rectangle or circle into two or four equal parts, the parts become smaller as the number of parts increases. | Grade 2 |
| South Carolina | 2.MDA.1 | Select and use appropriate tools (e.g., rulers, yardsticks, meter sticks, measuring tapes) to measure the length of an object. | Grade 2 |
| South Carolina | 2.MDA.2 | Measure the same object or distance using a standard unit of one length and then a standard unit of a different length and explain verbally and in writing how and why the measurements differ. | Grade 2 |
| South Carolina | 2.MDA.4 | Measure to determine how much longer one object is than another, using standard length units. | Grade 2 |
| South Carolina | 2.MDA.6 | Use analog and digital clocks to tell and record time to the nearest five-minute interval using a.m. and p.m. | Grade 2 |
| South Carolina | 2.MDA.7 | Solve real-world/story problems involving dollar bills using the $ symbol or involving quarters, dimes, nickels, and pennies using the ¢ symbol. | Grade 2 |
| South Carolina | 2.MDA.8 | Generate data by measuring objects in whole unit lengths and organize the data in a line plot using a horizontal scale marked in whole number units. | Grade 2 |
| South Carolina | 2.MDA.9 | Collect, organize, and represent data with up to four categories using picture graphs and bar graphs with a single-unit scale. | Grade 2 |
| South Carolina | 2.MDA.10 | Draw conclusions from t-charts, object graphs, picture graphs, and bar graphs. | Grade 2 |
| South Carolina | 2.NSBT.1 | Understand place value through 999. | Grade 2 |
| South Carolina | 2.NSBT.2 | Count by tens and hundreds to 1,000 starting with any number. | Grade 2 |
| South Carolina | 2.NSBT.3 | Read, write and represent numbers through 999 using concrete models, standard form, and equations in expanded form. | Grade 2 |
| South Carolina | 2.NSBT.4 | Compare two numbers with up to three digits using words and symbols (i.e., >, =, or <). | Grade 2 |
| South Carolina | 2.NSBT.5 | Add and subtract fluently through 99 using knowledge of place value and properties of operations. | Grade 2 |
| South Carolina | 2.NSBT.6 | Add up to four two-digit numbers using strategies based on knowledge of place value and properties of operations. | Grade 2 |
| South Carolina | 2.NSBT.7 | Add and subtract through 999 using concrete models, drawings, and symbols which convey strategies connected to place value understanding. | Grade 2 |
| South Carolina | 2.NSBT.8 | Determine the number that is 10 or 100 more or less than a given number through 1,000 and explain the reasoning verbally and in writing. | Grade 2 |
| South Carolina | 3.ATO.1 | Use concrete objects, drawings and symbols to represent multiplication facts of two single-digit whole numbers and explain the relationship between the factors (i.e., 0 - 10) and the product. | Grade 3 |
| South Carolina | 3.ATO.2 | Use concrete objects, drawings and symbols to represent division without remainders and explain the relationship among the whole number quotient (i.e., 0 - 10), divisor (i.e., 0 - 10), and dividend. | Grade 3 |
| South Carolina | 3.ATO.3 | Solve real-world problems involving equal groups, area/array, and number line models using basic multiplication and related division facts. Represent the problem situation using an equation with a symbol for the unknown. | Grade 3 |
| South Carolina | 3.ATO.4 | Determine the unknown whole number in a multiplication or division equation relating three whole numbers when the unknown is a missing factor, product, dividend, divisor, or quotient. | Grade 3 |
| South Carolina | 3.ATO.5 | Apply properties of operations (i.e., Commutative Property of Multiplication, Associative Property of Multiplication, Distributive Property) as strategies to multiply and divide and explain the reasoning. | Grade 3 |
| South Carolina | 3.ATO.6 | Understand division as a missing factor problem. | Grade 3 |
| South Carolina | 3.ATO.7 | Demonstrate fluency with basic multiplication and related division facts of products and dividends through 100. | Grade 3 |
| South Carolina | 3.ATO.8 | Solve two-step real-world problems using addition, subtraction, multiplication and division of whole numbers and having whole number answers. Represent these problems using equations with a letter for the unknown quantity. | Grade 3 |
| South Carolina | 3.ATO.9 | Identify a rule for an arithmetic pattern (e.g., patterns in the addition table or multiplication table). | Grade 3 |
| South Carolina | 3.G.1 | Understand that shapes in different categories (e.g., rhombus, rectangle, square, and other 4-sided shapes) may share attributes (e.g., 4-sided figures) and the shared attributes can define a larger category (e.g., quadrilateral). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories. | Grade 3 |
| South Carolina | 3.G.2 | Partition two-dimensional shapes into 2, 3, 4, 6, or 8 parts with equal areas and express the area of each part using the same unit fraction. Recognize that equal parts of identical wholes need not have the same shape. | Grade 3 |
| South Carolina | 3.G.3 | Use a right angle as a benchmark to identify and sketch acute and obtuse angles. | Grade 3 |
| South Carolina | 3.G.4 | Identify a three-dimensional shape (i.e., right rectangular prism, right triangular prism, pyramid) based on a given two-dimensional net and explain the relationship between the shape and the net. | Grade 3 |
| South Carolina | 3.MDA.1 | Use analog and digital clocks to determine and record time to the nearest minute, using a.m. and p.m.; measure time intervals in minutes; and solve problems involving addition and subtraction of time intervals within 60 minutes. | Grade 3 |
| South Carolina | 3.MDA.2 | Estimate and measure liquid volumes (capacity) in customary units (i.e., c., pt., qt., gal.) and metric units (mL, L) to the nearest whole unit. | Grade 3 |
| South Carolina | 3.MDA.3 | Collect, organize, classify, and interpret data with multiple categories and draw a scaled picture graph and a scaled bar graph to represent the data. | Grade 3 |
| South Carolina | 3.MDA.4 | Generate data by measuring length to the nearest inch, half-inch and quarter-inch and organize the data in a line plot using a horizontal scale marked off in appropriate units. | Grade 3 |
| South Carolina | 3.MDA.5 | Understand the concept of area measurement. | Grade 3 |
| South Carolina | 3.MDA.6 | Solve real-world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters. | Grade 3 |
| South Carolina | 3.NSBT.1 | Use place value understanding to round whole numbers to the nearest 10 or 100. | Grade 3 |
| South Carolina | 3.NSBT.2 | Add and subtract whole numbers fluently to 1,000 using knowledge of place value and properties of operations. | Grade 3 |
| South Carolina | 3.NSBT.3 | Multiply one-digit whole numbers by multiples of 10 in the range 10 - 90, using knowledge of place value and properties of operations. | Grade 3 |
| South Carolina | 3.NSBT.4 | Read and write numbers through 999,999 in standard form and equations in expanded form. | Grade 3 |
| South Carolina | 3.NSBT.5 | Compare and order numbers through 999,999 and represent the comparison using the symbols >, =, or <. | Grade 3 |
| South Carolina | 3.NSF.1 | Develop an understanding of fractions (i.e. denominators 2, 3, 4, 6, 8, 10) as numbers. | Grade 3 |
| South Carolina | 3.NSF.2 | Explain fraction equivalence (i.e., denominators 2, 3, 4, 6, 8, 10). | Grade 3 |
| South Carolina | 3.NSF.3 | Develop an understanding of mixed numbers (i.e., denominators 2, 3, 4, 6, 8, 10) as iterations of unit fractions on a number line. | Grade 3 |
| South Carolina | 4.ATO.1 | Interpret a multiplication equation as a comparison (e.g. interpret 35 = 5x7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5.) Represent verbal statements of multiplicative comparisons as multiplication equations. | Grade 4 |
| South Carolina | 4.ATO.2 | Solve real-world problems using multiplication (product unknown) and division (group size unknown, number of groups unknown). | Grade 4 |
| South Carolina | 4.ATO.3 | Solve multi-step, real-world problems using the four operations. Represent the problem using an equation with a variable as the unknown quantity. | Grade 4 |
| South Carolina | 4.ATO.4 | Recognize that a whole number is a multiple of each of its factors. Find all factors for a whole number in the range 1 - 100 and determine whether the whole number is prime or composite. | Grade 4 |
| South Carolina | 4.ATO.5 | Generate a number or shape pattern that follows a given rule and determine a term that appears later in the sequence. | Grade 4 |
| South Carolina | 4.G.1 | Draw points, lines, line segments, rays, angles (i.e., right, acute, obtuse), and parallel and perpendicular lines. Identify these in two-dimensional figures. | Grade 4 |
| South Carolina | 4.G.2 | Classify quadrilaterals based on the presence or absence of parallel or perpendicular lines. | Grade 4 |
| South Carolina | 4.G.3 | Recognize right triangles as a category, and identify right triangles. | Grade 4 |
| South Carolina | 4.G.4 | Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify line-symmetric figures and draw lines of symmetry. | Grade 4 |
| South Carolina | 4.MDA.1 | Convert measurements within a single system of measurement, customary (i.e., in., ft., yd., oz., lb., sec., min., hr.) or metric (i.e., cm, m, km, g, kg, mL, L) from a larger to a smaller unit. | Grade 4 |
| South Carolina | 4.MDA.2 | Solve real-world problems involving distance/length, intervals of time within 12 hours, liquid volume, mass, and money using the four operations. | Grade 4 |
| South Carolina | 4.MDA.3 | Apply the area and perimeter formulas for rectangles. | Grade 4 |
| South Carolina | 4.MDA.4 | Create a line plot to display a data set (i.e., generated by measuring length to the nearest quarter-inch and eighth-inch) and interpret the line plot. | Grade 4 |
| South Carolina | 4.MDA.5 | Understand the relationship of an angle measurement to a circle. | Grade 4 |
| South Carolina | 4.MDA.6 | Measure and draw angles in whole number degrees using a protractor. | Grade 4 |
| South Carolina | 4.MDA.7 | Solve addition and subtraction problems to find unknown angles in real-world and mathematical problems. | Grade 4 |
| South Carolina | 4.MDA.8 | Determine the value of a collection of coins and bills greater than $1.00. | Grade 4 |
| South Carolina | 4.NSBT.1 | Understand that, in a multi-digit whole number, a digit represents ten times what the same digit represents in the place to its right. | Grade 4 |
| South Carolina | 4.NSBT.2 | Recognize math periods and number patterns within each period to read and write in standard form large numbers through 999,999,999. | Grade 4 |
| South Carolina | 4.NSBT.3 | Use rounding as one form of estimation and round whole numbers to any given place value. | Grade 4 |
| South Carolina | 4.NSBT.4 | Fluently add and subtract multi-digit whole numbers using strategies to include a standard algorithm. | Grade 4 |
| South Carolina | 4.NSBT.5 | Multiply up to a four-digit number by a one-digit number and multiply a two-digit number by a two-digit number using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using rectangular arrays, area models and/or equations. | Grade 4 |
| South Carolina | 4.NSBT.6 | Divide up to a four-digit dividend by a one-digit divisor using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. | Grade 4 |
| South Carolina | 4.NSF.1 | Explain why a fraction (i.e., denominators 2, 3, 4, 5, 6, 8, 10, 12, 25, 100), a/b, is equivalent to a fraction, n x a/n x b, by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. | Grade 4 |
| South Carolina | 4.NSF.2 | Compare two given fractions (i.e., denominators 2, 3, 4, 5, 6, 8, 10, 12, 25, 100) by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2 and represent the comparison using the symbols >, =, or <. | Grade 4 |
| South Carolina | 4.NSF.3 | Develop an understanding of addition and subtraction of fractions (i.e., denominators 2, 3, 4, 5, 6, 8, 10, 12, 25, 100 based on unit fractions. | Grade 4 |
| South Carolina | 4.NSF.4 | Apply and extend an understanding of multiplication by multiplying a whole number and a fraction (i.e., denominators 2, 3, 4, 5, 6, 8, 10, 12, 25, 100). | Grade 4 |
| South Carolina | 4.NSF.5 | Express a fraction with a denominator of 10 as an equivalent fraction with a denominator of 100 and use this technique to add two fractions with respective denominators of 10 and 100. | Grade 4 |
| South Carolina | 4.NSF.6 | Write a fraction with a denominator of 10 or 100 using decimal notation, and read and write a decimal number as a fraction. | Grade 4 |
| South Carolina | 4.NSF.7 | Compare and order decimal numbers to hundredths, and justify using concrete and visual models. | Grade 4 |
| South Carolina | 5.ATO.1 | Evaluate numerical expressions involving grouping symbols (i.e., parentheses, brackets, braces). | Grade 5 |
| South Carolina | 5.ATO.2 | Translate verbal phrases into numerical expressions and interpret numerical expressions as verbal phrases. | Grade 5 |
| South Carolina | 5.ATO.3 | Investigate the relationship between two numerical patterns. | Grade 5 |
| South Carolina | 5.G.1 | Define a coordinate system. | Grade 5 |
| South Carolina | 5.G.2 | Plot and interpret points in the first quadrant of the coordinate plane to represent real-world and mathematical situations. | Grade 5 |
| South Carolina | 5.G.3 | Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. | Grade 5 |
| South Carolina | 5.G.4 | Classify two-dimensional figures in a hierarchy based on their attributes. | Grade 5 |
| South Carolina | 5.MDA.1 | Convert measurements within a single system of measurement: customary (i.e., in., ft., yd., oz., lb., sec., min., hr.) or metric (i.e., mm, cm, m, km, g, kg, mL, L) from a larger to a smaller unit and a smaller to a larger unit. | Grade 5 |
| South Carolina | 5.MDA.2 | Create a line plot consisting of unit fractions and use operations on fractions to solve problems related to the line plot. | Grade 5 |
| South Carolina | 5.MDA.3 | Understand the concept of volume measurement. | Grade 5 |
| South Carolina | 5.MDA.4 | Differentiate among perimeter, area and volume and identify which application is appropriate for a given situation. | Grade 5 |
| South Carolina | 5.NSBT.1 | Understand that, in a multi-digit whole number, a digit in one place represents 10 times what the same digit represents in the place to its right, and represents 1/10 times what the same digit represents in the place to its left. | Grade 5 |
| South Carolina | 5.NSBT.2 | Use whole number exponents to explain patterns in the number of zeroes of the product when multiplying a number by powers of 10; patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. | Grade 5 |
| South Carolina | 5.NSBT.3 | Read and write decimals in standard and expanded form. Compare two decimal numbers to the thousandths using the symbols >, =, or <. | Grade 5 |
| South Carolina | 5.NSBT.4 | Round decimals to any given place value within thousandths. | Grade 5 |
| South Carolina | 5.NSBT.5 | Fluently multiply multi-digit whole numbers using strategies to include a standard algorithm. | Grade 5 |
| South Carolina | 5.NSBT.6 | Divide up to a four-digit dividend by a two-digit divisor, using strategies based on place value, the properties of operations, and the relationship between multiplication and division. | Grade 5 |
| South Carolina | 5.NSBT.7 | Add, subtract, multiply, and divide decimal numbers to hundredths using concrete area models and drawings. | Grade 5 |
| South Carolina | 5.NSF.1 | Add and subtract fractions with unlike denominators (including mixed numbers) using a variety of models, including an area model and number line. | Grade 5 |
| South Carolina | 5.NSF.2 | Solve real-world problems involving addition and subtraction of fractions with unlike denominators. | Grade 5 |
| South Carolina | 5.NSF.3 | Understand the relationship between fractions and division of whole numbers by interpreting a fraction as the numerator divided by the denominator (i.e., a/b = a divided by b). | Grade 5 |
| South Carolina | 5.NSF.4 | Extend the concept of multiplication to multiply a fraction or whole number by a fraction. | Grade 5 |
| South Carolina | 5.NSF.5 | Justify the reasonableness of a product when multiplying with fractions. | Grade 5 |
| South Carolina | 5.NSF.6 | Solve real-world problems involving multiplication of a fraction by a fraction, improper fraction and a mixed number. | Grade 5 |
| South Carolina | 5.NSF.7 | Extend the concept of division to divide unit fractions and whole numbers by using visual fraction models and equations. | Grade 5 |
| South Carolina | 5.NSF.8 | Solve real-world problems involving division of unit fractions and whole numbers, using visual fraction models and equations. | Grade 5 |
| South Carolina | 6.DS.5 | Describe numerical data sets in relation to their real-world context. | Grade 6 |
| South Carolina | 6.EEI.1 | Write and evaluate numerical expressions involving whole-number exponents and positive rational number bases using the Order of Operations. | Grade 6 |
| South Carolina | 6.EEI.2 | Extend the concepts of numerical expressions to algebraic expressions involving positive rational numbers. | Grade 6 |
| South Carolina | 6.EEI.3 | Apply mathematical properties (e.g., commutative, associative, distributive) to generate equivalent expressions. | Grade 6 |
| South Carolina | 6.EEI.4 | Apply mathematical properties (e.g., commutative, associative, distributive) to justify that two expressions are equivalent. | Grade 6 |
| South Carolina | 6.EEI.5 | Understand that if any solutions exist, the solution set for an equation or inequality consists of values that make the equation or inequality true. | Grade 6 |
| South Carolina | 6.EEI.6 | Write expressions using variables to represent quantities in real-world and mathematical situations. Understand the meaning of the variable in the context of the situation. | Grade 6 |
| South Carolina | 6.EEI.7 | Write and solve one-step linear equations in one variable involving nonnegative rational numbers for real-world and mathematical situations. | Grade 6 |
| South Carolina | 6.EEI.8 | Extend knowledge of inequalities used to compare numerical expressions to include algebraic expressions in real-world and mathematical situations. | Grade 6 |
| South Carolina | 6.EEI.9 | Investigate multiple representations of relationships in real-world and mathematical situations. | Grade 6 |
| South Carolina | 6.GM.1 | Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems. | Grade 6 |
| South Carolina | 6.GM.2 | Use visual models (e.g., model by packing) to discover that the formulas for the volume of a right rectangular prism (V = lwh, V = Bh) are the same for whole or fractional edge lengths. Apply these formulas to solve real-world and mathematical problems. | Grade 6 |
| South Carolina | 6.GM.3 | Apply the concepts of polygons and the coordinate plane to real-world and mathematical situations. | Grade 6 |
| South Carolina | 6.GM.4 | Unfold three-dimensional figures into two-dimensional rectangles and triangles (nets) to find the surface area and to solve real-world and mathematical problems. | Grade 6 |
| South Carolina | 6.NS.1 | Compute and represent quotients of positive fractions using a variety of procedures (e.g., visual models, equations, and real-world situations). | Grade 6 |
| South Carolina | 6.NS.2 | Fluently divide multi-digit whole numbers using a standard algorithmic approach. | Grade 6 |
| South Carolina | 6.NS.3 | Fluently add, subtract, multiply and divide multi-digit decimal numbers using a standard algorithmic approach. | Grade 6 |
| South Carolina | 6.NS.5 | Understand that the positive and negative representations of a number are opposites in direction and value. Use integers to represent quantities in real-world situations and explain the meaning of zero in each situation. | Grade 6 |
| South Carolina | 6.NS.6 | Extend the understanding of the number line to include all rational numbers and apply this concept to the coordinate plane. | Grade 6 |
| South Carolina | 6.NS.7 | Understand and apply the concepts of comparing, ordering, and finding absolute value to rational numbers. | Grade 6 |
| South Carolina | 6.NS.8 | Extend knowledge of the coordinate plane to solve real-world and mathematical problems involving rational numbers. | Grade 6 |
| South Carolina | 6.NS.9 | Investigate and translate among multiple representations of rational numbers (fractions, decimal numbers, percentages). Fractions should be limited to those with denominators of 2, 3, 4, 5, 8, 10, and 100. | Grade 6 |
| South Carolina | 6.RP.1 | Interpret the concept of a ratio as the relationship between two quantities, including part to part and part to whole. | Grade 6 |
| South Carolina | 6.RP.2 | Investigate relationships between ratios and rates. | Grade 6 |
| South Carolina | 6.RP.3 | Apply the concepts of ratios and rates to solve real-world and mathematical problems. | Grade 6 |
| South Carolina | 7.EEI.1 | Apply mathematical properties (e.g., commutative, associative, distributive) to simplify and to factor linear algebraic expressions with rational coefficients. | Grade 7 |
| South Carolina | 7.EEI.2 | Recognize that algebraic expressions may have a variety of equivalent forms and determine an appropriate form for a given real-world situation. | Grade 7 |
| South Carolina | 7.EEI.3 | Extend previous understanding of Order of Operations to solve multi-step real-world and mathematical problems involving rational numbers. Include fraction bars as a grouping symbol. | Grade 7 |
| South Carolina | 7.EEI.4 | Apply the concepts of linear equations and inequalities in one variable to real-world and mathematical situations. | Grade 7 |
| South Carolina | 7.EEI.5 | Understand and apply the laws of exponents (i.e., product rule, quotient rule, power to a power, product to a power, quotient to a power, zero power property) to simplify numerical expressions that include whole-number exponents. | Grade 7 |
| South Carolina | 7.GM.1 | Determine the scale factor and translate between scale models and actual measurements (e.g., lengths, area) of real-world objects and geometric figures using proportional reasoning. | Grade 7 |
| South Carolina | 7.GM.2 | Construct triangles and special quadrilaterals using a variety of tools (e.g., freehand, ruler and protractor, technology). | Grade 7 |
| South Carolina | 7.GM.3 | Describe two-dimensional cross-sections of three-dimensional figures, specifically right rectangular prisms and right rectangular pyramids. | Grade 7 |
| South Carolina | 7.GM.4 | Investigate the concept of circles. | Grade 7 |
| South Carolina | 7.GM.5 | Write equations to solve problems involving the relationships between angles formed by two intersecting lines, including supplementary, complementary, vertical, and adjacent. | Grade 7 |
| South Carolina | 7.GM.6 | Apply the concepts of two- and three-dimensional figures to real-world and mathematical situations. | Grade 7 |
| South Carolina | 7.NS.1 | Extend prior knowledge of operations with positive rational numbers to add and to subtract all rational numbers and represent the sum or difference on a number line. | Grade 7 |
| South Carolina | 7.NS.2 | Extend prior knowledge of operations with positive rational numbers to multiply and to divide all rational numbers. | Grade 7 |
| South Carolina | 7.NS.3 | Apply the concepts of all four operations with rational numbers to solve real-world and mathematical problems. | Grade 7 |
| South Carolina | 7.NS.4 | Understand and apply the concepts of comparing and ordering to rational numbers. | Grade 7 |
| South Carolina | 7.NS.5 | Extend prior knowledge to translate among multiple representations of rational numbers (fractions, decimal numbers, percentages). Exclude the conversion of repeating decimal numbers to fractions. | Grade 7 |
| South Carolina | 7.RP.1 | Compute unit rates, including those involving complex fractions, with like or different units. | Grade 7 |
| South Carolina | 7.RP.2 | Identify and model proportional relationships given multiple representations, including tables, graphs, equations, diagrams, verbal descriptions, and real-world situations. | Grade 7 |
| South Carolina | 7.RP.3 | Solve real-world and mathematical problems involving ratios and percentages using proportional reasoning (e.g., multi-step dimensional analysis, percent increase/decrease, tax). | Grade 7 |
| South Carolina | 8.DSP.1 | Investigate bivariate data. | Grade 8 |
| South Carolina | 8.DSP.2 | Draw an approximate line of best fit on a scatter plot that appears to have a linear association and informally assess the fit of the line to the data points. | Grade 8 |
| South Carolina | 8.EEI.1 | Understand and apply the laws of exponents (i.e. product rule, quotient rule, power to a power, product to a power, quotient to a power, zero power property, negative exponents) to simplify numerical expressions that include integer exponents. | Grade 8 |
| South Carolina | 8.EEI.2 | Investigate concepts of square and cube roots. | Grade 8 |
| South Carolina | 8.EEI.3 | Explore the relationship between quantities in decimal and scientific notation. | Grade 8 |
| South Carolina | 8.EEI.4 | Apply the concepts of decimal and scientific notation to solve real-world and mathematical problems. | Grade 8 |
| South Carolina | 8.EEI.5 | Apply concepts of proportional relationships to real-world and mathematical situations. | Grade 8 |
| South Carolina | 8.EEI.6 | Apply concepts of slope and y-intercept to graphs, equations, and proportional relationships. | Grade 8 |
| South Carolina | 8.EEI.7 | Extend concepts of linear equations and inequalities in one variable to more complex multi-step equations and inequalities in real-world and mathematical situations. | Grade 8 |
| South Carolina | 8.EEI.8 | Investigate and solve real-world and mathematical problems involving systems of linear equations in two variables with integer coefficients and solutions. | Grade 8 |
| South Carolina | 8.F.1 | Explore the concept of functions. | Grade 8 |
| South Carolina | 8.F.2 | Compare multiple representations of two functions, including mappings, tables, graphs, equations, and verbal descriptions, in order to draw conclusions. | Grade 8 |
| South Carolina | 8.F.3 | Investigate the differences between linear and nonlinear functions using multiple representations (i.e., tables, graphs, equations, and verbal descriptions). | Grade 8 |
| South Carolina | 8.F.4 | Apply the concepts of linear functions to real-world and mathematical situations. | Grade 8 |
| South Carolina | 8.F.5 | Apply the concepts of linear and nonlinear functions to graphs in real-world and mathematical situations. | Grade 8 |
| South Carolina | 8.GM.1 | Investigate the properties of rigid transformations (rotations, reflections, translations) using a variety of tools (e.g., grid paper, reflective devices, graphing paper, technology). | Grade 8 |
| South Carolina | 8.GM.2 | Apply the properties of rigid transformations (rotations, reflections, translations). | Grade 8 |
| South Carolina | 8.GM.3 | Investigate the properties of transformations (rotations, reflections, translations, dilations) using a variety of tools (e.g., grid paper, reflective devices, graphing paper, dynamic software). | Grade 8 |
| South Carolina | 8.GM.4 | Apply the properties of transformations (rotations, reflections, translations, dilations). | Grade 8 |
| South Carolina | 8.GM.5 | Extend and apply previous knowledge of angles to properties of triangles, similar figures, and parallel lines cut by a transversal. | Grade 8 |
| South Carolina | 8.GM.7 | Apply the Pythagorean Theorem to model and solve real-world and mathematical problems in two and three dimensions involving right triangles. | Grade 8 |
| South Carolina | 8.GM.8 | Find the distance between any two points in the coordinate plane using the Pythagorean Theorem. | Grade 8 |
| South Carolina | 8.GM.9 | Solve real-world and mathematical problems involving volumes of cones, cylinders, and spheres and the surface area of cylinders. | Grade 8 |
| South Carolina | 8.NS.2 | Estimate and compare the value of irrational numbers by plotting them on a number line. | Grade 8 |
| South Carolina | 8.NS.3 | Extend prior knowledge to translate among multiple representations of rational numbers (fractions, decimal numbers, percentages). Include the conversion of repeating decimal numbers to fractions. | Grade 8 |
| South Carolina | A1.ACE.2 | Create equations in two or more variables to represent relationships between quantities. Graph the equations on coordinate axes using appropriate labels, units, and scales. (Limit to linear; quadratic; exponential with integer exponents; direct and indirect variation.) | Algebra 1 |
| South Carolina | A1.AREI.3 | Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. | Algebra 1 |
| South Carolina | A1.ASE.2 | Analyze the structure of binomials, trinomials, and other polynomials in order to rewrite equivalent expressions. | Algebra 1 |
| South Carolina | A1.ASE.3 | Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression. | Algebra 1 |
| South Carolina | A1.FIF.2 | Evaluate functions and interpret the meaning of expressions involving function notation from a mathematical perspective and in terms of the context when the function describes a real-world situation. | Algebra 1 |
| South Carolina | A1.FIF.4 | Interpret key features of a function that models the relationship between two quantities when given in graphical or tabular form. Sketch the graph of a function from a verbal description showing key features. Key features include intercepts; intervals where the function is increasing, decreasing, constant, positive, or negative; relative maximums and minimums; symmetries; end behavior and periodicity. (Limit to linear; quadratic; exponential.) | Algebra 1 |
| South Carolina | A1.FIF.7 | Graph functions from their symbolic representations. Indicate key features including intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior and periodicity. Graph simple cases by hand and use technology for complicated cases. (Limit to linear; quadratic; exponential only in the form y = a^x + k.) | Algebra 1 |
| South Carolina | A1.SPID.6 | Using technology, create scatterplots and analyze those plots to compare the fit of linear, quadratic, or exponential models to a given data set. Select the appropriate model, fit a function to the data set, and use the function to solve problems in the context of the data. | Algebra 1 |
| South Carolina | FA.ACE.2 | Create equations in two or more variables to represent relationships between quantities. Graph the equations on coordinate axes using appropriate labels, units, and scales. (Limit to linear; quadratic; exponential with integer exponents; direct and indirect variation.) | Foundations in Algebra |
| South Carolina | FA.FIF.2 | Evaluate functions and interpret the meaning of expressions involving function notation from a mathematical perspective and in terms of the context when the function describes a real-world situation. | Foundations in Algebra |
| South Carolina | FA.FIF.4 | Interpret key features of a function that models the relationship between two quantities when given in graphical or tabular form. Sketch the graph of a function from a verbal description showing key features. Key features include intercepts; intervals where the function is increasing, decreasing, constant, positive, or negative; relative maximums and minimums; symmetries; end behavior and periodicity. (Limit to linear; quadratic; exponential.) | Foundations in Algebra |
| South Carolina | FA.FIF.7 | Graph functions from their symbolic representations. Indicate key features including intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior and periodicity. Graph simple cases by hand and use technology for complicated cases. (Limit to linear; quadratic; exponential only in the form y = a^x + k.) | Foundations in Algebra |
| South Carolina | FA.SPID.6 | Using technology, create scatterplots and analyze those plots to compare the fit of linear, quadratic, or exponential models to a given data set. Select the appropriate model, fit a function to the data set, and use the function to solve problems in the context of the data. | Foundations in Algebra |
| South Carolina | IA.ACE.2 | Create equations in two or more variables to represent relationships between quantities. Graph the equations on coordinate axes using appropriate labels, units, and scales. | Intermediate Algebra |
| South Carolina | IA.ASE.2 | Analyze the structure of binomials, trinomials, and other polynomials in order to rewrite equivalent expressions. | Intermediate Algebra |
| South Carolina | IA.ASE.3 | Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression. | Intermediate Algebra |
| South Carolina | IA.FBF.1 | Write a function that describes a relationship between two quantities. | Intermediate Algebra |
| South Carolina | IA.FIF.4 | Interpret key features of a function that models the relationship between two quantities when given in graphical or tabular form. Sketch the graph of a function from a verbal description showing key features. Key features include intercepts; intervals where the function is increasing, decreasing, constant, positive, or negative; relative maximums and minimums; symmetries; end behavior and periodicity. | Intermediate Algebra |
| South Carolina | IA.FIF.7 | Graph functions from their symbolic representations. Indicate key features including intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior and periodicity. Graph simple cases by hand and use technology for complicated cases. | Intermediate Algebra |
| South Carolina | A2.AAPR.3 | Graph polynomials identifying zeros when suitable factorizations are available and indicating end behavior. Write a polynomial function of least degree corresponding to a given graph. (Limit to polynomials with degrees 3 or less.) | Algebra 2 |
| South Carolina | A2.ACE.2 | Create equations in two or more variables to represent relationships between quantities. Graph the equations on coordinate axes using appropriate labels, units, and scales. | Algebra 2 |
| South Carolina | A2.ACE.3 | Use systems of equations and inequalities to represent constraints arising in real- world situations. Solve such systems using graphical and analytical methods, including linear programing. Interpret the solution within the context of the situation. (Limit to linear programming.) | Algebra 2 |
| South Carolina | A2.ASE.2 | Analyze the structure of binomials, trinomials, and other polynomials in order to rewrite equivalent expressions. | Algebra 2 |
| South Carolina | A2.ASE.3 | Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression. | Algebra 2 |
| South Carolina | A2.FBF.1 | Write a function that describes a relationship between two quantities. | Algebra 2 |
| South Carolina | A2.FIF.4 | Interpret key features of a function that models the relationship between two quantities when given in graphical or tabular form. Sketch the graph of a function from a verbal description showing key features. Key features include intercepts; intervals where the function is increasing, decreasing, constant, positive, or negative; relative maximums and minimums; symmetries; end behavior and periodicity. | Algebra 2 |
| South Carolina | A2.FIF.7 | Graph functions from their symbolic representations. Indicate key features including intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior and periodicity. Graph simple cases by hand and use technology for complicated cases. | Algebra 2 |
| South Carolina | PS.SPID.6 | Using technology, create scatterplots and analyze those plots to compare the fit of linear, quadratic, or exponential models to a given data set. Select the appropriate model, fit a function to the data set, and use the function to solve problems in the context of the data. | Probability and Statistics |
| South Carolina | PC.AAPR.3 | Graph polynomials identifying zeros when suitable factorizations are available and indicating end behavior. Write a polynomial function of least degree corresponding to a given graph. | Pre-Calculus |
| South Carolina | PC.ASE.2 | Analyze the structure of binomials, trinomials, and other polynomials in order to rewrite equivalent expressions. | Pre-Calculus |
| South Carolina | PC.FBF.1 | Write a function that describes a relationship between two quantities. | Pre-Calculus |
| South Carolina | PC.FIF.4 | Interpret key features of a function that models the relationship between two quantities when given in graphical or tabular form. Sketch the graph of a function from a verbal description showing key features. Key features include intercepts; intervals where the function is increasing, decreasing, constant, positive, or negative; relative maximums and minimums; symmetries; end behavior and periodicity. | Pre-Calculus |
| South Carolina | PC.FIF.7 | Graph functions from their symbolic representations. Indicate key features including intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior and periodicity. Graph simple cases by hand and use technology for complicated cases. | Pre-Calculus |
| South Dakota | K.CC.A.1 | Count to 100 by ones and by tens. | Kindergarten |
| South Dakota | K.CC.A.2 | Count forward beginning from any given number within 100 (instead of having to begin at 1). Count backwards beginning from any given number within 20. | Kindergarten |
| South Dakota | K.CC.A.3 | Write numbers from 0 to 20. Represent a number of objects with a written numeral 0-20 (with 0 representing a count of no objects). | Kindergarten |
| South Dakota | K.CC.B.4 | Understand the relationship between numbers and quantities; connect counting to cardinality. a. When counting objects, say the number names in the standard order, pairing each object with one and only one number name and each number name with one and only one object. (one-to-one correspondence) b. Understand that the last number name said tells the number of objects counted. (cardinality) The number of objects is the same regardless of their arrangement or the order in which they were counted. c. Understand that each successive number name refers to a quantity that is one larger. | Kindergarten |
| South Dakota | K.CC.B.5 | Count to answer “how many?” a. When counting, answer questions about as many as 20 things arranged in a line, a rectangular array, or a circle, or and as many as 10 things in a scattered configuration. b. Given a number(s) from 1–20, count out that many objects. | Kindergarten |
| South Dakota | K.CC.C.6 | Identify whether the number of objects in one group is greater than, less than, or equal to the number of objects in another group. Include groups with up to ten objects. | Kindergarten |
| South Dakota | K.CC.C.7 | Compare two numbers between 1 and 10 presented as written numerals. | Kindergarten |
| South Dakota | K.OA.A.1 | Represent addition and subtraction with objects, fingers, mental images, drawings, sounds (e.g., claps), acting out situations, verbal explanations, expressions, or equations. (Drawings need not show details, but should show the mathematics in the problem.) | Kindergarten |
| South Dakota | K.OA.A.2 | Solve addition and subtraction word problems. a. Solve addition and subtraction word problems (within 10), involving result unknown problems, put together/take apart total unknown, and put together/take apart addend unknown, e.g., using objects or drawings to represent the problem. (see appendix for K-2 Common Addition and Subtraction Situations) b. Add and subtract within 10, eg., by using objects or drawings to represent the problem. | Kindergarten |
| South Dakota | K.OA.A.3 | Decompose numbers less than or equal to 10 into pairs in more than one way, e.g., by using objects or drawings, and record each decomposition by a drawing or equation (e.g., 5 = 2 + 3 and 5 = 4 + 1). | Kindergarten |
| South Dakota | K.OA.A.4 | For any number from 1 to 9, find the number that makes 10 when added to the given number, e.g., by using objects or drawings, and record the answer with a drawing or equation. | Kindergarten |
| South Dakota | K.OA.A.5 | Fluently add and subtract within 5. | Kindergarten |
| South Dakota | K.NBT.A.1 | Compose and decompose numbers from 11 to 19 into ten ones and some further ones, e.g., by using objects or drawings, and record each composition or decomposition by a drawing or equation (e.g., 18 = 10 + 8); understand that these numbers are composed of ten ones and one, two, three, four, five, six, seven, eight, or nine ones. | Kindergarten |
| South Dakota | K.MD.A.1 | Describe measurable attributes of a single object or objects, such as length, weight, or size. | Kindergarten |
| South Dakota | K.MD.A.2 | Directly compare two objects with a measurable attribute in common, to see which object has “more of”/“less of” the attribute, and describe the difference. | Kindergarten |
| South Dakota | K.MD.B.3 | Classify objects into given categories; count the number of objects in each category and sort the categories by count. Limit category counts to be less than or equal to 10. | Kindergarten |
| South Dakota | K.MD.C.4 | Identify a penny and understand that the value is one. Count pennies within 20. | Kindergarten |
| South Dakota | K.G.A.1 | Describe objects in the environment using names of shapes, and describe the relative positions of these objects using terms such as above, below, beside, in front of, behind, and next to. | Kindergarten |
| South Dakota | K.G.A.2 | Correctly name shapes regardless of their orientations or overall size. | Kindergarten |
| South Dakota | K.G.A.3 | Identify shapes as two-dimensional (lying in a plane, “flat”) or three-dimensional (“solid”). | Kindergarten |
| South Dakota | K.G.B.4 | Analyze and compare two- and three-dimensional shapes, in different sizes and orientations, using informal language to describe their similarities, differences, parts (e.g., number of sides and vertices/“corners”) and other attributes (e.g., having sides of equal length). | Kindergarten |
| South Dakota | K.G.B.6 | Compose simple shapes to form larger shapes. | Kindergarten |
| South Dakota | 1.OA.A.1 | Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem. | Grade 1 |
| South Dakota | 1.OA.B.3 | Apply commutative, associative, and additive identity properties of operations as strategies to add. (Students need not use formal terms for these properties.) Examples: If 8 + 3 = 11 is known, then 3 + 8 = 11 is also known. (Commutative property of addition.) To add 2 + 6 + 4, the second two numbers can be added to make a ten, so 2 + 6 + 4 = 2 + 10 = 12. (Associative property of addition.) 8 + 0 = 8 (Additive Identity property) | Grade 1 |
| South Dakota | 1.OA.B.4 | Understand subtraction as an unknown-addend problem. For example, subtract 10 – 8 by finding the number that makes 10 when added to 8. | Grade 1 |
| South Dakota | 1.OA.C.5 | Understand counting on as addition and counting back as subtraction e.g. 5, (6,7,8) means 5 + 3 and 5, (4,3,2) means 5-3. | Grade 1 |
| South Dakota | 1.OA.C.6 | Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to a ten (e.g., 13 – 4 = 13 – 3 – 1 = 10 – 1 = 9); using the relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 – 8 = 4); and creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13). | Grade 1 |
| South Dakota | 1.OA.D.7 | Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false. For example, which of the following equations are true and which are false? 6 = 6, 7 = 8 – 1, 5 + 2 = 2 + 5, 4 + 1 = 5 + 2. | Grade 1 |
| South Dakota | 1.OA.D.8 | Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations 8 + ? = 11, 5 = ? – 3, 6 + 6 = ? . | Grade 1 |
| South Dakota | 1.NBT.A.1 | In the range of 0 - 120 a. Count on from any given number. b. Read and write numerals. c. Represent a number of objects with a written numeral. | Grade 1 |
| South Dakota | 1.NBT.B.2 | Understand that the two digits of a two-digit number represent amounts of tens and ones. Understand the following as special cases: a. 10 can be thought of as a bundle of ten ones — called a “ten.” b. The numbers from 11 to 19 are composed of a ten and one, two, three, four, five, six, seven, eight, or nine ones. c. The numbers 10, 20, 30, 40, 50, 60, 70, 80, 90 refer to one, two, three, four, five, six, seven, eight, or nine tens (and 0 ones). | Grade 1 |
| South Dakota | 1.NBT.B.3 | Compare two two-digit numbers based on meanings of the tens and ones digits, recording the results of comparisons with the symbols . | Grade 1 |
| South Dakota | 1.NBT.C.4 | Add and subtract within 100. a. Add within 100, including adding a two-digit number and a one-digit number, and adding a two-digit number and a multiple of 10, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. b. Understand that in adding two-digit numbers (sums within 100) add tens and tens, ones and ones; and sometimes it is necessary to compose a ten. | Grade 1 |
| South Dakota | 1.NBT.C.5 | Given a two-digit number, mentally find 10 more or 10 less than the number, without having to count; explain the reasoning used. | Grade 1 |
| South Dakota | 1.NBT.C.6 | Subtract multiples of 10 in the range 10-90 from multiples of 10 in the range 10-90 (positive or zero differences), using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. | Grade 1 |
| South Dakota | 1.MD.A.1 | Order three objects by length; compare the lengths of two objects indirectly by using a third object. | Grade 1 |
| South Dakota | 1.MD.A.2 | Express the length of an object as a whole number of length units, by laying multiple copies of a shorter object (the length unit) end to end; understand that the length measurement of an object is the number of same-size length units that span it with no gaps or overlaps. | Grade 1 |
| South Dakota | 1.MD.B.3 | Tell and write about time in hours and half-hours using analog and digital clocks. | Grade 1 |
| South Dakota | 1.MD.B.5 | Identify nickels and understand that five pennies can be thought of as a nickel. Identify dimes and understand ten pennies can be thought of as a dime. Count the value of a set of coins comprised of pennies, nickels, and dimes. | Grade 1 |
| South Dakota | 1.MD.C.4 | Organize, represent, and interpret data with up to three categories; ask and answer questions about the total number of data points, how many in each category, and how many more or less are in one category than in another. | Grade 1 |
| South Dakota | 1.G.A.1 | Distinguish between defining attributes (e.g., triangles are closed and three-sided) versus non-defining attributes (e.g., color, orientation, overall size); build and draw shapes to possess defining attributes. | Grade 1 |
| South Dakota | 1.G.A.2 | Compose and Identify regular and irregular two-dimensional shapes (rectangles, squares, trapezoids, triangles, half-circles, and quarter-circles) and compose three-dimensional shapes (cubes, spheres, right rectangular prisms, right circular cones, and right circular cylinders) to create a composite shape, and compose new shapes from the composite shape. (Students do not need to master formal names such as “right rectangular prism.”) | Grade 1 |
| South Dakota | 1.G.A.3 | Partition circles and rectangles into two and four equal shares, describe the shares using the words halves, fourths, and quarters, and use the phrases half of, fourth of, and quarter of. Describe the whole as two of, or four of the shares. Understand for these examples that decomposing into more equal shares creates smaller shares. | Grade 1 |
| South Dakota | 2.OA.A.1 | Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem. | Grade 2 |
| South Dakota | 2.OA.B.2 | Add and subtract within 20. a. Fluently add and subtract within 20 using mental strategies. (See standard 1.OA.6 for a list of mental strategies.) b. By end of Grade 2, know from memory all sums of two one-digit numbers | Grade 2 |
| South Dakota | 2.OA.C.3 | Determine whether a group of objects (up to 20) has an odd or even number of members, e.g., by pairing objects or counting them by 2s; write an equation to express an even number as a sum of two equal addends. | Grade 2 |
| South Dakota | 2.OA.C.4 | Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends | Grade 2 |
| South Dakota | 2.NBT.A.1 | Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones. Understand the following as special cases: a. 100 can be thought of as a bundle of ten tens — called a “hundred.” b. The numbers 100, 200, 300, 400, 500, 600, 700, 800, 900 refer to one, two, three, four, five, six, seven, eight, or nine hundreds (and 0 tens and 0 ones). | Grade 2 |
| South Dakota | 2.NBT.A.2 | Count within 1000; skip-count by 5s, 10s, and 100s, starting from any number in its skip counting sequence. | Grade 2 |
| South Dakota | 2.NBT.A.3 | Read and write numbers to 1000 using base-ten numerals (standard form), number names (word form), and expanded form. | Grade 2 |
| South Dakota | 2.NBT.A.4 | Compare, two three-digit numbers based on meanings of the hundreds, tens, and ones digits, using >, =, and <, symbols to record the results of comparisons. | Grade 2 |
| South Dakota | 2.NBT.B.5 | Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction. | Grade 2 |
| South Dakota | 2.NBT.B.6 | Add up to four two-digit numbers using strategies based on place value and properties of operations. | Grade 2 |
| South Dakota | 2.NBT.B.7 | Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method. Understand that in adding or subtracting three-digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds. | Grade 2 |
| South Dakota | 2.NBT.B.8 | Mentally add 10 or 100 to a given number 100–900, and mentally subtract 10 or 100 from a given number 100–900. | Grade 2 |
| South Dakota | 2.MD.A.1 | Measure the length of an object by selecting and using appropriate tools such as rulers, yardsticks, meter sticks, and measuring tapes. | Grade 2 |
| South Dakota | 2.MD.A.2 | Measure the length of an object twice, using length units of different lengths for the two measurements; describe how the two measurements relate to the size of the unit chosen. | Grade 2 |
| South Dakota | 2.MD.A.4 | Measure to determine how much longer one object is than another, expressing the length difference in terms of a standard length unit. | Grade 2 |
| South Dakota | 2.MD.B.5 | Use addition and subtraction within 100 to solve word problems involving lengths that are given in the same units, e.g., by using drawings (such as drawings of rulers) and equations with a symbol for the unknown number to represent the problem. | Grade 2 |
| South Dakota | 2.MD.C.7 | Tell and write time from analog and digital clocks to the nearest five minutes, using a.m. and p.m. | Grade 2 |
| South Dakota | 2.MD.C.8 | Identify and count coins and bills and apply that understanding to solve word problems. a. Recognize and know the value of coins up to one dollar. b. Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies, using $ and ¢ symbols appropriately. | Grade 2 |
| South Dakota | 2.MD.D.9 | Generate measurement data by measuring lengths of several objects to the nearest whole unit, or by making repeated measurements of the same object. Show the measurements by making a line plot, where the horizontal scale is marked off in whole-number units. | Grade 2 |
| South Dakota | 2.MD.D.10 | Draw a picture graph and a bar graph (with single-unit scale) to represent a data set with up to four categories. Solve simple put together, take-apart, and compare problems using information presented in a bar graph. | Grade 2 |
| South Dakota | 2.G.A.1 | Recognize, identify, and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces; to include triangles, quadrilaterals, pentagons, hexagons, and cubes. (Sizes are compared directly or visually, not compared by measuring.) | Grade 2 |
| South Dakota | 2.G.A.2 | Partition a rectangle into rows and columns of same-size squares and count to find the total number of them. | Grade 2 |
| South Dakota | 2.G.A.3 | Partition circles and rectangles into two, three, or four equal shares, describe the shares using the words halves, thirds, half of, a third of, etc., and describe the whole as two halves, three thirds, four fourths. Recognize that equal shares of identical wholes need not have the same shape.. | Grade 2 |
| South Dakota | 3.OA.A.1 | Interpret products of whole numbers, e.g., interpret 5x7 as the total number of objects in 5 groups of 7 objects each. For example, describe a context in which a total number of objects can be expressed as 5x7. | Grade 3 |
| South Dakota | 3.OA.A.2 | Interpret whole-number quotients of whole numbers, e.g., interpret 56 ÷ 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each. | Grade 3 |
| South Dakota | 3.OA.A.3 | Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem. | Grade 3 |
| South Dakota | 3.OA.A.4 | Determine the unknown whole number in a multiplication or division equation relating three whole numbers. | Grade 3 |
| South Dakota | 3.OA.B.5 | Apply properties of operations as strategies to multiply and divide. (Students need not use formal terms for these properties.) | Grade 3 |
| South Dakota | 3.OA.B.6 | Understand division as an unknown-factor problem. For example, find 32÷8 by finding the number that makes 32 when multiplied by 8. | Grade 3 |
| South Dakota | 3.OA.C.7 | Multiply and divide within 100. a. Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 × 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. b. Demonstrate fluency (skill in carrying out procedures flexibly, appropriately, efficiently, and accurately) for all products of two one-digit numbers. | Grade 3 |
| South Dakota | 3.OA.D.8 | Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. (This standard is limited to problems posed with whole numbers and having whole number answers; students should know how to perform operations in the conventional order when there are no parentheses to specify a particular order [Order of Operations]). | Grade 3 |
| South Dakota | 3.OA.D.9 | Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations. | Grade 3 |
| South Dakota | 3.NBT.A.1 | Use place value understanding to round whole numbers to the nearest 10 or 100. | Grade 3 |
| South Dakota | 3.NBT.A.2 | Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction. | Grade 3 |
| South Dakota | 3.NBT.A.3 | Multiply one-digit whole numbers by multiples of 10 in the range 10–90 (e.g., 9 × 80, 5 × 60) using strategies based on place value and properties of operations. | Grade 3 |
| South Dakota | 3.NF.A.1 | Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts (example: 1 part out of 4 equal parts is the same as 1/4); understand a fraction a/b as the quantity formed by a parts of size 1/b. (example: 3/4 is the same as 3 one-fourths (1/4, 1/4, 1/4) | Grade 3 |
| South Dakota | 3.NF.A.2 | Understand a fraction as a number on the number line; represent fractions on a number line diagram. a. Represent a fraction 1/b on a number line diagram by defining the interval from 0 to 1 as the whole and partitioning it into b equal parts. Recognize that each part has size 1/b and that the endpoint of the part based at 0 locates the number 1/b on the number line. b. Represent a fraction a/b on a number line diagram by marking off a lengths 1/b from 0. Recognize that the resulting interval has size a/b and that its endpoint locates the number a/b on the number line. | Grade 3 |
| South Dakota | 3.NF.A.3 | Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size. Note - Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, and 8. a. Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line. b. Recognize and generate simple equivalent fractions, e.g., 1/2 = 2/4, 4/6 = 2/3. Explain why the fractions are equivalent, e.g., by using a visual fraction model. c. Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers. d. Compare two fractions with the same numerator or the same denominator by reasoning about their size. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with the symbols . | Grade 3 |
| South Dakota | 3.MD.A.1 | Tell and write time to the nearest minute and measure time intervals in minutes, using an analog and digital clock. Solve word problems involving addition and subtraction of time intervals in minutes, e.g., by representing the problem on a number line diagram. | Grade 3 |
| South Dakota | 3.MD.A.2 | Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l). (Excludes compound units such as cm³ and finding the geometric volume of a container.) Add, subtract, multiply, or divide to solve one-step word problems involving masses or volumes that are given in the same units, e.g., by using drawings (such as a beaker with a measurement scale) to represent the problem. | Grade 3 |
| South Dakota | 3.MD.B.3 | Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and two-step “how many more” and “how many less” problems using information presented in scaled bar graphs. | Grade 3 |
| South Dakota | 3.MD.B.4 | Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Show the data by making a line plot, where the horizontal scale is marked off in appropriate units— whole numbers, halves, or quarters. | Grade 3 |
| South Dakota | 3.MD.C.5 | Recognize area as an attribute of plane figures and understand concepts of area measurement. a. A square with side length 1 unit, called “a unit square,” is said to have “one square unit” of area, and can be used to measure area. b. A plane figure which can be covered without gaps or overlaps by n unit squares is said to have an area of n square units. | Grade 3 |
| South Dakota | 3.MD.C.6 | Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units). | Grade 3 |
| South Dakota | 3.MD.C.7 | Relate area to the operations of multiplication and addition. a. Find the area of a rectangle with whole-number side lengths by tiling it, and show that the area is the same as would be found by multiplying the side lengths. b. Multiply side lengths to find areas of rectangles with whole number side lengths in the context of solving real world and mathematical problems, and represent whole-number products as rectangular areas in mathematical reasoning. c. Use tiling to show in a concrete case that the area of a rectangle with whole-number side lengths a and b + c is the sum of a × b and a × c. Use area models to represent the distributive property in mathematical reasoning. d. Recognize area as additive. Find areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas of the non-overlapping parts, applying this technique to solve real world problems. | Grade 3 |
| South Dakota | 3.MD.C.8 | Solve real world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters. | Grade 3 |
| South Dakota | 3.G.A.1 | Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories. | Grade 3 |
| South Dakota | 3.G.A.2 | Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole. For example, partition a shape into 4 parts with equal area, and describe the area of each part as 1/4 of the area of a shape. | Grade 3 |
| South Dakota | 4.OA.A.1 | Use and interpret multiplicative equations. a. Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 × 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal or written statements of multiplicative comparisons as multiplication equations. Example: Tom has 7 toy cars; Joe has 5 times as many. How many toy cars does Joe have? Answer: 35, because 7 x 5 = 35 or 5 x 7 = 35. b. Know from memory (quick effortless recall of facts) all products of two one-digit numbers. | Grade 4 |
| South Dakota | 4.OA.A.2 | Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, and distinguish multiplicative comparison from additive comparison. | Grade 4 |
| South Dakota | 4.OA.A.3 | Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. | Grade 4 |
| South Dakota | 4.OA.B.4 | Using whole number in the range 1–100. a. Find all factor pairs for a given whole number. b. Recognize that a whole number is a multiple of each of its factors. c. Determine whether a given whole number is a multiple of each of a given one-digit number. d. Determine whether a given whole number is prime or composite. | Grade 4 |
| South Dakota | 4.OA.C.5 | Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. For example, given the rule 'Add 3' and the starting number is 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way. | Grade 4 |
| South Dakota | 4.NBT.A.1 | Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. For example, recognize that the 7 in 700 is 10 times greater than the 7 in 70 because 700 ÷ 70 =10 and 70 x 10=700. | Grade 4 |
| South Dakota | 4.NBT.A.2 | Read and write multi-digit whole numbers. a. Read and write multi-digit whole numbers using base-ten numerals (standard form), number names (word form), and expanded form. b. Compare two multi-digit numbers based on values of the digits in each place, using , and = symbols to record the results of comparisons. a. Read and write multi-digit whole numbers using base-ten numerals (standard form), number names (word form), and expanded form. b. Compare two multi-digit numbers based on values of the digits in each place, using , and = symbols to record the results of comparisons. | Grade 4 |
| South Dakota | 4.NBT.A.3 | Use place value understanding to round multi-digit whole numbers to any place. | Grade 4 |
| South Dakota | 4.NBT.B.4 | Fluently add and subtract multi-digit whole numbers using an algorithm including, but not limited to, the standard algorithm. | Grade 4 |
| South Dakota | 4.NBT.B.5 | Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. | Grade 4 |
| South Dakota | 4.NBT.B.6 | Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. | Grade 4 |
| South Dakota | 4.NF.A.1 | Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. | Grade 4 |
| South Dakota | 4.NF.A.2 | Compare two fractions with different numerators and different denominators, by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols , =, and justify the conclusions. | Grade 4 |
| South Dakota | 4.NF.B.3 | Understand a fraction a/b with a > 1 as a sum of fractions 1/b. For example, 4/5 = 1/5 + 1/5 + 1/5 + 1/5 a. Add and subtract of fractions e.g., joining and separating parts referring to the same whole. b. Decompose a fraction into a sum of fractions with like denominators in more than one way, recording each decomposition by an equation. Justify decompositions, e.g., by using a visual fraction model. c. Add and subtract mixed numbers with like denominators, e.g., by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. d. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators, e.g., by using visual fraction models and equations to represent the problem. | Grade 4 |
| South Dakota | 4.NF.B.4 | Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. a. Understand a fraction a/b as a multiple of 1/b. For example, use a visual fraction model to represent 5/4 as the product 5 x (1/4), recording the conclusion by the equation 5/4 = 5 x (1/4). b. Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number. For example, use a visual fraction model to express 3 x (2/5) as 6 x (1/5), recognizing this product as 6/5. (In general, n x (a/b) = (n x a)/b = (n x a) x 1/b.) c. Solve word problems involving multiplication of a fraction by a whole number, e.g., by using visual fraction models and equations to represent the problem. For example, if each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie? | Grade 4 |
| South Dakota | 4.NF.C.5 | Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100. For example, express 3/10 as 30/100, and add 3/10 + 4/100 = 34/100. | Grade 4 |
| South Dakota | 4.NF.C.6 | Read and write decimal notation for fractions with denominators 10 or 100. Locate these decimals on a number line. | Grade 4 |
| South Dakota | 4.NF.C.7 | Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, <, or =, and justify the conclusions. | Grade 4 |
| South Dakota | 4.MD.A.1 | Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two column table. For example, know that 1ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36),... | Grade 4 |
| South Dakota | 4.MD.A.2 | Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. | Grade 4 |
| South Dakota | 4.MD.A.3 | Apply the area and perimeter formulas for rectangles in real world and mathematical problems. | Grade 4 |
| South Dakota | 4.MD.B.4 | Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots. | Grade 4 |
| South Dakota | 4.MD.C.5 | Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement. a. An angle is measured with reference to a circle with its center at the common endpoint of the rays, by considering the fraction of the circular arc between the points where the two rays intersect the circle. An angle that turns through 1/360 of a circle is called a “one-degree angle,” and can be used to measure angles. b. An angle that turns through in one-degree angles is said to have an angle measure of n degrees. | Grade 4 |
| South Dakota | 4.MD.C.6 | Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure. | Grade 4 |
| South Dakota | 4.MD.C.7 | Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems, e.g., by using an equation with a symbol for the unknown angle measure. | Grade 4 |
| South Dakota | 4.G.A.1 | Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures. | Grade 4 |
| South Dakota | 4.G.A.2 | Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize, and identify categories of right, acute, and obtuse triangles. | Grade 4 |
| South Dakota | 4.G.A.3 | Recognize and draw lines of symmetry for two-dimensional figures. | Grade 4 |
| South Dakota | 5.OA.A.1 | Use and explain parentheses, in numerical expressions, and evaluate expressions with these symbols. | Grade 5 |
| South Dakota | 5.OA.A.2 | Write simple expressions that record calculations with numbers to represent real world problems, and interpret numerical expressions without evaluating them. | Grade 5 |
| South Dakota | 5.OA.B.3 | Generate two numerical patterns using two given rules. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. Identify the relationship between the two patterns. | Grade 5 |
| South Dakota | 5.NBT.A.1 | Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. | Grade 5 |
| South Dakota | 5.NBT.A.2 | Explain and apply patterns in the number of zeros of the product when multiplying a number by powers of 10. Explain and apply patterns in the placement of the decimal point with respect to the values of the digits in the product or the quotient, when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. | Grade 5 |
| South Dakota | 5.NBT.A.3 | Read, write, and compare decimals to thousandths. a. Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 × 100 + 4 × 10 + 7 × 1 + 3 × (1/10) + 9 × (1/100) + 2 × (1/1000). b. Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. | Grade 5 |
| South Dakota | 5.NBT.A.4 | Use place value understanding to round decimals to any place. | Grade 5 |
| South Dakota | 5.NBT.B.5 | Fluently multiply multi-digit whole numbers using an algorithm, including but not limited to the standard algorithm. | Grade 5 |
| South Dakota | 5.NBT.B.6 | Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Explain the calculation by using equations, rectangular arrays, illustrations, area models, or other representations based on place value. | Grade 5 |
| South Dakota | 5.NBT.B.7 | Use the four operations with decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; justify the reasoning used with a written explanation. a. Add and subtract decimals b. Multiply and divide decimals. | Grade 5 |
| South Dakota | 5.NF.A.1 | Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference with a like denominator. It is not necessary at this grade level to simplify the sum or difference. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) | Grade 5 |
| South Dakota | 5.NF.A.2 | Solve word problems involving addition and subtraction of fractions. a. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. b. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. | Grade 5 |
| South Dakota | 5.NF.B.3 | Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie? | Grade 5 |
| South Dakota | 5.NF.B.4 | Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. a. Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = ac/bd.) b. Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas. | Grade 5 |
| South Dakota | 5.NF.B.5 | Interpret multiplication as scaling (resizing), by: a. Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication. b. Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (n×a)/(n×b) to the effect of multiplying a/b by 1. | Grade 5 |
| South Dakota | 5.NF.B.7 | Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. a. Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3. b. Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4. c. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins? | Grade 5 |
| South Dakota | 5.MD.A.1 | Convert customary and metric measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m). Use these conversions in solving multi-step, real world problems involving distances, intervals of time, liquid volumes, masses of objects, and money (including problems involving simple fractions or decimals). For example, 3.6 liters and 4.1 liters can be combined as 7.7 liters or 7700 milliliters. | Grade 5 |
| South Dakota | 5.MD.B.2 | Make a line plot to display a data set. a. Use operations on fractions of a unit (1/2, 1/4, 1/8) for this grade to solve problems involving information presented in line plots. b. Use information from a line plot representing an unequal situation and redistribute whole or fractional parts to create an equal distribution. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally | Grade 5 |
| South Dakota | 5.MD.C.3 | Recognize volume as an attribute of solid figures and understand concepts of volume measurement. a. A cube with side length 1 unit, called a “unit cube,” is said to have “one cubic unit” of volume, and can be used to measure volume. b. A solid figure which can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units. | Grade 5 |
| South Dakota | 5.MD.C.4 | Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. | Grade 5 |
| South Dakota | 5.MD.C.5 | Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume. a. Find the volume of a right rectangular prism with whole-number side lengths by packing it with unit cubes, and show that the volume is the same as would be found by multiplying the edge lengths, equivalently by multiplying the height by the area of the base. b. Represent threefold whole-number products as volumes, e.g., to represent the associative property of multiplication. c. Apply the formulas V = l × w × h and V = B × h (where B is the area of the base) for rectangular prisms to find volumes of right rectangular prisms with whole number edge lengths in the context of solving real world and mathematical problems. d. Recognize volume as additive. Find volumes of solid figures composed of two non-overlapping right rectangular prisms by adding the volumes of the non-overlapping parts, applying this technique to solve real world problems. | Grade 5 |
| South Dakota | 5.G.A.1 | Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate). | Grade 5 |
| South Dakota | 5.G.A.2 | Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. | Grade 5 |
| South Dakota | 5.G.B.3 | Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. | Grade 5 |
| South Dakota | 5.G.B.4 | Classify two-dimensional figures in a hierarchy based on properties. For example, all rectangles are parallelograms, because they are all quadrilaterals with two pairs of opposite, parallel, equal-length sides. | Grade 5 |
| South Dakota | 6.RP.A.1 | Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. | Grade 6 |
| South Dakota | 6.RP.A.2 | Understand the concept of a unit rate a/b associated with a ratio a:b with b not equal to 0, and use rate language in the context of a ratio relationship. | Grade 6 |
| South Dakota | 6.RP.A.3 | Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. a. Make tables of equivalent ratios relating quantities with whole number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios. b. Solve unit rate problems including those involving unit pricing and constant speed. For example, if it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed c. Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent. d. Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities. | Grade 6 |
| South Dakota | 6.NS.A.1 | Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. For example, create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi? | Grade 6 |
| South Dakota | 6.NS.B.2 | Fluently divide multi-digit numbers using an algorithm including but not limited to the standard algorithm. | Grade 6 |
| South Dakota | 6.NS.B.3 | Fluently add, subtract, multiply, and divide multi-digit decimals using an algorithm including but not limited to the standard algorithm for each operation. | Grade 6 |
| South Dakota | 6.NS.C.5 | Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation. | Grade 6 |
| South Dakota | 6.NS.C.6 | Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates. a. Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line; recognize that the opposite of the opposite of a number is the number itself, e.g., –(–3) = 3, and that 0 is its own opposite. b. Understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane; recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes. c. Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. | Grade 6 |
| South Dakota | 6.NS.C.7 | Understand ordering and absolute value of rational numbers. a. Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram. b. Write, interpret, and explain statements of order for rational numbers in real-world contexts. c. Understand the absolute value of a rational number as its distance from 0 on the number line; interpret absolute value as magnitude for a positive or negative quantity in a real-world situation. d. Distinguish comparisons of absolute value from statements about order. | Grade 6 |
| South Dakota | 6.NS.C.8 | Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. | Grade 6 |
| South Dakota | 6.EE.A.1 | Write and evaluate numerical expressions involving whole-number exponents (e.g. parentheses, brackets, or braces). | Grade 6 |
| South Dakota | 6.EE.A.2 | Write, read, and evaluate expressions in which letters stand for numbers. a. Write expressions that record operations with numbers and with letters standing for numbers. For example, express the calculation Subtract y from 5 as 5-y. b. Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient); view one or more parts of an expression as a single entity. For example, describe the expression 2 (8 + 7) as a product of two factors; view (8 +7) as both a single entity and a sum of two terms. c. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. d. Perform arithmetic operations following the order of operations with and without parentheses, including those involving whole-number exponents. | Grade 6 |
| South Dakota | 6.EE.A.3 | Apply the properties of operations to generate equivalent expressions with an emphasis on the distributive property. | Grade 6 |
| South Dakota | 6.EE.A.4 | Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). | Grade 6 |
| South Dakota | 6.EE.B.5 | Understand solving an equation or inequality is a process in which you determine values from a set that make an equation or inequality true. Use substitution to determine whether a given number in a specified set makes an equation or inequality true. | Grade 6 |
| South Dakota | 6.EE.B.6 | Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set. | Grade 6 |
| South Dakota | 6.EE.B.7 | Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers. | Grade 6 |
| South Dakota | 6.EE.B.8 | Write an inequality of the form x > c, x > c, x < c or x < c which represents a condition or constraint in a real-world or mathematical problem. Recognize that inequalities have infinitely many solutions; represent solutions of inequalities on number line diagrams. | Grade 6 |
| South Dakota | 6.EE.C.9 | Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. | Grade 6 |
| South Dakota | 6.G.A.1 | Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems. | Grade 6 |
| South Dakota | 6.G.A.2 | Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas V = lwh and V = Bh where B is the area of the base to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems. | Grade 6 |
| South Dakota | 6.G.A.3 | Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems. | Grade 6 |
| South Dakota | 6.G.A.4 | Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems. | Grade 6 |
| South Dakota | 6.SP.B.5 | Summarize numerical data sets in relation to their context, such as by: a. Reporting the number of observations. b. Describing the nature of the attribute under investigation, including how it was measured and its units of measurement. c. Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered. d. Relating the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered. | Grade 6 |
| South Dakota | 7.RP.A.1 | Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. For example, if a person walks 1/2 mile in each 1/4 hour, compute the unit rate as the complex fraction 1/2/1/4 miles per hour, equivalently 2 miles per hour. | Grade 7 |
| South Dakota | 7.RP.A.2 | Recognize and represent proportional relationships between quantities. a. Decide whether two quantities are in a proportional relationship. For example, by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin. b. Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships. c. Represent proportional relationships by equations. For example, if total cost t is proportional to the number n of items. Purchased at a constant price p, the relationship between the total cost and the number of items can be expressed as t = pn. d. Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r) where r is the unit rate. | Grade 7 |
| South Dakota | 7.RP.A.3 | Use proportional relationships to solve multistep ratio and percent problems. For example, simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error. | Grade 7 |
| South Dakota | 7.NS.A.1 | Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram. a. Describe situations in which opposite quantities combine to make 0. For example, if you get paid $5 for babysitting but you owe your friend $5, you have $0. b. Understand p + q as the number located a distance |q| from p, in the positive or negative direction depending on whether q is positive or negative. Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing real-world contexts. c. Understand subtraction of rational numbers as adding the additive inverse, p – q = p + (–q). Show that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in real-world contexts. d. Apply properties of operations as strategies to add and subtract rational numbers. | Grade 7 |
| South Dakota | 7.NS.A.2 | Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers. a. Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as (–1)(–1) = 1 and the rules for multiplying signed numbers. Interpret products of rational numbers by describing real-world contexts. b. Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with non-zero divisor) is a rational number. If p and q are integers, then –(p/q) = (–p)/q = p/(–q). Interpret quotients of rational numbers by describing real world contexts. c. Apply properties of operations as strategies to multiply and divide rational numbers. d. Convert a rational number to a decimal using long division; know that the decimal form of a rational number terminates in 0s or eventually repeats. | Grade 7 |
| South Dakota | 7.NS.A.3 | Solve real-world and mathematical problems involving the four operations with rational numbers. (Computations with rational numbers extend the rules for manipulating fractions to complex fractions.) | Grade 7 |
| South Dakota | 7.EE.A.1 | Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients to include multiple grouping symbols (parentheses, brackets, and/or braces). | Grade 7 |
| South Dakota | 7.EE.A.2 | Understand the reason for rewriting an expression in different forms in contextual problems is to provide multiple ways of interpreting the problem, and how the quantities in it are related. For example, a + 0.05a=1.05a means that increase by 5% is the same as "multiply by 1.05". | Grade 7 |
| South Dakota | 7.EE.A.3 | Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. a. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate. For example, if a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $27.50. b. Assess the reasonableness of answers using mental computation and estimation strategies. For example, if you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation. | Grade 7 |
| South Dakota | 7.EE.A.4 | Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. a. Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. b. Solve word problems leading to inequalities of the form px + q > r, px + q ≥ r, px + q < r, and px + q ≤ r where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem. For example, as a salesperson, you are paid $50 per week plus $3 per sale. This week you want your pay to be at least $100. Write an inequality for the number of sales you need to make, and describe the solutions. | Grade 7 |
| South Dakota | 7.G.A.1 | Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale. | Grade 7 |
| South Dakota | 7.G.A.2 | Draw (freehand, with ruler and protractor/angle ruler, and/or with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle. | Grade 7 |
| South Dakota | 7.G.A.3 | Describe the two-dimensional figures that result from slicing three-dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids. | Grade 7 |
| South Dakota | 7.G.B.4 | Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle. | Grade 7 |
| South Dakota | 7.G.B.5 | Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure. | Grade 7 |
| South Dakota | 7.G.B.6 | Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. | Grade 7 |
| South Dakota | 8.NS.A.2 | Use rational approximations of irrational numbers to compare the size of irrational numbers. Locate irrational numbers approximately on a number line diagram, and estimate the value of expressions such as (π²). For example, by truncating the decimal expansion of √2, show that √2 is between 1 and 2, then between 1.4 and 1.5, and explain how to continue on to get better approximations. | Grade 8 |
| South Dakota | 8.EE.A.1 | Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, 32 × 3-5 = 3-3 = 1/33 = 1/27. | Grade 8 |
| South Dakota | 8.EE.A.2 | Use square root and cube root symbols to represent solutions to equations of the form x² = p and x³ = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. | Grade 8 |
| South Dakota | 8.EE.A.3 | Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other. For example, estimate the population of the United States as 3 times 108 and the population of the world as 7 times 109, and determine that the world population is more than 20 times larger. | Grade 8 |
| South Dakota | 8.EE.A.4 | Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology. | Grade 8 |
| South Dakota | 8.EE.B.5 | Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed. | Grade 8 |
| South Dakota | 8.EE.B.6 | Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b. | Grade 8 |
| South Dakota | 8.EE.C.7 | Solve linear equations in one variable. a. Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x = a, a = a, or a = b results (where a and b are different numbers). b. Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and combining like terms. | Grade 8 |
| South Dakota | 8.EE.C.8 | Analyze and solve pairs of simultaneous linear equations. a. Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously. b. Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection. For an inspection example, 3x + 2y = 5 and 3x + 2y = 6 have no solution because 3x + 2y cannot simultaneously be 5 and 6. c. Solve real-world and mathematical problems involving leading to two linear equations in one and/or two variables. | Grade 8 |
| South Dakota | 8.F.A.1 | Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output. (Function notation is not required in Grade 8). | Grade 8 |
| South Dakota | 8.F.A.2 | Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a linear function represented by a table of values and a linear function represented by an algebraic expression, determine which function has the greater rate of change. | Grade 8 |
| South Dakota | 8.F.A.3 | Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. | Grade 8 |
| South Dakota | 8.F.B.4 | Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values. 5. | Grade 8 |
| South Dakota | 8.F.B.5 | Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally. | Grade 8 |
| South Dakota | 8.G.A.1 | Verify experimentally the properties of rotations, reflections, and translations. a. Lines are mapped to lines, and line segments to line segments of the same length. b. Angles are mapped to angles of the same measure. c. Parallel lines are mapped to parallel lines. | Grade 8 |
| South Dakota | 8.G.A.2 | Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them. | Grade 8 |
| South Dakota | 8.G.A.3 | Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates. | Grade 8 |
| South Dakota | 8.G.A.4 | Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two-dimensional figures, describe a sequence that exhibits the similarity between them. | Grade 8 |
| South Dakota | 8.G.A.5 | Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. For example, arrange three copies of the same triangle so that the sum of the three angles appears to form a line, and give an argument in terms of transversals why this is so. | Grade 8 |
| South Dakota | 8.G.B.7 | Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions. | Grade 8 |
| South Dakota | 8.G.B.8 | Apply the Pythagorean Theorem to find the distance between two points in a coordinate system. | Grade 8 |
| South Dakota | 8.G.C.9 | Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems. | Grade 8 |
| South Dakota | 8.SP.A.1 | Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association. | Grade 8 |
| South Dakota | 8.SP.A.2 | Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line (i.e. line of fit), and informally assess the model fit by judging the closeness of the data points to the line. | Grade 8 |
| South Dakota | A1.A.SSE.A.2 | Recognize and use the structure of an expression to identify ways to rewrite it. | Algebra I |
| South Dakota | A1.A.SSE.B.3 | Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression. | Algebra I |
| South Dakota | A1.A.CED.A.2 | Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. | Algebra I |
| South Dakota | A1.A.CED.A.3 | Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. | Algebra I |
| South Dakota | A1.A.REI.B.3 | Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. | Algebra I |
| South Dakota | A1.F.IF.A.2 | Use function notation, evaluate functions, and interpret statements that use function notation in terms of a context. | Algebra I |
| South Dakota | A1.F.IF.B.4 | For functions, including linear, quadratic, and exponential, that model a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing or decreasing, including using interval notation; maximums and minimums; symmetries. | Algebra I |
| South Dakota | A1.S.ID.B.6 | Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. | Algebra I |
| South Dakota | A2.A.SSE.A.2 | Recognize and use the structure of an expression to identify ways to rewrite it. | Algebra II |
| South Dakota | A2.A.APR.B.3 | Identify zeros of polynomials by factoring. | Algebra II |
| South Dakota | A2.F.IF.B.4 | For functions that model a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries (including even, odd, or neither); end behavior; and periodicity. | Algebra II |
| South Dakota | A2.F.BF.A.1 | Write a function that describes a relationship between two quantities. | Algebra II |
| South Dakota | 4Y.F.IF.C.7 | Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. | 4th Year Math |
| South Dakota | 4Y.F.BF.A.1 | Write a function that describes a relationship between two quantities. | 4th Year Math |
| Texas | K.2.A | Count forward and backward to at least 20 with and without objects. | Kindergarten |
| Texas | K.2.B | Read, write, and represent whole numbers from 0 to at least 20 with and without objects or pictures. | Kindergarten |
| Texas | K.2.C | Count a set of objects up to at least 20 and demonstrate that the last number said tells the number of objects in the set regardless of their arrangement or order. | Kindergarten |
| Texas | K.2.D | Recognize instantly the quantity of a small group of objects in organized and random arrangements. | Kindergarten |
| Texas | K.2.E | Generate a set using concrete and pictorial models that represents a number that is more than, less than, and equal to a given number up to 20. | Kindergarten |
| Texas | K.2.F | Generate a number that is one more than or one less than another number up to at least 20. | Kindergarten |
| Texas | K.2.G | Compare sets of objects up to at least 20 in each set using comparative language. | Kindergarten |
| Texas | K.2.H | Use comparative language to describe two numbers up to 20 presented as written numerals. | Kindergarten |
| Texas | K.2.I | Compose and decompose numbers up to 10 with objects and pictures. | Kindergarten |
| Texas | K.3.A | Model the action of joining to represent addition and the action of separating to represent subtraction. | Kindergarten |
| Texas | K.3.B | Solve word problems using objects and drawings to find sums up to 10 and differences within 10 | Kindergarten |
| Texas | K.4.A | Identify U.S. coins by name, including pennies, nickels, dimes, and quarters. | Kindergarten |
| Texas | K.5.A | Recite numbers up to at least 100 by ones and tens beginning with any given number. | Kindergarten |
| Texas | K.6.A | Identify two-dimensional shapes, including circles, triangles, rectangles, and squares as special rectangles. | Kindergarten |
| Texas | K.6.B | Identify three-dimensional solids, including cylinders, cones, spheres, and cubes, in the real world. | Kindergarten |
| Texas | K.6.C | Identify two-dimensional components of three-dimensional objects. | Kindergarten |
| Texas | K.6.D | Identify attributes of two-dimensional shapes using informal and formal geometric language interchangeably | Kindergarten |
| Texas | K.6.E | Classify and sort a variety of regular and irregular two- and three-dimensional figures regardless of orientation or size | Kindergarten |
| Texas | K.7.A | Give an example of a measurable attribute of a given object, including length, capacity, and weight. | Kindergarten |
| Texas | K.7.B | Compare two objects with a common measurable attribute to see which object has more of/less of the attribute and describe the difference. | Kindergarten |
| Texas | K.8.A | Collect, sort, and organize data into two or three categories. | Kindergarten |
| Texas | K.8.B | Use data to create real-object and picture graphs | Kindergarten |
| Texas | K.8.C | Draw conclusions from real-object and picture graphs. | Kindergarten |
| Texas | 1.2.A | Recognize instantly the quantity of structured arrangements. | Grade 1 |
| Texas | 1.2.B | Use concrete and pictorial models to compose and decompose numbers up to 120 in more than one way as so many hundreds, so many tens, and so many ones. | Grade 1 |
| Texas | 1.2.C | Use objects, pictures, and expanded and standard forms to represent numbers up to 120. | Grade 1 |
| Texas | 1.2.D | Generate a number that is greater than or less than a given whole number up to 120. | Grade 1 |
| Texas | 1.2.E | Use place value to compare whole numbers up to 120 using comparative language. | Grade 1 |
| Texas | 1.2.F | Order whole numbers up to 120 using place value and open number lines. | Grade 1 |
| Texas | 1.2.G | Represent the comparison of two numbers to 100 using the symbols >, <, or =. | Grade 1 |
| Texas | 1.3.A | Use concrete and pictorial models to determine the sum of a multiple of 10 and a one-digit number in problems up to 99. | Grade 1 |
| Texas | 1.3.B | Use objects and pictorial models to solve word problems involving joining, separating, and comparing sets within 20 and unknowns as any one of the terms in the problem such as 2 + 4 = [ ]; 3 + [ ] = 7; and 5 = [ ] - 3 | Grade 1 |
| Texas | 1.3.C | Compose 10 with two or more addends with and without concrete objects. | Grade 1 |
| Texas | 1.3.D | Apply basic fact strategies to add and subtract within 20, including making 10 and decomposing a number leading to a 10. | Grade 1 |
| Texas | 1.3.E | Explain strategies used to solve addition and subtraction problems up to 20 using spoken words, objects, pictorial models, and number sentences | Grade 1 |
| Texas | 1.3.F | Generate and solve problem situations when given a number sentence involving addition or subtraction of numbers within 20. | Grade 1 |
| Texas | 1.4.A | Identify U.S. coins, including pennies, nickels, dimes, and quarters, by value and describe the relationships among them. | Grade 1 |
| Texas | 1.5.A | Recite numbers forward and backward from any given number between 1 and 120. | Grade 1 |
| Texas | 1.5.B | Skip count by twos, fives, and tens to determine the total number of objects up to 120 in a set. | Grade 1 |
| Texas | 1.5.C | Use relationships to determine the number that is 10 more and 10 less than a given number up to 120. | Grade 1 |
| Texas | 1.5.D | Represent word problems involving addition and subtraction of whole numbers up to 20 using concrete and pictorial models and number sentences | Grade 1 |
| Texas | 1.5.E | Understand that the equal sign represents a relationship where expressions on each side of the equal sign represent the same value(s). | Grade 1 |
| Texas | 1.5.F | Determine the unknown whole number in an addition or subtraction equation when the unknown may be any one of the three or four terms in the equation. | Grade 1 |
| Texas | 1.5.G | Apply properties of operations to add and subtract two or three numbers. | Grade 1 |
| Texas | 1.6.A | Classify and sort regular and irregular two-dimensional shapes based on attributes using informal geometric language. | Grade 1 |
| Texas | 1.6.B | Distinguish between attributes that define a two-dimensional or three-dimensional figure and attributes that do not define the shape. | Grade 1 |
| Texas | 1.6.D | Identify two-dimensional shapes, including circles, triangles, rectangles, and squares, as special rectangles, rhombuses, and hexagons and describe their attributes using formal geometric language. | Grade 1 |
| Texas | 1.6.E | Identify three-dimensional solids, including spheres, cones, cylinders, rectangular prisms (including cubes), and triangular prisms, and describe their attributes using formal geometric language. | Grade 1 |
| Texas | 1.6.F | Compose two-dimensional shapes by joining two, three, or four figures to produce a target shape in more than one way if possible. | Grade 1 |
| Texas | 1.6.G | Partition two-dimensional figures into two and four fair shares or equal parts and describe the parts using words. | Grade 1 |
| Texas | 1.6.H | Identify examples and non-examples of halves and fourths. | Grade 1 |
| Texas | 1.7.A | Use measuring tools to measure the length of objects to reinforce the continuous nature of linear measurement. | Grade 1 |
| Texas | 1.7.B | Illustrate that the length of an object is the number of same-size units of length that, when laid end-to-end with no gaps or overlaps, reach from one end of the object to the other. | Grade 1 |
| Texas | 1.7.C | Measure the same object/distance with units of two different lengths and describe how and why the measurements differ. | Grade 1 |
| Texas | 1.7.D | Describe a length to the nearest whole unit using a number and a unit. | Grade 1 |
| Texas | 1.7.E | Tell time to the hour and half hour using analog and digital clocks. | Grade 1 |
| Texas | 1.8.A | Collect, sort, and organize data in up to three categories using models/representations such as tally marks or T-charts | Grade 1 |
| Texas | 1.8.B | Use data to create picture and bar-type graphs | Grade 1 |
| Texas | 1.8.C | Draw conclusions and generate and answer questions using information from picture and bar-type graphs. | Grade 1 |
| Texas | 2.10.A | Explain that the length of a bar in a bar graph or the number of pictures in a pictograph represents the number of data points for a given category | Grade 2 |
| Texas | 2.10.B | Organize a collection of data with up to four categories using pictographs and bar graphs with intervals of one or more. | Grade 2 |
| Texas | 2.10.C | Write and solve one-step word problems involving addition or subtraction using data represented within pictographs and bar graphs with intervals of one | Grade 2 |
| Texas | 2.10.D | Draw conclusions and make predictions from information in a graph. | Grade 2 |
| Texas | 2.2.A | Use concrete and pictorial models to compose and decompose numbers up to 1,200 in more than one way as a sum of so many thousands, hundreds, tens, and ones. | Grade 2 |
| Texas | 2.2.B | Use standard, word, and expanded forms to represent numbers up to 1,200 | Grade 2 |
| Texas | 2.2.C | Generate a number that is greater than or less than a given whole number up to 1,200. | Grade 2 |
| Texas | 2.2.D | Use place value to compare and order whole numbers up to 1,200 using comparative language, numbers, and symbols (>, <, or =). | Grade 2 |
| Texas | 2.2.E | Locate the position of a given whole number on an open number line. | Grade 2 |
| Texas | 2.2.F | Name the whole number that corresponds to a specific point on a number line. | Grade 2 |
| Texas | 2.3.A | Partition objects into equal parts and name the parts, including halves, fourths, and eighths, using words | Grade 2 |
| Texas | 2.3.B | Explain that the more fractional parts used to make a whole, the smaller the part; and the fewer the fractional parts, the larger the part. | Grade 2 |
| Texas | 2.3.C | Use concrete models to count fractional parts beyond one whole using words and recognize how many parts it takes to equal one whole. | Grade 2 |
| Texas | 2.3.D | Identify examples and non-examples of halves, fourths, and eighths. | Grade 2 |
| Texas | 2.4.A | Recall basic facts to add and subtract within 20 with automaticity. | Grade 2 |
| Texas | 2.4.B | Add up to four two-digit numbers and subtract two-digit numbers using mental strategies and algorithms based on knowledge of place value and properties of operations. | Grade 2 |
| Texas | 2.4.C | Solve one-step and multi-step word problems involving addition and subtraction within 1,000 using a variety of strategies based on place value, including algorithms. | Grade 2 |
| Texas | 2.4.D | Generate and solve problem situations for a given mathematical number sentence involving addition and subtraction of whole numbers within 1,000. | Grade 2 |
| Texas | 2.5.A | Determine the value of a collection of coins up to one dollar | Grade 2 |
| Texas | 2.5.B | Use the cent symbol, dollar sign, and the decimal point to name the value of a collection of coins. | Grade 2 |
| Texas | 2.6.A | Model, create, and describe contextual multiplication situations in which equivalent sets of concrete objects are joined | Grade 2 |
| Texas | 2.6.B | Model, create, and describe contextual division situations in which a set of concrete objects is separated into equivalent sets. | Grade 2 |
| Texas | 2.7.A | Determine whether a number up to 40 is even or odd using pairings of objects to represent the number | Grade 2 |
| Texas | 2.7.B | Use an understanding of place value to determine the number that is 10 or 100 more or less than a given number up to 1,200 | Grade 2 |
| Texas | 2.8.A | Create two dimensional shpaes based on given attributes including number of sides and vertices. | Grade 2 |
| Texas | 2.8.B | Classify and sort three-dimensional solids, including spheres, cones, cylinders, rectangular prisms (including cubes as special rectangular prisms), and triangular prisms, based on attributes using formal geometric language. | Grade 2 |
| Texas | 2.8.C | Classify and sort polygons with 12 or fewer sides according to attributes, including identifying the number of sides and number of vertices. | Grade 2 |
| Texas | 2.8.D | Compose two-dimensional shapes and three-dimensional solids with given properties or attributes | Grade 2 |
| Texas | 2.8.E | Decompose two-dimensional shapes such as cutting out a square from a rectangle, dividing a shape in half, or partitioning a rectangle into identical triangles and identify the resulting geometric parts. | Grade 2 |
| Texas | 2.9.A | Find the length of objects using concrete models for standard units of length. | Grade 2 |
| Texas | 2.9.B | Describe the inverse relationship between the size of the unit and the number of units needed to equal the length of an object | Grade 2 |
| Texas | 2.9.C | Represent whole numbers as distances from any given location on a number line. | Grade 2 |
| Texas | 2.9.D | Determine the length of an object to the nearest marked unit using rulers, yardsticks, meter sticks, or measuring tapes. | Grade 2 |
| Texas | 2.9.E | Determine a solution to a problem involving length, including estimating lengths. | Grade 2 |
| Texas | 2.9.F | Use concrete models of square units to find the area of a rectangle by covering it with no gaps or overlaps, counting to find the total number of square units, and describing the measurement using a number and the unit. | Grade 2 |
| Texas | 2.9.G | Read and write time to the nearest one-minute increment using analog and digital clocks and distinguish between a.m. and p.m. | Grade 2 |
| Texas | 3.2.A | Compose and decompose numbers up to 100,000 as a sum of so many ten thousands, so many thousands, so many hundreds, so many tens, and so many ones using objects, pictorial models, and numbers, including expanded notation as appropriate. | Grade 3 |
| Texas | 3.2.C | Represent a number on a number line as being between two consecutive multiples of 10; 100; 1,000; or 10,000 and use words to describe relative size of numbers in order to round whole numbers. | Grade 3 |
| Texas | 3.2.D | Compare and order whole numbers up to 100,000 and represent comparisons using the symbols >, <, or =. | Grade 3 |
| Texas | 3.3.A | Represent fractions greater than zero and less than or equal to one with denominators of 2, 3, 4, 6, and 8 using concrete objects and pictorial models, including strip diagrams and number lines. | Grade 3 |
| Texas | 3.3.B | Determine the corresponding fraction greater than zero and less than or equal to one with denominators of 2, 3, 4, 6, and 8 given a specified point on a number line. | Grade 3 |
| Texas | 3.3.C | Explain that the unit fraction 1/b represents the quantity formed by one part of a whole that has been partitioned into b equal parts where b is a non-zero whole number. | Grade 3 |
| Texas | 3.3.D | Compose and decompose a fraction a/b with a numerator greater than zero and less than or equal to b as a sum of parts 1/b. | Grade 3 |
| Texas | 3.3.E | Solve problems involving partitioning an object or a set of objects among two or more recipients using pictorial representations of fractions with denominators of 2, 3, 4, 6, and 8. | Grade 3 |
| Texas | 3.3.F | Represent equivalent fractions with denominators of 2, 3, 4, 6, and 8 using a variety of objects and pictorial models, including number lines. | Grade 3 |
| Texas | 3.3.G | Explain that two fractions are equivalent if and only if they are both represented by the same point on the number line or represent the same portion of a same size whole for an area model. | Grade 3 |
| Texas | 3.3.H | Compare two fractions having the same numerator or denominator in problems by reasoning about their sizes and justifying the conclusion using symbols, words, objects, and pictorial models. | Grade 3 |
| Texas | 3.4.A | Solve with fluency one-step and two-step problems involving addition and subtraction within 1,000 using strategies based on place value, properties of operations, and the relationship between addition and subtraction. | Grade 3 |
| Texas | 3.4.B | Round to the nearest 10 or 100 or use compatible numbers to estimate solutions to addition and subtraction problems. | Grade 3 |
| Texas | 3.4.D | Determine the total number of objects when equally-sized groups of objects are combined or arranged in arrays up to 10 by 10. | Grade 3 |
| Texas | 3.4.E | Represent multiplication facts by using a variety of approaches such as repeated addition, equal-sized groups, arrays, area models, equal jumps on a number line, and skip counting. | Grade 3 |
| Texas | 3.4.F | Recall facts to multiply up to 10 by 10 with automaticity and recall the corresponding division facts. | Grade 3 |
| Texas | 3.4.G | Use strategies and algorithms, including the standard algorithm, to multiply a two-digit number by a one-digit number. Strategies may include mental math, partial products, and the commutative, associative, and distributive properties. | Grade 3 |
| Texas | 3.4.H | Determine the number of objects in each group when a set of objects is partitioned into equal shares or a set of objects is shared equally. | Grade 3 |
| Texas | 3.4.I | Determine if a number is even or odd using divisibility rules. | Grade 3 |
| Texas | 3.4.J | Determine a quotient using the relationship between multiplication and division. | Grade 3 |
| Texas | 3.4.K | Solve one-step and two-step problems involving multiplication and division within 100 using strategies based on objects; pictorial models, including arrays, area models, and equal groups; properties of operations; or recall of facts. | Grade 3 |
| Texas | 3.5.A | Represent one- and two-step problems involving addition and subtraction of whole numbers to 1,000 using pictorial models, number lines, and equations. | Grade 3 |
| Texas | 3.5.B | Represent and solve one- and two-step multiplication and division problems within 100 using arrays, strip diagrams, and equations. | Grade 3 |
| Texas | 3.5.C | Describe a multiplication expression as a comparison such as 3 x 24 represents 3 times as much as 24. | Grade 3 |
| Texas | 3.5.D | Determine the unknown whole number in a multiplication or division equation relating three whole numbers when the unknown is either a missing factor or product. | Grade 3 |
| Texas | 3.6.A | Classify and sort two- and three-dimensional figures, including cones, cylinders, spheres, triangular and rectangular prisms, and cubes, based on attributes using formal geometric language. | Grade 3 |
| Texas | 3.6.B | Use attributes to recognize rhombuses, parallelograms, trapezoids, rectangles, and squares as examples of quadrilaterals and draw examples of quadrilaterals that do not belong to any of these subcategories. | Grade 3 |
| Texas | 3.6.C | Determine the area of rectangles with whole number side lengths in problems using multiplication related to the number of rows times the number of unit squares in each row. | Grade 3 |
| Texas | 3.6.D | Decompose composite figures formed by rectangles into non-overlapping rectangles to determine the area of the original figure using the additive property of area. | Grade 3 |
| Texas | 3.6.E | Decompose two congruent two-dimensional figures into parts with equal areas and express the area of each part as a unit fraction of the whole and recognize that equal shares of identical wholes need not have the same shape. | Grade 3 |
| Texas | 3.7.A | Represent fractions of halves, fourths, and eighths as distances from zero on a number line. | Grade 3 |
| Texas | 3.7.B | Determine the perimeter of a polygon or a missing length when given perimeter and remaining side lengths in problems. | Grade 3 |
| Texas | 3.7.C | Determine the solutions to problems involving addition and subtraction of time intervals in minutes using pictorial models or tools such as a 15-minute event plus a 30-minute event equals 45 minutes. | Grade 3 |
| Texas | 3.7.D | Determine when it is appropriate to use measurements of liquid volume (capacity) or weight. | Grade 3 |
| Texas | 3.7.E | Determine liquid volume (capacity) or weight using appropriate units and tools. | Grade 3 |
| Texas | 3.8.A | Summarize a data set with multiple categories using a frequency table, dot plot, pictograph, or bar graph with scaled intervals. | Grade 3 |
| Texas | 3.8.B | Solve one- and two-step problems using categorical data represented with a frequency table, dot plot, pictograph, or bar graph with scaled intervals. | Grade 3 |
| Texas | 4.2.A | Interpret the value of each place-value position as 10 times the position to the right and as one-tenth of the value of the place to its left. | Grade 4 |
| Texas | 4.2.B | Represent the value of the digit in whole numbers through 1,000,000,000 and decimals to the hundredths using expanded notation and numerals. | Grade 4 |
| Texas | 4.2.C | Compare and order whole numbers to 1,000,000,000 and represent comparisons using the symbols >, <, or =. | Grade 4 |
| Texas | 4.2.D | Round whole numbers to a given place value through the hundred thousands place. | Grade 4 |
| Texas | 4.2.E | Represent decimals, including tenths and hundredths, using concrete and visual models and money. | Grade 4 |
| Texas | 4.2.F | Compare and order decimals using concrete and visual models to the hundredths. | Grade 4 |
| Texas | 4.2.G | Relate decimals to fractions that name tenths and hundredths. | Grade 4 |
| Texas | 4.2.H | Determine the corresponding decimal to the tenths or hundredths place of a specified point on a number line. | Grade 4 |
| Texas | 4.3.A | Represent a fraction a/b as a sum of fractions 1/b, where a and b are whole numbers and b > 0, including when a > b. | Grade 4 |
| Texas | 4.3.B | Decompose a fraction in more than one way into a sum of fractions with the same denominator using concrete and pictorial models and recording results with symbolic representations. | Grade 4 |
| Texas | 4.3.C | Determine if two given fractions are equivalent using a variety of methods. | Grade 4 |
| Texas | 4.3.D | Compare two fractions with different numerators and different denominators and represent the comparison using the symbols >, =, or <. | Grade 4 |
| Texas | 4.3.E | Represent and solve addition and subtraction of fractions with equal denominators using objects and pictorial models that build to the number line and properties of operations. | Grade 4 |
| Texas | 4.3.G | Represent fractions and decimals to the tenths or hundredths as distances from zero on a number line. | Grade 4 |
| Texas | 4.4.A | Add and subtract whole numbers and decimals to the hundredths place using the standard algorithm. | Grade 4 |
| Texas | 4.4.B | Determine products of a number and 10 or 100 using properties of operations and place value understandings. | Grade 4 |
| Texas | 4.4.C | Represent the product of 2 two-digit numbers using arrays, area models, or equations, including perfect squares through 15 by 15. | Grade 4 |
| Texas | 4.4.D | Use strategies and algorithms, including the standard algorithm, to multiply up to a four-digit number by a one-digit number and to multiply a two-digit number by a two-digit number. Strategies may include mental math, partial products, and the commutative, associative, and distributive properties. | Grade 4 |
| Texas | 4.4.E | Represent the quotient of up to a four-digit whole number divided by a one-digit whole number using arrays, area models, or equations. | Grade 4 |
| Texas | 4.4.F | Use strategies and algorithms, including the standard algorithm, to divide up to a four- digit dividend by a one-digit divisor. | Grade 4 |
| Texas | 4.4.G | Round to the nearest 10, 100, or 1,000 or use compatible numbers to estimate solutions involving whole numbers. | Grade 4 |
| Texas | 4.4.H | Solve with fluency one- and two-step problems involving multiplication and division, including interpreting remainders. | Grade 4 |
| Texas | 4.5.A | Represent multi-step problems involving the four operations with whole numbers using strip diagrams and equations with a letter standing for the unknown quantity. | Grade 4 |
| Texas | 4.5.B | Represent problems using an input-output table and numerical expressions to generate a number pattern that follows a given rule representing the relationship of the values in the resulting sequencing and their position in the sequence. | Grade 4 |
| Texas | 4.5.C | Use models to determine the formulas for the perimeter of a rectangle (l + w + l + w or 2l + 2w), including the special form for perimeter of a square (4s) and the area of a rectangle (l x w). | Grade 4 |
| Texas | 4.5.D | Solve problems related to perimeter and area of rectangles where dimensions are whole numbers. | Grade 4 |
| Texas | 4.6.A | Identify points, lines, line segments, rays, angles, and perpendicular and parallel lines. | Grade 4 |
| Texas | 4.6.B | Identify and draw one or more lines of symmetry, if they exist, for a two-dimensional figure. | Grade 4 |
| Texas | 4.6.C | Apply knowledge of right angles to identify acute, right, and obtuse triangles. | Grade 4 |
| Texas | 4.6.D | Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines or the presence or absence of angles of specified size. | Grade 4 |
| Texas | 4.7.A | Illustrate the measure of an angle as the part of a circle whose center is at the vertex of the angle that is cut out by the rays of the angle. Angle measures are limited to whole numbers. | Grade 4 |
| Texas | 4.7.B | Illustrate degrees as the units used to measure an angle, where 1/360 of any circle is one degree and an angle that cuts n/360 out of any circle whose center is at the angle's vertex has a measure of n degrees. Angle measures are limited to whole numbers. | Grade 4 |
| Texas | 4.7.C | Determine the approximate measures of angles in degrees to the nearest whole number using a protractor. | Grade 4 |
| Texas | 4.7.D | Draw an angle with a given measure. | Grade 4 |
| Texas | 4.7.E | Determine the measure of an unknown angle formed by two non overlapping adjacent angles given one or both angle measures. | Grade 4 |
| Texas | 4.8.A | Identify relative sizes of measurement units within the customary and metric systems. | Grade 4 |
| Texas | 4.8.B | Convert measurements within the same measurement system, customary or metric, from a smaller unit into a larger unit or a larger unit into a smaller unit when given other equivalent measures represented in a table. | Grade 4 |
| Texas | 4.8.C | Solve problems that deal with measurements of length, intervals of time, liquid volumes, mass, and money using addition, subtraction, multiplication, or division as appropriate. | Grade 4 |
| Texas | 4.9.A | Represent data on a frequency table, dot plot, or stem-and-leaf plot marked with whole numbers and fractions. | Grade 4 |
| Texas | 4.9.B | Solve one- and two-step problems using data in whole number, decimal, and fraction form in a frequency table, dot plot, or stem-and-leaf plot. | Grade 4 |
| Texas | 5.2.A | Represent the value of the digit in decimals through the thousandths using expanded notation and numerals. | Grade 5 |
| Texas | 5.2.B | Compare and order two decimals to thousandths and represent comparisons using the symbols >, <, or =. | Grade 5 |
| Texas | 5.2.C | Round decimals to tenths or hundredths. | Grade 5 |
| Texas | 5.3.A | Estimate to determine solutions to mathematical and real-world problems involving addition, subtraction, multiplication, or division. | Grade 5 |
| Texas | 5.3.B | Multiply with fluency a three-digit number by a two-digit number using the standard algorithm. | Grade 5 |
| Texas | 5.3.C | Solve with proficiency for quotients of up to a four-digit dividend by a two-digit divisor using strategies and the standard algorithm. | Grade 5 |
| Texas | 5.3.D | Represent multiplication of decimals with products to the hundredths using objects and pictorial models, including area models. | Grade 5 |
| Texas | 5.3.E | Solve for products of decimals to the hundredths, including situations involving money, using strategies based on place-value understandings, properties of operations, and the relationship to the multiplication of whole numbers. | Grade 5 |
| Texas | 5.3.F | Represent quotients of decimals to the hundredths, up to four-digit dividends and two- digit whole number divisors, using objects and pictorial models, including area models. | Grade 5 |
| Texas | 5.3.G | Solve for quotients of decimals to the hundredths, up to four-digit dividends and two-digit whole number divisors, using strategies and algorithms, including the standard algorithm. | Grade 5 |
| Texas | 5.3.H | Represent and solve addition and subtraction of fractions with unequal denominators referring to the same whole using objects and pictorial models and properties of operations. | Grade 5 |
| Texas | 5.3.I | Represent and solve multiplication of a whole number and a fraction that refers to the same whole using objects and pictorial models, including area models. | Grade 5 |
| Texas | 5.3.J | Represent division of a unit fraction by a whole number and the division of a whole number by a unit fraction such as 1/3 ? 7 and 7 ? 1/3 using objects and pictorial models, including area models. | Grade 5 |
| Texas | 5.3.K | Add and subtract positive rational numbers fluently. | Grade 5 |
| Texas | 5.3.L | Divide whole numbers by unit fractions and unit fractions by whole numbers. | Grade 5 |
| Texas | 5.4.A | Identify prime and composite numbers. | Grade 5 |
| Texas | 5.4.B | Represent and solve multi-step problems involving the four operations with whole numbers using equations with a letter standing for the unknown quantity. | Grade 5 |
| Texas | 5.4.E | Describe the meaning of parentheses and brackets in a numeric expression. | Grade 5 |
| Texas | 5.4.F | Simplify numerical expressions that do not involve exponents, including up to two levels of grouping. | Grade 5 |
| Texas | 5.4.G | Use concrete objects and pictorial models to develop the formulas for the volume of a rectangular prism, including the special form for a cube 5.4.V = l x w x h, V = s x s x s, and V = Bh). | Grade 5 |
| Texas | 5.4.H | Represent and solve problems related to perimeter and/or area and related to volume. | Grade 5 |
| Texas | 5.5.A | Classify two-dimensional figures in a hierarchy of sets and subsets using graphic organizers based on their attributes and properties. | Grade 5 |
| Texas | 5.6.A | Recognize a cube with side length of one unit as a unit cube having one cubic unit of volume and the volume of a three-dimensional figure as the number of unit cubes (n cubic units) needed to fill it with no gaps or overlaps if possible. | Grade 5 |
| Texas | 5.6.B | Determine the volume of a rectangular prism with whole number side lengths in problems related to the number of layers times the number of unit cubes in the area of the base. | Grade 5 |
| Texas | 5.7.A | Solve problems by calculating conversions within a measurement system, customary or metric. | Grade 5 |
| Texas | 5.8.A | Describe the key attributes of the coordinate plane, including perpendicular number lines (axes) where the intersection (origin) of the two lines coincides with zero on each number line and the given point (0, 0); the x-coordinate, the first number in an ordered pair, indicates movement parallel to the x-axis starting at the origin; and the y-coordinate, the second number, indicates movement parallel to the y-axis starting at the origin. | Grade 5 |
| Texas | 5.8.B | Describe the process for graphing ordered pairs of numbers in the first quadrant of the coordinate plane. | Grade 5 |
| Texas | 5.8.C | Graph in the first quadrant of the coordinate plane ordered pairs of numbers arising from mathematical and real-world problems, including those generated by number patterns or found in an input-output table. | Grade 5 |
| Texas | 5.9.A | Represent categorical data with bar graphs or frequency tables and numerical data, including data sets of measurements in fractions or decimals, with dot plots or stem-and-leaf plots. | Grade 5 |
| Texas | 5.9.C | Solve one- and two-step problems using data from a frequency table, dot plot, bar graph, stem-and-leaf plot, or scatterplot. | Grade 5 |
| Texas | 6.10.A | Model and solve one-variable, one-step equations and inequalities that represent problems, including geometric concepts. | Grade 6 |
| Texas | 6.10.B | Determine if the given value(s) make(s) one-variable, one-step equations or inequalities true. | Grade 6 |
| Texas | 6.11.A | Graph points in all four quadrants using ordered pairs of rational numbers. | Grade 6 |
| Texas | 6.12.C | Summarize numeric data with numerical summaries, including the mean and median (measures of center) and the range and interquartile range (IQR) (measures of spread), and use these summaries to describe the center, spread, and shape of the data distribution. | Grade 6 |
| Texas | 6.2.B | Identify a number, its opposite, and its absolute value. | Grade 6 |
| Texas | 6.2.C | Locate, compare, and order integers and rational numbers using a number line. | Grade 6 |
| Texas | 6.2.D | Order a set of rational numbers arising from mathematical and real-world contexts. | Grade 6 |
| Texas | 6.2.E | Extend representations for division to include fraction notation such as a/b represents the same number as a ? b where b ? 0. | Grade 6 |
| Texas | 6.3.C | Represent integer operations with concrete models and connect the actions with the models to standardized algorithms. | Grade 6 |
| Texas | 6.3.D | Add, subtract, multiply, and divide integers fluently. | Grade 6 |
| Texas | 6.3.E | Multiply and divide positive rational numbers fluently. | Grade 6 |
| Texas | 6.4.A | Compare two rules verbally, numerically, graphically, and symbolically in the form of y = ax or y = x + a in order to differentiate between additive and multiplicative relationships. | Grade 6 |
| Texas | 6.4.B | Apply qualitative and quantitative reasoning to solve prediction and comparison of real-world problems involving ratios and rates. | Grade 6 |
| Texas | 6.4.C | Give examples of ratios as multiplicative comparisons of two quantities describing the same attribute. | Grade 6 |
| Texas | 6.4.E | Represent ratios and percents with concrete models, fractions, and decimals. | Grade 6 |
| Texas | 6.4.F | Represent benchmark fractions and percents such as 1%, 10%, 25%, 33 1/3%, and multiples of these values using 10 by 10 grids, strip diagrams, number lines, and numbers. | Grade 6 |
| Texas | 6.4.H | Convert units within a measurement system, including the use of proportions and unit rates. | Grade 6 |
| Texas | 6.5.A | Represent mathematical and real-world problems involving ratios and rates using scale factors, tables, graphs, and proportions. | Grade 6 |
| Texas | 6.5.B | Solve real-world problems to find the whole given a part and the percent, to find the part given the whole and the percent, and to find the percent given the part and the whole, including the use of concrete and pictorial models. | Grade 6 |
| Texas | 6.5.C | Use equivalent fractions, decimals, and percents to show equal parts of the same whole. | Grade 6 |
| Texas | 6.6.B | Write an equation that represents the relationship between independent and dependent quantities from a table. | Grade 6 |
| Texas | 6.6.C | Represent a given situation using verbal descriptions, tables, graphs, and equations in the form y = kx or y = x + b. | Grade 6 |
| Texas | 6.7.A | Generate equivalent numerical expressions using order of operations, including whole number exponents and prime factorization. | Grade 6 |
| Texas | 6.7.C | Determine if two expressions are equivalent using concrete models, pictorial models, and algebraic representations. | Grade 6 |
| Texas | 6.7.D | Generate equivalent expressions using the properties of operations: inverse, identity, commutative, associative, and distributive properties. | Grade 6 |
| Texas | 6.8.A | Extend previous knowledge of triangles and their properties to include the sum of angles of a triangle, the relationship between the lengths of sides and measures of angles in a triangle, and determining when three lengths form a triangle. | Grade 6 |
| Texas | 6.8.C | Write equations that represent problems related to the area of rectangles, parallelograms, trapezoids, and triangles and volume of right rectangular prisms where dimensions are positive rational numbers. | Grade 6 |
| Texas | 6.8.D | Determine solutions for problems involving the area of rectangles, parallelograms, trapezoids, and triangles and volume of right rectangular prisms where dimensions are positive rational numbers. | Grade 6 |
| Texas | 6.9.A | Write one-variable, one-step equations and inequalities to represent constraints or conditions within problems. | Grade 6 |
| Texas | 6.9.B | Represent solutions for one-variable, one-step equations and inequalities on number lines. | Grade 6 |
| Texas | 7.10.A | Write one-variable, two-step equations and inequalities to represent constraints or conditions within problems. | Grade 7 |
| Texas | 7.10.B | Represent solutions for one-variable, two-step equations and inequalities on number lines. | Grade 7 |
| Texas | 7.10.C | Write a corresponding real-world problem given a one-variable, two-step equation or inequality. | Grade 7 |
| Texas | 7.11.A | Model and solve one-variable, two-step equations and inequalities. | Grade 7 |
| Texas | 7.11.B | Determine if the given value(s) make(s) one-variable, two-step equations and inequalities true. | Grade 7 |
| Texas | 7.11.C | Write and solve equations using geometry concepts, including the sum of the angles in a triangle and angle relationships. | Grade 7 |
| Texas | 7.3.A | Add, subtract, multiply, and divide rational numbers fluently. | Grade 7 |
| Texas | 7.3.B | Apply and extend previous understandings of operations to solve problems using addition, subtraction, multiplication, and division of rational numbers. | Grade 7 |
| Texas | 7.5.A | Generalize the critical attributes of similarity, including ratios within and between similar shapes. | Grade 7 |
| Texas | 7.5.C | Solve mathematical and real-world problems involving similar shape and scale drawings. | Grade 7 |
| Texas | 7.7.A | Represent linear relationships using verbal descriptions, tables, graphs, and equations that simplify to the form y = mx + b. | Grade 7 |
| Texas | 7.8.A | Model the relationship between the volume of a rectangular prism and a rectangular pyramid having both congruent bases and heights and connect that relationship to the formulas. | Grade 7 |
| Texas | 7.8.B | Explain verbally and symbolically the relationship between the volume of a triangular prism and a triangular pyramid having both congruent bases and heights and connect that relationship to the formulas. | Grade 7 |
| Texas | 7.8.C | Use models to determine the approximate formulas for the circumference and area of a circle and connect the models to the actual formulas. | Grade 7 |
| Texas | 7.9.A | Solve problems involving the volume of rectangular prisms, triangular prisms, rectangular pyramids, and triangular pyramids. | Grade 7 |
| Texas | 7.9.B | Determine the circumference and area of circles. | Grade 7 |
| Texas | 7.9.D | Solve problems involving the lateral and total surface area of a rectangular prism, rectangular pyramid, triangular prism, and triangular pyramid by determining the area of the shape's net. | Grade 7 |
| Texas | 8.10.A | Generalize the properties of orientation and congruence of rotations, reflections, translations, and dilations of two-dimensional shapes on a coordinate plane. | Grade 8 |
| Texas | 8.10.C | Explain the effect of translations, reflections over the x- or y-axis, and rotations limited to 90 degrees, 180 degrees, 270 degrees, and 360 degrees as applied to two-dimensional shapes on a coordinate plane using an algebraic representation. | Grade 8 |
| Texas | 8.11.A | Construct a scatterplot and describe the observed data to address questions of association such as linear, non-linear, and no association between bivariate data. | Grade 8 |
| Texas | 8.2.B | Approximate the value of an irrational number, including pi and square roots of numbers less than 225, and locate that rational number approximation on a number line. | Grade 8 |
| Texas | 8.2.C | Convert between standard decimal notation and scientific notation. | Grade 8 |
| Texas | 8.4.A | Use similar right triangles to develop an understanding that slope, m, given as the rate comparing the change in y-values to the change in x-values, (y2 - y1)/ (x2 - x1), is the same for any two points (x1, y1) and (x2, y2) on the same line. | Grade 8 |
| Texas | 8.4.B | Graph proportional relationships, interpreting the unit rate as the slope of the line that models the relationship. | Grade 8 |
| Texas | 8.4.C | Use data from a table or graph to determine the rate of change or slope and y-intercept in mathematical and real-world problems. | Grade 8 |
| Texas | 8.5.A | Represent linear proportional situations with tables, graphs, and equations in the form of y = kx. | Grade 8 |
| Texas | 8.5.B | Represent linear non-proportional situations with tables, graphs, and equations in the form of y = mx + b, where b ? 0. | Grade 8 |
| Texas | 8.5.I | Write an equation in the form y = mx + b to model a linear relationship between two quantities using verbal, numerical, tabular, and graphical representations. | Grade 8 |
| Texas | 8.6.A | Describe the volume formula V = Bh of a cylinder in terms of its base area and its height. | Grade 8 |
| Texas | 8.6.B | Model the relationship between the volume of a cylinder and a cone having both congruent bases and heights and connect that relationship to the formulas. | Grade 8 |
| Texas | 8.7.A | Solve problems involving the volume of cylinders, cones, and spheres. | Grade 8 |
| Texas | 8.7.C | Use the Pythagorean Theorem and its converse to solve problems. | Grade 8 |
| Texas | 8.7.D | Determine the distance between two points on a coordinate plane using the Pythagorean Theorem. | Grade 8 |
| Texas | 8.8.A | Write one-variable equations or inequalities with variables on both sides that represent problems using rational number coefficients and constants. | Grade 8 |
| Texas | 8.8.B | Write a corresponding real-world problem when given a one-variable equation or inequality with variables on both sides of the equal sign using rational number coefficients and constants. | Grade 8 |
| Texas | 8.8.C | Model and solve one-variable equations with variables on both sides of the equal sign that represent mathematical and real-world problems using rational number coefficients and constants. | Grade 8 |
| Texas | 8.8.D | Use informal arguments to establish facts about the angle sum and exterior angle of triangles, the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. | Grade 8 |
| Texas | 8.9.A | Identify and verify the values of x and y that simultaneously satisfy two linear equations in the form y = mx + b from the intersections of the graphed equations. | Grade 8 |
| Texas | A.10.B | Multiply polynomials of degree one and degree two. | Algebra |
| Texas | A.10.D | Rewrite polynomial expressions of degree one and degree two in equivalent forms using the distributive property. | Algebra |
| Texas | A.10.E | Factor, if possible, trinomials with real factors in the form ax^2 + bx + c, including perfect square trinomials of degree two. | Algebra |
| Texas | A.11.A | Simplify numerical radical expressions involving square roots. | Algebra |
| Texas | A.11.B | Simplify numeric and algebraic expressions using the laws of exponents, including integral and rational exponents. | Algebra |
| Texas | A.2.B | Write linear equations in two variables in various forms, including y = mx + b, Ax + By = C, and y - y1 = m(x - x1), given one point and the slope and given two points. | Algebra |
| Texas | A.2.C | Write linear equations in two variables given a table of values, a graph, and a verbal description. | Algebra |
| Texas | A.2.D | Write and solve equations involving direct variation. | Algebra |
| Texas | A.3.A | Determine the slope of a line given a table of values, a graph, two points on the line, and an equation written in various forms, including y = mx + b, Ax + By = C, and y - y1 = m(x - x1). | Algebra |
| Texas | A.3.B | Calculate the rate of change of a linear function represented tabularly, graphically, or algebraically in context of mathematical and real-world problems. | Algebra |
| Texas | A.3.C | Graph linear functions on the coordinate plane and identify key features, including x-intercept, y-intercept, zeros, and slope, in mathematical and real-world problems. | Algebra |
| Texas | A.3.E | Determine the effects on the graph of the parent function f(x) = x when f(x) is replaced by af(x), f(x) + d, f(x - c), f(bx) for specific values of a, b, c, and d. | Algebra |
| Texas | A.3.F | Graph systems of two linear equations in two variables on the coordinate plane and determine the solutions if they exist. | Algebra |
| Texas | A.4.C | Write, with and without technology, linear functions that provide a reasonable fit to data to estimate solutions and make predictions for real-world problems. | Algebra |
| Texas | A.5.A | Solve linear equations in one variable, including those for which the application of the distributive property is necessary and for which variables are included on both sides. | Algebra |
| Texas | A.6.B | Write equations of quadratic functions given the vertex and another point on the graph, write the equation in vertex form (f(x) = a(x - h)^2+ k), and rewrite the equation from vertex form to standard form (f(x) = ax^2+ bx + c). | Algebra |
| Texas | A.7.A | Graph quadratic functions on the coordinate plane and use the graph to identify key attributes, if possible, including x-intercept, y-intercept, zeros, maximum value, minimum values, vertex, and the equation of the axis of symmetry. | Algebra |
| Texas | A.7.B | Describe the relationship between the linear factors of quadratic expressions and the zeros of their associated quadratic functions. | Algebra |
| Texas | A.7.C | Determine the effects on the graph of the parent function f(x) = x^2 when f(x) is replaced by af(x), f(x) + d, f(x - c), f(bx) for specific values of a, b, c, and d. | Algebra |
| Texas | A.8.B | Write, using technology, quadratic functions that provide a reasonable fit to data to estimate solutions and make predictions for real-world problems. | Algebra |
| Texas | A2.4.A | Write the quadratic function given three specified points in the plane. | Algebra |
| Texas | A2.6.A | Analyze the effect on the graphs of f(x) = x^3 and f(x) = x^(1/3) when f(x) is replaced by af(x), f(bx), f(x - c), and f(x) + d for specific positive and negative real values of a, b, c, and d. | Algebra |
| Tennessee | K.CC.A.1 | Count to 100 by ones, fives, and tens. Count backward from 10. | Kindergarten |
| Tennessee | K.CC.A.2 | Count forward by ones beginning from any given number within the known sequence (instead of having to begin at 1). | Kindergarten |
| Tennessee | K.CC.A.3 | Write numbers from 0 to 20. Represent a quantity of objects with a written number 0-20. | Kindergarten |
| Tennessee | K.CC.B.5 | Understand the relationship between numbers and quantities; connect counting to cardinality. a. When counting objects 1-20, say the number names in the standard order, using one-to-one correspondence. b. Recognize that the last number name said tells the number of objects counted. The number of objects is the same regardless of their arrangement or the order in which they were counted. c. Recognize that each successive number name refers to a quantity that is one greater and each previous number is one less. | Kindergarten |
| Tennessee | K.CC.B.6 | Count to answer “how many?” questions about as many as 20 things arranged in a line, a rectangular array, a circle, or as many as 10 things in a scattered configuration. Given a number from 1-20, count out that many objects. | Kindergarten |
| Tennessee | K.CC.C.7 | Identify whether the number of objects in one group is greater than, less than, or equal to the number of objects in another group. | Kindergarten |
| Tennessee | K.CC.C.8 | Compare two given numbers up to 10, when written as numerals, using the terms greater than, less than, or equal to. (Students need not use comparison symbols here.) | Kindergarten |
| Tennessee | K.OA.A.1 | Represent addition and subtraction with objects, fingers, drawings, acting out situations, verbal explanations, expressions, or equations. | Kindergarten |
| Tennessee | K.OA.A.2 | Add and subtract within 10 to solve contextual problems with result/total unknown involving situations of add to, take from, and put together/take apart. Use objects, drawings, or equations to represent the problem. | Kindergarten |
| Tennessee | K.OA.A.3 | Decompose numbers less than or equal to 10 into addend pairs in more than one way (e.g., 5 = 2 + 3 and 5 = 4 + 1) by using objects or drawings. Record each decomposition using a drawing or writing an equation. | Kindergarten |
| Tennessee | K.OA.A.4 | Find the number that makes 10, when added to any given number, from 1 to 9 using objects or drawings. Record the answer using a drawing or writing an equation. | Kindergarten |
| Tennessee | K.OA.A.5 | Use mental strategies flexibly to develop fluency in addition and subtraction within 10. | Kindergarten |
| Tennessee | K.NBT.A.1 | Compose and decompose numbers from 11 to 19 into a group of ten ones and some more ones by using objects or drawings (e.g., 18 equals 10 + 8). Record the composition or decomposition using a drawing or by writing an equation. | Kindergarten |
| Tennessee | K.MD.A.1 | Describe the measurable attributes of an object, such as length (long/short), height (tall/short), or weight (heavy/light). | Kindergarten |
| Tennessee | K.MD.A.2 | Directly compare two objects with a measurable attribute in common, to describe which object has more of/less of the attribute. For example, directly compare the heights of two children and describe one child as taller/shorter. | Kindergarten |
| Tennessee | K.MD.C.4 | Sort a collection of objects into a given category, with 10 or fewer in each category. Compare the categories by group size. | Kindergarten |
| Tennessee | K.G.A.1 | Describe objects in the environment using names of shapes and solids (squares, circles, triangles, rectangles, hexagons, cubes, cones, cylinders, and spheres). Describe the relative positions of these objects using terms such as above, below, beside, in front of, behind, between, and next to. | Kindergarten |
| Tennessee | K.G.A.2 | Correctly name shapes and solids (squares, circles, triangles, rectangles, hexagons, cubes, cones, cylinders, and spheres) regardless of their orientations or overall size. | Kindergarten |
| Tennessee | K.G.A.3 | Identify shapes/solids (squares, circles, triangles, rectangles, hexagons, cubes, cones, cylinders, and spheres) as two-dimensional or three-dimensional. | Kindergarten |
| Tennessee | K.G.B.4 | Describe similarities and differences between two- and three-dimensional shapes/solids, in different sizes and orientations. | Kindergarten |
| Tennessee | K.G.B.6 | Compose a figure using simple shapes/solids and identify smaller shapes/solids within the figure. | Kindergarten |
| Tennessee | 1.OA.A.1 | Add and subtract within 20 to solve contextual problems, with unknowns in all positions, involving situations of add to, take from, put together/take apart, and compare. Use objects, drawings, and equations with a symbol for the unknown number to represent the problem. NOTE: While start unknown situations may be introduced in first grade, they are not expected to be mastered until second grade. | Grade 1 |
| Tennessee | 1.OA.B.3 | Apply properties of operations (additive identity, commutative, and associative) as strategies to add and subtract. (Students need not use formal terms for these properties.) | Grade 1 |
| Tennessee | 1.OA.B.4 | Understand the relationship between addition and subtraction by representing subtraction as an unknown-addend problem. For example, to solve 10 – 8 = __, a student can use 8 + __ = 10. | Grade 1 |
| Tennessee | 1.OA.C.5 | Add and subtract within 20 using strategies such as counting on, counting back, making 10, related known facts, and composing/decomposing numbers with an emphasis on making ten (e.g., 13 – 4 = 13 – 3 – 1 = 10 – 1 = 9 or adding 6 + 7 by creating the known equivalent 6 + 4 + 3 = 10 + 3 = 13 OR 6 + 6 + 1 = 12 + 1). | Grade 1 |
| Tennessee | 1.OA.D.7 | Understand the meaning of the equal sign (e.g., 6 = 6; 5 + 2 = 4 + 3; 7 = 8 – 1). Determine if equations involving addition and subtraction are true or false. | Grade 1 |
| Tennessee | 1.OA.D.8 | Determine the unknown whole number in an addition or subtraction equation with sums/differences within 20, with the unknown in any position (e.g., 8 + ? = 11, 5 = ? – 3, 6 + 6 = ?). | Grade 1 |
| Tennessee | 1.NBT.A.1 | Count to 120, by ones, twos, and fives starting at any multiple of that number. Count backward from 20. Read and write numbers to 120 and represent a quantity of objects with a written number. | Grade 1 |
| Tennessee | 1.NBT.B.3 | Know that the digits of a two-digit number represent groups of tens and ones (e.g., 39 can be represented as 39 ones, 2 tens and 19 ones, or 3 tens and 9 ones). | Grade 1 |
| Tennessee | 1.NBT.B.4 | Compare two two-digit numbers based on the meanings of the digits in each place and use the symbols >, =, and < to show the relationship. | Grade 1 |
| Tennessee | 1.NBT.C.5 | Add a two-digit number to a one-digit number and a two-digit number to a multiple of ten (within 100). Use concrete models, drawings, strategies based on place value, properties of operations, and/or the relationship between addition and subtraction to explain the reasoning used. | Grade 1 |
| Tennessee | 1.NBT.C.6 | Mentally find 10 more or 10 less than a given two-digit number without having to count by ones and explain the reasoning used. | Grade 1 |
| Tennessee | 1.NBT.C.7 | Subtract multiples of 10 from any number in the range of 10-99 using concrete models, drawings, strategies based on place value, properties of operations, and/or the relationship between addition and subtraction. | Grade 1 |
| Tennessee | 1.MD.A.1 | Order three objects by length. Compare the lengths of two objects indirectly by using a third object. For example, to compare indirectly the heights of Bill and Susan: if Bill is taller than mother and mother is taller than Susan, then Bill is taller than Susan. | Grade 1 |
| Tennessee | 1.MD.A.2 | Measure the length of an object using non-standard units (paper clips, cubes, etc.) and express this length as a whole number of units. | Grade 1 |
| Tennessee | 1.MD.B.3 | Recognize a clock as a measurement tool. Tell and write time in hours and half-hours using analog and digital clocks. | Grade 1 |
| Tennessee | 1.MD.C.5 | Organize, represent, and interpret data with up to three categories using pictographs, bar graphs, and tally charts. Ask and answer questions about the total number of data points, how many in each category, and how many more or less are in one category than in another. | Grade 1 |
| Tennessee | 1.G.A.1 | Distinguish between attributes that define a shape (e.g., number of sides and vertices) versus attributes that do not define the shape (e.g., color, orientation, overall size); build and draw two-dimensional shapes to possess defining attributes. | Grade 1 |
| Tennessee | 1.G.A.2 | Create a composite figure and use the composite figure to make new figures by using two-dimensional shapes (rectangles, squares, hexagons, trapezoids, triangles, half-circles, and quarter-circles) or three-dimensional solids (cubes, spheres, rectangular prisms, cones, and cylinders). | Grade 1 |
| Tennessee | 1.G.A.3 | Partition circles and rectangles into two and four equal shares, describe the shares using the words halves, fourths, and quarters, and use the phrases half of, fourth of, and quarter of. Describe the whole as two of, or four of, the shares. Understand for these examples that partitioning into more equal shares creates smaller shares. | Grade 1 |
| Tennessee | 2.OA.A.1 | Add and subtract within 100 to solve one- and two-step contextual problems, with unknowns in all positions, involving situations of add to, take from, put together/take apart, and compare. Use objects, drawings, and equations with a symbol for the unknown number to represent the problem. | Grade 2 |
| Tennessee | 2.OA.B.2 | Fluently add and subtract within 30 using mental strategies. By the end of 2nd grade, know all sums of two one-digit numbers and related subtraction facts. | Grade 2 |
| Tennessee | 2.OA.C.3 | Determine whether a group of objects (up to 20) has an odd or even number of members by pairing objects or counting them by 2s. Write an equation to express an even number as a sum of two equal addends. | Grade 2 |
| Tennessee | 2.OA.C.4 | Use repeated addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends. For example, a 3 by 4 array can be expressed as 3 + 3 + 3 + 3 = 12 or 4 + 4 + 4 = 12. | Grade 2 |
| Tennessee | 2.NBT.A.1 | Know that the three digits of a three-digit number represent amounts of hundreds, tens, and ones (e.g., 706 can be represented in multiple ways as 7 hundreds, 0 tens, and 6 ones; 706 ones; or 70 tens and 6 ones). | Grade 2 |
| Tennessee | 2.NBT.A.2 | Recognize, describe, extend, and create patterns when counting by ones, twos, fives, tens, and hundreds and use those patterns to predict the next number in the counting sequence up to 1000 through counting. For example: 111, 113, 115, ...; 82, 84, 86, ...; 370, 380, 390....; 100, 200, 300,…; etc. | Grade 2 |
| Tennessee | 2.NBT.A.3 | Read and write numbers to 1000 using standard form, word form, and expanded form. For example, write 234 as 200 + 30 + 4. | Grade 2 |
| Tennessee | 2.NBT.A.4 | Compare two three-digit numbers based on the meanings of the digits in each place and use the symbols >, =, and < to show the relationship. | Grade 2 |
| Tennessee | 2.NBT.B.5 | Fluently add and subtract within 100 using properties of operations, strategies based on place value, and/or the relationship between addition and subtraction. | Grade 2 |
| Tennessee | 2.NBT.B.6 | Add up to four two-digit numbers using properties of operations and strategies based on place value. | Grade 2 |
| Tennessee | 2.NBT.B.7 | Add and subtract within 1000 using concrete models, drawings, strategies based on place value, properties of operations, and/or the relationship between addition and subtraction to explain the reasoning used. (Explanations may include words, drawing, or objects.) | Grade 2 |
| Tennessee | 2.NBT.B.8 | Mentally add or subtract 10 or 100 to/from any given number within 1000. | Grade 2 |
| Tennessee | 2.MD.A.1 | Measure the length of an object in whole number units by selecting and using appropriate tools such as rulers, yardsticks, meter sticks, and measuring tapes. | Grade 2 |
| Tennessee | 2.MD.A.2 | Measure the length of an object using two different whole number units of measure and describe how the two measurements relate to the size of the unit chosen. | Grade 2 |
| Tennessee | 2.MD.A.4 | Measure, using whole number lengths, to determine how much longer one object is than another and express the difference in terms of a standard unit of length. | Grade 2 |
| Tennessee | 2.MD.B.5 | Add and subtract within 100 to solve contextual problems, with the unknown in any position, involving lengths that are given in the same units by using drawings and equations with a symbol for the unknown to represent the problem. | Grade 2 |
| Tennessee | 2.MD.C.7 | Tell and write time in quarter hours and to the nearest five minutes (in a.m. and p.m.) using analog and digital clocks. | Grade 2 |
| Tennessee | 2.MD.C.8 | Solve contextual problems involving amounts less than one dollar including quarters, dimes, nickels, and pennies using the ¢ symbol appropriately. Solve contextual problems involving whole number dollar amounts up to $100 using the $ symbol appropriately. | Grade 2 |
| Tennessee | 2.MD.D.9 | Given a set of data, create a line plot, where the horizontal scale is marked off in whole-number units. | Grade 2 |
| Tennessee | 2.MD.D.10 | Draw a pictograph (with a key of values of 1, 2, 5, or 10) and a bar graph (with intervals of one) to represent a data set with up to four categories. Solve addition and subtraction problems related to the data in a graph. | Grade 2 |
| Tennessee | 2.G.A.1 | Identify triangles, quadrilaterals, pentagons, and hexagons. Draw two-dimensional shapes having specified attributes (as determined directly or visually, not by measuring), such as a given number of angles/vertices or a given number of sides of equal length. | Grade 2 |
| Tennessee | 2.G.A.2 | Partition a rectangle into rows and columns of same-sized squares and find the total number of squares. | Grade 2 |
| Tennessee | 2.G.A.3 | Partition circles and rectangles into two, three, and four equal shares. Describe the shares using the words halves, thirds, fourths, half of, a third of, and a fourth of, and describe the whole as two halves, three thirds, four fourths. Recognize that equal shares of identical wholes need not have the same shape. | Grade 2 |
| Tennessee | 3.OA.A.1 | Interpret the factors and products in whole number multiplication equations (e.g., 4 x 7 is 4 groups of 7 objects with a total of 28 objects or 4 strings measuring 7 inches each with a total length of 28 inches). | Grade 3 |
| Tennessee | 3.OA.A.2 | Interpret the dividend, divisor, and quotient in whole number division equations (e.g., 28 ÷ 7 can be interpreted as 28 objects divided into 7 equal groups with 4 objects in each group or 28 objects divided so there are 7 objects in each of the 4 equal groups). | Grade 3 |
| Tennessee | 3.OA.A.3 | Multiply and divide within 100 to solve contextual problems, with the unknown in any positions, in situations involving equal groups, arrays/area, and measurement quantities using strategies based on place value, the properties of operations, and the relationship between multiplication and division (e.g., contexts including computations such as 3 x ? = 24, 6 x 16 = ?, ? ÷ 8 = 3, or 96 ÷ 6 = ?). | Grade 3 |
| Tennessee | 3.OA.A.4 | Determine the unknown whole number in a multiplication or division equation relating three whole numbers within 100. For example, determine the unknown number that makes the equation true in each of the equations: 8 x ? = 48, 5 = ? ÷ 3, 6 x 6 =?. | Grade 3 |
| Tennessee | 3.OA.B.5 | Apply properties of operations as strategies to multiply and divide. (Students need not use formal terms for these properties.) Examples: If 6 x 4 = 24 is known, then 4 x 6 = 24 is also known (commutative property of multiplication). 3 x 5 x 2 can be solved by (3 x 5) x 2 or 3 x (5 x 2) (associative property of multiplication). One way to find 8 x 7 is by using 8 x (5 + 2) = (8 x 5) + (8 x 2). By knowing that 8 x 5 = 40 and 8 x 2 = 16, then 8 x 7 = 40 + 16 = 56 (distributive property of multiplication over addition). | Grade 3 |
| Tennessee | 3.OA.B.6 | Understand division as an unknown-factor problem. For example, find 32 ÷ 8 by finding the number that makes 32 when multiplied by 8. | Grade 3 |
| Tennessee | 3.OA.C.7 | Fluently multiply and divide within 100, using strategies such as the properties of operations or the relationship between multiplication and division (e.g., knowing that 8 x 5 = 40, one knows 40 ÷ 5 = 8). By the end of 3rd grade, know all products of two one-digit numbers and related division facts. | Grade 3 |
| Tennessee | 3.OA.D.8 | Solve two-step contextual problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. | Grade 3 |
| Tennessee | 3.OA.D.9 | Identify patterns in a multiplication chart and explain them using properties of operations. For example, in the multiplication chart, observe that 4 times a number is always even (because 4 x 6 = (2 x 2) x 6 = 2 x (2 x 6), which uses the associative property of multiplication) or, for example, observe that 6 times 7 is one more group of 7 than 5 times 7 (because 6 x 7 = (5 + 1) x 7 = (5 x 7) + (1 x 7), which uses the distributive property of multiplication over addition). | Grade 3 |
| Tennessee | 3.NBT.A.1 | Round whole numbers to the nearest 10 or 100 using understanding of place value and use a number line to explain how the number was rounded. | Grade 3 |
| Tennessee | 3.NBT.A.2 | Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction. | Grade 3 |
| Tennessee | 3.NBT.A.3 | Multiply one-digit whole numbers by multiples of 10 in the range 10–90 (e.g., 9 x 80, 5 x 60) using strategies based on place value and properties of operations. | Grade 3 |
| Tennessee | 3.NF.A.1 | Understand a unit fraction, 1/b, as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a non-unit fraction, n/b, as the quantity formed by n parts of size 1/b. For example, 3/4 represents a quantity formed by 3 parts of size 1/4. | Grade 3 |
| Tennessee | 3.NF.A.2 | Understand a fraction as a number on the number line. Represent fractions on a number line. a. Represent a fraction 1/b on a number line diagram by defining the interval from 0 to 1 as the whole and partitioning it into b equal parts. Recognize that each part has size 1/b and that the endpoint locates the number 1/b on the number line. For example, on a number line from 0 to 1, students can partition it into 4 equal parts and recognize that each part represents a length of 1/4 and the first part has an endpoint at 1/4 on the number line. b. Represent a fraction n/b on a number line diagram by marking off n lengths 1/b from 0. Recognize that the resulting interval has size n/b and that its endpoint locates the number n/b on the number line. For example, 5/3 is the distance from 0 when there are 5 iterations of 1/3. | Grade 3 |
| Tennessee | 3.NF.A.3 | Explain equivalence of fractions and compare fractions by reasoning about their size. a. Understand two fractions as equivalent (equal) if they are the same size or the same point on a number line. b. Recognize and generate simple equivalent fractions (e.g., 1/2 = 2/4, 4/6 = 2/3) and explain why the fractions are equivalent using a visual fraction model. c. Express whole numbers as fractions and recognize fractions that are equivalent to whole numbers. For example, express 3 in the form 3 = 3/1; recognize that 6/1= 6; locate 4/4 and 1 at the same point on a number line diagram. d. Compare two fractions with the same numerator or the same denominator by reasoning about their size. Recognize that comparisons are valid only when the two fractions refer to the same whole. Use the symbols >, =, or < to show the relationship and justify the conclusions. | Grade 3 |
| Tennessee | 3.MD.A.1 | Solve contextual problems in time and money. a. Tell and write time to the nearest minute and measure time intervals in minutes. Solve contextual problems involving addition and subtraction of time intervals in minutes. b. Solve one-step contextual problems involving amounts less than one dollar including quarters, dimes, nickels, and pennies using the ¢ symbol appropriately. Solve contextual problems involving whole number dollar amounts up to $1000 using the $ symbol appropriately. | Grade 3 |
| Tennessee | 3.MD.A.2 | Measure the mass of objects and liquid volume using standard units of grams (g), kilograms (kg), milliliters (ml), and liters (l). Estimate the mass of objects and liquid volume using benchmarks. For example, a large paper clip is about one gram, so a box of about 100 large clips is about 100 grams. | Grade 3 |
| Tennessee | 3.MD.B.3 | Draw a pictograph and a scaled bar graph to represent a data set with several categories. Solve one- and two-step 'how many more' and 'how many less' problems using information presented in graphs. | Grade 3 |
| Tennessee | 3.MD.B.4 | Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Show the data by making a line plot, where the horizontal scale is marked off in appropriate units: whole numbers, halves, or quarters. | Grade 3 |
| Tennessee | 3.MD.C.5 | Recognize that plane figures have an area and understand concepts of area measurement. a. Understand that a square with side length 1 unit, called 'a unit square,' is said to have 'one square unit' of area and can be used to measure area. b. Understand that a plane figure which can be covered without gaps or overlaps by n unit squares is said to have an area of n square units. | Grade 3 |
| Tennessee | 3.MD.C.6 | Measure areas by counting unit squares (square centimeters, square meters, square inches, square feet, and improvised units). | Grade 3 |
| Tennessee | 3.MD.C.7 | Relate area of rectangles to the operations of multiplication and addition. a. Find the area of a rectangle with whole-number side lengths by tiling it and show that the area is the same as would be found by multiplying the side lengths. b. Multiply side lengths to find areas of rectangles with whole number side lengths in the context of solving real-world and mathematical problems and represent whole-number products as rectangular areas in mathematical reasoning. c. Use tiling to show in a concrete case that the area of a rectangle with whole number side lengths a and (b + c) is the sum of (a x b) and (a x c). Use area models to represent the distributive property in mathematical reasoning. For example, in a rectangle with dimensions 4 by 6, students can decompose the rectangle into 4 x 3 and 4 x 3 to find the total area of 4 x 6. d. Recognize area as additive. Find areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas of the non-overlapping parts, applying this technique to solve real-world problems. | Grade 3 |
| Tennessee | 3.MD.D.8 | Solve real-world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exploring rectangles with the same perimeter and different areas or with the same area and different perimeters. | Grade 3 |
| Tennessee | 3.G.A.1 | Understand that shapes in different categories may share attributes and that the shared attributes can define a larger category. Recognize rhombuses, rectangles, and squares as examples of quadrilaterals and recognize examples of quadrilaterals that do not belong to any of these subcategories. | Grade 3 |
| Tennessee | 3.G.A.2 | Partition shapes into parts with equal areas. Recognize that equal shares of identical wholes need not have the same shape. Express the area of each part as a unit fraction of the whole. | Grade 3 |
| Tennessee | 4.OA.A.1 | Interpret a multiplication equation as a comparison (e.g., interpret 35 = 5 x 7 as a statement that 35 is 5 times as many as 7 and 7 times as much as 5). Represent verbal/written statements of multiplicative comparisons as multiplication equations. | Grade 4 |
| Tennessee | 4.OA.A.2 | Multiply or divide to solve contextual problems involving multiplicative comparison, and distinguish multiplicative comparison from additive comparison. For example, school A has 300 students and school B has 600 students: to say that school B has two times as many students is an example of multiplicative comparison; to say that school B has 300 more students is an example of additive comparison. | Grade 4 |
| Tennessee | 4.OA.A.3 | Solve multi-step contextual problems (posed with whole numbers and having whole-number answers using the four operations) including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. | Grade 4 |
| Tennessee | 4.OA.B.4 | Find factor pairs for whole numbers in the range 1–100 using models. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number is prime or composite and whether the given number is a multiple of a given one-digit number. | Grade 4 |
| Tennessee | 4.OA.C.5 | Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. For example, given the rule 'Add 3' and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way. | Grade 4 |
| Tennessee | 4.NBT.A.1 | Recognize that in a multi-digit whole number (less than or equal to 1,000,000), a digit in one place represents 10 times as much as it represents in the place to its right. For example, recognize that 7 in 700 is 10 times bigger than the 7 in 70 because 700 ÷ 70 = 10 and 70 x 10 = 700. | Grade 4 |
| Tennessee | 4.NBT.A.2 | Read and write multi-digit whole numbers (less than or equal to 1,000,000) using standard form, word form, and expanded notation (e.g. the expanded notation of 4256 is written as (4 x 1000) + (2 x 100) + (5 x 10) + (6 x 1)). Compare two multi-digit numbers based on meanings of the digits in each place and use the symbols >, =, and < to show the relationship. | Grade 4 |
| Tennessee | 4.NBT.A.3 | Round multi-digit whole numbers to any place (up to and including the hundred-thousand place) using understanding of place value and use a number line to explain how the number was rounded. | Grade 4 |
| Tennessee | 4.NBT.B.4 | Fluently add and subtract within 1,000,000 using efficient strategies and algorithms. | Grade 4 |
| Tennessee | 4.NBT.B.5 | Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. | Grade 4 |
| Tennessee | 4.NBT.B.6 | Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. | Grade 4 |
| Tennessee | 4.NF.A.1 | Explain why a fraction a/b is equivalent to a fraction (a x n)/(b x n) or (a ÷ n)/(b ÷ n) using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. For example, 3/4 = (3 x 2)/(4 x 2) = 6/8. | Grade 4 |
| Tennessee | 4.NF.A.2 | Compare two fractions with different numerators and different denominators by creating common denominators or common numerators or by comparing to a benchmark such as 0 or 1/2 or 1. Recognize that comparisons are valid only when the two fractions refer to the same whole. Use the symbols >, =, or < to show the relationship and justify the conclusions. | Grade 4 |
| Tennessee | 4.NF.B.3 | Understand a fraction a/b with a > 1 as a sum of fractions 1/b. For example, 4/5 = 1/5 +1/5 + 1/5 + 1/5. a. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. b. Decompose a fraction into a sum of fractions with the same denominator in more than one way (e.g., 3/8 = 1/8 + 1/8 + 1/8; 3/8 = 1/8 + 2/8; 2 1/8 = 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8) recording each decomposition by an equation. Justify decompositions using a visual fraction model. c. Add and subtract mixed numbers with like denominators by replacing each mixed number with an equivalent fraction and/or by using properties of operations and the relationship between addition and subtraction. d. Solve contextual problems involving addition and subtraction of fractions referring to the same whole and having like denominators | Grade 4 |
| Tennessee | 4.NF.B.4 | Apply and extend understanding of multiplication as repeated addition to multiply a whole number by a fraction. a. Understand a fraction a/b as a multiple of 1/b. For example, use a visual fraction model to represent 5/4 as the product 5 × 1/4, recording the conclusion by the equation 5/4 = 5 x 1/4. b. Understand a multiple of a/b as a multiple of 1/b and use this understanding to multiply a whole number by a fraction. For example, use a visual fraction model to express 3 × 2/5 as 6 × 1/5, recognizing this product as 6/5. (In general, n x a/b = (n x a)/b = (n x a) x 1/b.) c. Solve contextual problems involving multiplication of a whole number by a fraction (e.g., by using visual fraction models and equations to represent the problem). For example, if each person at a party will eat 3/8 of a pound of roast beef, and there will be 4 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie? | Grade 4 |
| Tennessee | 4.NF.C.5 | Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100. | Grade 4 |
| Tennessee | 4.NF.C.6 | Read and write decimal notation for fractions with denominators 10 or 100. Locate these decimals on a number line. | Grade 4 |
| Tennessee | 4.NF.C.7 | Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Use the symbols >, =, or < to show the relationship and justify the conclusions. | Grade 4 |
| Tennessee | 4.MD.A.1 | Measure and estimate to determine relative sizes of measurement units within a single system of measurement involving length, liquid volume, and mass/weight of objects using customary and metric units. | Grade 4 |
| Tennessee | 4.MD.A.2 | Solve one- or two-step real-world problems involving whole number measurements (including length, liquid volume, mass/weight, time, and money) with all four operations within a single system of measurement. (Contexts need not include conversions.) | Grade 4 |
| Tennessee | 4.MD.A.3 | Know and apply the area and perimeter formulas for rectangles in real-world and mathematical contexts. For example, find the width of a rectangular room given the area of the flooring and the length, by viewing the area formula as a multiplication equation with an unknown factor. | Grade 4 |
| Tennessee | 4.MD.B.4 | Make a line plot to display a data set of measurements in fractions of the same unit (1/2 or 1/4 or 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, from a line plot find and interpret the difference in length between the longest and shortest specimens in an insect collection. | Grade 4 |
| Tennessee | 4.MD.C.5 | Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint; and understand concepts of angle measurement. a. Understand that an angle is measured with reference to a circle with its center at the common endpoint of the rays, by considering the fraction of the circular arc between the points where the two rays intersect the circle. b. Understand that an angle that turns through 1/360 of a circle is called a 'one degree angle,' and can be used to measure angles. An angle that turns through n one-degree angles is said to have an angle measure of n degrees and represents a fractional portion of the circle. | Grade 4 |
| Tennessee | 4.MD.C.6 | Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure. | Grade 4 |
| Tennessee | 4.MD.C.7 | Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real-world and mathematical problems. (e.g., by using an equation with a symbol for the unknown angle measure). | Grade 4 |
| Tennessee | 4.G.A.1 | Draw points, lines, line segments, rays, angles (right, acute, obtuse, straight, reflex), and perpendicular and parallel lines. Identify these in two-dimensional figures. | Grade 4 |
| Tennessee | 4.G.A.2 | Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines or the presence or absence of angles of a specified size. Classify triangles based on the measure of the angles as right, acute, or obtuse. | Grade 4 |
| Tennessee | 4.G.A.3 | Recognize and draw lines of symmetry for two-dimensional figures. | Grade 4 |
| Tennessee | 5.OA.A.1 | Use parentheses and/or brackets in numerical expressions involving whole numbers and evaluate expressions having these symbols using the conventional order by applying the Order of Operations. (When applying the order of operations, the evaluation of exponents need not be included.) | Grade 5 |
| Tennessee | 5.OA.A.2 | Write numerical expressions that record calculations with numbers and interpret numerical expressions without evaluating them. For example, express the calculation 'add 8 and 7, then multiply by 2' as 2 x (8 + 7). Recognize that 3 x (18,932 + 921) is three times as large as 18,932 + 921, without having to calculate the indicated sum or product. | Grade 5 |
| Tennessee | 5.OA.B.3 | Generate two numerical patterns using two given rules. For example, given the rule 'Add 3' and the starting number 0, and given the rule 'Add 6' and the starting number 0, generate terms in the resulting sequences. a. Identify relationships between corresponding terms in two numerical patterns. b. Form ordered pairs (limited to first quadrant) consisting of corresponding terms from two numerical patterns and graph the ordered pairs on a coordinate plane. | Grade 5 |
| Tennessee | 5.NBT.A.1 | Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. | Grade 5 |
| Tennessee | 5.NBT.A.2 | Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. | Grade 5 |
| Tennessee | 5.NBT.A.3 | Read and write decimals to thousandths using standard form, word form, and expanded notation (e.g., the expanded notation of 347.392 is written as (3 x 100) + (4 x 10) + (7 x 1) + (3 x (1/10)) + (9 x (1/100)) + (2 x (1/1000))). Compare two decimals to thousandths based on meanings of the digits in each place and use the symbols >, =, and < to show the relationship. | Grade 5 |
| Tennessee | 5.NBT.A.4 | Round decimals to the nearest hundredth, tenth, or whole number using understanding of place value, and use a number line to explain how the number was rounded. | Grade 5 |
| Tennessee | 5.NBT.B.5 | Fluently multiply multi-digit whole numbers (up to three-digit by four-digit factors) using efficient strategies and algorithms. | Grade 5 |
| Tennessee | 5.NBT.B.6 | Find whole-number quotients and remainders of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. | Grade 5 |
| Tennessee | 5.NBT.B.7 | Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between operations. Assess the reasonableness of answers using estimation strategies. (Limit multiplication problems so that the product does not exceed thousandths. Limit division problems so that either the dividend or the divisor is a whole number.) | Grade 5 |
| Tennessee | 5.NF.A.1 | Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12 or 3/5 + 7/10 = 6/10 + 7/10 = 13/10. | Grade 5 |
| Tennessee | 5.NF.A.2 | Solve contextual problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. | Grade 5 |
| Tennessee | 5.NF.B.3 | Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). For example, 3/4 = 3 ÷ 4 so when 3 wholes are shared equally among 4 people, each person has a share of size 3/4. Solve contextual problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers by using visual fraction models or equations to represent the problem. For example, if 8 people want to share 49 sheets of construction paper equally, how many sheets will each person receive? Between what two whole numbers does your answer lie? | Grade 5 |
| Tennessee | 5.NF.B.4 | Apply and extend previous understandings of multiplication to multiply a fraction by a whole number or a fraction by a fraction. a. Interpret the product a/b x q as a x (q ÷ b) (partition the quantity q into b equal parts and then multiply by a). Interpret the product a/b x q as (a x q) ÷ b (multiply a times the quantity q and then partition the product into b equal parts). For example, use a visual fraction model or write a story context to show that 2/3 x 6 can be interpreted as 2 x (6 ÷ 3) or (2 x 6) ÷ 3. Do the same with 2/3 x 4/5 = 8/15. (In general, a/b x c/d = ac/bd.) b. Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles and represent fraction products as rectangular areas. | Grade 5 |
| Tennessee | 5.NF.B.5 | Interpret multiplication as scaling (resizing). a. Compare the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication. For example, know if the product will be greater than, less than, or equal to the factors. b. Explain why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explain why multiplying a given number by a fraction between 0 and 1 results in a product less than the given number; and relate the principle of fraction equivalence a/b = (a x n)/(b x n) to the effect of multiplying a/b by 1. | Grade 5 |
| Tennessee | 5.NF.B.6 | Solve real-world problems involving multiplication of fractions and mixed numbers by using visual fraction models or equations to represent the problem. | Grade 5 |
| Tennessee | 5.NF.B.7 | Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. a. Interpret division of a unit fraction by a non-zero whole number and compute such quotients. For example, use visual models and the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) x 4 = 1/3. In other words, when thirds are partitioned into 4 equal groups, they become twelfths. b. Interpret division of a whole number by a unit fraction and compute such quotients. For example, use visual models and the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 x (1/5) = 4 (i.e., there are 20 groups of 1/5 inside 4 wholes and connect this to ? x (1/5) = 4). c. Solve real-world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions and non-unit fractions by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb. of chocolate equally? How many 1/3 cup servings are in 2 cups of raisins? | Grade 5 |
| Tennessee | 5.MD.A.1 | Convert customary and metric measurement units within a single system by expressing measurements of a larger unit in terms of a smaller unit. Use these conversions to solve multi-step real-world problems involving distances, intervals of time, liquid volumes, masses of objects, and money (including problems involving simple fractions or decimals). For example, 3.6 liters and 4.1 liters can be combined as 7.7 liters or 7700 milliliters. | Grade 5 |
| Tennessee | 5.MD.B.2 | Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. | Grade 5 |
| Tennessee | 5.MD.C.3 | Recognize volume as an attribute of solid figures and understand concepts of volume measurement. a. Understand that a cube with side length 1 unit, called a 'unit cube,' is said to have 'one cubic unit' of volume and can be used to measure volume. b. Understand that a solid figure which can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units. | Grade 5 |
| Tennessee | 5.MD.C.4 | Measure volume by counting unit cubes, using cubic centimeters, cubic inches, cubic feet, and improvised units. | Grade 5 |
| Tennessee | 5.MD.C.5 | Relate volume to the operations of multiplication and addition and solve real-world and mathematical problems involving volume of right rectangular prisms. a. Find the volume of a right rectangular prism with whole-number side lengths by packing it with unit cubes and show that the volume is the same as would be found by multiplying the edge lengths, equivalently by multiplying the height by the area of the base. Represent whole-number products of three factors as volumes (e.g., to represent the associative property of multiplication). b. Know and apply the formulas V = l x w x h and V = B x h (where B represents the area of the base) for rectangular prisms with whole number edge lengths in the context of solving real-world and mathematical problems. c. Recognize volume as additive. Find volumes of solid figures composed of two non-overlapping right rectangular prisms by adding the volumes of the nonoverlapping parts, applying this technique to solve real-world problems. | Grade 5 |
| Tennessee | 5.G.A.1 | Graph ordered pairs and label points using the first quadrant of the coordinate plane. Understand in the ordered pair that the first number indicates the horizontal distance traveled along the x-axis from the origin and the second number indicates the vertical distance traveled along the y-axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate). | Grade 5 |
| Tennessee | 5.G.A.2 | Represent real-world and mathematical problems by graphing points in the first quadrant of the coordinate plane and interpret coordinate values of points in the context of the situation. | Grade 5 |
| Tennessee | 5.G.B.3 | Classify two-dimensional figures in a hierarchy based on properties. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. | Grade 5 |
| Tennessee | 6.RP.A.1 | Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. Make a distinction between ratios and fractions. For example, the ratio of wings to beaks in a bird house at the zoo was 2:1, because for every 2 wings there was 1 beak. Another example could be for every vote candidate A received, candidate C received nearly three votes. | Grade 6 |
| Tennessee | 6.RP.A.2 | Understand the concept of a unit rate a/b associated with a ratio a:b with b ≠ 0. Use rate language in the context of a ratio relationship. For example, this recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar. Also, we paid $75 for 15 hamburgers, which is a rate of $5 per hamburger. (Expectations for unit rates in 6th grade are limited to non-complex fractions). | Grade 6 |
| Tennessee | 6.RP.A.3 | Use ratio and rate reasoning to solve real-world and mathematical problems (e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations). a. Make tables of equivalent ratios relating quantities with whole number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios. b. Solve unit rate problems including those involving unit pricing and constant speed. For example, if a runner ran 10 miles in 90 minutes, running at that speed, how long will it take him to run 6 miles? How fast is he running in miles per hour? c. Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent. d. Use ratio reasoning to convert customary and metric measurement units (within the same system); manipulate and transform units appropriately when multiplying or dividing quantities. | Grade 6 |
| Tennessee | 6.NS.A.1 | Interpret and compute quotients of fractions, and solve real-world and mathematical problems involving division of fractions by fractions (e.g., connecting visual fraction models and equations to represent the problem is suggested). For example, create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 times 8/9 is 2/3 ((a/b) ÷ (c/d) = ad/bc). Further example: How much chocolate will each person get if 3 people share 1/2 lb. of chocolate equally? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi? | Grade 6 |
| Tennessee | 6.NS.B.2 | Fluently divide multi-digit numbers using a standard algorithm. | Grade 6 |
| Tennessee | 6.NS.B.3 | Fluently add, subtract, multiply, and divide multi-digit decimals using a standard algorithm and making connections to previous conceptual work with each operation. | Grade 6 |
| Tennessee | 6.NS.C.5 | Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation as well as describing situations in which opposite quantities can combine to make 0. | Grade 6 |
| Tennessee | 6.NS.C.6 | Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates. a. Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line; recognize that the opposite of the opposite of a number is the number itself. For example, – (–3) = 3, and that 0 is its own opposite. b. Understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane; recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes. c. Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. | Grade 6 |
| Tennessee | 6.NS.C.7 | Understand ordering and absolute value of rational numbers. a. Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram. For example, interpret –3 > –7 as a statement that –3 is located to the right of –7 on a number line oriented from left to right. b. Write, interpret, and explain statements of order for rational numbers in real-world contexts. For example, write –3º C > –7º C to express the fact that –3º C is warmer than –7º C. c. Understand the absolute value of a rational number as its distance from 0 on the number line and distinguish comparisons of absolute value from statements about order in a real-world context. For example, an account balance of -24 dollars represents a greater debt than an account balance - 14 dollars because -24 is located to the left of -14 on the number line. | Grade 6 |
| Tennessee | 6.NS.C.8 | Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. | Grade 6 |
| Tennessee | 6.EE.A.1 | Write and evaluate numerical expressions involving whole-number exponents. | Grade 6 |
| Tennessee | 6.EE.A.2 | Write, read, and evaluate expressions in which variables stand for numbers. a. Write expressions that record operations with numbers and with variables. For example, express the calculation 'Subtract y from 5' as 5 – y. b. Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient); view one or more parts of an expression as a single entity. For example, describe the expression 2 (8 + 7) as a product of two factors; view (8 + 7) as both a single entity and a sum of two terms. c. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations). | Grade 6 |
| Tennessee | 6.EE.A.3 | Apply the properties of operations (including, but not limited to, commutative, associative, and distributive properties) to generate equivalent expressions. (The distributive property of multiplication over addition is prominent here. Negative coefficients are not an expectation at this grade level.) For example, apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y. | Grade 6 |
| Tennessee | 6.EE.A.4 | Identify when expressions are equivalent (i.e., when the expressions name the same number regardless of which value is substituted into them). For example, the expression 5b + 3b is equivalent to (5 +3) b, which is equivalent to 8b. | Grade 6 |
| Tennessee | 6.EE.B.5 | Understand that a solution to an equation or inequality is the value(s) that makes that statement true. Use substitution to determine whether a given number in a specified set makes an equation or inequality true. | Grade 6 |
| Tennessee | 6.EE.B.6 | Use variables to represent numbers and write expressions when solving real-world and mathematical problems; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set. | Grade 6 |
| Tennessee | 6.EE.B.7 | Solve real-world and mathematical problems by writing and solving one-step equations of the form x + p = q, px = q, x – p = q, and x/p = q for cases in which p, q, and x are all nonnegative rational numbers and p ≠ 0. (Complex fractions are not an expectation at this grade level.) | Grade 6 |
| Tennessee | 6.EE.B.8 | Interpret and write an inequality of the form x > c, x < c, x ≤ c, or x ≥ c which represents a condition or constraint in a real-world or mathematical problem. Recognize that inequalities have infinitely many solutions; represent solutions of inequalities on number line diagrams. | Grade 6 |
| Tennessee | 6.EE.C.9 | Use variables to represent two quantities in a real-world problem that change in relationship to one another. For example, Susan is putting money in her savings account by depositing a set amount each week ($50). Represent her savings account balance with respect to the number of weekly deposits (s = 50w, illustrating the relationship between balance amount s and number of weeks w). a. Write an equation in the form of y = px where y, p, and x are all non-negative and p ≠ 0, to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. b. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. | Grade 6 |
| Tennessee | 6.G.A.1 | Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; know and apply these techniques in the context of solving real-world and mathematical problems. | Grade 6 |
| Tennessee | 6.G.A.2 | Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas V = lwh and V = Bh where B is the area of the base to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems. | Grade 6 |
| Tennessee | 6.G.A.3 | Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side that joins two vertices (vertical or horizontal segments only). Apply these techniques in the context of solving real-world and mathematical problems. | Grade 6 |
| Tennessee | 6.G.A.4 | Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems. | Grade 6 |
| Tennessee | 6.SP.B.5 | Summarize numerical data sets in relation to their context. a. Report the number of observations. b. Describe the nature of the attribute under investigation, including how it was measured and its units of measurement. c. Give quantitative measures of center (median and/or mean) and variability (range) as well as describing any overall pattern with reference to the context in which the data were gathered. d. Relate the choice of measures of center to the shape of the data distribution and the context in which the data were gathered. | Grade 6 |
| Tennessee | 7.RP.A.1 | Compute unit rates associated with ratios of fractions, including ratios of lengths, areas, and other quantities measured in like or different units. For example, if a person walks 1/2 mile in each 15 minutes, compute the unit rate as the complex fraction (1/2) / (1/4) miles per hour, equivalently 2 miles per hour. | Grade 7 |
| Tennessee | 7.RP.A.2 | Recognize and represent proportional relationships between quantities. a. Decide whether two quantities are in a proportional relationship (e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin). b. Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships. c. Use the concept of equality to represent proportional relationships with equations. For example, if total cost t is proportional to the number n of items purchased at a constant price p, the relationship between the total cost and the number of items can be expressed as t = pn. d. Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r) where r is the unit rate. | Grade 7 |
| Tennessee | 7.RP.A.3 | Use proportional relationships to solve multi-step ratio and percent problems. Examples: batting averages, recipes, simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error, etc. | Grade 7 |
| Tennessee | 7.NS.A.1 | Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram. a. Understand p + q as the number located a distance |q| from p, in the positive or negative direction depending on whether q is positive or negative. Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing real- world contexts. b. Understand subtraction of rational numbers as adding the additive inverse, p – q = p + (–q). Show that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in real-world contexts. c. Apply properties of operations as strategies to add and subtract rational numbers. | Grade 7 |
| Tennessee | 7.NS.A.2 | Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers. a. Understand that multiplication is extended from fractions to all rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as (– 1)(–1) = 1 and the rules for multiplying signed numbers. Interpret products of rational numbers by describing real-world contexts. b. Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with non-zero divisor) is a rational number. If p and q are integers, then –(p/q) = (–p)/q = p/(–q). Interpret quotients of rational numbers by describing real-world contexts. c. Apply properties of operations as strategies to multiply and divide rational numbers. d. Convert a rational number to a decimal using long division; know that the decimal form of a rational number terminates or eventually repeats. | Grade 7 |
| Tennessee | 7.NS.A.3 | Solve real-world and mathematical problems involving the four operations with rational numbers. (Computations with rational numbers extend the rules for manipulating fractions to complex fractions.) | Grade 7 |
| Tennessee | 7.EE.A.1 | Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients. | Grade 7 |
| Tennessee | 7.EE.A.2 | Rewrite and connect equivalent expressions in different forms in a contextual problem to provide multiple ways of interpreting the problem and investigating how the quantities in it are related. For example, shoes are on sale at a 25% discount. How is the discounted price P related to the original cost C of the shoes? C – 0.25C = P. In other words, P is 75% of the original cost since C – 0.25C can be written as 0.75C. | Grade 7 |
| Tennessee | 7.EE.B.3 | Solve multi-step real-world and mathematical problems posed with positive and negative rational numbers presented in any form (whole numbers, fractions, and decimals). a. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate. b. Assess the reasonableness of answers using mental computation and estimation strategies. | Grade 7 |
| Tennessee | 7.EE.B.4 | Use variables to represent quantities in a real-world and mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. a. Solve real-world and mathematical problems leading to equations of the form px + q = r and p(x + q) = r where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. For example, the perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width? b. Solve real-world and mathematical problems leading to inequalities of the form px + q > r, px + q < r, px + q ≥ r, and px + q ≤ r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality on a number line and interpret it in the context of the problem. For example: As a salesperson, you are paid $50 per week plus $3 per sale. This week you want your pay to be at least $100. Write an inequality for the number of sales you need to make, and describe the solutions. | Grade 7 |
| Tennessee | 7.G.A.1 | Solve problems involving scale drawings of congruent and similar geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale. | Grade 7 |
| Tennessee | 7.G.A.2 | Draw triangles with given conditions: three angle measures or three side measures. Notice when the conditions determine a unique triangle, more than one triangle, or no triangle. | Grade 7 |
| Tennessee | 7.G.B.3 | Know the formulas for the area and circumference of a circle and use them to solve problems. Explore the relationships between the radius, the circumference, and the area of a circle, and the number π. | Grade 7 |
| Tennessee | 7.G.B.4 | Know and use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure. | Grade 7 |
| Tennessee | 7.G.B.5 | Solve real-world and mathematical problems involving area of two-dimensional figures composed of triangles, quadrilaterals, and polygons, and volume and surface area of three-dimensional objects composed of cubes and right prisms. | Grade 7 |
| Tennessee | 8.NS.A.2 | Use rational approximations of irrational numbers to compare the size of irrational numbers by locating them approximately on a number line diagram. Estimate the value of irrational expressions (such as π² ). | Grade 8 |
| Tennessee | 8.EE.A.1 | Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, 3² x 3^-5 = 3^-3 = 1/3³ = 1/27. | Grade 8 |
| Tennessee | 8.EE.A.2 | Use square root and cube root symbols to represent solutions to equations of the form x² = p and x³ = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. | Grade 8 |
| Tennessee | 8.EE.A.3 | Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities and to express how many times as much one is than the other. For example, estimate the population of the United States as 3 x 10^8 and the population of the world as 7 x 10^9, and determine that the world population is more than 20 times larger. | Grade 8 |
| Tennessee | 8.EE.A.4 | Using technology, solve real-world problems with numbers expressed in decimal and scientific notation. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities (e.g., use millimeters per year for seafloor spreading). | Grade 8 |
| Tennessee | 8.EE.B.5 | Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed. | Grade 8 |
| Tennessee | 8.EE.B.6 | Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; know and apply the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b. | Grade 8 |
| Tennessee | 8.EE.C.7 | Solve linear equations in one variable. a. Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x = a, a = a, or a = b results (where a and b are different numbers). b. Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and combining like terms. | Grade 8 |
| Tennessee | 8.EE.C.8 | Analyze and solve systems of two linear equations graphically. a. Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously. b. Estimate solutions by graphing a system of two linear equations in two variables. Identify solutions by inspecting graphs of a system of linear equations in two variables. | Grade 8 |
| Tennessee | 8.F.A.1 | Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output. (Function notation is not required in 8th grade.) | Grade 8 |
| Tennessee | 8.F.A.2 | Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a linear function represented by a table of values and another linear function represented by an algebraic expression, determine which function has the greater rate of change. | Grade 8 |
| Tennessee | 8.F.A.3 | Know and interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. For example, the function A = s2 giving the area of a square as a function of its side length is not linear because its graph contains the points (1,1), (2,4) and (3,9), which are not on a straight line. | Grade 8 |
| Tennessee | 8.F.B.4 | Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models and in terms of its graph or a table of values. | Grade 8 |
| Tennessee | 8.F.B.5 | Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally. | Grade 8 |
| Tennessee | 8.G.A.1 | Describe the effect of translations, rotations, reflections, and dilations on two-dimensional figures using coordinates. a. Verify informally that lines are taken to lines, and determine when line segments are taken to line segments of the same length. b. Verify informally that angles are taken to angles of the same measure. c. Verify informally that parallel lines are taken to parallel lines. d. Make connections between dilations and scale factors. | Grade 8 |
| Tennessee | 8.G.A.2 | Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. | Grade 8 |
| Tennessee | 8.G.B.4 | Know and apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions. | Grade 8 |
| Tennessee | 8.G.B.5 | Apply the Pythagorean Theorem to find the distance between two points in a coordinate system. | Grade 8 |
| Tennessee | 8.G.C.6 | Apply the formulas for the volumes of cones, cylinders, and spheres to solve real-world and mathematical problems. | Grade 8 |
| Tennessee | 8.SP.A.1 | Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association. | Grade 8 |
| Tennessee | 8.SP.A.2 | Know that straight lines are widely used to model linear relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line and informally assess the model fit by judging the closeness of the data points to the line. | Grade 8 |
| Tennessee | A1.A.CED.A.2 | Create equations and inequalities in two variables to represent relationships between quantities and use them to solve problems in a real-world context. Graph equations with two variables on coordinate axes with labels and scales, and use the graphs to make predictions. | High School |
| Tennessee | A1.A.CED.A.3 | Create individual and systems of equations and/or inequalities to represent constraints in a contextual situation, and interpret solutions as viable or non-viable. | High School |
| Tennessee | A1.A.REI.B.2 | Solve linear and absolute value equations and inequalities in one variable. a. Solve linear equations and inequalities, including compound inequalities, in one variable. Represent solutions algebraically and graphically. b. Solve absolute value equations and inequalities in one variable. Represent solutions algebraically and graphically. | High School |
| Tennessee | A1.F.IF.A.2 | Use function notation. a. Use function notation to evaluate functions for inputs in their domains, including functions of two variables. b. Interpret statements that use function notation in terms of a context. | High School |
| Tennessee | A1.F.IF.B.4 | For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. | High School |
| Tennessee | A1.F.IF.C.7 | Graph functions expressed algebraically and show key features of the graph by hand and using technology. | High School |
| Tennessee | A1.F.BF.A.1 | Build a function that describes a relationship between two quantities. a. Determine steps for calculation, a recursive process, or an explicit expression from a context. | High School |
| Tennessee | A1.S.ID.B.4 | Represent data from two quantitative variables on a scatter plot, and describe how the variables are related. Fit a function to the data; use functions fitted to data to solve problems in the context of the data. | High School |
| Tennessee | A2.A.APR.A.2 | Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial. | High School |
| Tennessee | A2.F.IF.B.5 | Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.a. Rewrite quadratic functions to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a real-world context. b. Know and use the properties of exponents to interpret expressions for exponential functions in terms of a realworld context. | High School |
| Utah | K.CC.1 | Count to 100 by ones and by tens. | Kindergarten |
| Utah | K.CC.2 | Count forward beginning from a given number within the known sequence (instead of having to begin at 1). | Kindergarten |
| Utah | K.CC.3 | Read and write numbers using base ten numerals from 0 to 20. Represent a number of objects with a written numeral, in or out of sequence (0 represents a count of no objects). | Kindergarten |
| Utah | K.CC.4 | Understand the relationship between numbers and quantities; connect counting to cardinality. | Kindergarten |
| Utah | K.CC.5 | Use counting to answer questions about “how many.” For example, 20 or fewer objects arranged in a line, a rectangular array, or circle; 10 or fewer objects in a scattered configuration. Using a number from 1–20, count out that many objects. | Kindergarten |
| Utah | K.CC.6 | Use matching or counting strategies to identify whether the number of objects in one group is greater than, less than, or equal to the number of objects in another group. Include groups with up to ten objects. | Kindergarten |
| Utah | K.CC.7 | Compare two numbers between 1 and 10 presented as written numerals using “greater than,” “less than,” or “equal to.” | Kindergarten |
| Utah | K.G.1 | Describe objects in the environment using names of shapes, and describe the relative positions of these objects using terms such as above, below, beside, in front of, behind, and next to. | Kindergarten |
| Utah | K.G.2 | Correctly name shapes regardless of their orientations or overall sizes. | Kindergarten |
| Utah | K.G.3 | Identify shapes as two-dimensional ("flat") or three-dimensional ("solid"). | Kindergarten |
| Utah | K.G.4 | Analyze, compare, and sort two- and three-dimensional shapes and objects, in different sizes and orientations, using informal language to describe their similarities, differences, and other attributes (for example, color, size, shape, number of sides). | Kindergarten |
| Utah | K.G.6 | Compose simple shapes to form larger shapes. For example, “Can you join these two triangles with full sides touching to make a rectangle?” | Kindergarten |
| Utah | K.MD.1 | Describe measurable attributes of objects, such as length or weight. Describe several measurable attributes of a single object. | Kindergarten |
| Utah | K.MD.2 | Directly compare two objects with a measurable attribute in common, to see which object has "more of"/"less of" the attribute, and describe the difference. For example, directly compare the length of two pencils and describe one as shorter or longer. | Kindergarten |
| Utah | K.MD.3 | Classify objects into given categories; count the numbers of objects in each category and sort the categories by count. Limit the category counts to less than or equal to 10. | Kindergarten |
| Utah | K.NBT.1 | Compose and decompose numbers from 11–19 into ten ones and some further ones. Use objects or drawings and record each composition or decomposition by a drawing or equation. For example, 18 = 10 + 8. Understand that these numbers are composed of ten ones and one, two, three, four, five, six, seven, eight, or nine ones. | Kindergarten |
| Utah | K.OA.1 | Represent addition and subtraction with objects, fingers, mental images, simple drawings, or sounds. For example, use clapping, act out situations, and use verbal explanations, expressions, or equations. | Kindergarten |
| Utah | K.OA.2 | Solve addition and subtraction word problems within 10. Use objects or drawings to represent the problem. | Kindergarten |
| Utah | K.OA.3 | Decompose numbers less than or equal to 10 into pairs in more than one way by using objects or drawings. Record each decomposition by a drawing or equation. For example, 5 = 2 + 3 and 5 = 4 + 1. | Kindergarten |
| Utah | K.OA.4 | Make sums of 10 using any number from 1 to 9. For example, 2 + 8 = 10. Use objects or drawings to represent and record the answer. | Kindergarten |
| Utah | K.OA.5 | Fluently add and subtract using numbers within 5. | Kindergarten |
| Utah | 1.G.1 | Distinguish between defining attributes (for example, triangles are closed and three-sided) versus non-defining attributes (for example, color, orientation, overall size); build and draw shapes that possess defining attributes. | Grade 1 |
| Utah | 1.G.2 | Compose shapes. | Grade 1 |
| Utah | 1.G.3 | Partition circles and rectangles into two and four equal shares; describe the shares using the words halves, fourths, and quarters; and use the phrases half of, fourth of, and quarter of. Describe the whole as two or four of the shares. Understand that, for these examples, decomposing into more equal shares creates smaller shares. | Grade 1 |
| Utah | 1.MD.1 | Order three objects by length; compare the lengths of two objects indirectly by using a third object. | Grade 1 |
| Utah | 1.MD.2 | Express the length of an object as a whole number of length units, by laying multiple copies of a shorter object (the length unit) end to end; understand that the length measurement of an object is the number of same-size length units that span it with no gaps or overlaps. Limit to contexts where the object being measured is spanned by a whole number of length units with no gaps or overlaps. | Grade 1 |
| Utah | 1.MD.3 | Tell and write time in hours and half-hours using analog and digital clocks. | Grade 1 |
| Utah | 1.MD.4 | Organize, represent, and interpret data with up to three categories; ask and answer questions about the total number of data points, how many in each category, and how many more or less are in one category than in another. | Grade 1 |
| Utah | 1.MD.5 | Identify the values of pennies, nickels, dimes and quarters, and know their comparative values. (For example, a dime is of greater value than a nickel.) Use appropriate notation to designate a coin’s value. (For example, 5¢.) | Grade 1 |
| Utah | 1.NBT.1 | Count to 120, starting at any number less than 120. In this range, read and write numerals and represent a number of objects with a written numeral. | Grade 1 |
| Utah | 1.NBT.2 | Understand that the two digits of a two-digit number represent amounts of tens and ones. Understand the following as special cases: | Grade 1 |
| Utah | 1.NBT.3 | Compare two two-digit numbers based on meanings of the tens and ones digits, recording the results of comparisons with the symbols >, =, and <. | Grade 1 |
| Utah | 1.NBT.4 | Add within 100, including adding a two-digit number and a one-digit number, and adding a two-digit number and a multiple of 10, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Understand that in adding two-digit numbers, one adds tens to tens and ones to ones, and that it is sometimes necessary to compose a ten. | Grade 1 |
| Utah | 1.NBT.5 | Given a two-digit number, mentally find 10 more or 10 less than the number, without having to count; explain the reasoning used. | Grade 1 |
| Utah | 1.NBT.6 | Subtract multiples of 10 in the range 10–90 from multiples of 10 in the range 10–90 (positive or zero differences), using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. | Grade 1 |
| Utah | 1.OA.1 | Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions. For example, use objects, drawings, and equations with a symbol for the unknown number to represent the problem. | Grade 1 |
| Utah | 1.OA.3 | Apply properties of operations as strategies to add and subtract. For example: If 8 + 3 = 11 is known, then 3 + 8 = 11 is also known. (Commutative property of addition.) To add 2 + 6 + 4, the second two numbers can be added to make a ten, so 2 + 6 + 4 = 2 + 10 =12. (Associative property of addition.) First grade students need not use formal terms for these properties. | Grade 1 |
| Utah | 1.OA.4 | Understand subtraction as an unknown-addend problem. For example, subtract 10 – 8 by finding the number that makes 10 when added to 8. | Grade 1 |
| Utah | 1.OA.5 | Relate counting to addition and subtraction. For example, by counting on 2 to add 2. | Grade 1 |
| Utah | 1.OA.6 | Add and subtract within 20. | Grade 1 |
| Utah | 1.OA.7 | Understand the meaning of the equal sign, and determine whether equations involving addition and subtraction are true or false. For example, which of the following equations are true and which are false? 6 = 6, 7 = 8 – 1, 5 + 2 = 2 + 5, 4 + 1 = 5 + 2. | Grade 1 |
| Utah | 1.OA.8 | Determine the unknown whole number in an addition or subtraction equation relating three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations 8 + ? = 11, 5 = ? – 3, 6 + 6 = ? | Grade 1 |
| Utah | 2.G.1 | Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces. Sizes are compared directly or visually, not compared by measuring. Identify triangles, quadrilaterals, pentagons, hexagons, and cubes. | Grade 2 |
| Utah | 2.G.2 | Partition a rectangle into rows and columns of same-size squares and count to find the total number of squares. | Grade 2 |
| Utah | 2.G.3 | Partition circles and rectangles into two, three, or four equal shares; describe the shares using the words halves, thirds, half of, a third of, etc.; and describe the whole as two halves, three thirds, or four fourths. Recognize that equal shares of identical wholes need not have the same shape. | Grade 2 |
| Utah | 2.MD.1 | Measure the length of an object by selecting and using appropriate tools such as rulers, yardsticks, meter sticks, and measuring tapes. | Grade 2 |
| Utah | 2.MD.2 | Measure the length of an object twice, using length units of different lengths for the two measurements; describe how the two measurements relate to the size of the unit chosen. | Grade 2 |
| Utah | 2.MD.4 | Measure to determine how much longer one object is than another, expressing the length difference in terms of a standard length unit. For example, after measuring a pencil and a crayon, a student uses the measurements to determine that the pencil is two inches longer than the crayon. | Grade 2 |
| Utah | 2.MD.5 | Use addition and subtraction within 100 to solve word problems involving lengths that are given in the same units. For example, use drawings (such as drawings of rulers) and equations with a symbol for the unknown number to represent the problem. | Grade 2 |
| Utah | 2.MD.7 | Tell and write time from analog and digital clocks to the nearest five minutes, using a.m. and p.m. | Grade 2 |
| Utah | 2.MD.8 | Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies, using $ and ¢ symbols appropriately. For example, if you have 2 dimes and 3 pennies, how many cents do you have? | Grade 2 |
| Utah | 2.MD.9 | Generate measurement data by measuring lengths of several objects to the nearest whole unit, or by making repeated measurements of the same object. Show the measurements by making a line plot, where the horizontal scale is marked off in whole-number units. | Grade 2 |
| Utah | 2.MD.10 | Draw a picture graph and a bar graph (with single-unit scale) to represent a data set with up to four categories. Solve simple put-together, take-apart, and comparison problems using information presented in a bar graph. | Grade 2 |
| Utah | 2.NBT.1 | Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones; for example, 706 equals 7 hundreds, 0 tens, and 6 ones. Understand the following as special cases: | Grade 2 |
| Utah | 2.NBT.2 | Count within 1,000; skip-count by fives, tens, and hundreds. | Grade 2 |
| Utah | 2.NBT.3 | Read and write numbers to 1,000 using base-ten numerals, number names, and expanded form. | Grade 2 |
| Utah | 2.NBT.4 | Compare two three-digit numbers based on meanings of the hundreds, tens, and ones digits, using >, =, and < symbols to record the results of comparisons. | Grade 2 |
| Utah | 2.NBT.5 | Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction. | Grade 2 |
| Utah | 2.NBT.6 | Add up to four two-digit numbers using strategies based on place value and properties of operations. | Grade 2 |
| Utah | 2.NBT.7 | Add and subtract within 1,000 using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method. Understand that in adding or subtracting three-digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, and ones and ones, and that it is sometimes necessary to compose or decompose tens or hundreds. | Grade 2 |
| Utah | 2.NBT.8 | Mentally add 10 or 100 to a given number 100-900, and mentally subtract 10 or 100 from a given number 100-900. | Grade 2 |
| Utah | 2.OA.1 | Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing with unknowns in all positions, for example, by using drawings and equations with a symbol for the unknown number to represent the problem. | Grade 2 |
| Utah | 2.OA.2 | Fluently add and subtract within 20. | Grade 2 |
| Utah | 2.OA.3 | Determine whether a group of objects (up to 20) has an odd or even number of members, (for example, by pairing objects or counting them by twos). Write an equation to express an even number as a sum of two equal addends. | Grade 2 |
| Utah | 2.OA.4 | Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends. | Grade 2 |
| Utah | 3.G.1 | Understand that shapes in different categories (for example, rhombuses, rectangles, and others) may share attributes (for example, having four sides), and that the shared attributes can define a larger category (for example, quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories. | Grade 3 |
| Utah | 3.G.2 | Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole. For example, partition a shape into four parts with equal area, and describe the area of each part as 1/4 of the area of the shape. | Grade 3 |
| Utah | 3.MD.1 | Tell and write time to the nearest minute and measure time intervals in minutes. Solve word problems involving addition and subtraction of time intervals in minutes, for example, by representing the problem on a number line diagram. | Grade 3 |
| Utah | 3.MD.2 | Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), milliliters (ml), and liters (l). (Excludes compound units such as cubic centimeters [cc or cm3] and finding the geometric volume of a container.) Add, subtract, multiply, or divide to solve one-step word problems involving masses of objects or volumes of liquids that are given in the same units, for example, by using drawings (such as a beaker with a measurement scale) to represent the problem. (Excludes multiplicative comparison problems.) | Grade 3 |
| Utah | 3.MD.3 | Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and two-step "how many more" and "how many less" problems using information presented in scaled bar graphs. For example, draw a bar graph in which each square in the bar graph might represent five pets. | Grade 3 |
| Utah | 3.MD.4 | Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Show the data by making a line plot where the horizontal scale is marked off in appropriate units-whole numbers, halves, or quarters. | Grade 3 |
| Utah | 3.MD.5 | Recognize area as an attribute of plane figures and understand concepts of area measurement. | Grade 3 |
| Utah | 3.MD.6 | Measure area by counting unit squares (square centimeters, square meters, square inches, square feet, and improvised units). | Grade 3 |
| Utah | 3.MD.7 | Relate area to the operations of multiplication and addition (refer to 3.OA.5). | Grade 3 |
| Utah | 3.MD.8 | Solve real-world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters. | Grade 3 |
| Utah | 3.NBT.1 | Use place value understanding to round whole numbers to the nearest 10 or 100. | Grade 3 |
| Utah | 3.NBT.2 | Fluently add and subtract within 1,000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction. | Grade 3 |
| Utah | 3.NBT.3 | Multiply one-digit whole numbers by multiples of 10 in the range 10–90 (for example, 9 x 80 and 5 x 60) using strategies based on place value and properties of operations. | Grade 3 |
| Utah | 3.NF.1 | Understand that a unit fraction has a numerator of one and a non-zero denominator. | Grade 3 |
| Utah | 3.NF.2 | Understand a fraction as a number on the number line; represent fractions on a number line diagram. | Grade 3 |
| Utah | 3.NF.3 | Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size. | Grade 3 |
| Utah | 3.OA.1 | Interpret the products of whole numbers, such as interpreting 5 × 7 as the total number of objects in 5 groups of 7 objects each. For example, describe a context in which a total number of objects can be expressed as 5 × 7. | Grade 3 |
| Utah | 3.OA.2 | Interpret whole-number quotients of whole numbers. For example, interpret 56 ÷ 8 as the number of objects in each share when 56 objects are partitioned equally into eight shares (partitive), or as a number of shares when 56 objects are partitioned into equal shares of eight objects each (quotative). | Grade 3 |
| Utah | 3.OA.3 | Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities. For example, use drawings and equations with a symbol for the unknown number to represent the problem. | Grade 3 |
| Utah | 3.OA.4 | Determine the unknown whole number in a multiplication or division equation relating three whole numbers. For example, determine the unknown number—product, factor, quotient, dividend, or divisor—that makes the equation true in each of the equations 8 × ? = 48, 5 = ? ÷ 3, 6 × 6 = ?. | Grade 3 |
| Utah | 3.OA.5 | Apply properties of operations as strategies to multiply and divide. For example: If 6 × 4 = 24 is known, then 4 × 6 = 24 is also known (commutative property of multiplication). 3 × 5 × 2 can be found by 3 × 5 = 15, then 15 × 2 = 30, or by 5 × 2 = 10, then 3 × 10 = 30 (associative property of multiplication). Knowing that 8 × 5 = 40 and 8 × 2 = 16, one can find 8 × 7 as 8 × (5 + 2) = (8 × 5) + (8 × 2) = 40 + 16 = 56 (distributive property). (Third grade students may, but need not, use formal terms for these properties.) | Grade 3 |
| Utah | 3.OA.6 | Understand division as an unknown-factor problem. Understand the relationship between multiplication and division (multiplication and division are inverse operations). For example, find 32 ÷ 8 by finding the number that makes 32 when multiplied by 8. | Grade 3 |
| Utah | 3.OA.7 | Fluently multiply and divide. | Grade 3 |
| Utah | 3.OA.8 | Solve two-step word problems. | Grade 3 |
| Utah | 3.OA.9 | Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations. For example, observe that four times a number is always even, and explain why four times a number can be decomposed into two equal addends. | Grade 3 |
| Utah | 4.G.1 | Draw points, lines, line segments, rays, angles (right, acute, and obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures. | Grade 4 |
| Utah | 4.G.2 | Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles. | Grade 4 |
| Utah | 4.G.3 | Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify line-symmetric figures and draw lines of symmetry. | Grade 4 |
| Utah | 4.MD.1 | Know relative sizes of measurement units within each system of units (standard and metric), including kilometers, meters, and centimeters; liters and milliliters; kilograms and grams; pounds and ounces; hours, minutes, and seconds. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table. For example, know that one foot is 12 times as long as one inch. Express the length of a four-foot snake as 48 inches. Know that one meter is 100 times as long as one centimeter. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36)… | Grade 4 |
| Utah | 4.MD.2 | Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money. | Grade 4 |
| Utah | 4.MD.3 | Apply the area and perimeter formulas for rectangles in real-world and mathematical problems. For example, find the width of a rectangular room given the area of the flooring and the length, by viewing the area formula as a multiplication equation with an unknown factor. | Grade 4 |
| Utah | 4.MD.4 | Make a line plot to display a data set of measurements in fractions of a unit (halves, quarters, and eighths). Solve problems involving addition and subtraction with like denominators of fractions by using information presented in line plots. For example, use a line plot to find and interpret the difference in length between the longest and shortest pencils in a classroom. | Grade 4 |
| Utah | 4.MD.5 | Recognize angles as geometric figures that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement. | Grade 4 |
| Utah | 4.MD.6 | Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure. | Grade 4 |
| Utah | 4.MD.7 | Recognize angle measure as additive. | Grade 4 |
| Utah | 4.NBT.1 | Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. For example, recognize that 700 ÷ 70 = 10 by applying concepts of place value and division. | Grade 4 |
| Utah | 4.NBT.2 | Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. | Grade 4 |
| Utah | 4.NBT.3 | Use place value understanding to round multi-digit whole numbers to any place. | Grade 4 |
| Utah | 4.NBT.4 | Fluently add and subtract multi-digit whole numbers using the standard algorithm. | Grade 4 |
| Utah | 4.NBT.5 | Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. | Grade 4 |
| Utah | 4.NBT.6 | Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. | Grade 4 |
| Utah | 4.NF.1 | Explain why a fraction a/b is equivalent to a fraction (n x a)/(n x b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. | Grade 4 |
| Utah | 4.NF.2 | Compare two fractions with different numerators and different denominators, for example, by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, for example, by using a visual fraction model. | Grade 4 |
| Utah | 4.NF.3 | Understand a fraction a/b with a >1 as a sum of fractions 1/b. In other words, any fraction is a sum of unit fractions. | Grade 4 |
| Utah | 4.NF.4 | Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. | Grade 4 |
| Utah | 4.NF.5 | Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100. For example, express 3/10 as 30/100, and add 3/10 + 4/100 = 34/100. | Grade 4 |
| Utah | 4.NF.6 | Use decimal notation for fractions with denominators 10 or 100. For example, rewrite 0.62 as 62/100, describe a length as 0.62 meters; locate 0.62 on a number line diagram. | Grade 4 |
| Utah | 4.NF.7 | Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, for example, by using a visual model. | Grade 4 |
| Utah | 4.OA.1 | Interpret a multiplication equation as a comparison (for example, interpret 35 = 5 × 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5). Represent verbal statements of multiplicative comparisons as multiplication equations. | Grade 4 |
| Utah | 4.OA.2 | Multiply or divide to solve word problems involving multiplicative comparison, for example, by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison. | Grade 4 |
| Utah | 4.OA.3 | Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. | Grade 4 |
| Utah | 4.OA.4 | Find all factor pairs for a whole number in the range 1-100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1-100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1-100 is prime or composite. | Grade 4 |
| Utah | 4.OA.5 | Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. For example, given the rule "add 3" and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way. | Grade 4 |
| Utah | 5.G.1 | Compose and understand the coordinate plane. | Grade 5 |
| Utah | 5.G.2 | Represent real-world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. | Grade 5 |
| Utah | 5.G.3 | Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and all squares are rectangles, so all squares have four right angles. For example, all rectangles have four right angles and all squares are rectangles, so all squares have four right angles. | Grade 5 |
| Utah | 5.G.4 | Classify two-dimensional figures in a hierarchy based on properties. | Grade 5 |
| Utah | 5.MD.1 | Convert among different-sized standard measurement units within a given measurement system (for example, convert 5 cm to 0.05 m); use these conversions in solving multi-step, real-world problems. | Grade 5 |
| Utah | 5.MD.2 | Make a line plot to display a data set of measurements in fractions of a unit (halves, quarters, eighths). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given graduated cylinders with different measures of liquid in each, find the amount of liquid each cylinder would contain if the total amount in all the cylinders were redistributed equally. | Grade 5 |
| Utah | 5.MD.3 | Recognize volume as an attribute of solid figures and understand concepts of volume measurement. | Grade 5 |
| Utah | 5.MD.4 | Measure volumes by counting unit cubes, using cubic cm, cubic in., cubic ft., and improvised units. | Grade 5 |
| Utah | 5.MD.5 | Relate volume to the operations of multiplication and addition and solve real-world and mathematical problems involving volume. | Grade 5 |
| Utah | 5.NBT.1 | Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. | Grade 5 |
| Utah | 5.NBT.2 | Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. | Grade 5 |
| Utah | 5.NBT.3 | Read, write, and compare decimals to thousandths. | Grade 5 |
| Utah | 5.NBT.4 | Use place value understanding to round decimals to any place. | Grade 5 |
| Utah | 5.NBT.5 | Fluently multiply multi-digit whole numbers using the standard algorithm. | Grade 5 |
| Utah | 5.NBT.6 | Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. | Grade 5 |
| Utah | 5.NBT.7 | Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. In this standard, dividing decimals is limited to a whole number dividend with a decimal divisor or a decimal dividend with a whole number divisor. Compare the value of the quotient on the basis of the values of the dividend and divisor. | Grade 5 |
| Utah | 5.NF.1 | Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) | Grade 5 |
| Utah | 5.NF.2 | Solve real-world problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators by, for example, using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize 2/5 + 1/2 = 3/7 as an incorrect result, by observing that 3/7 < 1/2. | Grade 5 |
| Utah | 5.NF.3 | Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve real-world problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, through the use of visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing three by four, noting that 3/4 multiplied by four equals three, and that when three wholes are shared equally among four people each person has a share of size 3/4. If nine people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie? | Grade 5 |
| Utah | 5.NF.4 | Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. | Grade 5 |
| Utah | 5.NF.5 | Interpret multiplication as scaling. | Grade 5 |
| Utah | 5.NF.6 | Solve real-world problems involving multiplication of fractions and mixed numbers, for example, by using visual fraction models or equations to represent the problem. | Grade 5 |
| Utah | 5.NF.7 | Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. Use strategies to divide fractions by reasoning about the relationship between multiplication and division. Division of a fraction by a fraction is not a requirement at this grade. | Grade 5 |
| Utah | 5.OA.1 | Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. | Grade 5 |
| Utah | 5.OA.2 | Write and interpret simple numerical expressions. | Grade 5 |
| Utah | 5.OA.3 | Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. For example, given the rule "add 3" and the starting number 0, and given the rule "add 6" and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so. | Grade 5 |
| Utah | 6.EE.1 | Write and evaluate numerical expressions involving whole-number exponents. | Grade 6 |
| Utah | 6.EE.2 | Write, read, and evaluate expressions in which letters represent numbers. | Grade 6 |
| Utah | 6.EE.3 | Apply the properties of operations to generate equivalent expressions. For example, apply the distributive property to the expression 3(2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6(4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y. | Grade 6 |
| Utah | 6.EE.4 | Identify when two expressions are equivalent. For example, the expressions y + y + y and 3y are equivalent because they name the same number, regardless of which number y represents. | Grade 6 |
| Utah | 6.EE.5 | Understand solving an equation or inequality as a process of answering the question: Which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true. | Grade 6 |
| Utah | 6.EE.6 | Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set. | Grade 6 |
| Utah | 6.EE.7 | Solve real-world and mathematical problems by writing and solving equations of the form x + a = b and ax = b for cases in which a, b and x are all non-negative rational numbers. | Grade 6 |
| Utah | 6.EE.8 | Write an inequality of the form x > c or x c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams. | Grade 6 |
| Utah | 6.EE.9 | Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. For example, in a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to represent the relationship between distance and time. | Grade 6 |
| Utah | 6.G.1 | Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing and decomposing into rectangles, triangles and/or other shapes; apply these techniques in the context of solving real-world and mathematical problems. | Grade 6 |
| Utah | 6.G.2 | Find the volume of a right rectangular prism with appropriate unit fraction edge lengths by packing it with cubes of the appropriate unit fraction edge lengths (for example, 3½ × 2 × 6), and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas V = lwh and V = bh to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems. (Note: Model the packing using drawings and diagrams.) | Grade 6 |
| Utah | 6.G.3 | Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same x coordinate or the same y coordinate. Apply these techniques in the context of solving real-world and mathematical problems. | Grade 6 |
| Utah | 6.G.4 | Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems. | Grade 6 |
| Utah | 6.RP.1 | Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. The following are examples of ratio language: “The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every two wings there was one beak.” “For every vote candidate A received, candidate C received nearly three votes.” | Grade 6 |
| Utah | 6.RP.2 | Understand the concept of a unit rate a/b associated with a ratio a:b with b ≠ 0, and use rate language in the context of a ratio relationship. The following are examples of rate language: "This recipe has a ratio of four cups of flour to two cups of sugar, so the rate is two cups of flour for each cup of sugar.” “We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger.” (In sixth grade, unit rates are limited to non-complex fractions.) | Grade 6 |
| Utah | 6.RP.3 | Use ratio and rate reasoning to solve real-world (with a context) and mathematical (void of context) problems, using strategies such as reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations involving unit rate problems. | Grade 6 |
| Utah | 6.SP.5 | Summarize numerical data sets in relation to their context, such as by: | Grade 6 |
| Utah | 6.NS.1 | Interpret and compute quotients of fractions. | Grade 6 |
| Utah | 6.NS.2 | Fluently divide multi-digit numbers using the standard algorithm. | Grade 6 |
| Utah | 6.NS.3 | Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation. | Grade 6 |
| Utah | 6.NS.5 | Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (for example, temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of zero in each situation. | Grade 6 |
| Utah | 6.NS.6 | Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates. | Grade 6 |
| Utah | 6.NS.7 | Understand ordering and absolute value of rational numbers. | Grade 6 |
| Utah | 6.NS.8 | Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same x-coordinate or the same y-coordinate. | Grade 6 |
| Utah | 7.EE.1 | Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients. | Grade 7 |
| Utah | 7.EE.2 | Understand that rewriting an expression in different forms in a problem context can shed light on the problem, and how the quantities in it are related. For example, a + 0.05a = 1.05a means that “increase by 5%” is the same as “multiply by 1.05.” | Grade 7 |
| Utah | 7.EE.3 | Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form, convert between forms as appropriate, and assess the reasonableness of answers using mental computation and estimation strategies. For example: If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation. | Grade 7 |
| Utah | 7.EE.4 | Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. | Grade 7 |
| Utah | 7.G.1 | Solve problems involving scale drawings of geometric figures, such as computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale. | Grade 7 |
| Utah | 7.G.2 | Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle. | Grade 7 |
| Utah | 7.G.3 | Describe the two-dimensional figures that result from slicing three-dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids. | Grade 7 |
| Utah | 7.G.4 | Know the formulas for the area and circumference of a circle, and solve problems; give an informal derivation of the relationship between the circumference and area of a circle. | Grade 7 |
| Utah | 7.G.5 | Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write, and use them to solve simple equations for an unknown angle in a figure. | Grade 7 |
| Utah | 7.G.6 | Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. | Grade 7 |
| Utah | 7.RP.1 | Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. For example, if a person walks ½ mile in each ¼ hour, compute the unit rate as the complex fraction ½/¼ miles per hour, equivalently 2 miles per hour. | Grade 7 |
| Utah | 7.RP.2 | Recognize and represent proportional relationships between quantities. | Grade 7 |
| Utah | 7.RP.3 | Use proportional relationships to solve multi-step ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error. | Grade 7 |
| Utah | 7.NS.1 | Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram. | Grade 7 |
| Utah | 7.NS.2 | Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers. | Grade 7 |
| Utah | 7.NS.3 | Solve real-world and mathematical problems involving the four operations with rational numbers. Computations with rational numbers extend the rules for manipulating fractions to complex fractions. | Grade 7 |
| Utah | 8.EE.1 | Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, 3² × (3⁻⁵) = (3⁻³) = 1/3³ = 1/27. | Grade 8 |
| Utah | 8.EE.2 | Use square root and cube root symbols to represent solutions to equations of the form x² = p and x³ = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that √2 is irrational. | Grade 8 |
| Utah | 8.EE.3 | Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other. For example, estimate the population of the United States as 3 × 10⁸ and the population of the world as 7 × 10⁹, and determine that the world population is more than 20 times larger. | Grade 8 |
| Utah | 8.EE.4 | Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology. | Grade 8 |
| Utah | 8.EE.5 | Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed. | Grade 8 |
| Utah | 8.EE.6 | Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b. | Grade 8 |
| Utah | 8.EE.7 | Solve linear equations and inequalities in one variable. | Grade 8 |
| Utah | 8.EE.8 | Analyze and solve pairs of simultaneous linear equations. | Grade 8 |
| Utah | 8.F.1 | Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output. | Grade 8 |
| Utah | 8.F.2 | Compare properties of two functions, each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a linear function represented by a table of values and a linear function represented by an algebraic expression, determine which function has the greater rate of change. | Grade 8 |
| Utah | 8.F.3 | Interpret the equation y = mx + b as defining a linear function whose graph is a straight line; give examples of functions that are not linear. For example, the function A = s², giving the area of a square as a function of its side length, is not linear because its graph contains the points (1,1), (2,4) and (3,9), which are not on a straight line. | Grade 8 |
| Utah | 8.F.4 | Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values. | Grade 8 |
| Utah | 8.F.5 | Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally. | Grade 8 |
| Utah | 8.G.1 | Verify experimentally the properties of rotations, reflections, and translations: | Grade 8 |
| Utah | 8.G.2 | Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them. | Grade 8 |
| Utah | 8.G.3 | Observe that orientation of the plane is preserved in rotations and translations, but not with reflections. Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates. | Grade 8 |
| Utah | 8.G.4 | Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two-dimensional figures, describe a sequence that exhibits the similarity between them. | Grade 8 |
| Utah | 8.G.5 | Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. For example, arrange three copies of the same triangle so that the sum of the three angles appears to form a line, and give an argument in terms of transversals why this is so. | Grade 8 |
| Utah | 8.G.7 | Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions. | Grade 8 |
| Utah | 8.G.8 | Apply the Pythagorean Theorem to find the distance between two points in a coordinate system. | Grade 8 |
| Utah | 8.G.9 | Know the formulas for the volumes of cones, cylinders, and spheres, and use them to solve real-world and mathematical problems. | Grade 8 |
| Utah | 8.NS.2 | Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g., π²). For example, by truncating the decimal expansion of √2, show that √2 is between 1 and 2, then between 1.4 and 1.5, and explain how to continue on to get better approximations. | Grade 8 |
| Utah | 8.SP.1 | Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association. | Grade 8 |
| Utah | 8.SP.2 | Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line. | Grade 8 |
| Utah | A.CED.2 | Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. | Mathematics I |
| Utah | A.CED.3 | Represent constraints by equations or inequalities and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context. For example, represent inequalities describing nutritional and cost constraints on combinations of different foods. | Mathematics I |
| Utah | A.REI.3 | Solve equations and inequalities in one variable. | Mathematics I |
| Utah | F.IF.2 | Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. | Mathematics I |
| Utah | F.IF.4 | For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; and end behavior. | Mathematics I |
| Utah | F.IF.7 | Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. | Mathematics I |
| Utah | F.BF.1 | Write a function that describes a relationship between two quantities. | Mathematics I |
| Utah | S.ID.6 | Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. | Mathematics I |
| Utah | S.ID.8 | Compute (using technology) and interpret the correlation coefficient of a linear fit. | Mathematics I |
| Vermont | K.CC.A.1 | Count to 100 by ones and by tens. | Kindergarten |
| Vermont | K.CC.A.2 | Count forward beginning from a given number within the known sequence (instead of having to begin at 1). | Kindergarten |
| Vermont | K.CC.A.3 | Write numbers from 0 to 20. Represent a number of objects with a written numeral 0-20 (with 0 representing a count of no objects). | Kindergarten |
| Vermont | K.CC.B.4 | Understand the relationship between numbers and quantities; connect counting to cardinality. | Kindergarten |
| Vermont | K.CC.B.5 | Count to answer “how many?” questions about as many as 20 things arranged in a line, a rectangular array, or a circle, or as many as 10 things in a scattered configuration; given a number from 1-20, count out that many objects. | Kindergarten |
| Vermont | K.CC.C.6 | Identify whether the number of objects in one group is greater than, less than, or equal to the number of objects in another group, e.g., by using matching and counting strategies. | Kindergarten |
| Vermont | K.CC.C.7 | Compare two numbers between 1 and 10 presented as written numerals. | Kindergarten |
| Vermont | K.G.A.1 | Describe objects in the environment using names of shapes, and describe the relative positions of these objects using terms such as above, below, beside, in front of, behind, and next to. | Kindergarten |
| Vermont | K.G.A.2 | Correctly name shapes regardless of their orientations or overall size. | Kindergarten |
| Vermont | K.G.A.3 | Identify shapes as two-dimensional (lying in a plane, “flat”) or three-dimensional (“solid”). | Kindergarten |
| Vermont | K.G.B.4 | Analyze and compare two- and three-dimensional shapes, in different sizes and orientations, using informal language to describe their similarities, differences, parts (e.g., number of sides and vertices/“corners”) and other attributes (e.g., having sides of equal length). | Kindergarten |
| Vermont | K.G.B.6 | Compose simple shapes to form larger shapes. | Kindergarten |
| Vermont | K.MD.A.1 | Describe measurable attributes of objects, such as length or weight. Describe several measurable attributes of a single object. | Kindergarten |
| Vermont | K.MD.A.2 | Directly compare two objects with a measurable attribute in common, to see which object has “more of”/“less of” the attribute, and describe the difference. | Kindergarten |
| Vermont | K.MD.B.3 | Classify objects into given categories; count the numbers of objects in each category and sort the categories by count. | Kindergarten |
| Vermont | K.NBT.A.1 | Compose and decompose numbers from 11 to 19 into ten ones and some further ones, e.g., by using objects or drawings, and record each composition or decomposition by a drawing or equation (e.g., 18 = 10 + 8); understand that these numbers are composed of ten ones and one, two, three, four, five, six, seven, eight, or nine ones. | Kindergarten |
| Vermont | K.OA.A.1 | Represent addition and subtraction with objects, fingers, mental images, drawings, sounds (e.g., claps), acting out situations, verbal explanations, expressions, or equations. | Kindergarten |
| Vermont | K.OA.A.2 | Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem. | Kindergarten |
| Vermont | K.OA.A.3 | Decompose numbers less than or equal to 10 into pairs in more than one way, e.g., by using objects or drawings, and record each decomposition by a drawing or equation (e.g., 5 = 2 + 3 and 5 = 4 + 1). | Kindergarten |
| Vermont | K.OA.A.4 | For any number from 1 to 9, find the number that makes 10 when added to the given number, e.g., by using objects or drawings, and record the answer with a drawing or equation. | Kindergarten |
| Vermont | K.OA.A.5 | Fluently add and subtract within 5. | Kindergarten |
| Vermont | 1.G.A.1 | Distinguish between defining attributes (e.g., triangles are closed and three-sided) versus non-defining attributes (e.g., color, orientation, overall size); build and draw shapes to possess defining attributes. | Grade 1 |
| Vermont | 1.G.A.2 | Compose two-dimensional shapes (rectangles, squares, trapezoids, triangles, half-circles, and quarter-circles) or three-dimensional shapes (cubes, right rectangular prisms, right circular cones, and right circular cylinders) to create a composite shape, and compose new shapes from the composite shape. | Grade 1 |
| Vermont | 1.G.A.3 | Partition circles and rectangles into two and four equal shares, describe the shares using the words halves, fourths, and quarters, and use the phrases half of, fourth of, and quarter of. Describe the whole as two of, or four of the shares. Understand for these examples that decomposing into more equal shares creates smaller shares. | Grade 1 |
| Vermont | 1.MD.A.1 | Order three objects by length; compare the lengths of two objects indirectly by using a third object. | Grade 1 |
| Vermont | 1.MD.A.2 | Express the length of an object as a whole number of length units, by laying multiple copies of a shorter object (the length unit) end to end; understand that the length measurement of an object is the number of same-size length units that span it with no gaps or overlaps. | Grade 1 |
| Vermont | 1.MD.B.3 | Tell and write time in hours and half-hours using analog and digital clocks. | Grade 1 |
| Vermont | 1.MD.C.4 | Organize, represent, and interpret data with up to three categories; ask and answer questions about the total number of data points, how many in each category, and how many more or less are in one category than in another. | Grade 1 |
| Vermont | 1.NBT.A.1 | Count to 120, starting at any number less than 120. In this range, read and write numerals and represent a number of objects with a written numeral. | Grade 1 |
| Vermont | 1.NBT.B.2 | Understand that the two digits of a two-digit number represent amounts of tens and ones. Understand the following as special cases: | Grade 1 |
| Vermont | 1.NBT.B.3 | Compare two two-digit numbers based on meanings of the tens and ones digits, recording the results of comparisons with the symbols >, =, and <. | Grade 1 |
| Vermont | 1.NBT.C.4 | Add within 100, including adding a two-digit number and a one-digit number, and adding a two-digit number and a multiple of 10, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Understand that in adding two-digit numbers, one adds tens and tens, ones and ones; and sometimes it is necessary to compose a ten. | Grade 1 |
| Vermont | 1.NBT.C.5 | Given a two-digit number, mentally find 10 more or 10 less than the number, without having to count; explain the reasoning used. | Grade 1 |
| Vermont | 1.NBT.C.6 | Subtract multiples of 10 in the range 10-90 from multiples of 10 in the range 10-90 (positive or zero differences), using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. | Grade 1 |
| Vermont | 1.OA.A.1 | Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem. | Grade 1 |
| Vermont | 1.OA.B.3 | Apply properties of operations as strategies to add and subtract. | Grade 1 |
| Vermont | 1.OA.B.4 | Understand subtraction as an unknown-addend problem. | Grade 1 |
| Vermont | 1.OA.C.5 | Relate counting to addition and subtraction (e.g., by counting on 2 to add 2). | Grade 1 |
| Vermont | 1.OA.C.6 | Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to a ten (e.g., 13 - 4 = 13 - 3 - 1 = 10 - 1 = 9); using the relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 - 8 = 4); and creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13). | Grade 1 |
| Vermont | 1.OA.D.7 | Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false. | Grade 1 |
| Vermont | 1.OA.D.8 | Determine the unknown whole number in an addition or subtraction equation relating three whole numbers. | Grade 1 |
| Vermont | 2.G.A.1 | Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces. Identify triangles, quadrilaterals, pentagons, hexagons, and cubes. | Grade 2 |
| Vermont | 2.G.A.2 | Partition a rectangle into rows and columns of same-size squares and count to find the total number of them. | Grade 2 |
| Vermont | 2.G.A.3 | Partition circles and rectangles into two, three, or four equal shares, describe the shares using the words halves, thirds, half of, a third of, etc., and describe the whole as two halves, three thirds, four fourths. Recognize that equal shares of identical wholes need not have the same shape. | Grade 2 |
| Vermont | 2.MD.A.1 | Measure the length of an object by selecting and using appropriate tools such as rulers, yardsticks, meter sticks, and measuring tapes. | Grade 2 |
| Vermont | 2.MD.A.2 | Measure the length of an object twice, using length units of different lengths for the two measurements; describe how the two measurements relate to the size of the unit chosen. | Grade 2 |
| Vermont | 2.MD.A.4 | Measure to determine how much longer one object is than another, expressing the length difference in terms of a standard length unit. | Grade 2 |
| Vermont | 2.MD.B.5 | Use addition and subtraction within 100 to solve word problems involving lengths that are given in the same units, e.g., by using drawings (such as drawings of rulers) and equations with a symbol for the unknown number to represent the problem. | Grade 2 |
| Vermont | 2.MD.C.7 | Tell and write time from analog and digital clocks to the nearest five minutes, using a.m. and p.m. | Grade 2 |
| Vermont | 2.MD.C.8 | Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies, using $ and ¢ symbols appropriately. | Grade 2 |
| Vermont | 2.MD.D.9 | Generate measurement data by measuring lengths of several objects to the nearest whole unit, or by making repeated measurements of the same object. Show the measurements by making a line plot, where the horizontal scale is marked off in whole-number units. | Grade 2 |
| Vermont | 2.MD.D.10 | Draw a picture graph and a bar graph (with single-unit scale) to represent a data set with up to four categories. Solve simple put-together, take-apart, and compare problems using information presented in a bar graph. | Grade 2 |
| Vermont | 2.NBT.A.1 | Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones. Understand the following as special cases: | Grade 2 |
| Vermont | 2.NBT.A.2 | Count within 1000; skip-count by 5s, 10s, and 100s. | Grade 2 |
| Vermont | 2.NBT.A.3 | Read and write numbers to 1000 using base-ten numerals, number names, and expanded form. | Grade 2 |
| Vermont | 2.NBT.A.4 | Compare two three-digit numbers based on meanings of the hundreds, tens, and ones digits, using >, =, and < symbols to record the results of comparisons. | Grade 2 |
| Vermont | 2.NBT.B.5 | Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction. | Grade 2 |
| Vermont | 2.NBT.B.6 | Add up to four two-digit numbers using strategies based on place value and properties of operations. | Grade 2 |
| Vermont | 2.NBT.B.7 | Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method. Understand that in adding or subtracting three-digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds. | Grade 2 |
| Vermont | 2.NBT.B.8 | Mentally add 10 or 100 to a given number 100–900, and mentally subtract 10 or 100 from a given number 100–900. | Grade 2 |
| Vermont | 2.OA.A.1 | Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem. | Grade 2 |
| Vermont | 2.OA.B.2 | Fluently add and subtract within 20 using mental strategies. By end of Grade 2, know from memory all sums of two one-digit numbers. | Grade 2 |
| Vermont | 2.OA.C.3 | Determine whether a group of objects (up to 20) has an odd or even number of members, e.g., by pairing objects or counting them by 2s; write an equation to express an even number as a sum of two equal addends. | Grade 2 |
| Vermont | 2.OA.C.4 | Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends. | Grade 2 |
| Vermont | 3.G.A.1 | Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories. | Grade 3 |
| Vermont | 3.G.A.2 | Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole. | Grade 3 |
| Vermont | 3.MD.A.1 | Tell and write time to the nearest minute and measure time intervals in minutes. Solve word problems involving addition and subtraction of time intervals in minutes, e.g., by representing the problem on a number line diagram. | Grade 3 |
| Vermont | 3.MD.A.2 | Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l). Add, subtract, multiply, or divide to solve one-step word problems involving masses or volumes that are given in the same units, e.g., by using drawings (such as a beaker with a measurement scale) to represent the problem. | Grade 3 |
| Vermont | 3.MD.B.3 | Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and two-step “how many more” and “how many less” problems using information presented in scaled bar graphs. | Grade 3 |
| Vermont | 3.MD.B.4 | Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Show the data by making a line plot, where the horizontal scale is marked off in appropriate units-whole numbers, halves, or quarters. | Grade 3 |
| Vermont | 3.MD.C.5 | Recognize area as an attribute of plane figures and understand concepts of area measurement. | Grade 3 |
| Vermont | 3.MD.C.6 | Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units). | Grade 3 |
| Vermont | 3.MD.C.7 | Relate area to the operations of multiplication and addition. | Grade 3 |
| Vermont | 3.MD.D.8 | Solve real world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters. | Grade 3 |
| Vermont | 3.NBT.A.1 | Use place value understanding to round whole numbers to the nearest 10 or 100. | Grade 3 |
| Vermont | 3.NBT.A.2 | Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction. | Grade 3 |
| Vermont | 3.NBT.A.3 | Multiply one-digit whole numbers by multiples of 10 in the range 10–90 (e.g., 9 × 80, 5 × 60) using strategies based on place value and properties of operations. | Grade 3 |
| Vermont | 3.NF.A.1 | Understand a fraction 1/𝘣 as the quantity formed by 1 part when a whole is partitioned into 𝘣 equal parts; understand a fraction 𝘢/𝑏 as the quantity formed by 𝘢 parts of size 1/𝘣. | Grade 3 |
| Vermont | 3.NF.A.2 | Understand a fraction as a number on the number line; represent fractions on a number line diagram. | Grade 3 |
| Vermont | 3.NF.A.3 | Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size. | Grade 3 |
| Vermont | 3.OA.A.1 | Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each. | Grade 3 |
| Vermont | 3.OA.A.2 | Interpret whole-number quotients of whole numbers, e.g., interpret 56 ÷ 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each. | Grade 3 |
| Vermont | 3.OA.A.3 | Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem. | Grade 3 |
| Vermont | 3.OA.A.4 | Determine the unknown whole number in a multiplication or division equation relating three whole numbers. | Grade 3 |
| Vermont | 3.OA.B.5 | Apply properties of operations as strategies to multiply and divide. | Grade 3 |
| Vermont | 3.OA.B.6 | Understand division as an unknown-factor problem. | Grade 3 |
| Vermont | 3.OA.C.7 | Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 × 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers. | Grade 3 |
| Vermont | 3.OA.D.8 | Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. | Grade 3 |
| Vermont | 3.OA.D.9 | Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations. | Grade 3 |
| Vermont | 4.G.A.1 | Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures. | Grade 4 |
| Vermont | 4.G.A.2 | Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles. | Grade 4 |
| Vermont | 4.G.A.3 | Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify line-symmetric figures and draw lines of symmetry. | Grade 4 |
| Vermont | 4.MD.A.1 | Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table. | Grade 4 |
| Vermont | 4.MD.A.2 | Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. | Grade 4 |
| Vermont | 4.MD.A.3 | Apply the area and perimeter formulas for rectangles in real world and mathematical problems. | Grade 4 |
| Vermont | 4.MD.B.4 | Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots. | Grade 4 |
| Vermont | 4.MD.C.5 | Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement: | Grade 4 |
| Vermont | 4.MD.C.6 | Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure. | Grade 4 |
| Vermont | 4.MD.C.7 | Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems, e.g., by using an equation with a symbol for the unknown angle measure. | Grade 4 |
| Vermont | 4.NBT.A.1 | Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. | Grade 4 |
| Vermont | 4.NBT.A.2 | Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. | Grade 4 |
| Vermont | 4.NBT.A.3 | Use place value understanding to round multi-digit whole numbers to any place. | Grade 4 |
| Vermont | 4.NBT.B.4 | Fluently add and subtract multi-digit whole numbers using the standard algorithm. | Grade 4 |
| Vermont | 4.NBT.B.5 | Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. | Grade 4 |
| Vermont | 4.NBT.B.6 | Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. | Grade 4 |
| Vermont | 4.NF.A.1 | Explain why a fraction 𝘢/𝘣 is equivalent to a fraction (𝘯 × 𝘢)/(𝘯 × 𝘣) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. | Grade 4 |
| Vermont | 4.NF.A.2 | Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model. | Grade 4 |
| Vermont | 4.NF.B.3 | Understand a fraction 𝘢/𝘣 with 𝘢 > 1 as a sum of fractions 1/𝘣. | Grade 4 |
| Vermont | 4.NF.B.4 | Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. | Grade 4 |
| Vermont | 4.NF.C.5 | Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100. | Grade 4 |
| Vermont | 4.NF.C.6 | Use decimal notation for fractions with denominators 10 or 100. | Grade 4 |
| Vermont | 4.NF.C.7 | Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual model. | Grade 4 |
| Vermont | 4.OA.A.1 | Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 × 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations. | Grade 4 |
| Vermont | 4.OA.A.2 | Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison. | Grade 4 |
| Vermont | 4.OA.A.3 | Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. | Grade 4 |
| Vermont | 4.OA.B.4 | Find all factor pairs for a whole number in the range 1-100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1-100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1-100 is prime or composite. | Grade 4 |
| Vermont | 4.OA.C.5 | Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. | Grade 4 |
| Vermont | 5.G.A.1 | Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., 𝘹-axis and 𝘹-coordinate, 𝘺-axis and 𝘺-coordinate). | Grade 5 |
| Vermont | 5.G.A.2 | Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. | Grade 5 |
| Vermont | 5.G.B.3 | Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. | Grade 5 |
| Vermont | 5.G.B.4 | Classify two-dimensional figures in a hierarchy based on properties. | Grade 5 |
| Vermont | 5.MD.A.1 | Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. | Grade 5 |
| Vermont | 5.MD.B.2 | Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. | Grade 5 |
| Vermont | 5.MD.C.3 | Recognize volume as an attribute of solid figures and understand concepts of volume measurement. | Grade 5 |
| Vermont | 5.MD.C.4 | Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. | Grade 5 |
| Vermont | 5.MD.C.5 | Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume. | Grade 5 |
| Vermont | 5.NBT.A.1 | Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. | Grade 5 |
| Vermont | 5.NBT.A.2 | Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. | Grade 5 |
| Vermont | 5.NBT.A.3 | Read, write, and compare decimals to thousandths. | Grade 5 |
| Vermont | 5.NBT.A.4 | Use place value understanding to round decimals to any place. | Grade 5 |
| Vermont | 5.NBT.B.5 | Fluently multiply multi-digit whole numbers using the standard algorithm. | Grade 5 |
| Vermont | 5.NBT.B.6 | Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. | Grade 5 |
| Vermont | 5.NBT.B.7 | Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. | Grade 5 |
| Vermont | 5.NF.A.1 | Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. | Grade 5 |
| Vermont | 5.NF.A.2 | Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. | Grade 5 |
| Vermont | 5.NF.B.3 | Interpret a fraction as division of the numerator by the denominator (𝘢/𝘣 = 𝘢 ÷ 𝘣). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. | Grade 5 |
| Vermont | 5.NF.B.4 | Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. | Grade 5 |
| Vermont | 5.NF.B.5 | Interpret multiplication as scaling (resizing), by: | Grade 5 |
| Vermont | 5.NF.B.6 | Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. | Grade 5 |
| Vermont | 5.NF.B.7 | Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. | Grade 5 |
| Vermont | 5.OA.A.1 | Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. | Grade 5 |
| Vermont | 5.OA.A.2 | Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. | Grade 5 |
| Vermont | 5.OA.B.3 | Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. | Grade 5 |
| Vermont | 6.EE.A.1 | Write and evaluate numerical expressions involving whole-number exponents. | Grade 6 |
| Vermont | 6.EE.A.2 | Write, read, and evaluate expressions in which letters stand for numbers. | Grade 6 |
| Vermont | 6.EE.A.3 | Apply the properties of operations to generate equivalent expressions. | Grade 6 |
| Vermont | 6.EE.A.4 | Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). | Grade 6 |
| Vermont | 6.EE.B.5 | Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true. | Grade 6 |
| Vermont | 6.EE.B.6 | Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set. | Grade 6 |
| Vermont | 6.EE.B.7 | Solve real-world and mathematical problems by writing and solving equations of the form 𝘹 + 𝘱 = 𝘲 and 𝘱𝘹 = 𝘲 for cases in which 𝘱, 𝘲 and 𝘹 are all nonnegative rational numbers. | Grade 6 |
| Vermont | 6.EE.B.8 | Write an inequality of the form 𝘹 > 𝘤 or 𝘹 𝘤 or 𝘹 < 𝘤 have infinitely many solutions; represent solutions of such inequalities on number line diagrams. | Grade 6 |
| Vermont | 6.EE.C.9 | Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. | Grade 6 |
| Vermont | 6.G.A.1 | Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems. | Grade 6 |
| Vermont | 6.G.A.2 | Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas 𝘝 = 𝘭 𝘸 𝘩 and 𝘝 = 𝘣 𝘩 to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems. | Grade 6 |
| Vermont | 6.G.A.3 | Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems. | Grade 6 |
| Vermont | 6.G.A.4 | Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems. | Grade 6 |
| Vermont | 6.RP.A.1 | Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. | Grade 6 |
| Vermont | 6.RP.A.2 | Understand the concept of a unit rate 𝘢/𝘣 associated with a ratio 𝘢:𝘣 with 𝘣 ≠ 0, and use rate language in the context of a ratio relationship. | Grade 6 |
| Vermont | 6.RP.A.3 | Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. | Grade 6 |
| Vermont | 6.SP.B.5 | Summarize numerical data sets in relation to their context, such as by: | Grade 6 |
| Vermont | 6.NS.A.1 | Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. | Grade 6 |
| Vermont | 6.NS.B.2 | Fluently divide multi-digit numbers using the standard algorithm. | Grade 6 |
| Vermont | 6.NS.B.3 | Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation. | Grade 6 |
| Vermont | 6.NS.C.5 | Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation. | Grade 6 |
| Vermont | 6.NS.C.6 | Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates. | Grade 6 |
| Vermont | 6.NS.C.7 | Understand ordering and absolute value of rational numbers. | Grade 6 |
| Vermont | 6.NS.C.8 | Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. | Grade 6 |
| Vermont | 7.EE.A.1 | Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients. | Grade 7 |
| Vermont | 7.EE.A.2 | Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. | Grade 7 |
| Vermont | 7.EE.B.3 | Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. | Grade 7 |
| Vermont | 7.EE.B.4 | Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. | Grade 7 |
| Vermont | 7.G.A.1 | Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale. | Grade 7 |
| Vermont | 7.G.A.2 | Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle. | Grade 7 |
| Vermont | 7.G.A.3 | Describe the two-dimensional figures that result from slicing three-dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids. | Grade 7 |
| Vermont | 7.G.B.4 | Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle. | Grade 7 |
| Vermont | 7.G.B.5 | Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure. | Grade 7 |
| Vermont | 7.G.B.6 | Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. | Grade 7 |
| Vermont | 7.RP.A.1 | Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. | Grade 7 |
| Vermont | 7.RP.A.2 | Recognize and represent proportional relationships between quantities. | Grade 7 |
| Vermont | 7.RP.A.3 | Use proportional relationships to solve multistep ratio and percent problems. | Grade 7 |
| Vermont | 7.NS.A.1 | Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram. | Grade 7 |
| Vermont | 7.NS.A.2 | Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers. | Grade 7 |
| Vermont | 7.NS.A.3 | Solve real-world and mathematical problems involving the four operations with rational numbers. | Grade 7 |
| Vermont | 8.EE.A.1 | Know and apply the properties of integer exponents to generate equivalent numerical expressions. | Grade 8 |
| Vermont | 8.EE.A.2 | Use square root and cube root symbols to represent solutions to equations of the form 𝘹² = 𝘱 and 𝘹³ = 𝘱, where 𝘱 is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that √2 is irrational. | Grade 8 |
| Vermont | 8.EE.A.3 | Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other. | Grade 8 |
| Vermont | 8.EE.A.4 | Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology. | Grade 8 |
| Vermont | 8.EE.B.5 | Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. | Grade 8 |
| Vermont | 8.EE.B.6 | Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation 𝘺 = 𝘮𝘹 for a line through the origin and the equation 𝘺 = 𝘮𝘹 + 𝘣 for a line intercepting the vertical axis at 𝘣. | Grade 8 |
| Vermont | 8.EE.C.7 | Solve linear equations in one variable. | Grade 8 |
| Vermont | 8.EE.C.8 | Analyze and solve pairs of simultaneous linear equations. | Grade 8 |
| Vermont | 8.F.A.1 | Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output. | Grade 8 |
| Vermont | 8.F.A.2 | Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). | Grade 8 |
| Vermont | 8.F.A.3 | Interpret the equation 𝘺 = 𝘮𝘹 + 𝘣 as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. | Grade 8 |
| Vermont | 8.F.B.4 | Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (𝘹, 𝘺) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values. | Grade 8 |
| Vermont | 8.F.B.5 | Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally. | Grade 8 |
| Vermont | 8.G.A.1 | Verify experimentally the properties of rotations, reflections, and translations: | Grade 8 |
| Vermont | 8.G.A.2 | Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them. | Grade 8 |
| Vermont | 8.G.A.3 | Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates. | Grade 8 |
| Vermont | 8.G.A.4 | Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two-dimensional figures, describe a sequence that exhibits the similarity between them. | Grade 8 |
| Vermont | 8.G.A.5 | Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. | Grade 8 |
| Vermont | 8.G.B.7 | Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions. | Grade 8 |
| Vermont | 8.G.B.8 | Apply the Pythagorean Theorem to find the distance between two points in a coordinate system. | Grade 8 |
| Vermont | 8.G.C.9 | Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems. | Grade 8 |
| Vermont | 8.SP.A.1 | Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association. | Grade 8 |
| Vermont | 8.SP.A.2 | Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line. | Grade 8 |
| Vermont | 8.NS.A.2 | Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g., π²). | Grade 8 |
| Vermont | A-APR.B.3 | Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial. | High School |
| Vermont | A-CED.A.2 | Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. | High School |
| Vermont | A-CED.A.3 | Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context. | High School |
| Vermont | A-REI.B.3 | Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. | High School |
| Vermont | A-SSE.A.2 | Use the structure of an expression to identify ways to rewrite it. | High School |
| Vermont | A-SSE.B.3 | Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression. | High School |
| Vermont | F-BF.A.1 | Write a function that describes a relationship between two quantities. | High School |
| Vermont | F-IF.A.2 | Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. | High School |
| Vermont | F-IF.B.4 | For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. | High School |
| Vermont | F-IF.C.7 | Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. | High School |
| Vermont | S-ID.B.6 | Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. | High School |
| Virginia | K.1.a | The student will tell how many are in a given set of 20 or fewer objects by counting orally. | Kindergarten |
| Virginia | K.1.b | The student will read, write, and represent numbers from 0 through 20. | Kindergarten |
| Virginia | K.2.a | The student, given no more than three sets, each set containing 10 or fewer concrete objects, will compare and describe one set as having more, fewer, or the same number of objects as the other set(s). | Kindergarten |
| Virginia | K.2.b | The student, given no more than three sets, each set containing 10 or fewer concrete objects, will compare and order sets from least to greatest and greatest to least. | Kindergarten |
| Virginia | K.3.a | The student will count forward orally by ones from 0 to 100. | Kindergarten |
| Virginia | K.3.c | The student will identify the number after, without counting, when given any number between 0 and 100 and identify the number before, without counting, when given any number between 1 and 10. | Kindergarten |
| Virginia | K.3.d | The student will count forward by tens to determine the total number of objects to 100. | Kindergarten |
| Virginia | K.4.a | The student will recognize and describe with fluency part-whole relationships for numbers up to 5. | Kindergarten |
| Virginia | K.4.b | The student will investigate and describe part-whole relationships for numbers up to 10. | Kindergarten |
| Virginia | K.5 | The student will investigate fractions by representing and solving practical problems involving equal sharing with two sharers. | Kindergarten |
| Virginia | K.6 | The student will model and solve single-step story and picture problems with sums to 10 and differences within 10, using concrete objects. | Kindergarten |
| Virginia | K.7 | The student will recognize the attributes of a penny, nickel, dime, and quarter and identify the number of pennies equivalent to a nickel, a dime, and a quarter. | Kindergarten |
| Virginia | K.9 | The student will compare two objects or events, using direct comparisons, according to one or more of the following attributes: length (longer, shorter), height (taller, shorter), weight (heavier, lighter), temperature (hotter, colder), volume (more, less), and time (longer, shorter). | Kindergarten |
| Virginia | K.10.a | The student will identify and describe plane figures (circle, triangle, square, and rectangle). | Kindergarten |
| Virginia | K.10.b | The student will compare the size (smaller, larger) and shape of plane figures (circle, triangle, square, and rectangle). | Kindergarten |
| Virginia | K.10.c | The student will describe the location of one object relative to another (above, below, next to) and identify representations of plane figures (circle, triangle, square, and rectangle) regardless of their positions and orientations in space. | Kindergarten |
| Virginia | K.11.a | The student will collect, organize, and represent data. | Kindergarten |
| Virginia | K.11.b | The student will read and interpret data in object graphs, picture graphs, and tables. | Kindergarten |
| Virginia | K.12 | The student will sort and classify objects according to one attribute. | Kindergarten |
| Virginia | K.13 | The student will identify, describe, extend, create, and transfer repeating patterns. | Kindergarten |
| Virginia | 1.1.a | The student will count forward orally by ones to 110, starting at any number between 0 and 110. | Grade 1 |
| Virginia | 1.1.b | The student will write the numerals 0 to 110 in sequence and out-of-sequence. | Grade 1 |
| Virginia | 1.1.c | The student will count backward orally by ones when given any number between 1 and 30. | Grade 1 |
| Virginia | 1.1.d | The student will count forward orally by ones, twos, fives, and tens to determine the total number of objects to 110. | Grade 1 |
| Virginia | 1.2.a | The student, given up to 110 objects, will group a collection into tens and ones and write the corresponding numeral. | Grade 1 |
| Virginia | 1.2.b | The student, given up to 110 objects, will compare two numbers between 0 and 110 represented pictorially or with concrete objects, using the words greater than, less than or equal to. | Grade 1 |
| Virginia | 1.2.c | The student, given up to 110 objects, will order three or fewer sets from least to greatest and greatest to least. | Grade 1 |
| Virginia | 1.3 | The student, given an ordered set of ten objects and/or pictures, will indicate the ordinal position of each object, first through tenth. | Grade 1 |
| Virginia | 1.4.a | The student will represent and solve practical problems involving equal sharing with two or four sharers. | Grade 1 |
| Virginia | 1.4.b | The student will represent and name fractions for halves and fourths, using models. | Grade 1 |
| Virginia | 1.6 | The student will create and solve single-step story and picture problems using addition and subtraction within 20. | Grade 1 |
| Virginia | 1.7.a | The student will recognize and describe with fluency part-whole relationships for numbers up to 10. | Grade 1 |
| Virginia | 1.7.b | The student will demonstrate fluency with addition and subtraction within 10. | Grade 1 |
| Virginia | 1.9.a | The student will investigate the passage of time and tell time to the hour and half-hour, using analog and digital clocks. | Grade 1 |
| Virginia | 1.1 | The student will use nonstandard units to measure and compare length, weight, and volume. | Grade 1 |
| Virginia | 1.11.a | The student will identify, trace, describe, and sort plane figures (triangles, squares, rectangles, and circles) according to number of sides, vertices, and angles. | Grade 1 |
| Virginia | 1.11.b | The student will identify and describe representations of circles, squares, rectangles, and triangles in different environments, regardless of orientation, and explain reasoning. | Grade 1 |
| Virginia | 1.12.a | The student will collect, organize, and represent various forms of data using tables, picture graphs, and object graphs. | Grade 1 |
| Virginia | 1.12.b | The student will read and interpret data displayed in tables, picture graphs, and object graphs, using the vocabulary more, less, fewer, greater than, less than, and equal to. | Grade 1 |
| Virginia | 1.13 | The student will sort and classify concrete objects according to one or two attributes. | Grade 1 |
| Virginia | 1.14 | The student will identify, describe, extend, create, and transfer growing and repeating patterns. | Grade 1 |
| Virginia | 1.15 | The student will demonstrate an understanding of equality through the use of the equal symbol. | Grade 1 |
| Virginia | 2.1.a | The student will read, write, and identify the place and value of each digit in a three-digit numeral, with and without models. | Grade 2 |
| Virginia | 2.1.b | The student will identify the number that is 10 more, 10 less, 100 more, and 100 less than a given number up to 999. | Grade 2 |
| Virginia | 2.1.c | The student will compare and order whole numbers between 0 and 999. | Grade 2 |
| Virginia | 2.1.d | The student will round two-digit numbers to the nearest ten. | Grade 2 |
| Virginia | 2.2.a | The student will count forward by twos, fives, and tens to 120, starting at various multiples of 2, 5, or 10. | Grade 2 |
| Virginia | 2.2.b | The student will count backward by tens from 120. | Grade 2 |
| Virginia | 2.2.c | The student will use objects to determine whether a number is even or odd. | Grade 2 |
| Virginia | 2.4.a | The student will name and write fractions represented by a set, region, or length model for halves, fourths, eighths, thirds, and sixths. | Grade 2 |
| Virginia | 2.4.b | The student will represent fractional parts with models and with symbols. | Grade 2 |
| Virginia | 2.4.c | The student will compare the unit fractions for halves, fourths, eighths, thirds, and sixths, with models. | Grade 2 |
| Virginia | 2.5.a | The student will recognize and use the relationships between addition and subtraction to solve single-step practical problems, with whole numbers to 20. | Grade 2 |
| Virginia | 2.5.b | The student will demonstrate fluency with addition and subtraction within 20. | Grade 2 |
| Virginia | 2.6.a | The student will estimate sums and differences. | Grade 2 |
| Virginia | 2.6.b | The student will determine sums and differences, using various methods. | Grade 2 |
| Virginia | 2.6.c | The student will create and solve single-step and two-step practical problems involving addition and subtraction. | Grade 2 |
| Virginia | 2.7.a | The student will count and compare a collection of pennies, nickels, dimes, and quarters whose total value is $2.00 or less. | Grade 2 |
| Virginia | 2.7.b | The student will use the cent symbol, dollar symbol, and decimal point to write a value of money. | Grade 2 |
| Virginia | 2.8.a | The student will estimate and measure length to the nearest inch. | Grade 2 |
| Virginia | 2.8.b | The student will estimate and measure weight to the nearest pound. | Grade 2 |
| Virginia | 2.9 | The student will tell time and write time to the nearest five minutes, using analog and digital clocks. | Grade 2 |
| Virginia | 2.12.a | The student will draw a line of symmetry in a figure. | Grade 2 |
| Virginia | 2.12.b | The student will identify and create figures with at least one line of symmetry. | Grade 2 |
| Virginia | 2.13 | The student will identify, describe, compare, and contrast plane and solid figures (circles/spheres, squares/cubes, and rectangles/rectangular prisms). | Grade 2 |
| Virginia | 2.15.a | The student will collect, organize, and represent data in pictographs and bar graphs. | Grade 2 |
| Virginia | 2.15.b | The student will read and interpret data represented in pictographs and bar graphs. | Grade 2 |
| Virginia | 2.16 | The student will identify, describe, create, extend, and transfer patterns found in objects, pictures, and numbers. | Grade 2 |
| Virginia | 2.17 | The student will demonstrate an understanding of equality through the use of the equal symbol and the use of the not equal symbol. | Grade 2 |
| Virginia | 3.1.a | The student will read, write, and identify the place and value of each digit in a six-digit whole number, with and without models. | Grade 3 |
| Virginia | 3.1.b | The student will round whole numbers, 9,999 or less, to the nearest ten, hundred, and thousand. | Grade 3 |
| Virginia | 3.1.c | The student will compare and order whole numbers, each 9,999 or less. | Grade 3 |
| Virginia | 3.2.a | The student will name and write fractions and mixed numbers represented by a model. | Grade 3 |
| Virginia | 3.2.b | The student will represent fractions and mixed numbers with models and symbols. | Grade 3 |
| Virginia | 3.2.c | The student will compare fractions having like and unlike denominators, using words and symbols (greater than, less than, equal to or not equal to) with models. | Grade 3 |
| Virginia | 3.3.a | The student will estimate and determine the sum or difference of two whole numbers. | Grade 3 |
| Virginia | 3.3.b | The student will create and solve single-step and multistep practical problems involving sums or differences of two whole numbers, each 9,999 or less. | Grade 3 |
| Virginia | 3.4.a | The student will represent multiplication and division through 10 x 10, using a variety of approaches and models. | Grade 3 |
| Virginia | 3.4.b | The student will create and solve single-step practical problems that involve multiplication and division through 10 x 10. | Grade 3 |
| Virginia | 3.4.c | The student will demonstrate fluency with multiplication facts of 0, 1, 2, 5, and 10. | Grade 3 |
| Virginia | 3.4.d | The student will solve single-step practical problems involving multiplication of whole numbers, where one factor is 99 or less and the second factor is 5 or less. | Grade 3 |
| Virginia | 3.5 | The student will solve practical problems that involve addition and subtraction with proper fractions having like denominators of 12 or less. | Grade 3 |
| Virginia | 3.7.a | The student will estimate and use U.S. Customary and metric units to measure length to the nearest 1/2 inch, inch, foot, yard, centimeter, and meter. | Grade 3 |
| Virginia | 3.7.b | The student will estimate and use U.S. Customary and metric units to measure liquid volume in cups, pints, quarts, gallons, and liters. | Grade 3 |
| Virginia | 3.8.a | The student will estimate and measure the distance around a polygon in order to determine its perimeter using U.S. Customary and metric units. | Grade 3 |
| Virginia | 3.8.b | The student will estimate and count the number of square units needed to cover a given surface in order to determine its area. | Grade 3 |
| Virginia | 3.9.a | The student will tell time to the nearest minute, using analog and digital clocks. | Grade 3 |
| Virginia | 3.9.b | The student will solve practical problems related to elapsed time in one-hour increments within a 12-hour period. | Grade 3 |
| Virginia | 3.9.c | The student will identify equivalent periods of time and solve practical problems related to equivalent periods of time. | Grade 3 |
| Virginia | 3.1 | The student will read temperature to the nearest degree. | Grade 3 |
| Virginia | 3.11 | The student will identify and draw representations of points, lines, line segments, rays, and angles. | Grade 3 |
| Virginia | 3.12.a | The student will define polygon. | Grade 3 |
| Virginia | 3.12.b | The student will identify and name polygons with 10 or fewer sides. | Grade 3 |
| Virginia | 3.12.c | The student will combine and subdivide polygons with three or four sides and name the resulting polygon(s). | Grade 3 |
| Virginia | 3.15.a | The student will collect, organize, and represent data in pictographs or bar graphs. | Grade 3 |
| Virginia | 3.15.b | The student will collect, organize, read, and interpret data represented in pictographs and bar graphs. | Grade 3 |
| Virginia | 3.16 | The student will identify, describe, create, and extend patterns found in objects, pictures, numbers and tables. | Grade 3 |
| Virginia | 4.1.a | The student will read, write, and identify the place and value of each digit in a nine-digit whole number. | Grade 4 |
| Virginia | 4.1.b | The student will compare and order whole numbers expressed through millions. | Grade 4 |
| Virginia | 4.1.c | The student will round whole numbers expressed through millions to the nearest thousand, ten thousand, and hundred thousand. | Grade 4 |
| Virginia | 4.2.a | The student will compare and order fractions and mixed numbers, with and without models. | Grade 4 |
| Virginia | 4.2.b | The student will represent equivalent fractions. | Grade 4 |
| Virginia | 4.2.c | The student will identify the division statement that represents a fraction, with models and in context. | Grade 4 |
| Virginia | 4.3.a | The student will read, write, represent, and identify decimals expressed through thousandths. | Grade 4 |
| Virginia | 4.3.b | The student will round decimals to the nearest whole number. | Grade 4 |
| Virginia | 4.3.c | The student will compare and order decimals. | Grade 4 |
| Virginia | 4.3.d | The student will, given a model, write the decimal and fraction equivalents. | Grade 4 |
| Virginia | 4.4.a | The student will demonstrate fluency with multiplication facts through 12 x 12, and the corresponding division facts. | Grade 4 |
| Virginia | 4.4.b | The student will estimate and determine sums, differences, and products of whole numbers. | Grade 4 |
| Virginia | 4.4.c | The student will estimate and determine quotients of whole numbers, with and without remainders. | Grade 4 |
| Virginia | 4.4.d | The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers. | Grade 4 |
| Virginia | 4.5.a | The student will determine common multiples and factors, including least common multiple and greatest common factor. | Grade 4 |
| Virginia | 4.5.b | The student will add and subtract fractions and mixed numbers having like and unlike denominators. | Grade 4 |
| Virginia | 4.5.c | The student will solve single-step practical problems involving addition and subtraction with fractions and mixed numbers. | Grade 4 |
| Virginia | 4.6.a | The student will add and subtract with decimals. | Grade 4 |
| Virginia | 4.6.b | The student will solve single-step and multistep practical problems involving addition and subtraction with decimals. | Grade 4 |
| Virginia | 4.7 | The student will solve practical problems that involve determining perimeter and area in U.S. Customary and metric units. | Grade 4 |
| Virginia | 4.8.a | The student will estimate and measure length and describe the result in U.S. Customary and metric units. | Grade 4 |
| Virginia | 4.8.b | The student will estimate and measure weight/mass and describe the result in U.S. Customary and metric units. | Grade 4 |
| Virginia | 4.8.c | The student will, given the equivalent measure of one unit, identify equivalent measures of length, weight/mass, and liquid volume between units within the U.S. Customary system. | Grade 4 |
| Virginia | 4.8.d | The student will solve practical problems that involve length, weight/mass, and liquid volume in U.S. Customary units. | Grade 4 |
| Virginia | 4.9 | The student will solve practical problems related to elapsed time in hours and minutes within a 12-hour period. | Grade 4 |
| Virginia | 4.10.a | The student will identify and describe points, lines, line segments, rays, and angles, including endpoints and vertices. | Grade 4 |
| Virginia | 4.10.b | The student will identify and describe intersecting, parallel, and perpendicular lines. | Grade 4 |
| Virginia | 4.11 | The student will identify, describe, compare, and contrast plane and solid figures according to their characteristics (number of angles, vertices, edges, and the number and shape of faces) using concrete models and pictorial representations. | Grade 4 |
| Virginia | 4.12 | The student will classify quadrilaterals as a parallelograms, rectangles, squares, rhombi, and/or trapezoids. | Grade 4 |
| Virginia | 4.14.a | The student will collect, organize, and represent data in bar graphs and line graphs. | Grade 4 |
| Virginia | 4.14.b | The student will interpret data represented in bar graphs and line graphs. | Grade 4 |
| Virginia | 4.15 | The student will identify, describe, create, and extend patterns found in objects, pictures, numbers, and tables. | Grade 4 |
| Virginia | 4.16 | The student will recognize and demonstrate the meaning of equality in an equation. | Grade 4 |
| Virginia | 5.1 | The student, given a decimal through thousandths, will round to the nearest whole number, tenth, or hundredth. | Grade 5 |
| Virginia | 5.2.a | The student will represent and identify equivalencies among fractions and decimals, with and without models. | Grade 5 |
| Virginia | 5.2.b | The student will compare and order fractions, mixed numbers, and/or decimals in a given set, from least to greatest and greatest to least. | Grade 5 |
| Virginia | 5.3.a | The student will identify and describe the characteristics of prime and composite numbers. | Grade 5 |
| Virginia | 5.3.b | identify and describe the characteristics of even and odd numbers. | Grade 5 |
| Virginia | 5.4 | The student will create and solve single-step and multistep practical problems involving addition, subtraction, multiplication, and division of whole numbers. | Grade 5 |
| Virginia | 5.5.a | The student will estimate and determine the product and quotient of two numbers involving decimals. | Grade 5 |
| Virginia | 5.5.b | The student will create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication of decimals, and create and solve single-step practical problems involving division of decimals. | Grade 5 |
| Virginia | 5.6.a | The student will solve single-step and multistep practical problems involving addition and subtraction with fractions and mixed numbers. | Grade 5 |
| Virginia | 5.6.b | The student will solve single-step practical problems involving multiplication of a whole number, limited to 12 or less, and a proper fraction, with models. | Grade 5 |
| Virginia | 5.7 | The student will simplify whole number numerical expressions using the order of operations. | Grade 5 |
| Virginia | 5.8.a | The student will solve practical problems that involve perimeter, area, and volume in standard units of measure. | Grade 5 |
| Virginia | 5.8.b | The student will differentiate among perimeter, area, and volume and identify whether the application of the concept of perimeter, area, or volume is appropriate for a given situation. | Grade 5 |
| Virginia | 5.9.a | The student will, given the equivalent measure of one unit, identify equivalent measurements within the metric system. | Grade 5 |
| Virginia | 5.9.b | The student will solve practical problems involving length, mass, and liquid volume using metric units. | Grade 5 |
| Virginia | 5.11 | The student will solve practical problems related to elapsed time in hours and minutes within a 24-hour period. | Grade 5 |
| Virginia | 5.12 | The student will classify and measure right, acute, obtuse, and straight angles. | Grade 5 |
| Virginia | 5.13.a | The student will classify triangles as right, acute, or obtuse and equilateral, scalene, or isosceles. | Grade 5 |
| Virginia | 5.13.b | The student will investigate the sum of the interior angles in a triangle and determine an unknown angle measure. | Grade 5 |
| Virginia | 5.14.a | The student will recognize and apply transformations, such as translation, reflection, and rotation. | Grade 5 |
| Virginia | 5.16.a | The student, given a practical problem, will represent data in line plots and stem-and-leaf plots. | Grade 5 |
| Virginia | 5.16.b | The student, given a practical problem, will interpret data represented in line plots and stem-and-leaf plots. | Grade 5 |
| Virginia | 5.17.a | The student, given a practical problem, will describe mean, median, and mode as measures of center. | Grade 5 |
| Virginia | 5.17.d | The student, given a practical problem, will determine the mean, median, mode, and range of a set of data. | Grade 5 |
| Virginia | 5.18 | The student will identify, describe, create, express, and extend number patterns found in objects, pictures, numbers and tables. | Grade 5 |
| Virginia | 5.19.a | The student will investigate and describe the concept of variable. | Grade 5 |
| Virginia | 5.19.b | The student will write an equation to represent a given mathematical relationship, using a variable. | Grade 5 |
| Virginia | 5.19.c | The student will use an expression with a variable to represent a given verbal expression involving one operation. | Grade 5 |
| Virginia | 6.1 | The student will represent relationships between quantities using ratios, and will use appropriate notations, such as a/b, a to b, and a:b. | Grade 6 |
| Virginia | 6.2.a | The student will represent and determine equivalencies among fractions, mixed numbers, decimals, and percents. | Grade 6 |
| Virginia | 6.2.b | The student will compare and order positive rational numbers. | Grade 6 |
| Virginia | 6.3.a | The student will identify and represent integers. | Grade 6 |
| Virginia | 6.3.b | The student will compare and order integers. | Grade 6 |
| Virginia | 6.3.c | The student will identify and describe absolute value of integers. | Grade 6 |
| Virginia | 6.4 | The student will recognize and represent patterns with whole number exponents and perfect squares. | Grade 6 |
| Virginia | 6.5.a | The student will multiply and divide fractions and mixed numbers. | Grade 6 |
| Virginia | 6.5.b | The student will solve single-step and multistep practical problems involving addition, subtraction, multiplication, and division of fractions and mixed numbers. | Grade 6 |
| Virginia | 6.5.c | The student will solve multistep practical problems involving addition, subtraction, multiplication, and division of decimals. | Grade 6 |
| Virginia | 6.6.a | The student will add, subtract, multiply, and divide integers. | Grade 6 |
| Virginia | 6.6.b | The student will solve practical problems involving operations with integers. | Grade 6 |
| Virginia | 6.6.c | The student will simplify numerical expressions involving integers. | Grade 6 |
| Virginia | 6.7.b | The student will solve problems, including practical problems, involving circumference and area of a circle. | Grade 6 |
| Virginia | 6.7.c | The student will solve problems, including practical problems, involving area and perimeter of triangles and rectangles. | Grade 6 |
| Virginia | 6.8.a | The student will identify the components of the coordinate plane. | Grade 6 |
| Virginia | 6.8.b | The student will identify the coordinates of a point and graph ordered pairs in a coordinate plane. | Grade 6 |
| Virginia | 6.9 | The student will determine congruence of segments, angles, and polygons. | Grade 6 |
| Virginia | 6.12.a | The student will represent a proportional relationship between two quantities, including those arising from practical situations. | Grade 6 |
| Virginia | 6.12.b | The student will determine the unit rate of a proportional relationship and use it to find a missing value in a ratio table. | Grade 6 |
| Virginia | 6.12.c | The student will determine whether a proportional relationship exists between two quantities. | Grade 6 |
| Virginia | 6.12.d | The student will make connections between and among representations of a proportional relationship between two quantities using verbal descriptions, ratio tables, and graphs. | Grade 6 |
| Virginia | 6.13 | The student will solve one-step linear equations in one variable, including practical problems that require the solution of a one-step linear equation in one variable. | Grade 6 |
| Virginia | 6.14.a | The student will represent a practical situation with a linear inequality in one variable. | Grade 6 |
| Virginia | 6.14.b | The student will solve one-step linear inequalities in one variable, involving addition or subtraction, and graph the solution on a number line. | Grade 6 |
| Virginia | 7.1.a | The student will investigate and describe the concept of negative exponents for powers of ten. | Grade 7 |
| Virginia | 7.1.b | The student will compare and order numbers greater than zero written in scientific notation. | Grade 7 |
| Virginia | 7.1.c | The student will compare and order rational numbers. | Grade 7 |
| Virginia | 7.1.d | The student will determine square roots of perfect squares. | Grade 7 |
| Virginia | 7.1.e | The student will identify and describe absolute value of rational numbers. | Grade 7 |
| Virginia | 7.2 | The student will solve practical problems involving operations with rational numbers. | Grade 7 |
| Virginia | 7.3 | The student will solve single-step and multistep practical problems, using proportional reasoning. | Grade 7 |
| Virginia | 7.4.a | The student will describe and determine the volume and surface area of rectangular prisms and cylinders. | Grade 7 |
| Virginia | 7.4.b | The student will solve problems, including practical problems, involving the volume and surface area of rectangular prisms and cylinders. | Grade 7 |
| Virginia | 7.5 | The student will solve problems, including practical problems, involving the relationship between corresponding sides and corresponding angles of similar quadrilaterals and triangles. | Grade 7 |
| Virginia | 7.6.a | The student will compare and contrast quadrilaterals based on their properties. | Grade 7 |
| Virginia | 7.6.b | The student will determine unknown side lengths or angle measures of quadrilaterals. | Grade 7 |
| Virginia | 7.7 | The student will apply translations and reflections of right triangles or rectangles in the coordinate plane. | Grade 7 |
| Virginia | 7.10.a | The student will determine the slope, m, as rate of change in a proportional relationship between two quantities and write an equation in the form y = mx to represent the relationship. | Grade 7 |
| Virginia | 7.10.b | The student will graph a line representing a proportional relationship between two quantities given the slope and an ordered pair, or given the equation in y = mx form where m represents the slope as rate of change. | Grade 7 |
| Virginia | 7.10.d | The student will graph a line representing an additive relationship between two quantities given the y-intercept and an ordered pair, or given the equation in the form y = x + b, where b represents the y-intercept. | Grade 7 |
| Virginia | 7.10.e | The student will make connections between and among representations of a proportional or additive relationship between two quantities using verbal descriptions, tables, equations, and graphs. | Grade 7 |
| Virginia | 7.11 | The student will evaluate algebraic expressions for given replacement values of the variables. | Grade 7 |
| Virginia | 7.12 | The student will solve two-step linear equations in one variable, including practical problems that require the solution of a two-step linear equation in one variable. | Grade 7 |
| Virginia | 7.13 | The student will solve one- and two-step linear inequalities in one variable, including practical problems, involving addition, subtraction, multiplication, and division, and graph the solution on a number line. | Grade 7 |
| Virginia | 8.1 | The student will compare and order real numbers. | Grade 8 |
| Virginia | 8.2 | The student will describe the relationships between the subsets of the real number system. | Grade 8 |
| Virginia | 8.3.a | The student will estimate and determine the two consecutive integers between which a square root lies. | Grade 8 |
| Virginia | 8.3.b | The student will determine both the positive and negative square roots of a given perfect square. | Grade 8 |
| Virginia | 8.4 | The student will solve practical problems involving consumer applications. | Grade 8 |
| Virginia | 8.5 | The student will use the relationships among pairs of angles that are vertical angles, adjacent angles, supplementary angles, and complementary angles to determine the measure of unknown angles. | Grade 8 |
| Virginia | 8.6.a | The student will solve problems, including practical problems, involving volume and surface area of cones and square-based pyramids. | Grade 8 |
| Virginia | 8.6.b | The student will describe how changing one measured attribute of a rectangular prism affects the volume and surface area. | Grade 8 |
| Virginia | 8.7.a | The student will, given a polygon, apply transformations, to include translations, reflections, and dilations, in the coordinate plane. | Grade 8 |
| Virginia | 8.9.a | The student will verify the Pythagorean Theorem. | Grade 8 |
| Virginia | 8.9.b | The student will apply the Pythagorean Theorem. | Grade 8 |
| Virginia | 8.1 | The student will solve area and perimeter problems, including practical problems, involving composite plane figures. | Grade 8 |
| Virginia | 8.13.a | The student will represent data in scatterplots. | Grade 8 |
| Virginia | 8.13.b | The student will make observations about data represented in scatterplots. | Grade 8 |
| Virginia | 8.13.c | The student will use a drawing to estimate the line of best fit for data represented in a scatterplot. | Grade 8 |
| Virginia | 8.14.a | The student will evaluate an algebraic expression for given replacement values of the variables. | Grade 8 |
| Virginia | 8.14.b | The student will simplify algebraic expressions in one variable. | Grade 8 |
| Virginia | 8.15.a | The student will determine whether a given relation is a function. | Grade 8 |
| Virginia | 8.16.a | The student will recognize and describe the graph of a linear function with a slope that is positive, negative, or zero. | Grade 8 |
| Virginia | 8.16.b | The student will identify the slope and y-intercept of a linear function, given a table of values, a graph, or an equation in y = mx + b form. | Grade 8 |
| Virginia | 8.16.c | The student will determine the independent and dependent variable, given a practical situation modeled by a linear function. | Grade 8 |
| Virginia | 8.16.d | The student will graph a linear function given the equation in y = mx + b form. | Grade 8 |
| Virginia | 8.16.e | The student will make connections between and among representations of a linear function using verbal descriptions, tables, equations, and graphs. | Grade 8 |
| Virginia | 8.17 | The student will solve multistep linear equations in one variable with the variable on one or both sides of the equation, including practical problems that require the solution of a multistep linear equation in one variable. | Grade 8 |
| Virginia | 8.18 | The student will solve multistep linear inequalities in one variable with the variable on one or both sides of the inequality symbol, including practical problems, and graph the solution on a number line. | Grade 8 |
| Virginia | EI.A.4.a | The student will solve multistep linear equations in one variable algebraically. | Algebra |
| Virginia | A.4.c | The student will solve literal equations for a specified variable. | Algebra |
| Virginia | A.4.d | The student will solve systems of two linear equations in two variables algebraically and graphically. | Algebra |
| Virginia | A.4.e | The student will solve practical problems involving equations and systems of equations. | Algebra |
| Virginia | A.5.a | The student will solve multistep linear inequalities in one variable algebraically and represent the solution graphically. | Algebra |
| Virginia | A.5.c | The student will solve practical problems involving inequalities. | Algebra |
| Virginia | A.6.a | The student will determine the slope of a line when given an equation of the line, the graph of the line, or two points on the line. | Algebra |
| Virginia | A.6.b | The student will write the equation of a line when given the graph of the line, two points on the line, or the slope and a point on the line. | Algebra |
| Virginia | A.1.a | The student will represent verbal quantitative situations algebraically. | Algebra |
| Virginia | A.2.a | The student will perform operations on polynomials, including applying the laws of exponents to perform operations on expressions. | Algebra |
| Virginia | A.2.b | The student will perform operations on polynomials, including adding, subtracting, multiplying, and dividing polynomials. | Algebra |
| Virginia | A.2.c | The student will perform operations on polynomials, including factoring completely first- and second-degree binomials and trinomials in one variable. | Algebra |
| Virginia | A.3.c | The student will simplify numerical expressions containing square or cube roots. | Algebra |
| Virginia | A.7.a | The student will investigate and analyze linear and quadratic function families and their characteristics both algebraically and graphically, including determining whether a relation is a function. | Algebra |
| Virginia | A.7.c | The student will investigate and analyze linear and quadratic function families and their characteristics both algebraically and graphically, including zeros. | Algebra |
| Virginia | A.7.d | The student will investigate and analyze linear and quadratic function families and their characteristics both algebraically and graphically, including intercepts. | Algebra |
| Virginia | A.7.e | The student will investigate and analyze linear and quadratic function families and their characteristics both algebraically and graphically, including values of a function for elements in its domain. | Algebra |
| Virginia | A.7.f | The student will investigate and analyze linear and quadratic function families and their characteristics both algebraically and graphically, including connections between and among multiple representations of functions using verbal descriptions, tables, equations, and graphs. | Algebra |
| Virginia | A.8 | The student, given a data set or practical situation, will analyze a relation to determine whether a direct or inverse variation exists, and represent a direct variation algebraically and graphically and an inverse variation algebraically. | Algebra |
| Virginia | A.9 | The student will collect and analyze data, determine the equation of the curve of best fit in order to make predictions, and solve practical problems, using mathematical models of linear and quadratic functions. | Algebra |
| Virginia | AII.3.a | The student will solve absolute value linear equations and inequalities. | Algebra II |
| Virginia | AII.3.c | The student will solve equations containing rational algebraic expressions. | Algebra II |
| Virginia | AII.1.b | The student will add, subtract, multiply, divide, and simplify radical expressions containing rational numbers and variables, and expressions containing rational exponents. | Algebra II |
| Virginia | AII.1.c | The student will factor polynomials completely in one or two variables. | Algebra II |
| Virginia | AII.5 | The student will investigate and apply the properties of arithmetic and geometric sequences and series to solve practical problems, including writing the first n terms, determining then nth term, and evaluating summation formulas. Notation will include summation and a sub n. | Algebra II |
| Virginia | AII.6.a | For absolute value, square root, cube root, rational, polynomial, exponential, and logarithmic functions, the student will recognize the general shape of function families. | Algebra II |
| Virginia | AII.6.b | For absolute value, square root, cube root, rational, polynomial, exponential, and logarithmic functions, the student will use knowledge of transformations to convert between equations and the corresponding graphs of functions. | Algebra II |
| Virginia | AII.7.b | The student will investigate and analyze linear, quadratic, absolute value, square root, cube root, rational, polynomial, exponential, and logarithmic function families algebraically and graphically. Key concepts include intervals in which a function is increasing or decreasing. | Algebra II |
| Virginia | AII.7.c | The student will investigate and analyze linear, quadratic, absolute value, square root, cube root, rational, polynomial, exponential, and logarithmic function families algebraically and graphically. Key concepts include extrema. | Algebra II |
| Virginia | AII.7.d | The student will investigate and analyze linear, quadratic, absolute value, square root, cube root, rational, polynomial, exponential, and logarithmic function families algebraically and graphically. Key concepts include zeros. | Algebra II |
| Virginia | AII.7.e | The student will investigate and analyze linear, quadratic, absolute value, square root, cube root, rational, polynomial, exponential, and logarithmic function families algebraically and graphically. Key concepts include intercepts. | Algebra II |
| Virginia | AII.7.g | The student will investigate and analyze linear, quadratic, absolute value, square root, cube root, rational, polynomial, exponential, and logarithmic function families algebraically and graphically. Key concepts include connections between and among multiple representations of functions using verbal descriptions, tables, equations, and graphs. | Algebra II |
| Virginia | AII.7.k | The student will investigate and analyze linear, quadratic, absolute value, square root, cube root, rational, polynomial, exponential, and logarithmic function families algebraically and graphically. Key concepts include composition of functions algebraically and graphically. | Algebra II |
| Virginia | AII.8 | The student will investigate and describe the relationships among solutions of an equation, zeros of a function, x-intercepts of a graph, and factors of a polynomial expression. | Algebra II |
| Virginia | AII.10 | The student will represent and solve problems, including practical problems, involving inverse variation, joint variation, and a combination of direct and inverse variations. | Algebra II |
| Virginia | AII.9 | The student will collect and analyze data, determine the equation of the curve of best fit in order to make predictions, and solve practical problems, using mathematical models of quadratic and exponential functions. | Algebra II |
| Virginia | G.10.a | The student will solve problems, including practical problems, involving angles of convex polygons. This will include determining the sum of the interior and/or exterior angles. | Geometry |
| Virginia | G.10.b | The student will solve problems, including practical problems, involving angles of convex polygons. This will include determining the measure of an interior and/or exterior angle. | Geometry |
| Virginia | G.9 | The student will verify and use properties of quadrilaterals to solve problems, including practical problems. | Geometry |
| Virginia | G.2.a | The student will use the relationships between angles formed by two lines intersected by a transversal to prove two or more lines are parallel. | Geometry |
| Virginia | G.2.b | The student will use the relationships between angles formed by two lines intersected by a transversal to solve problems, including practical problems, involving angles formed when parallel lines are intersected by a transversal. | Geometry |
| Virginia | G.3.a | The student will solve problems involving symmetry and transformation. This will include investigating and using formulas for determining distance, midpoint, and slope. | Geometry |
| Virginia | G.3.d | The student will solve problems involving symmetry and transformation. This will include determining whether a figure has been translated, reflected, rotated, or dilated, using coordinate methods. | Geometry |
| Virginia | G.5.c | The student, given information concerning the lengths of sides and/or measures of angles in triangles, will solve problems, including practical problems. This will include determining whether a triangle exists. | Geometry |
| Virginia | G.7 | The student, given information in the form of a figure or statement, will prove two triangles are similar. | Geometry |
| Virginia | G.8.a | The student will solve problems, including practical problems, involving right triangles. This will include applying the Pythagorean Theorem and its converse. | Geometry |
| Virginia | G.13 | The student will use surface area and volume of three-dimensional objects to solve practical problems. | Geometry |
| Virginia | G.14.b | The student will apply the concepts of similarity to two- or three-dimensional geometric figures. This will include determining how changes in one or more dimensions of a figure affect area and/or volume of the figure. | Geometry |
| Virginia | G.14.c | The student will apply the concepts of similarity to two- or three-dimensional geometric figures. This will include determining how changes in area and/or volume of a figure affect one or more dimensions of the figure. | Geometry |
| Virginia | PS.4 | The student will analyze scatterplots to identify and describe the relationship between two variables, using shape; strength of relationship; clusters; positive, negative, or no association; outliers; and influential points. | Probability and Statistics |
| Virginia | PS.5 | The student will determine and interpret linear correlation, use the method of least squares regression to model the linear relationship between two variables, and use the residual plots to assess linearity. | Probability and Statistics |
| Washington | K.CC.A.1 | Count to 100 by ones and by tens. | Kindergarten |
| Washington | K.CC.A.2 | Count forward beginning from a given number within the known sequence (instead of having to begin at 1). | Kindergarten |
| Washington | K.CC.A.3 | Write numbers from 0 to 20. Represent a number of objects with a written numeral 0-20 (with 0 representing a count of no objects). | Kindergarten |
| Washington | K.CC.B.4 | Understand the relationship between numbers and quantities; connect counting to cardinality. | Kindergarten |
| Washington | K.CC.B.5 | Count to answer “how many?” questions about as many as 20 things arranged in a line, a rectangular array, or a circle, or as many as 10 things in a scattered configuration; given a number from 1-20, count out that many objects. | Kindergarten |
| Washington | K.CC.C.6 | Identify whether the number of objects in one group is greater than, less than, or equal to the number of objects in another group, e.g., by using matching and counting strategies. | Kindergarten |
| Washington | K.CC.C.7 | Compare two numbers between 1 and 10 presented as written numerals. | Kindergarten |
| Washington | K.G.A.1 | Describe objects in the environment using names of shapes, and describe the relative positions of these objects using terms such as above, below, beside, in front of, behind, and next to. | Kindergarten |
| Washington | K.G.A.2 | Correctly name shapes regardless of their orientations or overall size. | Kindergarten |
| Washington | K.G.A.3 | Identify shapes as two-dimensional (lying in a plane, “flat”) or three-dimensional (“solid”). | Kindergarten |
| Washington | K.G.B.4 | Analyze and compare two- and three-dimensional shapes, in different sizes and orientations, using informal language to describe their similarities, differences, parts (e.g., number of sides and vertices/“corners”) and other attributes (e.g., having sides of equal length). | Kindergarten |
| Washington | K.G.B.6 | Compose simple shapes to form larger shapes. | Kindergarten |
| Washington | K.MD.A.1 | Describe measurable attributes of objects, such as length or weight. Describe several measurable attributes of a single object. | Kindergarten |
| Washington | K.MD.A.2 | Directly compare two objects with a measurable attribute in common, to see which object has “more of”/“less of” the attribute, and describe the difference. | Kindergarten |
| Washington | K.MD.B.3 | Classify objects into given categories; count the numbers of objects in each category and sort the categories by count. | Kindergarten |
| Washington | K.NBT.A.1 | Compose and decompose numbers from 11 to 19 into ten ones and some further ones, e.g., by using objects or drawings, and record each composition or decomposition by a drawing or equation (e.g., 18 = 10 + 8); understand that these numbers are composed of ten ones and one, two, three, four, five, six, seven, eight, or nine ones. | Kindergarten |
| Washington | K.OA.A.1 | Represent addition and subtraction with objects, fingers, mental images, drawings, sounds (e.g., claps), acting out situations, verbal explanations, expressions, or equations. | Kindergarten |
| Washington | K.OA.A.2 | Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem. | Kindergarten |
| Washington | K.OA.A.3 | Decompose numbers less than or equal to 10 into pairs in more than one way, e.g., by using objects or drawings, and record each decomposition by a drawing or equation (e.g., 5 = 2 + 3 and 5 = 4 + 1). | Kindergarten |
| Washington | K.OA.A.4 | For any number from 1 to 9, find the number that makes 10 when added to the given number, e.g., by using objects or drawings, and record the answer with a drawing or equation. | Kindergarten |
| Washington | K.OA.A.5 | Fluently add and subtract within 5. | Kindergarten |
| Washington | 1.G.A.1 | Distinguish between defining attributes (e.g., triangles are closed and three-sided) versus non-defining attributes (e.g., color, orientation, overall size); build and draw shapes to possess defining attributes. | Grade 1 |
| Washington | 1.G.A.2 | Compose two-dimensional shapes (rectangles, squares, trapezoids, triangles, half-circles, and quarter-circles) or three-dimensional shapes (cubes, right rectangular prisms, right circular cones, and right circular cylinders) to create a composite shape, and compose new shapes from the composite shape. | Grade 1 |
| Washington | 1.G.A.3 | Partition circles and rectangles into two and four equal shares, describe the shares using the words halves, fourths, and quarters, and use the phrases half of, fourth of, and quarter of. Describe the whole as two of, or four of the shares. Understand for these examples that decomposing into more equal shares creates smaller shares. | Grade 1 |
| Washington | 1.MD.A.1 | Order three objects by length; compare the lengths of two objects indirectly by using a third object. | Grade 1 |
| Washington | 1.MD.A.2 | Express the length of an object as a whole number of length units, by laying multiple copies of a shorter object (the length unit) end to end; understand that the length measurement of an object is the number of same-size length units that span it with no gaps or overlaps. | Grade 1 |
| Washington | 1.MD.B.3 | Tell and write time in hours and half-hours using analog and digital clocks. | Grade 1 |
| Washington | 1.MD.C.4 | Organize, represent, and interpret data with up to three categories; ask and answer questions about the total number of data points, how many in each category, and how many more or less are in one category than in another. | Grade 1 |
| Washington | 1.NBT.A.1 | Count to 120, starting at any number less than 120. In this range, read and write numerals and represent a number of objects with a written numeral. | Grade 1 |
| Washington | 1.NBT.B.2 | Understand that the two digits of a two-digit number represent amounts of tens and ones. Understand the following as special cases: | Grade 1 |
| Washington | 1.NBT.B.3 | Compare two two-digit numbers based on meanings of the tens and ones digits, recording the results of comparisons with the symbols >, =, and <. | Grade 1 |
| Washington | 1.NBT.C.4 | Add within 100, including adding a two-digit number and a one-digit number, and adding a two-digit number and a multiple of 10, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Understand that in adding two-digit numbers, one adds tens and tens, ones and ones; and sometimes it is necessary to compose a ten. | Grade 1 |
| Washington | 1.NBT.C.5 | Given a two-digit number, mentally find 10 more or 10 less than the number, without having to count; explain the reasoning used. | Grade 1 |
| Washington | 1.NBT.C.6 | Subtract multiples of 10 in the range 10-90 from multiples of 10 in the range 10-90 (positive or zero differences), using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. | Grade 1 |
| Washington | 1.OA.A.1 | Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem. | Grade 1 |
| Washington | 1.OA.B.3 | Apply properties of operations as strategies to add and subtract. | Grade 1 |
| Washington | 1.OA.B.4 | Understand subtraction as an unknown-addend problem. | Grade 1 |
| Washington | 1.OA.C.5 | Relate counting to addition and subtraction (e.g., by counting on 2 to add 2). | Grade 1 |
| Washington | 1.OA.C.6 | Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to a ten (e.g., 13 - 4 = 13 - 3 - 1 = 10 - 1 = 9); using the relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 - 8 = 4); and creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13). | Grade 1 |
| Washington | 1.OA.D.7 | Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false. | Grade 1 |
| Washington | 1.OA.D.8 | Determine the unknown whole number in an addition or subtraction equation relating three whole numbers. | Grade 1 |
| Washington | 2.G.A.1 | Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces. Identify triangles, quadrilaterals, pentagons, hexagons, and cubes. | Grade 2 |
| Washington | 2.G.A.2 | Partition a rectangle into rows and columns of same-size squares and count to find the total number of them. | Grade 2 |
| Washington | 2.G.A.3 | Partition circles and rectangles into two, three, or four equal shares, describe the shares using the words halves, thirds, half of, a third of, etc., and describe the whole as two halves, three thirds, four fourths. Recognize that equal shares of identical wholes need not have the same shape. | Grade 2 |
| Washington | 2.MD.A.1 | Measure the length of an object by selecting and using appropriate tools such as rulers, yardsticks, meter sticks, and measuring tapes. | Grade 2 |
| Washington | 2.MD.A.2 | Measure the length of an object twice, using length units of different lengths for the two measurements; describe how the two measurements relate to the size of the unit chosen. | Grade 2 |
| Washington | 2.MD.A.4 | Measure to determine how much longer one object is than another, expressing the length difference in terms of a standard length unit. | Grade 2 |
| Washington | 2.MD.B.5 | Use addition and subtraction within 100 to solve word problems involving lengths that are given in the same units, e.g., by using drawings (such as drawings of rulers) and equations with a symbol for the unknown number to represent the problem. | Grade 2 |
| Washington | 2.MD.C.7 | Tell and write time from analog and digital clocks to the nearest five minutes, using a.m. and p.m. | Grade 2 |
| Washington | 2.MD.C.8 | Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies, using $ and ¢ symbols appropriately. | Grade 2 |
| Washington | 2.MD.D.9 | Generate measurement data by measuring lengths of several objects to the nearest whole unit, or by making repeated measurements of the same object. Show the measurements by making a line plot, where the horizontal scale is marked off in whole-number units. | Grade 2 |
| Washington | 2.MD.D.10 | Draw a picture graph and a bar graph (with single-unit scale) to represent a data set with up to four categories. Solve simple put-together, take-apart, and compare problems using information presented in a bar graph. | Grade 2 |
| Washington | 2.NBT.A.1 | Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones. Understand the following as special cases: | Grade 2 |
| Washington | 2.NBT.A.2 | Count within 1000; skip-count by 5s, 10s, and 100s. | Grade 2 |
| Washington | 2.NBT.A.3 | Read and write numbers to 1000 using base-ten numerals, number names, and expanded form. | Grade 2 |
| Washington | 2.NBT.A.4 | Compare two three-digit numbers based on meanings of the hundreds, tens, and ones digits, using >, =, and < symbols to record the results of comparisons. | Grade 2 |
| Washington | 2.NBT.B.5 | Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction. | Grade 2 |
| Washington | 2.NBT.B.6 | Add up to four two-digit numbers using strategies based on place value and properties of operations. | Grade 2 |
| Washington | 2.NBT.B.7 | Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method. Understand that in adding or subtracting three-digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds. | Grade 2 |
| Washington | 2.NBT.B.8 | Mentally add 10 or 100 to a given number 100–900, and mentally subtract 10 or 100 from a given number 100–900. | Grade 2 |
| Washington | 2.OA.A.1 | Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem. | Grade 2 |
| Washington | 2.OA.B.2 | Fluently add and subtract within 20 using mental strategies. By end of Grade 2, know from memory all sums of two one-digit numbers. | Grade 2 |
| Washington | 2.OA.C.3 | Determine whether a group of objects (up to 20) has an odd or even number of members, e.g., by pairing objects or counting them by 2s; write an equation to express an even number as a sum of two equal addends. | Grade 2 |
| Washington | 2.OA.C.4 | Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends. | Grade 2 |
| Washington | 3.G.A.1 | Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories. | Grade 3 |
| Washington | 3.G.A.2 | Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole. | Grade 3 |
| Washington | 3.MD.A.1 | Tell and write time to the nearest minute and measure time intervals in minutes. Solve word problems involving addition and subtraction of time intervals in minutes, e.g., by representing the problem on a number line diagram. | Grade 3 |
| Washington | 3.MD.A.2 | Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l). Add, subtract, multiply, or divide to solve one-step word problems involving masses or volumes that are given in the same units, e.g., by using drawings (such as a beaker with a measurement scale) to represent the problem. | Grade 3 |
| Washington | 3.MD.B.3 | Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and two-step “how many more” and “how many less” problems using information presented in scaled bar graphs. | Grade 3 |
| Washington | 3.MD.B.4 | Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Show the data by making a line plot, where the horizontal scale is marked off in appropriate units-whole numbers, halves, or quarters. | Grade 3 |
| Washington | 3.MD.C.5 | Recognize area as an attribute of plane figures and understand concepts of area measurement. | Grade 3 |
| Washington | 3.MD.C.6 | Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units). | Grade 3 |
| Washington | 3.MD.C.7 | Relate area to the operations of multiplication and addition. | Grade 3 |
| Washington | 3.MD.D.8 | Solve real world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters. | Grade 3 |
| Washington | 3.NBT.A.1 | Use place value understanding to round whole numbers to the nearest 10 or 100. | Grade 3 |
| Washington | 3.NBT.A.2 | Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction. | Grade 3 |
| Washington | 3.NBT.A.3 | Multiply one-digit whole numbers by multiples of 10 in the range 10–90 (e.g., 9 × 80, 5 × 60) using strategies based on place value and properties of operations. | Grade 3 |
| Washington | 3.NF.A.1 | Understand a fraction 1/𝘣 as the quantity formed by 1 part when a whole is partitioned into 𝘣 equal parts; understand a fraction 𝘢/𝑏 as the quantity formed by 𝘢 parts of size 1/𝘣. | Grade 3 |
| Washington | 3.NF.A.2 | Understand a fraction as a number on the number line; represent fractions on a number line diagram. | Grade 3 |
| Washington | 3.NF.A.3 | Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size. | Grade 3 |
| Washington | 3.OA.A.1 | Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each. | Grade 3 |
| Washington | 3.OA.A.2 | Interpret whole-number quotients of whole numbers, e.g., interpret 56 ÷ 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each. | Grade 3 |
| Washington | 3.OA.A.3 | Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem. | Grade 3 |
| Washington | 3.OA.A.4 | Determine the unknown whole number in a multiplication or division equation relating three whole numbers. | Grade 3 |
| Washington | 3.OA.B.5 | Apply properties of operations as strategies to multiply and divide. | Grade 3 |
| Washington | 3.OA.B.6 | Understand division as an unknown-factor problem. | Grade 3 |
| Washington | 3.OA.C.7 | Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 × 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers. | Grade 3 |
| Washington | 3.OA.D.8 | Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. | Grade 3 |
| Washington | 3.OA.D.9 | Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations. | Grade 3 |
| Washington | 4.G.A.1 | Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures. | Grade 4 |
| Washington | 4.G.A.2 | Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles. | Grade 4 |
| Washington | 4.G.A.3 | Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify line-symmetric figures and draw lines of symmetry. | Grade 4 |
| Washington | 4.MD.A.1 | Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table. | Grade 4 |
| Washington | 4.MD.A.2 | Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. | Grade 4 |
| Washington | 4.MD.A.3 | Apply the area and perimeter formulas for rectangles in real world and mathematical problems. | Grade 4 |
| Washington | 4.MD.B.4 | Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots. | Grade 4 |
| Washington | 4.MD.C.5 | Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement: | Grade 4 |
| Washington | 4.MD.C.6 | Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure. | Grade 4 |
| Washington | 4.MD.C.7 | Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems, e.g., by using an equation with a symbol for the unknown angle measure. | Grade 4 |
| Washington | 4.NBT.A.1 | Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. | Grade 4 |
| Washington | 4.NBT.A.2 | Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. | Grade 4 |
| Washington | 4.NBT.A.3 | Use place value understanding to round multi-digit whole numbers to any place. | Grade 4 |
| Washington | 4.NBT.B.4 | Fluently add and subtract multi-digit whole numbers using the standard algorithm. | Grade 4 |
| Washington | 4.NBT.B.5 | Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. | Grade 4 |
| Washington | 4.NBT.B.6 | Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. | Grade 4 |
| Washington | 4.NF.A.1 | Explain why a fraction 𝘢/𝘣 is equivalent to a fraction (𝘯 × 𝘢)/(𝘯 × 𝘣) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. | Grade 4 |
| Washington | 4.NF.A.2 | Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model. | Grade 4 |
| Washington | 4.NF.B.3 | Understand a fraction 𝘢/𝘣 with 𝘢 > 1 as a sum of fractions 1/𝘣. | Grade 4 |
| Washington | 4.NF.B.4 | Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. | Grade 4 |
| Washington | 4.NF.C.5 | Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100. | Grade 4 |
| Washington | 4.NF.C.6 | Use decimal notation for fractions with denominators 10 or 100. | Grade 4 |
| Washington | 4.NF.C.7 | Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual model. | Grade 4 |
| Washington | 4.OA.A.1 | Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 × 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations. | Grade 4 |
| Washington | 4.OA.A.2 | Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison. | Grade 4 |
| Washington | 4.OA.A.3 | Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. | Grade 4 |
| Washington | 4.OA.B.4 | Find all factor pairs for a whole number in the range 1-100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1-100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1-100 is prime or composite. | Grade 4 |
| Washington | 4.OA.C.5 | Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. | Grade 4 |
| Washington | 5.G.A.1 | Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., 𝘹-axis and 𝘹-coordinate, 𝘺-axis and 𝘺-coordinate). | Grade 5 |
| Washington | 5.G.A.2 | Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. | Grade 5 |
| Washington | 5.G.B.3 | Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. | Grade 5 |
| Washington | 5.G.B.4 | Classify two-dimensional figures in a hierarchy based on properties. | Grade 5 |
| Washington | 5.MD.A.1 | Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. | Grade 5 |
| Washington | 5.MD.B.2 | Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. | Grade 5 |
| Washington | 5.MD.C.3 | Recognize volume as an attribute of solid figures and understand concepts of volume measurement. | Grade 5 |
| Washington | 5.MD.C.4 | Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. | Grade 5 |
| Washington | 5.MD.C.5 | Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume. | Grade 5 |
| Washington | 5.NBT.A.1 | Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. | Grade 5 |
| Washington | 5.NBT.A.2 | Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. | Grade 5 |
| Washington | 5.NBT.A.3 | Read, write, and compare decimals to thousandths. | Grade 5 |
| Washington | 5.NBT.A.4 | Use place value understanding to round decimals to any place. | Grade 5 |
| Washington | 5.NBT.B.5 | Fluently multiply multi-digit whole numbers using the standard algorithm. | Grade 5 |
| Washington | 5.NBT.B.6 | Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. | Grade 5 |
| Washington | 5.NBT.B.7 | Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. | Grade 5 |
| Washington | 5.NF.A.1 | Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. | Grade 5 |
| Washington | 5.NF.A.2 | Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. | Grade 5 |
| Washington | 5.NF.B.3 | Interpret a fraction as division of the numerator by the denominator (𝘢/𝘣 = 𝘢 ÷ 𝘣). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. | Grade 5 |
| Washington | 5.NF.B.4 | Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. | Grade 5 |
| Washington | 5.NF.B.5 | Interpret multiplication as scaling (resizing), by: | Grade 5 |
| Washington | 5.NF.B.6 | Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. | Grade 5 |
| Washington | 5.NF.B.7 | Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. | Grade 5 |
| Washington | 5.OA.A.1 | Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. | Grade 5 |
| Washington | 5.OA.A.2 | Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. | Grade 5 |
| Washington | 5.OA.B.3 | Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. | Grade 5 |
| Washington | 6.EE.A.1 | Write and evaluate numerical expressions involving whole-number exponents. | Grade 6 |
| Washington | 6.EE.A.2 | Write, read, and evaluate expressions in which letters stand for numbers. | Grade 6 |
| Washington | 6.EE.A.3 | Apply the properties of operations to generate equivalent expressions. | Grade 6 |
| Washington | 6.EE.A.4 | Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). | Grade 6 |
| Washington | 6.EE.B.5 | Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true. | Grade 6 |
| Washington | 6.EE.B.6 | Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set. | Grade 6 |
| Washington | 6.EE.B.7 | Solve real-world and mathematical problems by writing and solving equations of the form 𝘹 + 𝘱 = 𝘲 and 𝘱𝘹 = 𝘲 for cases in which 𝘱, 𝘲 and 𝘹 are all nonnegative rational numbers. | Grade 6 |
| Washington | 6.EE.B.8 | Write an inequality of the form 𝘹 > 𝘤 or 𝘹 𝘤 or 𝘹 < 𝘤 have infinitely many solutions; represent solutions of such inequalities on number line diagrams. | Grade 6 |
| Washington | 6.EE.C.9 | Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. | Grade 6 |
| Washington | 6.G.A.1 | Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems. | Grade 6 |
| Washington | 6.G.A.2 | Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas 𝘝 = 𝘭 𝘸 𝘩 and 𝘝 = 𝘣 𝘩 to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems. | Grade 6 |
| Washington | 6.G.A.3 | Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems. | Grade 6 |
| Washington | 6.G.A.4 | Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems. | Grade 6 |
| Washington | 6.RP.A.1 | Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. | Grade 6 |
| Washington | 6.RP.A.2 | Understand the concept of a unit rate 𝘢/𝘣 associated with a ratio 𝘢:𝘣 with 𝘣 ≠ 0, and use rate language in the context of a ratio relationship. | Grade 6 |
| Washington | 6.RP.A.3 | Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. | Grade 6 |
| Washington | 6.SP.B.5 | Summarize numerical data sets in relation to their context, such as by: | Grade 6 |
| Washington | 6.NS.A.1 | Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. | Grade 6 |
| Washington | 6.NS.B.2 | Fluently divide multi-digit numbers using the standard algorithm. | Grade 6 |
| Washington | 6.NS.B.3 | Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation. | Grade 6 |
| Washington | 6.NS.C.5 | Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation. | Grade 6 |
| Washington | 6.NS.C.6 | Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates. | Grade 6 |
| Washington | 6.NS.C.7 | Understand ordering and absolute value of rational numbers. | Grade 6 |
| Washington | 6.NS.C.8 | Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. | Grade 6 |
| Washington | 7.EE.A.1 | Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients. | Grade 7 |
| Washington | 7.EE.A.2 | Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. | Grade 7 |
| Washington | 7.EE.B.3 | Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. | Grade 7 |
| Washington | 7.EE.B.4 | Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. | Grade 7 |
| Washington | 7.G.A.1 | Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale. | Grade 7 |
| Washington | 7.G.A.2 | Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle. | Grade 7 |
| Washington | 7.G.A.3 | Describe the two-dimensional figures that result from slicing three-dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids. | Grade 7 |
| Washington | 7.G.B.4 | Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle. | Grade 7 |
| Washington | 7.G.B.5 | Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure. | Grade 7 |
| Washington | 7.G.B.6 | Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. | Grade 7 |
| Washington | 7.RP.A.1 | Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. | Grade 7 |
| Washington | 7.RP.A.2 | Recognize and represent proportional relationships between quantities. | Grade 7 |
| Washington | 7.RP.A.3 | Use proportional relationships to solve multistep ratio and percent problems. | Grade 7 |
| Washington | 7.NS.A.1 | Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram. | Grade 7 |
| Washington | 7.NS.A.2 | Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers. | Grade 7 |
| Washington | 7.NS.A.3 | Solve real-world and mathematical problems involving the four operations with rational numbers. | Grade 7 |
| Washington | 8.EE.A.1 | Know and apply the properties of integer exponents to generate equivalent numerical expressions. | Grade 8 |
| Washington | 8.EE.A.2 | Use square root and cube root symbols to represent solutions to equations of the form 𝘹² = 𝘱 and 𝘹³ = 𝘱, where 𝘱 is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that √2 is irrational. | Grade 8 |
| Washington | 8.EE.A.3 | Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other. | Grade 8 |
| Washington | 8.EE.A.4 | Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology. | Grade 8 |
| Washington | 8.EE.B.5 | Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. | Grade 8 |
| Washington | 8.EE.B.6 | Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation 𝘺 = 𝘮𝘹 for a line through the origin and the equation 𝘺 = 𝘮𝘹 + 𝘣 for a line intercepting the vertical axis at 𝘣. | Grade 8 |
| Washington | 8.EE.C.7 | Solve linear equations in one variable. | Grade 8 |
| Washington | 8.EE.C.8 | Analyze and solve pairs of simultaneous linear equations. | Grade 8 |
| Washington | 8.F.A.1 | Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output. | Grade 8 |
| Washington | 8.F.A.2 | Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). | Grade 8 |
| Washington | 8.F.A.3 | Interpret the equation 𝘺 = 𝘮𝘹 + 𝘣 as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. | Grade 8 |
| Washington | 8.F.B.4 | Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (𝘹, 𝘺) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values. | Grade 8 |
| Washington | 8.F.B.5 | Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally. | Grade 8 |
| Washington | 8.G.A.1 | Verify experimentally the properties of rotations, reflections, and translations: | Grade 8 |
| Washington | 8.G.A.2 | Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them. | Grade 8 |
| Washington | 8.G.A.3 | Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates. | Grade 8 |
| Washington | 8.G.A.4 | Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two-dimensional figures, describe a sequence that exhibits the similarity between them. | Grade 8 |
| Washington | 8.G.A.5 | Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. | Grade 8 |
| Washington | 8.G.B.7 | Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions. | Grade 8 |
| Washington | 8.G.B.8 | Apply the Pythagorean Theorem to find the distance between two points in a coordinate system. | Grade 8 |
| Washington | 8.G.C.9 | Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems. | Grade 8 |
| Washington | 8.SP.A.1 | Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association. | Grade 8 |
| Washington | 8.SP.A.2 | Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line. | Grade 8 |
| Washington | 8.NS.A.2 | Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g., π²). | Grade 8 |
| Washington | A-APR.B.3 | Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial. | High School |
| Washington | A-CED.A.2 | Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. | High School |
| Washington | A-CED.A.3 | Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context. | High School |
| Washington | A-REI.B.3 | Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. | High School |
| Washington | A-SSE.A.2 | Use the structure of an expression to identify ways to rewrite it. | High School |
| Washington | A-SSE.B.3 | Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression. | High School |
| Washington | F-BF.A.1 | Write a function that describes a relationship between two quantities. | High School |
| Washington | F-IF.A.2 | Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. | High School |
| Washington | F-IF.B.4 | For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. | High School |
| Washington | F-IF.C.7 | Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. | High School |
| Washington | S-ID.B.6 | Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. | High School |
| West Virginia | CC.M.K.1 | Count to 100 by ones and by tens. | Kindergarten |
| West Virginia | CC.M.K.2 | Count forward beginning from a given number within the known sequence (instead of having to begin at 1). | Kindergarten |
| West Virginia | CC.M.K.3 | Write numbers from 0 to 20. Represent a number of objects with a written numeral 0-20 (with 0 representing a count of no objects). | Kindergarten |
| West Virginia | CC.M.K.4 | Understand the relationship between numbers and quantities; connect counting to cardinality. | Kindergarten |
| West Virginia | CC.M.K.5 | Count to answer questions (e.g., “How many?”) about as many as 20 things arranged in a line, a rectangular array, a circle, or as many as 10 things in a scattered configuration; given a number from 1–20, count out that many objects. | Kindergarten |
| West Virginia | CC.M.K.6 | Identify whether the number of objects in one group is greater than, less than, or equal to the number of objects in another group (e.g., by using matching and counting strategies). | Kindergarten |
| West Virginia | CC.M.K.7 | Compare two numbers between 1 and 10 presented as written numerals. | Kindergarten |
| West Virginia | G.M.K.17 | Describe objects in the environment using names of shapes and describe the relative positions of these objects using terms such as above, below, beside, in front of, behind and next to. | Kindergarten |
| West Virginia | G.M.K.18 | Correctly name shapes regardless of their orientations or overall size. | Kindergarten |
| West Virginia | G.M.K.19 | Through the use of real-life objects, identify shapes as two-dimensional (lying in a plane, "flat") or three-dimensional ("solid"). | Kindergarten |
| West Virginia | G.M.K.20 | Analyze and compare two- and three-dimensional shapes, in different sizes and orientations, using informal language to describe their similarities, differences, parts (e.g., number of sides and vertices/“corners”), and other attributes (e.g., having sides of equal length). Instructional Note: Student focus should include real-world shapes. | Kindergarten |
| West Virginia | G.M.K.22 | Compose simple shapes to form larger shapes (e.g., “Can these two triangles, with full sides touching, join to make a rectangle?”). | Kindergarten |
| West Virginia | MD.M.K.14 | Describe measurable attributes of objects, such as length or weight and describe several measurable attributes of a single object. | Kindergarten |
| West Virginia | MD.M.K.15 | Directly compare two objects with a measurable attribute in common, to see which object has “more of” or “less of” the attribute, and describe the difference. | Kindergarten |
| West Virginia | MD.M.K.16 | Classify objects into given categories, count the numbers of objects in each category, and sort the categories by count. Category counts should be limited to less than or equal to 10. (e.g., Identify coins and sort them into groups of 5s or 10s.) | Kindergarten |
| West Virginia | NBT.M.K.13 | Compose and decompose numbers from 11 to 19 into ten ones and some further ones by using objects or drawings, and record each composition or decomposition by a drawing or equation (e.g., 18 = 10 + 8); understand that these numbers are composed of ten ones (one ten) and one, two, three, four, five, six, seven, eight, or nine ones. | Kindergarten |
| West Virginia | OA.M.K.8 | Represent addition and subtraction with objects, fingers, mental images, drawings, sounds (e.g., claps), and acting out situations, verbal explanations, expressions, or equations. | Kindergarten |
| West Virginia | OA.M.K.9 | Solve addition and subtraction word problems and add and subtract within 10 by using objects or drawings to represent the problem. | Kindergarten |
| West Virginia | OA.M.K.10 | Decompose numbers less than or equal to 10 into pairs in more than one way by using objects or drawings, and record each decomposition by a drawing or equation (e.g., 5 = 2 + 3 and 5 = 4 + 1). | Kindergarten |
| West Virginia | OA.M.K.11 | For any number from 1 to 9, find the number that makes 10 when added to the given number by using objects or drawings, and record the answer with a drawing or equation. | Kindergarten |
| West Virginia | OA.M.K.12 | Fluently add and subtract within 5. | Kindergarten |
| West Virginia | G.M.1.19 | Distinguish between defining attributes (e.g., triangles are closed and three-sided) versus non-defining attributes (e.g., color, orientation, and/or overall size); build and draw shapes to possess defining attributes. | Grade 1 |
| West Virginia | G.M.1.20 | Compose two-dimensional shapes (rectangles, squares, trapezoids, triangles, half-circles, and quarter-circles) or three-dimensional shapes (cubes, right rectangular prisms, right circular cones, and right circular cylinders) to create a composite shape and compose new shapes from the composite shape. | Grade 1 |
| West Virginia | G.M.1.21 | Partition circles and rectangles into two and four equal shares, describe the shares using the words halves, fourths and quarters and use the phrases half of, fourth of and quarter of. Describe the whole as two of, or four of the shares and understand for these examples that decomposing into more equal shares creates smaller shares. | Grade 1 |
| West Virginia | MD.M.1.15 | Order three objects by length and compare the lengths of two objects indirectly by using a third object. | Grade 1 |
| West Virginia | MD.M.1.16 | Express the length of an object as a whole number of length units, by laying multiple copies of a shorter object (the length unit) end to end; understand that the length measurement of an object is the number of same-size length units that span it with no gaps or overlaps. | Grade 1 |
| West Virginia | MD.M.1.17 | Tell and write time in hours and half-hours using analog and digital clocks. | Grade 1 |
| West Virginia | MD.M.1.18 | Organize, represent, interpret data with up to three categories; ask and answer questions about the total number of data points, how many in each category and how many more or less are in one category than in another. | Grade 1 |
| West Virginia | NBT.M.1.9 | Count to 120, starting at any number less than 120. In this range, read and write numerals and represent a number of objects with a written numeral. | Grade 1 |
| West Virginia | NBT.M.1.10 | Understand the two digits of a two-digit number represent amounts of tens and ones. | Grade 1 |
| West Virginia | NBT.M.1.11 | Compare two two-digit numbers based on meanings of the tens and ones digits, recording the results of comparisons with the symbols >, =, and <. | Grade 1 |
| West Virginia | NBT.M.1.12 | Add within 100, including adding a two-digit number and a one-digit number and adding a two-digit number and a multiple of 10, using concrete models or drawings and strategies based on place value, properties of operations and/or the relationship between addition and subtraction. Relate the strategy to a written method and explain the reasoning used. Understand that in adding two-digit numbers, one adds tens and tens, ones and ones, and sometimes it is necessary to compose a ten. | Grade 1 |
| West Virginia | NBT.M.1.13 | Given a two-digit number, mentally find 10 more or 10 less than the number, without having to count and explain the reasoning used. | Grade 1 |
| West Virginia | NBT.M.1.14 | Subtract multiples of 10 in the range 10-90 from multiples of 10 in the range 10-90 (positive or zero differences) using concrete models or drawings and strategies based on place value, properties of operations and/or the relationship between addition and subtraction. Relate the strategy to a written method and explain the reasoning used. | Grade 1 |
| West Virginia | OA.M.1.1 | Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions (e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem). | Grade 1 |
| West Virginia | OA.M.1.3 | Apply properties of operations as strategies to add and subtract (e.g., If 8 + 3 = 11 is known, then 3 + 8 = 11 is also known: Commutative Property of Addition. To add 2 + 6 + 4, the second two numbers can be added to make a ten, so 2 + 6 + 4 = 2 + 10 = 12: Associative Property of Addition). | Grade 1 |
| West Virginia | OA.M.1.4 | Understand subtraction as an unknown-addend problem (e.g., subtract 10 – 8 by finding the number that makes 10 when added to 8). | Grade 1 |
| West Virginia | OA.M.1.5 | Relate counting to addition and subtraction (e.g., by counting on 2 to add 2). | Grade 1 |
| West Virginia | OA.M.1.6 | Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. | Grade 1 |
| West Virginia | OA.M.1.7 | Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false (e.g., Which of the following equations are true and which are false? 6 = 6, 7 = 8 – 1, 5 + 2 = 2 + 5, 4 + 1 = 5 + 2). | Grade 1 |
| West Virginia | OA.M.1.8 | Determine the unknown whole number in an addition or subtraction equation relating three whole numbers (e.g., Determine the unknown number that makes the equation true in each of the equations. 8 + ? = 11, 5 = ? – 3, 6 + 6 = ?). | Grade 1 |
| West Virginia | G.M.2.24 | Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces (sizes are compared directly or visually, not compared by measuring). Identify triangles, quadrilaterals, pentagons, hexagons, and cubes. | Grade 2 |
| West Virginia | G.M.2.25 | Partition a rectangle into rows and columns of same-size squares and count to find the total number of them. | Grade 2 |
| West Virginia | G.M.2.26 | Partition circles and rectangles into two, three, or four equal shares, describe the shares using the words halves, thirds, half of, a third of, etc., describe the whole as two halves, three thirds, four fourths. Recognize that equal shares of identical wholes need not have the same shape. | Grade 2 |
| West Virginia | MD.M.2.14 | Measure the length of an object by selecting and using appropriate tools such as rulers, yardsticks, meter sticks, and measuring tapes. | Grade 2 |
| West Virginia | MD.M.2.15 | Measure the length of an object twice, using length units of different lengths for the two measurements, describe how the two measurements relate to the size of the unit chosen. | Grade 2 |
| West Virginia | MD.M.2.17 | Measure to determine how much longer one object is than another, expressing the length difference in terms of a standard length unit. | Grade 2 |
| West Virginia | MD.M.2.18 | Use addition and subtraction within 100 to solve word problems involving lengths that are given in the same units (e.g., by using drawings, such as drawings of rulers), and equations with a symbol for the unknown number to represent the problem. | Grade 2 |
| West Virginia | MD.M.2.20 | Tell and write time from analog and digital clocks to the nearest five minutes, using a.m. and p.m. | Grade 2 |
| West Virginia | MD.M.2.21 | Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies, using $ and ¢ symbols appropriately (e.g., If you have 2 dimes and 3 pennies, how many cents do you have?). | Grade 2 |
| West Virginia | MD.M.2.22 | Generate measurement data by measuring lengths of several objects to the nearest whole unit or by making repeated measurements of the same object. Show the measurements by making a line plot, where the horizontal scale is marked off in whole-number units. | Grade 2 |
| West Virginia | MD.M.2.23 | Draw a picture graph and a bar graph (with single-unit scale) to represent a data set with up to four categories. Solve simple put-together, take-apart, and compare problems using information presented in a bar graph. | Grade 2 |
| West Virginia | NBT.M.2.5 | Understand that the three digits of a three-digit number represent amounts of hundreds, tens and ones (e.g., 706 equals 7 hundreds, 0 tens and 6 ones). | Grade 2 |
| West Virginia | NBT.M.2.6 | Count within 1000 and skip-count by 5s, 10s and 100s. | Grade 2 |
| West Virginia | NBT.M.2.7 | Read and write numbers to 1000 using base-ten numerals, number names and expanded form. | Grade 2 |
| West Virginia | NBT.M.2.8 | Compare two three-digit numbers based on meanings of the hundreds, tens and ones digits, using >, = and < symbols to record the results of comparisons. | Grade 2 |
| West Virginia | NBT.M.2.9 | Fluently add and subtract within 100 using strategies based on place value, properties of operations and/or the relationship between addition and subtraction. | Grade 2 |
| West Virginia | NBT.M.2.10 | Add up to four two-digit numbers using strategies based on place value and properties of operations. | Grade 2 |
| West Virginia | NBT.M.2.11 | Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations and/or the relationship between addition and subtraction; relate the strategy to a written method. Understand that in adding or subtracting three-digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones and sometimes it is necessary to compose or decompose tens or hundreds. | Grade 2 |
| West Virginia | NBT.M.2.12 | Mentally add 10 or 100 to a given number 100-900 and mentally subtract 10 or 100 from a given number 100-900. | Grade 2 |
| West Virginia | OA.M.2.1 | Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions (e.g. by using drawings and equations with a symbol for the unknown number to represent the problem). | Grade 2 |
| West Virginia | OA.M.2.2 | Fluently add and subtract within 20 using mental strategies and by end of Grade 2, know from memory all sums of two one-digit numbers. | Grade 2 |
| West Virginia | OA.M.2.3 | Determine whether a group of objects (up to 20) has an odd or even number of members, e.g. by pairing objects or counting them by 2s; write an equation to express an even number as a sum of two equal addends. | Grade 2 |
| West Virginia | OA.M.2.4 | Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends. | Grade 2 |
| West Virginia | G.M.3.24 | Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), that the shared attributes can define a larger category (e.g. quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories. | Grade 3 |
| West Virginia | G.M.3.25 | Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole. For example, partition a shape into 4 parts with equal area, and describe the area of each part as ¼ or the area of the shape. | Grade 3 |
| West Virginia | MD.M.3.16 | Tell and write time to the nearest minute, measure time intervals in minutes. Solve word problems involving addition and subtraction of time intervals in minutes (e.g., by representing the problem on a number line diagram). | Grade 3 |
| West Virginia | MD.M.3.17 | Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg) and liters (l). Add, subtract, multiply or divide to solve one-step word problems involving masses or volumes that are given in the same units (e.g., by using drawings, such as a beaker with a measurement scale) to represent the problem. | Grade 3 |
| West Virginia | MD.M.3.18 | Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and two-step “how many more” and “how many less” problems using information presented in scaled bar graphs (e.g., draw a bar graph in which each square in the bar graph might represent 5 pets). | Grade 3 |
| West Virginia | MD.M.3.19 | Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Show the data by making a line plot, where the horizontal scale is marked off in appropriate units—whole numbers, halves or quarters. | Grade 3 |
| West Virginia | MD.M.3.20 | Recognize area as an attribute of plane figures and understand concepts of area measurement. | Grade 3 |
| West Virginia | MD.M.3.21 | Measure areas by counting unit squares (square cm, square m, square in, square ft. and improvised units). | Grade 3 |
| West Virginia | MD.M.3.22 | Relate area to the operations of multiplication and addition. | Grade 3 |
| West Virginia | MD.M.3.23 | Solve real world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters. | Grade 3 |
| West Virginia | NBT.M.3.10 | Use place value understanding to round whole numbers to the nearest 10 or 100. | Grade 3 |
| West Virginia | NBT.M.3.11 | Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction. | Grade 3 |
| West Virginia | NBT.M.3.12 | Multiply one-digit whole numbers by multiples of 10 in the range 10–90 (e.g., 9 × 80, 5 × 60) using strategies based on place value and properties of operations. | Grade 3 |
| West Virginia | NF.M.3.13 | Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b. | Grade 3 |
| West Virginia | NF.M.3.14 | Understand a fraction as a number on the number line and represent fractions on a number line diagram. | Grade 3 |
| West Virginia | NF.M.3.15 | Explain equivalence of fractions in special cases and compare fractions by reasoning about their size. | Grade 3 |
| West Virginia | OA.M.3.1 | Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each (e.g., describe context in which a total number of objects can be expressed as 5 × 7). | Grade 3 |
| West Virginia | OA.M.3.2 | Interpret whole-number quotients of whole numbers, e.g., interpret 56 ÷ 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each (e.g., describe a context in which a number of shares or a number of groups can be expressed as 56 ÷ 8). | Grade 3 |
| West Virginia | OA.M.3.3 | Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays and measurement quantities (e.g., by using drawings and equations with a symbol for the unknown number to represent the problem). | Grade 3 |
| West Virginia | OA.M.3.4 | Determine the unknown whole number in a multiplication or division equation relating three whole numbers (e.g., determine the unknown number that makes the equation true in each of the equations 8 × ? = 48, 5 = ? ÷ 3, 6 × 6 =?). | Grade 3 |
| West Virginia | OA.M.3.5 | Apply properties of operations as strategies to multiply and divide (e.g., If 6 × 4 = 24 is known, then 4 × 6 = 24 is also known: Commutative Property of Multiplication. 3 × 5 × 2 can be found by 3 × 5 = 15, then 15 × 2 = 30, or by 5 × 2 = 10, then 3 × 10 = 30: Associative Property of Multiplication. Knowing that 8 × 5 = 40 and 8 × 2 = 16, one can find 8 × 7 as 8 × (5 + 2) = (8 × 5) + (8 × 2) = 40 + 16 = 56: Distributive Property. | Grade 3 |
| West Virginia | OA.M.3.6 | Understand division as an unknown-factor problem (e.g., find 32 ÷ 8 by finding the number that makes 32 when multiplied by 8). | Grade 3 |
| West Virginia | OA.M.3.7 | Learn multiplication tables (facts) with speed and memory in order to fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 × 5 = 40, one knows that 40 ÷ 5 = 8) or properties of operations by the end of Grade 3. | Grade 3 |
| West Virginia | OA.M.3.8 | Solve two-step word problems using the four operations, represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. | Grade 3 |
| West Virginia | OA.M.3.9 | Identify arithmetic patterns (including patterns in the addition table or multiplication table) and explain those using properties of operations (e.g., observe that 4 times a number is always even and explain why 4 times a number can be decomposed into two equal addends). | Grade 3 |
| West Virginia | G.M.4.26 | Draw points, lines, line segments, rays, angles (right, acute, obtuse) and perpendicular and parallel lines. Identify these in two-dimensional figures. | Grade 4 |
| West Virginia | G.M.4.27 | Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles. | Grade 4 |
| West Virginia | G.M.4.28 | Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify line-symmetric figures and draw lines of symmetry. | Grade 4 |
| West Virginia | MD.M.4.19 | Know relative sizes of measurement units within a system of units, including the metric system (km, m, cm; kg, g; l, ml), the standard system (lb, oz), and time (hr, min, sec.). Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table. (e.g., Know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36),...) | Grade 4 |
| West Virginia | MD.M.4.20 | Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. | Grade 4 |
| West Virginia | MD.M.4.21 | Apply the area and perimeter formulas for rectangles in real world and mathematical problems by viewing the area formula as a multiplication equation with an unknown factor. (e.g., find the width of a rectangular room given the area of the flooring and the length.) | Grade 4 |
| West Virginia | MD.M.4.22 | Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots (e.g., from a line plot find and interpret the difference in length between the longest and shortest specimens in an insect collection). | Grade 4 |
| West Virginia | MD.M.4.23 | Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement. | Grade 4 |
| West Virginia | MD.M.4.24 | Measure angles in whole-number degrees using a protractor and sketch angles of specified measure. | Grade 4 |
| West Virginia | MD.M.4.25 | Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems (e.g., by using an equation with a symbol for the unknown angle measure). | Grade 4 |
| West Virginia | NBT.M.4.6 | Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right (e.g., recognize that 700 ÷ 70 = 10 by applying concepts of place value and division). | Grade 4 |
| West Virginia | NBT.M.4.7 | Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, = and < symbols to record the results of comparisons. | Grade 4 |
| West Virginia | NBT.M.4.8 | Use place value understanding to round multi-digit whole numbers to any place. | Grade 4 |
| West Virginia | NBT.M.4.9 | Fluently add and subtract multi-digit whole numbers using the standard algorithm. | Grade 4 |
| West Virginia | NBT.M.4.10 | Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value and the properties of operations and illustrate and explain the calculation by using equations, rectangular arrays and/or area models. | Grade 4 |
| West Virginia | NBT.M.4.11 | Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models. | Grade 4 |
| West Virginia | NF.M.4.12 | Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. | Grade 4 |
| West Virginia | NF.M.4.13 | Compare two fractions with different numerators and different denominators (e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as ½). Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, = or <, and justify the conclusions by using a visual fraction model. | Grade 4 |
| West Virginia | NF.M.4.14 | Understand the fraction a/b, with a > 1, as the sum of a of the fractions 1/b. | Grade 4 |
| West Virginia | NF.M.4.15 | Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. | Grade 4 |
| West Virginia | NF.M.4.16 | Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100 (e.g., express 3/10 as 30/100, and add 3/10 + 4/100 = 34/100). | Grade 4 |
| West Virginia | NF.M.4.17 | Use decimal notation for fractions with denominators 10 or 100 (e.g., rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram). | Grade 4 |
| West Virginia | NF.M.4.18 | Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, = or <, and justify the conclusions by using a visual model. | Grade 4 |
| West Virginia | OA.M.4.1 | Interpret a multiplication equation as a comparison (e.g., interpret 35 = 5 × 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5). Represent verbal statements of multiplicative comparisons as multiplication equations. | Grade 4 |
| West Virginia | OA.M.4.2 | Multiply or divide to solve word problems involving multiplicative comparison (e.g., by using drawings and equations with a symbol for the unknown number to represent the problem) and distinguish multiplicative comparison from additive comparison. | Grade 4 |
| West Virginia | OA.M.4.3 | Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. | Grade 4 |
| West Virginia | OA.M.4.4 | Find all factor pairs for a whole number in the range 1–100, recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1–100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1–100 is prime or composite. | Grade 4 |
| West Virginia | OA.M.4.5 | Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. (e.g., Given the rule “Add 3” and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way.) | Grade 4 |
| West Virginia | G.M.5.23 | Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines, the origin, arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate). | Grade 5 |
| West Virginia | G.M.5.24 | Represent real-world mathematical problems by graphing points in the first quadrant of the coordinate plane and interpret coordinate values of points in the context of the situation. | Grade 5 |
| West Virginia | G.M.5.25 | Understand that attributes belonging to a category of two dimensional figures also belong to all subcategories of that category (e.g., all rectangles have four right angles and squares are rectangles, so all squares have four right angles). | Grade 5 |
| West Virginia | G.M.5.26 | Classify two-dimensional figures in a hierarchy based on properties. | Grade 5 |
| West Virginia | MD.M.5.18 | Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m) and use these conversions in solving multi-step, real-world problems. | Grade 5 |
| West Virginia | MD.M.5.19 | Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. (e.g., Given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally). | Grade 5 |
| West Virginia | MD.M.5.20 | Recognize volume as an attribute of solid figures and understand concepts of volume measurement. | Grade 5 |
| West Virginia | MD.M.5.21 | Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. | Grade 5 |
| West Virginia | MD.M.5.22 | Relate volume to the operations of multiplication and addition and solve real-world and mathematical problems involving volume. | Grade 5 |
| West Virginia | NF.M.5.11 | Add and subtract fractions with unlike denominators, including mixed numbers, by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators (e.g., 2/3 + 5/4 = 8/12 + 15/12 = 23/12). | Grade 5 |
| West Virginia | NF.M.5.12 | Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers (e.g., recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2). | Grade 5 |
| West Virginia | NF.M.5.13 | Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers by using visual fraction models or equations to represent the problem. (e.g., Interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3 and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie?) | Grade 5 |
| West Virginia | NF.M.5.14 | Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. | Grade 5 |
| West Virginia | NF.M.5.15 | Interpret multiplication as scaling (resizing). | Grade 5 |
| West Virginia | NF.M.5.16 | Solve real-world problems involving multiplication of fractions and mixed numbers by using visual fraction models or equations to represent the problem. | Grade 5 |
| West Virginia | NF.M.5.17 | Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. | Grade 5 |
| West Virginia | NBT.M.5.4 | Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. | Grade 5 |
| West Virginia | NBT.M.5.5 | Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. | Grade 5 |
| West Virginia | NBT.M.5.6 | Read, write, and compare decimals to thousandths. | Grade 5 |
| West Virginia | NBT.M.5.7 | Use place value understanding to round decimals to any place. | Grade 5 |
| West Virginia | NBT.M.5.8 | Fluently multiply multi-digit whole numbers using the standard algorithm. | Grade 5 |
| West Virginia | NBT.M.5.9 | Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. | Grade 5 |
| West Virginia | NBT.M.5.10 | Add, subtract, multiply and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between related operations, relate the strategy to a written method and explain the reasoning used. | Grade 5 |
| West Virginia | OA.M.5.1 | Use parentheses, brackets or braces in numerical expressions and evaluate expressions with these symbols. | Grade 5 |
| West Virginia | OA.M.5.2 | Write simple expressions that record calculations with numbers and interpret numerical expressions without evaluating them. (e.g., Express the calculation “add 8 and 7, then multiply by 2” as 2 × (8 + 7). Recognize that 3 × (18932 + 921) is three times as large as 18932 + 921, without having to calculate the indicated sum or product.) | Grade 5 |
| West Virginia | OA.M.5.3 | Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. (e.g., Given the rule “Add 3” and the starting number 0 and given the rule “Add 6” and the starting number 0, generate terms in the resulting sequences and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so.) | Grade 5 |
| West Virginia | EE.M.6.12 | Write and evaluate numerical expressions involving whole-number exponents. | Grade 6 |
| West Virginia | EE.M.6.13 | Write, read and evaluate expressions in which letters stand for numbers. | Grade 6 |
| West Virginia | EE.M.6.14 | Apply the properties of operations to generate equivalent expressions (e.g., apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y). | Grade 6 |
| West Virginia | EE.M.6.15 | Identify when two expressions are equivalent; i.e., when the two expressions name the same number regardless of which value is substituted into them. (e.g., The expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for.) | Grade 6 |
| West Virginia | EE.M.6.16 | Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true. | Grade 6 |
| West Virginia | EE.M.6.17 | Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number or depending on the purpose at hand, any number in a specified set. | Grade 6 |
| West Virginia | EE.M.6.18 | Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers. | Grade 6 |
| West Virginia | EE.M.6.19 | Write an inequality of the form x > c or x c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams. | Grade 6 |
| West Virginia | EE.M.6.20 | Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. (e.g., In a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to represent the relationship between distance and time.) | Grade 6 |
| West Virginia | G.M.6.21 | Find the area of right triangles, other triangles, special quadrilaterals and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems. | Grade 6 |
| West Virginia | G.M.6.22 | Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas V = l w h and V = B h to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems. | Grade 6 |
| West Virginia | G.M.6.23 | Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems. | Grade 6 |
| West Virginia | G.M.6.24 | Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems. | Grade 6 |
| West Virginia | RP.M.6.1 | Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. (e.g., “The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak.” “For every vote candidate A received, candidate C received nearly three votes.”) | Grade 6 |
| West Virginia | RP.M.6.2 | Understand the concept of a unit rate a/b associated with a ratio a:b with b ≠ 0, and use rate language in the context of a ratio relationship. (e.g., “This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar.” “We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger.”) | Grade 6 |
| West Virginia | RP.M.6.3 | Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. | Grade 6 |
| West Virginia | SP.M.6.29 | Summarize numerical data sets in relation to their context, such as by: | Grade 6 |
| West Virginia | NS.M.6.4 | Interpret and compute quotients of fractions and solve word problems involving division of fractions by fractions by using visual fraction models and equations to represent the problem. (e.g., Create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area ½ square mi?) | Grade 6 |
| West Virginia | NS.M.6.5 | Fluently divide multi-digit numbers using the standard algorithm. | Grade 6 |
| West Virginia | NS.M.6.6 | Fluently add, subtract, multiply and divide multi-digit decimals using the standard algorithm for each operation. | Grade 6 |
| West Virginia | NS.M.6.8 | Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation. | Grade 6 |
| West Virginia | NS.M.6.9 | Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates. | Grade 6 |
| West Virginia | NS.M.6.10 | Understand ordering and absolute value of rational numbers. | Grade 6 |
| West Virginia | NS.M.6.11 | Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. | Grade 6 |
| West Virginia | EE.M.7.7 | Apply properties of operations as strategies to add, subtract, factor and expand linear expressions with rational coefficients. | Grade 7 |
| West Virginia | EE.M.7.8 | Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. (e.g., a + 0.05a = 1.05a means that “increase by 5%” is the same as “multiply by 1.05.”) | Grade 7 |
| West Virginia | EE.M.7.9 | Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. (e.g., If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation.) | Grade 7 |
| West Virginia | EE.M.7.10 | Use variables to represent quantities in a real-world or mathematical problem and construct simple equations and inequalities to solve problems by reasoning about the quantities. | Grade 7 |
| West Virginia | G.M.7.11 | Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale. | Grade 7 |
| West Virginia | G.M.7.12 | Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle. | Grade 7 |
| West Virginia | G.M.7.13 | Describe the two-dimensional figures that result from slicing three-dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids. | Grade 7 |
| West Virginia | G.M.7.14 | Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle. | Grade 7 |
| West Virginia | G.M.7.15 | Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure. | Grade 7 |
| West Virginia | G.M.7.16 | Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. | Grade 7 |
| West Virginia | RP.M.7.1 | Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. (e.g., If a person walks 1/2 mile in each 1/4 hour, compute the unit rate as the complex fraction 1/2/1/4 miles per hour, equivalently 2 miles per hour.) | Grade 7 |
| West Virginia | RP.M.7.2 | Recognize and represent proportional relationships between quantities. | Grade 7 |
| West Virginia | RP.M.7.3 | Use proportional relationships to solve multistep ratio and percent problems (e.g., simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, and/or percent error). | Grade 7 |
| West Virginia | NS.M.7.4 | Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram. | Grade 7 |
| West Virginia | NS.M.7.5 | Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers. | Grade 7 |
| West Virginia | NS.M.7.6 | Solve real-world and mathematical problems involving the four operations with rational numbers. Instructional Note: Computations with rational numbers extend the rules for manipulating fractions to complex fractions. | Grade 7 |
| West Virginia | EE.M.8.3 | Know and apply the properties of integer exponents to generate equivalent numerical expressions. (e.g., 3² × 3–⁵ = 3–³ = 1/3³ = 1/27.) | Grade 8 |
| West Virginia | EE.M.8.4 | Use square root and cube root symbols to represent solutions to equations of the form x² = p and x³ = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that √2 is irrational. | Grade 8 |
| West Virginia | EE.M.8.5 | Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other. (e.g., Estimate the population of the United States as 3 × 10⁸ and the population of the world as 7 × 10⁹, and determine that the world population is more than 20 times larger.) | Grade 8 |
| West Virginia | EE.M.8.6 | Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities. (e.g., Use millimeters per year for seafloor spreading.) Interpret scientific notation that has been generated by technology. | Grade 8 |
| West Virginia | EE.M.8.7 | Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. (e.g., Compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed.) | Grade 8 |
| West Virginia | EE.M.8.8 | Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b. | Grade 8 |
| West Virginia | EE.M.8.9 | Solve linear equations in one variable. | Grade 8 |
| West Virginia | EE.M.8.10 | Analyze and solve pairs of simultaneous linear equations. | Grade 8 |
| West Virginia | F.M.8.11 | Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output. | Grade 8 |
| West Virginia | F.M.8.12 | Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). (e.g., Given a linear function represented by a table of values and a linear function represented by an algebraic expression, determine which function has the greater rate of change.) | Grade 8 |
| West Virginia | F.M.8.13 | Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. (e.g., The function A = s² giving the area of a square as a function of its side length is not linear because its graph contains the points (1,1), (2,4) and (3,9), which are not on a straight line.) | Grade 8 |
| West Virginia | F.M.8.14 | Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values. | Grade 8 |
| West Virginia | F.M.8.15 | Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally. | Grade 8 |
| West Virginia | G.M.8.16 | Verify experimentally the properties of rotations, reflections and translations. | Grade 8 |
| West Virginia | G.M.8.17 | Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections and translations; given two congruent figures, describe a sequence that exhibits the congruence between them. | Grade 8 |
| West Virginia | G.M.8.18 | Describe the effect of dilations, translations, rotations and reflections on two-dimensional figures using coordinates. | Grade 8 |
| West Virginia | G.M.8.19 | Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations and dilations; given two similar two dimensional figures, describe a sequence that exhibits the similarity between them. | Grade 8 |
| West Virginia | G.M.8.20 | Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. (e.g., Arrange three copies of the same triangle so that the sum of the three angles appears to form a line, and give an argument in terms of transversals why this is so.) | Grade 8 |
| West Virginia | G.M.8.22 | Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions. | Grade 8 |
| West Virginia | G.M.8.23 | Apply the Pythagorean Theorem to find the distance between two points in a coordinate system. | Grade 8 |
| West Virginia | G.M.8.24 | Know the formulas for the volumes of cones, cylinders and spheres and use them to solve real-world and mathematical problems. | Grade 8 |
| West Virginia | SP.M.8.25 | Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association and nonlinear association. | Grade 8 |
| West Virginia | SP.M.8.26 | Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line and informally assess the model fit by judging the closeness of the data points to the line. | Grade 8 |
| West Virginia | NS.M.8.2 | Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram and estimate the value of expressions such as π². (e.g., By truncating the decimal expansion of √2, show that √2 is between 1 and 2, then between 1.4 and 1.5, and explain how to continue on to get better approximations.) | Grade 8 |
| West Virginia | RE.M.1HS.28 | Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. | High School Mathematics I |
| West Virginia | RQ.M.1HS.7 | Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context. (e.g., Represent inequalities describing nutritional and cost constraints on combinations of different foods.) | High School Mathematics I |
| West Virginia | MM.M.3HS.33 | Represent constraints by equations or inequalities and by systems of equations and/or inequalities and interpret solutions as viable or non-viable options in a modeling context. (e.g., Represent inequalities describing nutritional and cost constraints on combinations of different foods.) | High School Mathematics III LA |
| West Virginia | DS.M.A1HS.37 | Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. | High School Algebra I |
| West Virginia | EE.M.A1HS.42 | Use the structure of an expression to identify ways to rewrite it. | High School Algebra I |
| West Virginia | EE.M.A1HS.46 | Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. | High School Algebra I |
| West Virginia | LER.M.A1HS.19 | Use function notation, evaluate functions for inputs in their domains and interpret statements that use function notation in terms of a context. | High School Algebra I |
| West Virginia | LER.M.A1HS.21 | For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. | High School Algebra I |
| West Virginia | QFM.M.A1HS.51 | For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. | High School Algebra I |
| West Virginia | RQ.M.A1HS.6 | Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. | High School Algebra I |
| West Virginia | RQ.M.A1HS.7 | Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context. (e.g., Represent inequalities describing nutritional and cost constraints on combinations of different foods.) | High School Algebra I |
| West Virginia | RQ.M.A1HS.10 | Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. | High School Algebra I |
| West Virginia | MF.M.A2HS.25 | Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context. (e.g., Represent inequalities describing nutritional and cost constraints on combinations of different foods.) | High School Algebra II |
| West Virginia | A.C.M.TMS.13 | Represent constraints by equations or inequalities and by systems of equations and/or inequalities and interpret solutions as viable or nonviable options in a modeling context. | Transition Mathematics for Seniors |
| West Virginia | A.D.M.TMS.16 | Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. | Transition Mathematics for Seniors |
| Wisconsin | M.K.CC.A.1 | Count to 100 by ones and by tens. | Kindergarten |
| Wisconsin | M.K.CC.A.2 | Count forward beginning from a given number within the known sequence (instead of having to begin at 1). | Kindergarten |
| Wisconsin | M.K.CC.A.3 | Write numbers from 0 to 20. Represent a number of objects with a written numeral 0-20 (with 0 representing a count of no objects). | Kindergarten |
| Wisconsin | M.K.CC.A.4 | Understand the relationship between numbers and quantities; connect counting to cardinality. a. When counting objects, say the number names in the standard order, pairing each object with one and only one number name and each number name with one and only one object (one to one correspondence). b. Understand that the last number name said tells the number of objects counted (cardinality). The number of objects is the same regardless of their arrangement or the order in which they were counted (number conservation). c. Understand that each successive number name refers to a quantity that is one larger and the previous number is one smaller (hierarchical inclusion). | Kindergarten |
| Wisconsin | M.K.CC.B.6 | Count to answer how many? questions about as many as 20 things arranged in a line, a rectangular array, or a circle, or as many as 10 things in a scattered configuration; given a number from 1-20, count out that many objects. | Kindergarten |
| Wisconsin | M.K.CC.C.7 | Identify whether the number of objects (up to 10) in one group is greater than, less than, or equal to the number of objects in another group, e.g., by using matching and counting strategies. | Kindergarten |
| Wisconsin | M.K.CC.C.8 | Compare two numbers between 1 and 10 presented as written numerals using student generated ways to record the comparison. | Kindergarten |
| Wisconsin | M.K.OA.A.1 | Represent addition and subtraction with objects, fingers, mental images, drawings, sounds (e.g., claps), acting out situations, verbal explanations, or numbers. Drawings need not show details, but should show the mathematics in the problem. | Kindergarten |
| Wisconsin | M.K.OA.A.2 | Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem. | Kindergarten |
| Wisconsin | M.K.OA.A.3 | Compose and decompose quantities within 10. a. Decompose numbers less than or equal to 10 into pairs in more than one way, e.g., by using objects or drawings, and record each decomposition with drawings or numbers. b. Quickly name the quantity of objects briefly shown in structured arrangements anchored to 5 (e.g., fingers, ten frames, math rack/rekenrek) with totals up to 10 without counting by recognizing the arrangement or seeing the quantity in subgroups that are combined (conceptual subitizing). | Kindergarten |
| Wisconsin | M.K.OA.A.4 | For any number from 1 to 9, find the number that makes 10 when added to the given number, e.g., by using objects or drawings, and record the answer with a drawing or numbers. | Kindergarten |
| Wisconsin | M.K.NBT.A.1 | Compose and decompose numbers from 11 to 19 into ten ones and some further ones, e.g., by using objects or drawings, and record each composition or decomposition by a drawing or numbers; understand that these numbers are composed of ten ones and one, two, three, four, five, six, seven, eight, or nine ones. | Kindergarten |
| Wisconsin | M.K.MD.A.1 | Describe measurable attributes of objects, such as length or weight. Describe several measurable attributes of a single object. | Kindergarten |
| Wisconsin | M.K.MD.A.2 | Directly compare two objects with a measurable attribute in common, to see which object has more of/less of the attribute, and describe the difference. | Kindergarten |
| Wisconsin | M.K.MD.B.3 | Classify objects into given categories; count the numbers of objects in each category and sort the categories by count. Limit category counts to be less than or equal to 10. | Kindergarten |
| Wisconsin | M.K.G.A.1 | Describe objects in the environment using names of shapes, and describe the relative positions of these objects using terms such as above, below, beside, in front of, behind, and next to. | Kindergarten |
| Wisconsin | M.K.G.A.2 | Correctly name shapes regardless of their orientations or overall size. | Kindergarten |
| Wisconsin | M.K.G.A.3 | Identify shapes as two-dimensional (lying in a plane, flat) or three-dimensional (solid). | Kindergarten |
| Wisconsin | M.K.G.B.4 | Analyze and compare two- and three-dimensional shapes, in different sizes and orientations, using informal language to describe their similarities, differences, parts (e.g., number of sides and vertices/corners) and other attributes (e.g., having sides of equal length). | Kindergarten |
| Wisconsin | M.K.G.B.6 | Compose simple shapes to form larger shapes. | Kindergarten |
| Wisconsin | M.1.OA.A.1 | Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem. | Grade 1 |
| Wisconsin | M.1.OA.B.3 | Apply properties of operations as strategies to add and subtract. | Grade 1 |
| Wisconsin | M.1.OA.B.4 | Understand subtraction as an unknown-addend problem. | Grade 1 |
| Wisconsin | M.1.OA.C.5 | Use counting and subitizing strategies to explain addition and subtraction. a. Relate counting to addition and subtraction (e.g., by counting on 2 to add 2). b. Use conceptual subitizing in unstructured arrangements with totals up to 10 and structured arrangements anchored to 5 or 10 (e.g., 10 frames, double ten frames, math rack/rekenrek) with totals up to 20 to relate the compositions and decompositions to addition and subtraction. | Grade 1 |
| Wisconsin | M.1.OA.C.6 | Use multiple strategies to add and subtract within 20. a. Flexibly and efficiently add and subtract within 10 using strategies that may include mental images and composing and decomposing up to 10. b. Add and subtract within 20 using objects, drawings, or equations. Use multiple strategies that may include counting on; making a ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to a ten (e.g., 13 - 4 = 13 - 3 - 1 = 10 - 1 = 9); using the relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 - 8 = 4); and creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13). | Grade 1 |
| Wisconsin | M.1.OA.D.7 | Understand the meaning of the equal sign as has the same value/amount as and determine if equations involving addition and subtraction are true or false. | Grade 1 |
| Wisconsin | M.1.NBT.A.1 | Count to 120, starting at any number less than 120. In this range, read and write numerals and represent a number of objects with a written numeral. | Grade 1 |
| Wisconsin | M.1.NBT.B.2 | Understand that the two digits of a two-digit number represent amounts of tens and ones. Understand the following as special cases: Understand that the two digits of a two-digit number represent amounts of tens and ones. Understand the following as special cases: a. 10 can be thought of as a bundle of ten ones—called a ten. b. The numbers from 11 to 19 are composed of a ten and one, two, three, four, five, six, seven, eight, or nine ones. c. The numbers 10, 20, 30, 40, 50, 60, 70, 80, 90 refer to one, two, three, four, five, six, seven, eight, or nine tens (and 0 ones). | Grade 1 |
| Wisconsin | M.1.NBT.B.3 | Compare two two-digit numbers based on meanings of the tens and ones digits and describe the result of the comparison using words and symbols ( >, =, and < ). | Grade 1 |
| Wisconsin | M.1.NBT.C.4 | Add within 100, including adding a two-digit number and a one-digit number, and adding a two-digit number and a multiple of 10, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Understand that in adding two-digit numbers, one adds tens and tens, ones and ones; and sometimes it is necessary to compose a ten. | Grade 1 |
| Wisconsin | M.1.NBT.C.5 | Given a two-digit number, mentally find 10 more or 10 less than the number, without having to count; explain the reasoning used. | Grade 1 |
| Wisconsin | M.1.NBT.C.6 | Subtract multiples of 10 in the range 10-90 from multiples of 10 in the range 10-90 (positive or zero differences), using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. | Grade 1 |
| Wisconsin | M.1.MD.A.1 | Order three objects by length; compare the lengths of two objects indirectly by using a third object. | Grade 1 |
| Wisconsin | M.1.MD.A.2 | Express the length of an object as a whole number of length units, by laying multiple copies of a shorter object (the length unit) end to end; understand that the length measurement of an object is the number of same-size length units that span it with no gaps or overlaps. Limit to contexts where the object being measured is spanned by a whole number of length units with no gaps or overlaps. | Grade 1 |
| Wisconsin | M.1.MD.B.3 | Tell and write time in hours and half-hours using analog and digital clocks | Grade 1 |
| Wisconsin | M.1.MD.C.4 | Organize, represent, and interpret data with up to three categories; ask and answer questions about the total number of data points, how many in each category, and how many more or less are in one category than in another. | Grade 1 |
| Wisconsin | M.1.G.A.1 | Distinguish between defining attributes (e.g., triangles are closed and three-sided) versus non-defining attributes (e.g., color, orientation, overall size); build and draw shapes to possess defining attributes. | Grade 1 |
| Wisconsin | M.1.G.A.2 | Compose two-dimensional shapes (rectangles, squares, trapezoids, triangles, half-circles, and quarter-circles) or three-dimensional shapes (cubes, right rectangular prisms, right circular cones, and right circular cylinders) to create a composite shape, and compose new shapes from the composite shape. Student use of formal names such as right rectangular prism is not expected. | Grade 1 |
| Wisconsin | M.1.G.A.3 | Partition circles and rectangles into two and four equal shares, describe and count the shares using the words halves and fourths, and use the phrases half of and fourth of the whole. Describe the whole as being two of the shares, or four of the shares. Understand for these examples that decomposing into more equal shares creates smaller shares. | Grade 1 |
| Wisconsin | M.2.OA.A.1 | Use addition and subtraction within 100 to solve one and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem. | Grade 2 |
| Wisconsin | M.2.OA.B.2 | Flexibly and efficiently add and subtract within 20 using multiple mental strategies which may include counting on; making ten; decomposing a number leading to a ten; using the relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 - 8 = 4); and creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13). | Grade 2 |
| Wisconsin | M.2.OA.C.3 | Determine whether a group of objects (up to 20) has an odd or even number of members, e.g., by pairing objects or counting them by 2s; write an equation to express an even number as a sum of two equal addends. | Grade 2 |
| Wisconsin | M.2.OA.C.4 | Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends. | Grade 2 |
| Wisconsin | M.2.NBT.A.1 | Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones. Understand the following as special cases: a. 100 can be thought of as a bundle of ten tens -- called a hundred. b. The numbers 100, 200, 300, 400, 500, 600, 700, 800, 900 refer to one, two, three, four, five, six, seven, eight, or nine hundreds (and 0 tens and 0 ones). | Grade 2 |
| Wisconsin | M.2.NBT.A.2 | Count within 1000; skip-count by 5s, 10s, and 100s. | Grade 2 |
| Wisconsin | M.2.NBT.A.3 | Read and write numbers to 1000 using base-ten numerals, number names, and expanded form. | Grade 2 |
| Wisconsin | M.2.NBT.A.4 | Compare two three-digit numbers based on meanings of the hundreds, tens, and ones digits, and describe the result of the comparison using words and symbols ( >, =, and < ). | Grade 2 |
| Wisconsin | M.2.NBT.B.5 | Flexibly and efficiently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction. In Grade 2, subtraction with decomposition is an exception and may include drawings/representations. | Grade 2 |
| Wisconsin | M.2.NBT.B.6 | Add up to four two-digit numbers using strategies based on place value and properties of operations. | Grade 2 |
| Wisconsin | M.2.NBT.B.7 | Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method. Understand that in adding or subtracting three digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds. | Grade 2 |
| Wisconsin | M.2.NBT.B.8 | Mentally add 10 or 100 to a given number 100 - 900, and mentally subtract 10 or 100 from a given number 100 - 900. | Grade 2 |
| Wisconsin | M.2.MD.A.1 | Measure the length of an object by selecting and using appropriate tools such as rulers, yardsticks, meter sticks, and measuring tapes. | Grade 2 |
| Wisconsin | M.2.MD.A.2 | Measure the length of an object twice, using length units of different lengths for the two measurements; describe how the two measurements relate to the size of the unit chosen. | Grade 2 |
| Wisconsin | M.2.MD.A.4 | Measure to determine how much longer one object is than another, expressing the length difference in terms of a standard length unit. | Grade 2 |
| Wisconsin | M.2.MD.B.5 | Use addition and subtraction within 100 to solve word problems involving lengths that are given in the same units, e.g., by using drawings (such as number lines) and equations with a symbol for the unknown number to represent the problem. | Grade 2 |
| Wisconsin | M.2.MD.C.7 | Tell and write time from analog and digital clocks to the nearest five minutes, using a.m. and p.m. | Grade 2 |
| Wisconsin | M.2.MD.C.8 | Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies, using $ and ¢ symbols appropriately. | Grade 2 |
| Wisconsin | M.2.MD.D.9 | Generate measurement data by measuring lengths of several objects to the nearest whole unit, or by making repeated measurements of the same object. Show the measurements by making a line plot, where the horizontal scale is marked off in whole-number units. | Grade 2 |
| Wisconsin | M.2.MD.D.10 | Draw a picture graph and a bar graph (with single-unit scale) to represent a data set with up to four categories. Solve simple put together, take-apart, and compare problems using information presented in a bar graph. | Grade 2 |
| Wisconsin | M.2.G.A.1 | Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces. Identify triangles, quadrilaterals, pentagons, hexagons, and cubes. Sizes are compared directly or visually, not compared by measuring. | Grade 2 |
| Wisconsin | M.2.G.A.2 | Partition a rectangle into rows and columns of same-size squares and count to find the total number of them. | Grade 2 |
| Wisconsin | M.2.G.A.3 | Partition circles and rectangles into two, three, or four equal shares, describe and count the shares using the words halves, thirds, and fourths, and use phrases half of, a third of, and a fourth of the whole. Describe the whole as composed of two halves, three thirds, and four fourths. Recognize that equal shares of identical wholes need not have the same shape. | Grade 2 |
| Wisconsin | M.3.OA.A.1 | Interpret products of whole numbers, e.g., interpret 5 x 7 as the total number of objects in 5 groups of 7 objects each. | Grade 3 |
| Wisconsin | M.3.OA.A.2 | Interpret whole-number quotients of whole numbers. | Grade 3 |
| Wisconsin | M.3.OA.A.3 | Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem. | Grade 3 |
| Wisconsin | M.3.OA.B.4 | Apply properties of operations as strategies to multiply and divide. Student use of the formal terms for these properties is not necessary. | Grade 3 |
| Wisconsin | M.3.OA.B.5 | Understand division as an unknown-factor problem. | Grade 3 |
| Wisconsin | M.3.OA.C.6 | Use multiplicative thinking to multiply and divide within 100. a. Use the meanings of multiplication and division, the relationship between the operations (e.g., knowing that 8 x 5 = 40, one could reason that 40 ÷ 5 = 8), and properties of operations (e.g., the distributive property) to develop and understand strategies to multiply and divide within 100. b. Flexibly and efficiently use strategies, the relationship between the operations, and properties of operations to find products and quotients with multiples of 0, 1, 2, 5, & 10 within 100. | Grade 3 |
| Wisconsin | M.3.OA.D.7 | Solve two-step word problems, posed with whole numbers and having whole number answers, using the four operations. Represent these problems using one or two equations with a letter standing for the unknown quantity. If one equation is used, grouping symbols (i.e. parentheses) may be needed. Assess the reasonableness of answers using mental computation and estimation strategies. | Grade 3 |
| Wisconsin | M.3.OA.D.8 | Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations. | Grade 3 |
| Wisconsin | M.3.NBT.A.1 | Use place value understanding to generate estimates for problems in real-world situations, with whole numbers within 1,000, using strategies such as mental math, benchmark numbers, compatible numbers, and rounding. Assess the reasonableness of their estimates. | Grade 3 |
| Wisconsin | M.3.NBT.A.2 | Flexibly and efficiently add and subtract within 1,000 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction. | Grade 3 |
| Wisconsin | M.3.NBT.A.3 | Multiply one-digit whole numbers by multiples of 10 in the range 10-90 (e.g., 9 x 80, 5 x 60) using strategies based on place value and properties of operations. | Grade 3 |
| Wisconsin | M.3.NF.A.1 | Understand a unit fraction as the quantity formed when a whole is partitioned into equal parts and explain that a unit fraction is one of those parts (e.g., 1/4). Understand fractions are composed of unit fractions, for example, 7/4 is the quantity formed by 7 parts of the size 1/4. | Grade 3 |
| Wisconsin | M.3.NF.A.2 | Understand and represent a fraction as a number on the number line. a. Understand the whole on a number line is defined as the interval from 0 to 1 and the unit fraction is defined by partitioning the interval into equal parts (i.e., equal-sized lengths). b. Represent fractions on a number line by iterating lengths of the unit fraction from 0. Recognize that the resulting interval represents the size of the fraction and that its endpoint locates the fraction as a number on the number line. | Grade 3 |
| Wisconsin | M.3.NF.A.3 | Explain equivalence of fractions and compare fractions by reasoning about their size. a. Understand two fractions as equivalent (equal) if they are the same size or name the same point on a number line. b. Recognize and generate simple equivalent fractions, e.g., 1/2 = 2/4, 4/6 = 2/3) and explain why the fractions are equivalent by using a visual fraction model (e.g., tape diagram or number line). c. Express whole numbers as fractions (3 = 3/1), and recognize fractions that are equivalent to whole numbers (4/4 = 1). d. Compare two fractions with the same numerator or the same denominator by reasoning about their size. Recognize that comparisons are valid only when the two fractions refer to the same whole. Justify the conclusions by using a visual fraction model (e.g., tape diagram or number line) and describe the result of the comparison using words and symbols ( >, =, and < ). | Grade 3 |
| Wisconsin | M.3.MD.A.1 | Tell and write time to the nearest minute and measure time intervals in minutes. Solve word problems involving addition and subtraction of time intervals in minutes, e.g., by representing the problem on a number line. | Grade 3 |
| Wisconsin | M.3.MD.A.2 | Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l), excluding compound units such as cm³ and finding the geometric volume of a container. Add, subtract, multiply, or divide to solve one-step word problems involving masses or volumes that are given in the same units, e.g., by using drawings (such as a beaker with a measurement scale) to represent the problem. | Grade 3 |
| Wisconsin | M.3.MD.B.3 | Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and two-step how many more and how many less problems using information presented in scaled bar graphs. | Grade 3 |
| Wisconsin | M.3.MD.B.4 | Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Show the data by making a line plot, where the horizontal scale is marked off in appropriate units -- whole numbers, halves, fourths. | Grade 3 |
| Wisconsin | M.3.MD.C.5 | Recognize area as an attribute of plane figures and understand concepts of area measurement. a. A square with side length 1 unit, called a unit square is said to have one square unit of area, and can be used to measure area. b. A plane figure which can be covered without gaps or overlaps by n unit squares is said to have an area of n square units. | Grade 3 |
| Wisconsin | M.3.MD.C.6 | Measure areas by counting unit squares (square cm, square m, square in, square ft., and improvised units). | Grade 3 |
| Wisconsin | M.3.MD.C.7 | Relate area to the operations of multiplication and addition. a. Find the area of a rectangle with whole-number side lengths by tiling it, and show that the area is the same as would be found by multiplying the side lengths. b. Multiply side lengths to find areas of rectangles with whole number side lengths in the context of solving real world and mathematical problems, and represent whole-number products as rectangular areas in mathematical reasoning. c. Use tiling to show in a concrete case that the area of a rectangle with whole-number side lengths a and b + c is the sum of a x b and a x c. Use area models to represent the distributive property in mathematical reasoning. d. Recognize area as additive. Find areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas of the non-overlapping parts, applying this technique to solve real world problems. | Grade 3 |
| Wisconsin | M.3.MD.D.8 | Solve real world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters. | Grade 3 |
| Wisconsin | M.3.G.A.1 | Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories. | Grade 3 |
| Wisconsin | M.3.G.A.2 | Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole. | Grade 3 |
| Wisconsin | M.4.OA.A.1 | Interpret a multiplication equation as a multiplicative comparison, e.g., interpret 35 = 5 × 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations. | Grade 4 |
| Wisconsin | M.4.OA.A.2 | Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison. | Grade 4 |
| Wisconsin | M.4.OA.A.3 | Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies. | Grade 4 |
| Wisconsin | M.4.OA.B.4 | Find all factor pairs for a whole number in the range 1-100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1-100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1-100 is prime or composite. | Grade 4 |
| Wisconsin | M.4.OA.C.5 | Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. | Grade 4 |
| Wisconsin | M.4.NBT.A.1 | Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. | Grade 4 |
| Wisconsin | M.4.NBT.A.2 | Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place and describe the result of the comparison using words and symbols ( >, =, and < ). | Grade 4 |
| Wisconsin | M.4.NBT.A.3 | Use place value understanding to generate estimates for real-world problem situations, with multi-digit whole numbers, using strategies such as mental math, benchmark numbers, compatible numbers, and rounding. Assess the reasonableness of their estimates. | Grade 4 |
| Wisconsin | M.4.NBT.B.4 | Flexibly and efficiently add and subtract multi-digit whole numbers using strategies or algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction. | Grade 4 |
| Wisconsin | M.4.NBT.B.5 | Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. | Grade 4 |
| Wisconsin | M.4.NBT.B.6 | Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. | Grade 4 |
| Wisconsin | M.4.NF.A.1 | Understand fraction equivalence. a. Explain why a fraction is equivalent to another fraction by using visual fraction models (e.g., tape diagrams and number lines), with attention to how the number and the size of the parts differ even though the two fractions themselves are the same size. b. Understand and use a general principle to recognize and generate equivalent fractions that name the same amount. | Grade 4 |
| Wisconsin | M.4.NF.A.2 | Compare fractions with different numerators and different denominators while recognizing that comparisons are valid only when the fractions refer to the same whole. Justify the conclusions by using visual fraction models (e.g., tape diagrams and number lines) and by reasoning about the size of the fractions, using benchmark fractions (including whole numbers), or creating common denominators or numerators. Describe the result of the comparison using words and symbols ( >, =, and < ). | Grade 4 |
| Wisconsin | M.4.NF.B.3 | Understand composing and decomposing fractions. a. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. b. Decompose a fraction into a sum of unit fractions or multiples of that unit fraction in more than one way, recording each decomposition by an equation. Justify decompositions with explanations, visual fraction models, or equations. For example: 3/8 = 1/8 + 1/8 + 1/8; 3/8 = 1/8 + 2/8; 2 1/8 = 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8. c. Add and subtract fractions, including mixed numbers, with like denominators (e.g., 3/8 + 2/8) and related denominators (e.g., 1/2 +1/4, 1/3 + 1/6) by using visual fraction models (e.g., tape diagrams and number lines), properties of operations, and the relationship between addition and subtraction. d. Solve word problems involving addition and subtraction of fractions with like and related denominators, including mixed numbers, by using visual fraction models and equations to represent the problem. Students are not required to rename fractions in lowest terms nor use least common denominators. | Grade 4 |
| Wisconsin | M.4.NF.B.4 | Apply and extend previous understandings of multiplication to multiply a whole number times a fraction. a. Understand a fraction as a group of unit fractions or as a multiple of a unit fraction. b. Represent a whole number times a non-unit fraction (e.g., 3 x 2/5) using visual fraction models and understand this as combining equal groups of the non-unit fraction (3 groups of 2/5) and as a collection of unit fractions (6 groups of 1/5), recognizing this product as 6/5. c. Solve word problems involving multiplication of a whole number times a fraction by using visual fraction models and equations to represent the problem. Understand a reasonable answer range when multiplying with fractions. | Grade 4 |
| Wisconsin | M.4.NF.C.5 | Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100. | Grade 4 |
| Wisconsin | M.4.NF.C.6 | Use decimal notation for fractions with denominators 10 or 100, connect decimals to real-world contexts, and represent with visual models (e.g., number line or area model). | Grade 4 |
| Wisconsin | M.4.NF.C.7 | Compare decimals to hundredths by reasoning about their size and using benchmarks. Recognize that comparisons are valid only when the decimals refer to the same whole. Justify the conclusions, by using explanations or visual models (e.g., number line or area model) and describe the result of the comparison using words and symbols ( >, =, and < ). | Grade 4 |
| Wisconsin | M.4.MD.A.1 | Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb., oz.; l, ml; hr., min., sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two column table. | Grade 4 |
| Wisconsin | M.4.MD.A.2 | Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as a number line that feature a measurement scale. | Grade 4 |
| Wisconsin | M.4.MD.A.3 | Apply the area and perimeter formulas for rectangles in real world and mathematical problems. | Grade 4 |
| Wisconsin | M.4.MD.B.4 | Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots. | Grade 4 |
| Wisconsin | M.4.MD.C.5 | Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement: a. An angle is measured with reference to a circle with its center at the common endpoint of the rays, by considering the fraction of the circular arc between the points where the two rays intersect the circle. An angle that turns through 1/360 of a circle is called a one-degree angle and can be used to measure angles. b. An angle that turns through n one-degree angles is said to have an angle measure of n degrees. | Grade 4 |
| Wisconsin | M.4.MD.C.6 | Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure. | Grade 4 |
| Wisconsin | M.4.MD.C.7 | Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems, e.g., by using an equation with a symbol for the unknown angle measure | Grade 4 |
| Wisconsin | M.4.G.A.1 | Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures. | Grade 4 |
| Wisconsin | M.4.G.A.2 | Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles. | Grade 4 |
| Wisconsin | M.4.G.A.3 | Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify line-symmetric figures and draw lines of symmetry. | Grade 4 |
| Wisconsin | M.5.OA.A.1 | Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. | Grade 5 |
| Wisconsin | M.5.OA.A.2 | Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. | Grade 5 |
| Wisconsin | M.5.OA.B.3 | Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. | Grade 5 |
| Wisconsin | M.5.NBT.A.1 | Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. | Grade 5 |
| Wisconsin | M.5.NBT.A.2 | Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. | Grade 5 |
| Wisconsin | M.5.NBT.A.3 | Read, write, and compare decimals to thousandths. a. Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 x 100 + 4 x 10 + 7 x 1 + 3 x (1/10) + 9 x (1/100) + 2 x (1/1000). b. Compare decimals to thousandths based on meanings of the digits in each place and describe the result of the comparison using words and symbols ( >, =, and < ). | Grade 5 |
| Wisconsin | M.5.NBT.A.4 | Use place value understanding to generate estimates for problems in real-world situations, with decimals, using strategies such as mental math, benchmark numbers, compatible numbers, and rounding. Assess the reasonableness of their estimates. | Grade 5 |
| Wisconsin | M.5.NBT.B.5 | Flexibly and efficiently multiply multi-digit whole numbers using strategies or algorithms based on place value, area models, and the properties of operations. | Grade 5 |
| Wisconsin | M.5.NBT.B.6 | Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. | Grade 5 |
| Wisconsin | M.5.NBT.B.7 | Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. | Grade 5 |
| Wisconsin | M.5.NF.A.1 | Add and subtract fractions and mixed numbers using flexible and efficient strategies, including renaming fractions with equivalent] fractions. Justify using visual models (e.g., tape diagrams or number lines) and equations. | Grade 5 |
| Wisconsin | M.5.NF.A.2 | Solve word problems involving addition and subtraction of fractions referring to the same whole using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. | Grade 5 |
| Wisconsin | M.5.NF.B.3 | Interpret a fraction as an equal sharing division situation, where a quantity (the numerator) is divided into equal parts (the denominator). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, by using visual fraction models (e.g., tape diagrams or area models) or equations to represent the problem. | Grade 5 |
| Wisconsin | M.5.NF.B.4 | Apply and extend previous understandings of multiplication to multiply a fraction times a whole number (e.g., 2/3 x 4) or a fraction times a fraction (e.g., 2/3 x 4/5 ), including mixed numbers. a. Represent word problems involving multiplication of fractions using visual models to develop flexible and efficient strategies. b. Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles and represent fraction products as rectangular areas. | Grade 5 |
| Wisconsin | M.5.NF.B.5 | Interpret multiplication as scaling (resizing) by estimating whether a product will be larger or smaller than a given factor on the basis of the size of the other factor, without performing the indicated multiplication. a. Explain why multiplying a given number by a fraction greater than 1 results in a product greater than the given number and explain why multiplying a given number by a fraction less than 1 results in a product smaller than the given number. b. Relate the principle of fraction equivalence to the effect of multiplying or dividing a fraction by 1 or an equivalent form of 1 (e.g., 3/3, 5/5). | Grade 5 |
| Wisconsin | M.5.NF.B.6 | Solve real world problems involving multiplication of fractions and mixed numbers by using visual fraction models (e.g., tape diagrams, area models, or number lines) and equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. | Grade 5 |
| Wisconsin | M.5.NF.B.7 | Apply and extend previous understandings of division to divide unit fractions by whole numbers (e.g.,1/3 ÷ 4) and whole numbers by unit fractions (e.g., 4 ÷ 1/5). Students able to multiply fractions can develop strategies to divide fractions by reasoning about the relationship between multiplication and division. But division of a fraction by a fraction is not a requirement at this grade. a. Interpret and represent division of a unit fraction by a non-zero whole number as an equal sharing division situation. b. Interpret and represent division of a whole number by a unit fraction as a measurement division situation. c. Solve real-world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions by using visual fraction models and equations to represent the problem. | Grade 5 |
| Wisconsin | M.5.MD.A.1 | Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems | Grade 5 |
| Wisconsin | M.5.MD.B.2 | Make a line plot to display a data set of measurements in fractions of a unit (1/2,1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. | Grade 5 |
| Wisconsin | M.5.MD.C.3 | Recognize volume as an attribute of solid figures and understand concepts of volume measurement. a. A cube with side length 1 unit, called a unit cube, is said to have one cubic unit of volume, and can be used to measure volume. b. A solid figure which can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units. | Grade 5 |
| Wisconsin | M.5.MD.C.4 | Measure volumes by counting unit cubes, using cubic cm, cubic in., cubic ft., and improvised units. | Grade 5 |
| Wisconsin | M.5.MD.C.5 | Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume. a. Find the volume of a right rectangular prism with whole-number side lengths by packing it with unit cubes, and show that the volume is the same as would be found by multiplying the edge lengths, equivalently by multiplying the height by the area of the base. Represent threefold whole-number products as volumes, e.g., to represent the associative property of multiplication. b. Apply the formulas V = l x w x h and V = B x h for rectangular prisms to find volumes of right rectangular prisms with whole number edge lengths in the context of solving real-world and mathematical problems. c. Recognize volume as additive. Find volumes of solid figures composed of two nonoverlapping right rectangular prisms by adding the volumes of the non-overlapping parts, applying this technique to solve real-world problems. | Grade 5 |
| Wisconsin | M.5.G.A.1 | Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond. | Grade 5 |
| Wisconsin | M.5.G.A.2 | Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. | Grade 5 |
| Wisconsin | M.5.G.B.3 | Understand that attributes belonging to a category of two dimensional figures also belong to all subcategories of that category. . | Grade 5 |
| Wisconsin | M.5.G.B.4 | Classify two-dimensional figures in a hierarchy based on properties. | Grade 5 |
| Wisconsin | M.6.RP.A.1 | Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. | Grade 6 |
| Wisconsin | M.6.RP.A.2 | Understand the concept of a unit rate a/b associated with a ratio a:b with b ≠ 0, and use rate language in the context of a ratio relationship. | Grade 6 |
| Wisconsin | M.6.RP.A.3 | Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number lines, or equations. a. Make tables of equivalent ratios relating quantities with whole number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios. b. Solve unit rate problems including those involving unit pricing and constant speed. For example, if it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed? c. Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent. d. Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities. | Grade 6 |
| Wisconsin | M.6.NS.A.1 | Interpret, represent and compute division of fractions by fractions; and solve word problems by using visual fraction models (e.g., tape diagrams, area models, or number lines), equations, and the relationship between multiplication and division. | Grade 6 |
| Wisconsin | M.6.NS.B.2 | Flexibly and efficiently divide multi-digit whole numbers using strategies or algorithms based on place value, area models, and the properties of operations | Grade 6 |
| Wisconsin | M.6.NS.B.3 | Flexibly and efficiently add, subtract, multiply, and divide multi-digit decimals using strategies or algorithms based on place value, visual models, the relationship between operations and the properties of operations. | Grade 6 |
| Wisconsin | M.6.NS.C.5 | Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation. | Grade 6 |
| Wisconsin | M.6.NS.C.6 | Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates. a. Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line; recognize that the opposite of the opposite of a number is the number itself, e.g., -(-3) = 3, and that 0 is its own opposite. b. Understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane; recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes. c. Find and position integers and other rational numbers on a horizontal or vertical number line; find and position pairs of integers and other rational numbers on a coordinate plane. | Grade 6 |
| Wisconsin | M.6.NS.C.7 | Understand ordering and absolute value of rational numbers. a. Interpret statements of inequality as statements about the relative position of two numbers on a number line. b. Write, interpret, and explain statements of order for rational numbers in real-world contexts. c. Understand the absolute value of a rational number as its distance from 0 on the number line; interpret absolute value as magnitude for a positive or negative quantity in a real-world situation. d. Distinguish comparisons of absolute value from statements about order. | Grade 6 |
| Wisconsin | M.6.NS.C.8 | Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. | Grade 6 |
| Wisconsin | M.6.EE.A.1 | Write and evaluate numerical expressions involving whole-number exponents. | Grade 6 |
| Wisconsin | M.6.EE.A.2 | Write, read, and evaluate expressions in which letters stand for numbers. a. Write expressions that record operations with numbers and with letters standing for numbers. b. Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient); view one or more parts of an expression as a single entity. c. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations). | Grade 6 |
| Wisconsin | M.6.EE.A.3 | Apply the properties of operations to generate equivalent expressions. | Grade 6 |
| Wisconsin | M.6.EE.A.4 | Identify when two expressions are equivalent. | Grade 6 |
| Wisconsin | M.6.EE.B.5 | Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true. | Grade 6 |
| Wisconsin | M.6.EE.B.6 | Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set. | Grade 6 |
| Wisconsin | M.6.EE.B.7 | Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers. | Grade 6 |
| Wisconsin | M.6.EE.B.8 | Write an inequality of the form x > c or x c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams. | Grade 6 |
| Wisconsin | M.6.EE.C.9 | Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. | Grade 6 |
| Wisconsin | M.6.G.A.1 | Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems. | Grade 6 |
| Wisconsin | M.6.G.A.2 | Find volumes of right rectangular prisms with fractional edge lengths by using physical or virtual unit cubes. Develop (construct) and apply the formulas V = l w h and V = B h to find volumes of right rectangular prisms in the context of solving real-world and mathematical problems. | Grade 6 |
| Wisconsin | M.6.G.A.3 | Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems. | Grade 6 |
| Wisconsin | M.6.G.A.4 | Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems. | Grade 6 |
| Wisconsin | M.6.SP.B.5 | Summarize numerical data sets in relation to their context, such as by: a. Reporting the number of observations. b. Describing the nature of the attribute under investigation, including how it was measured and its units of measurement. c. Describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered and the quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation) were given. d. Relating the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered. | Grade 6 |
| Wisconsin | M.7.RP.A.1 | Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. | Grade 7 |
| Wisconsin | M.7.RP.A.2 | Recognize and represent proportional relationships between quantities. a. Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin. b. Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships. c. Represent proportional relationships by equations. For example, if total cost t is proportional to the number n of items purchased at a constant price p, the relationship between the total cost and the number of items can be expressed as t = pn. d. Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r) where r is the unit rate. | Grade 7 |
| Wisconsin | M.7.RP.A.3 | Use proportional relationships to solve multi-step ratio and percent problems. | Grade 7 |
| Wisconsin | M.7.NS.A.1 | Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line. a. Describe situations in which opposite quantities combine to make 0. b. Understand p + q as the number located a distance |q| from p, in the positive or negative direction depending on whether q is positive or negative. Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing real-world contexts. c. Understand subtraction of rational numbers as adding the additive inverse, p - q = p + (-q). Show that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in real-world contexts. d. Apply properties of operations as strategies to add and subtract rational numbers. | Grade 7 |
| Wisconsin | M.7.NS.A.2 | Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers. a. Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as (-1)(-1) = 1 and the rules for multiplying signed numbers. Interpret products of rational numbers by describing real-world contexts. b. Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with non-zero divisor) is a rational number. If p and q are integers, then -(p/q) = (-p)/q = p/(-q). Interpret quotients of rational numbers by describing real-world contexts. c. Apply properties of operations as strategies to multiply and divide rational numbers. d. Convert a rational number to a decimal using long division; know that the decimal form of a rational number terminates in 0s or eventually repeats. | Grade 7 |
| Wisconsin | M.7.NS.A.3 | Solve real-world and mathematical problems involving the four operations with rational numbers. Computations with rational numbers extend the rules for manipulating fractions to complex fractions. | Grade 7 |
| Wisconsin | M.7.EE.A.1 | Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients. | Grade 7 |
| Wisconsin | M.7.EE.A.2 | Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. | Grade 7 |
| Wisconsin | M.7.EE.B.3 | Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. | Grade 7 |
| Wisconsin | M.7.EE.B.4 | Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. a. Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Flexibly and efficiently apply the properties of operations and equality to solve equations of these forms. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. b. Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem. | Grade 7 |
| Wisconsin | M.7.G.A.1 | Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale. | Grade 7 |
| Wisconsin | M.7.G.A.2 | Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle. | Grade 7 |
| Wisconsin | M.7.G.A.3 | Describe the two-dimensional figures that result from slicing three dimensional figures parallel to the base, as in plane sections of right rectangular prisms and right rectangular pyramids. | Grade 7 |
| Wisconsin | M.7.G.B.4 | Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle. | Grade 7 |
| Wisconsin | M.7.G.B.5 | Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure. | Grade 7 |
| Wisconsin | M.7.G.B.6 | Solve real-world and mathematical problems involving area, volume and surface area of two- and three- dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. | Grade 7 |
| Wisconsin | M.8.NS.A.2 | Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line, and estimate the value of expressions (e.g., 𝝅² ). | Grade 8 |
| Wisconsin | M.8.EE.A.1 | Know and apply the properties of integer exponents to generate equivalent numerical expressions. | Grade 8 |
| Wisconsin | M.8.EE.A.2 | Use square root and cube root symbols to represent solutions to equations of the form x² = p and x = p³, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that √ 2 is irrational. | Grade 8 |
| Wisconsin | M.8.EE.A.3 | Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other. | Grade 8 |
| Wisconsin | M.8.EE.A.4 | Use technology to interpret and perform operations with numbers expressed in scientific notation. Choose units of appropriate size for measurements of very large or very small quantities. | Grade 8 |
| Wisconsin | M.8.EE.B.5 | Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. | Grade 8 |
| Wisconsin | M.8.EE.B.6 | Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b. | Grade 8 |
| Wisconsin | M.8.EE.C.7 | Solve linear equations in one variable. a. Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into equivalent forms. b. Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms. | Grade 8 |
| Wisconsin | M.8.EE.C.8 | Analyze and solve pairs of simultaneous linear equations. a. Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously. b. Solve systems of two linear equations in two variables by graphing and analyzing tables. Solve simple cases represented in algebraic symbols by inspection. c. Solve real-world and mathematical problems leading to two linear equations in two variables. | Grade 8 |
| Wisconsin | M.8.F.A.1 | Understand that a function is a rule that assigns to each input exactly one output. The graph of a numerically valued function is the set of ordered pairs consisting of an input and the corresponding output. | Grade 8 |
| Wisconsin | M.8.F.A.2 | Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). | Grade 8 |
| Wisconsin | M.8.F.A.3 | Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. | Grade 8 |
| Wisconsin | M.8.F.B.4 | Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values. | Grade 8 |
| Wisconsin | M.8.F.B.5 | Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear, continuous or discrete). Sketch a graph that exhibits the qualitative features of a function that has been described verbally. | Grade 8 |
| Wisconsin | M.8.G.A.1 | Verify experimentally the properties of rotations, reflections, and translations: a. Lines are taken to lines, and line segments to line segments of the same length. b. Angles are taken to angles of the same measure. c. Parallel lines are taken to parallel lines. | Grade 8 |
| Wisconsin | M.8.G.A.2 | Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them. | Grade 8 |
| Wisconsin | M.8.G.A.3 | Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates. | Grade 8 |
| Wisconsin | M.8.G.A.4 | Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two dimensional figures, describe a sequence that exhibits the similarity between them. | Grade 8 |
| Wisconsin | M.8.G.A.5 | Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. | Grade 8 |
| Wisconsin | M.8.G.B.7 | Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions. | Grade 8 |
| Wisconsin | M.8.G.B.8 | Apply the Pythagorean Theorem to find the distance between two points in a coordinate system. | Grade 8 |
| Wisconsin | M.8.G.C.9 | Know the relationship among the formulas for the volumes of cones, cylinders, and spheres (given the same height and diameter) and use them to solve real-world and mathematical problems. | Grade 8 |
| Wisconsin | M.8.SP.A.1 | Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association. | Grade 8 |
| Wisconsin | M.8.SP.A.2 | Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line. | Grade 8 |
| Wisconsin | M.A.SSE.A.2 | Use the structure of an expression to identify ways to rewrite it. | High School |
| Wisconsin | M.A.SSE.B.3 | Choose and use an efficient process to produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression. a. Factor a quadratic expression to reveal the zeros of the function it defines. b. Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines. c. Use the properties of exponents to transform expressions for exponential functions. | High School |
| Wisconsin | M.A.APR.B.3 | Identify zeros of higher degree polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial. | High School |
| Wisconsin | M.A.CED.A.2 | Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. | High School |
| Wisconsin | M.A.CED.A.3 | Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. | High School |
| Wisconsin | M.A.REI.B.3 | Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. | High School |
| Wisconsin | M.F.IF.A.2 | Use function notation, evaluate functions and interpret statements that use function notation in terms of a context. | High School |
| Wisconsin | M.F.IF.B.4 | For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. | High School |
| Wisconsin | M.F.IF.C.7 | Graph functions expressed symbolically and show key features of the graph using an efficient method. a. Graph linear and quadratic functions and show intercepts, maxima, and minima, and exponential functions, showing intercepts and end behavior. b. Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. c. Graph polynomial functions, identifying zeros when suitable factorizations are available and showing end behavior. d. Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available and showing end behavior. e. Graph logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude. | High School |
| Wisconsin | M.F.BF.A.1 | Write a function that describes a relationship between two quantities. a. Determine an explicit expression, a recursive process, or steps for calculation from a context. b. Combine standard function types using arithmetic operations. c. Work with composition of functions using tables, graphs, and symbols. | High School |
| Wisconsin | M.SP.ID.B.6 | Represent data on two quantitative variables on a scatter plot and describe how the variables are related. a. Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models. b. Informally assess the fit of a function by plotting and analyzing residuals. c. Fit a linear function for a scatter plot that suggests a linear association. | High School |
| WNCP | K.1.1.1 | Name the number that comes after a given number, one to nine | Kindergarten |
| WNCP | K.1.2.1 | Look briefly at a given familiar arrangement of 1 to 5 objects or dots and identify the number represented without counting | Kindergarten |
| WNCP | K.1.4.1 | Show a given number as two parts, using fingers, counters or other objects, and name the number of objects in each part | Kindergarten |
| WNCP | K.1.5.2 | Compare two given sets through direct comparison and describe the sets using words, such as more, fewer, as many as or the same number | Kindergarten |
| WNCP | 1.1.1.1 | Recite forward by 1s the number sequence between two given numbers (0 to 100) | Grade 1 |
| WNCP | 1.1.1.4 | Read a given numeral (0 to 100) when it is presented symbolically | Grade 1 |
| WNCP | 1.1.10.1 | Use and describe a personal strategy for determining a given sum | Grade 1 |
| WNCP | 1.1.10.2 | Use and describe a personal strategy for determining a given difference | Grade 1 |
| WNCP | 1.1.10.3 | Write the related subtraction fact for a given addition fact | Grade 1 |
| WNCP | 1.1.2.1 | Look briefly at a given familiar arrangement of objects or dots and identify the number represented without counting | Grade 1 |
| WNCP | 1.1.3.5 | Determine the total number of objects in a given set, starting from a known quantity and counting on | Grade 1 |
| WNCP | 1.1.3.6 | Count quantity using groups of 2s, 5s or 10s and counting on | Grade 1 |
| WNCP | 1.1.4.1 | Represent a given number up to 20 using a variety of manipulatives, including ten frames and base ten materials | Grade 1 |
| WNCP | 1.1.4.3 | Partition any given quantity up to 20 into 2 parts and identify the number of objects in each part | Grade 1 |
| WNCP | 1.1.5.4 | Compare two given sets using one-to-one correspondence and describe them using comparative words, such as more, fewer or as many | Grade 1 |
| WNCP | 1.1.5.5 | Compare a set to a given referent using comparative language | Grade 1 |
| WNCP | 1.1.7.1 | Represent a given number in a variety of equal groups with and without singles | Grade 1 |
| WNCP | 1.1.7.2 | Recognize that for a given number of counters, no matter how they are grouped, the total number of counters does not change | Grade 1 |
| WNCP | 1.1.8.1 | Name the number that is one more, two more, one less or two less than a given number, up to 20 | Grade 1 |
| WNCP | 1.1.8.2 | Represent a number on a ten frame that is one more, two more, one less or two less than a given number | Grade 1 |
| WNCP | 1.2.3.3 | Determine if two given concrete sets are equal or unequal and explain the process used | Grade 1 |
| WNCP | 2.1.1.1 | Extend a given skip counting sequence (by 2s, 5s or 10s) forward and backward | Grade 2 |
| WNCP | 2.1.1.2 | Skip count by 10s, given any number from 1 to 9 as a starting point | Grade 2 |
| WNCP | 2.1.1.5 | Count quantity using groups of 2s, 5s or 10s and counting on | Grade 2 |
| WNCP | 2.1.10.1 | Explain the mental mathematics strategy that could be used to determine a basic fact, such as doubles | Grade 2 |
| WNCP | 2.1.10.2 | Explain the mental mathematics strategy that could be used to determine a basic fact, such as doubles plus one | Grade 2 |
| WNCP | 2.1.10.3 | Explain the mental mathematics strategy that could be used to determine a basic fact, such as doubles take away one | Grade 2 |
| WNCP | 2.1.10.4 | Explain the mental mathematics strategy that could be used to determine a basic fact, such as doubles plus two | Grade 2 |
| WNCP | 2.1.10.5 | Explain the mental mathematics strategy that could be used to determine a basic fact, such as doubles take away two | Grade 2 |
| WNCP | 2.1.10.6 | Explain the mental mathematics strategy that could be used to determine a basic fact, such as making 10 | Grade 2 |
| WNCP | 2.1.10.7 | Explain the mental mathematics strategy that could be used to determine a basic fact, such as building on a known double | Grade 2 |
| WNCP | 2.1.4.1 | Represent a given number using concrete materials, such as ten frames and base ten materials | Grade 2 |
| WNCP | 2.1.5.1 | Order a given set of numbers in ascending or descending order and verify the result using a hundred chart, number line, ten frames or by making references to place value | Grade 2 |
| WNCP | 2.1.5.3 | Identify missing numbers in a given hundred chart | Grade 2 |
| WNCP | 2.1.7.2 | Count the number of objects in a given set using groups of 10s and 1s, and record the result as a 2-digit numeral under the headings of 10s and 1s | Grade 2 |
| WNCP | 2.1.7.3 | Describe a given 2-digit numeral in at least two ways | Grade 2 |
| WNCP | 2.1.7.4 | Illustrate using ten frames and diagrams that a given numeral consists of a certain number of groups of ten and a certain number of ones | Grade 2 |
| WNCP | 2.1.8.1 | Add zero to a given number and explain why the sum is the same as the addend | Grade 2 |
| WNCP | 2.1.8.2 | Subtract zero from a given number and explain why the difference is the same as the given number | Grade 2 |
| WNCP | 2.1.9.1 | Model addition and subtraction using concrete materials or visual representations and record the process symbolically | Grade 2 |
| WNCP | 2.1.9.3 | Solve a given problem involving a missing addend and describe the strategy used | Grade 2 |
| WNCP | 2.1.9.7 | Add a given set of numbers in two different ways, and explain why the sum is the same | Grade 2 |
| WNCP | 2.2.3.1 | Determine whether two given quantities of the same object (same shape and mass) are equal by using a balance scale | Grade 2 |
| WNCP | 2.3.8.2 | Identify common attributes of triangles, squares, rectangles and circles from given sets of the same type of 2-D shapes. | Grade 2 |
| WNCP | 2.3.8.3 | Identify given 2-D shapes with different dimensions. | Grade 2 |
| WNCP | 2.3.8.4 | Identify given 2-D shapes with different orientations. | Grade 2 |
| WNCP | 2.3.8.5 | Create a model to represent a given 2-D shape. | Grade 2 |
| WNCP | 2.3.8.6 | Create a pictorial representation of a given 2-D shape. | Grade 2 |
| WNCP | 2.4.1.2 | Organize data as it is collected using concrete objects, tallies, checkmarks, charts or lists. | Grade 2 |
| WNCP | 2.4.1.3 | Answer questions using collected data. | Grade 2 |
| WNCP | 2.4.2.3 | Answer questions pertaining to a given concrete graph or pictograph. | Grade 2 |
| WNCP | 2.4.2.4 | Create a concrete graph to display a given set of data and draw conclusions. | Grade 2 |
| WNCP | 2.4.2.5 | Create a pictograph to represent a given set of data using one-to-one correspondence. | Grade 2 |
| WNCP | 2.4.2.6 | Solve a given problem by constructing and interpreting a concrete graph or pictograph. | Grade 2 |
| WNCP | 3.1.1.1 | Extend a given skip counting sequence by 5s, 10s or 100s, forward and backward, using a given starting point | Grade 3 |
| WNCP | 3.1.1.2 | Extend a given skip counting sequence by 3s, forward and backward, starting at a given multiple of 3 | Grade 3 |
| WNCP | 3.1.1.3 | Extend a given skip counting sequence by 4s, forward and backward, starting at a given multiple of 4 | Grade 3 |
| WNCP | 3.1.10.1 | Describe a mental mathematics strategy that could be used to determine a given basic fact, such as doubles | Grade 3 |
| WNCP | 3.1.10.6 | Describe a mental mathematics strategy that could be used to determine a given basic fact, such as making 10 | Grade 3 |
| WNCP | 3.1.11.3 | Represent a given multiplication expression as repeated addition | Grade 3 |
| WNCP | 3.1.11.6 | Represent, concretely or pictorially, equal groups for a given number sentence | Grade 3 |
| WNCP | 3.1.11.7 | Represent a given multiplication expression using an array | Grade 3 |
| WNCP | 3.1.11.9 | Relate multiplication to division by using arrays and writing related number sentences | Grade 3 |
| WNCP | 3.1.12.10 | Solve a given problem involving division | Grade 3 |
| WNCP | 3.1.13.3 | Cut or fold a whole into equal parts, or draw a whole in equal parts; demonstrate that the parts are equal and name the parts | Grade 3 |
| WNCP | 3.1.13.5 | Represent a given fraction concretely or pictorially | Grade 3 |
| WNCP | 3.1.13.6 | Name and record the fraction represented by the shaded and non-shaded parts of a given region. | Grade 3 |
| WNCP | 3.1.2.4 | Represent a given number using manipulatives, such as base ten materials | Grade 3 |
| WNCP | 3.1.3.1 | Place a given set of numbers in ascending or descending order and verify the result by using a hundred chart | Grade 3 |
| WNCP | 3.1.4.3 | Estimate a given quantity by comparing it to a referent | Grade 3 |
| WNCP | 3.1.5.1 | Record, in more than one way, the number represented by given proportional and nonproportional concrete materials | Grade 3 |
| WNCP | 3.1.5.2 | Represent a given number in different ways using proportional and non-proportional concrete materials and explain how they are equivalent | Grade 3 |
| WNCP | 3.1.6.1 | Add two given 2-digit numerals using a mental mathematics strategy and explain or illustrate the strategy | Grade 3 |
| WNCP | 3.1.7.1 | Subtract two given 2-digit numerals using a mental mathematics strategy and explain or model the strategy used | Grade 3 |
| WNCP | 3.1.9.1 | Model the addition of two or more given numbers using concrete or visual representations and record the process symbolically | Grade 3 |
| WNCP | 3.1.9.2 | Model the subtraction of two given numbers using concrete or visual representations and record the process symbolically | Grade 3 |
| WNCP | 3.1.9.6 | Solve a given problem involving the sum or difference of two given numbers | Grade 3 |
| WNCP | 3.2.3.5 | Solve a given addition or subtraction equation with one unknown using a variety of strategies including guess and test | Grade 3 |
| WNCP | 3.3.3.4 | Show that 100 centimetres is equivalent to 1 metre by using concrete materials | Grade 3 |
| WNCP | 3.3.3.6 | Determine and record the length and width of a given 2-D shape | Grade 3 |
| WNCP | 3.3.3.8 | Draw a line segment of a given length using a ruler | Grade 3 |
| WNCP | 3.3.3.9 | Sketch a line segment of a given length without using a ruler | Grade 3 |
| WNCP | 3.3.4.4 | Explain the relationship between 1000 grams and 1 kilogram using a model | Grade 3 |
| WNCP | 3.3.7.1 | Classify a given set of regular and irregular polygons according to the number of side | Grade 3 |
| WNCP | 3.4.1.1 | Record the number of objects in a given set using tally marks | Grade 3 |
| WNCP | 3.4.1.3 | Organize a given set of data using tally marks, line plots, charts or lists | Grade 3 |
| WNCP | 3.4.1.4 | Collect and organize data using tally marks, line plots, charts and lists | Grade 3 |
| WNCP | 3.4.1.5 | Answer questions arising from a given line plot, chart or list | Grade 3 |
| WNCP | 3.4.1.6 | Answer questions using collected data | Grade 3 |
| WNCP | 3.4.2.2 | Create bar graphs from a given set of data including labelling the title and axes | Grade 3 |
| WNCP | 3.4.2.3 | Draw conclusions from a given bar graph to solve problems | Grade 3 |
| WNCP | 3.4.2.4 | Solve problems by constructing and interpreting a bar graph | Grade 3 |
| WNCP | 4.1.2.1 | Order a given set of numbers in ascending or descending order and explain the order by making references to place value | Grade 4 |
| WNCP | 4.1.3.4 | Estimate sums and differences using different strategies, e.g., front-end estimation and compensation | Grade 4 |
| WNCP | 4.1.5.1 | Provide examples for applying mental mathematics strategies: doubling | Grade 4 |
| WNCP | 4.1.5.2 | Provide examples for applying mental mathematics strategies: doubling and adding one more group | Grade 4 |
| WNCP | 4.1.5.4 | Provide examples for applying mental mathematics strategies: halving | Grade 4 |
| WNCP | 4.1.6.1 | Model a given multiplication problem using the distributive property | Grade 4 |
| WNCP | 4.1.6.2 | Use concrete materials, such as base ten blocks or their pictorial representations, to represent multiplication and record the process symbolically | Grade 4 |
| WNCP | 4.1.6.5 | Model and solve a given multiplication problem using an array and record the process | Grade 4 |
| WNCP | 4.1.7.3 | Solve a given division problem using a personal strategy and record the process | Grade 4 |
| WNCP | 4.1.8.6 | Represent a given fraction pictorially by shading parts of a given whole | Grade 4 |
| WNCP | 4.1.8.8 | Order a given set of fractions that have the same numerator and explain the ordering | Grade 4 |
| WNCP | 4.1.8.9 | Order a given set of fractions that have the same denominator and explain the ordering | Grade 4 |
| WNCP | 4.1.8.11 | Name fractions between two given benchmarks on a number line | Grade 4 |
| WNCP | 4.1.9.2 | Represent a given decimal using concrete materials or a pictorial representation | Grade 4 |
| WNCP | 4.1.9.3 | Explain the meaning of each digit in a given decimal with all digits the same | Grade 4 |
| WNCP | 4.1.10.4 | Express a given pictorial or concrete representation as a fraction or decimal | Grade 4 |
| WNCP | 4.1.11.1 | Predict sums and differences of decimals using estimation strategies | Grade 4 |
| WNCP | 4.2.5.3 | Identify the unknown in a story problem, represent the problem with an equation and solve the problem concretely, pictorially or symbolically | Grade 4 |
| WNCP | 4.3.1.2 | Express the time orally and numerically from a 12-hour analog clock | Grade 4 |
| WNCP | 4.3.1.3 | Express the time orally and numerically from a 24-hour analog clock | Grade 4 |
| WNCP | 4.3.1.4 | Express the time orally and numerically from a 12-hour digital clock | Grade 4 |
| WNCP | 4.3.3.2 | Identify and explain why the square is the most efficient unit for measuring area. | Grade 4 |
| WNCP | 4.3.5.2 | Sort a given set of 2-D shapes as symmetrical and non-symmetrical. | Grade 4 |
| WNCP | 4.3.5.3 | Complete a symmetrical 2-D shape given half the shape and its line of symmetry. | Grade 4 |
| WNCP | 4.3.5.4 | Identify lines of symmetry of a given set of 2-D shapes and explain why each shape is symmetrical. | Grade 4 |
| WNCP | 4.4.2.1 | Identify an interval and correspondence for displaying a given set of data in a graph and justify the choice | Grade 4 |
| WNCP | 4.4.2.2 | Create and label (with categories, title and legend) a pictograph to display a given set of data using many-to-one correspondence, and justify the choice of correspondence used | Grade 4 |
| WNCP | 4.4.2.3 | Create and label (with axes and title) a bar graph to display a given set of data using many-to one correspondence, and justify the choice of interval used | Grade 4 |
| WNCP | 4.4.2.4 | Answer a given question using a given graph in which data is displayed using many-to-one correspondence | Grade 4 |
| WNCP | 5.1.10.1 | Order a given set of decimals by placing them on a number line that contains benchmarks | Grade 5 |
| WNCP | 5.1.10.2 | Order a given set of decimals including only tenths using place value | Grade 5 |
| WNCP | 5.1.10.3 | Order a given set of decimals including only hundredths using place value | Grade 5 |
| WNCP | 5.1.11.5 | Solve a given problem that involves addition and subtraction of decimals, limited to thousandths | Grade 5 |
| WNCP | 5.1.3.1 | Describe the mental mathematics strategy used to determine a given basic fact, such as skip count up by one or two groups from a known fact | Grade 5 |
| WNCP | 5.1.3.3 | Describe the mental mathematics strategy used to determine a given basic fact, such as doubling | Grade 5 |
| WNCP | 5.1.3.5 | Describe the mental mathematics strategy used to determine a given basic fact, such as repeated doubling | Grade 5 |
| WNCP | 5.1.4.1 | Determine the products when one factor is a multiple of 10, 100 or 1000 by annexing zero or adding zeros | Grade 5 |
| WNCP | 5.1.4.2 | Apply halving and doubling when determining a given product | Grade 5 |
| WNCP | 5.1.4.3 | Apply the distributive property to determine a given product involving multiplying factors that are close to multiples of 10 | Grade 5 |
| WNCP | 5.1.6.2 | Explain that the interpretation of a remainder depends on the context: ignore the remainder | Grade 5 |
| WNCP | 5.1.6.3 | Explain that the interpretation of a remainder depends on the context: round up the quotient | Grade 5 |
| WNCP | 5.1.6.4 | Explain that the interpretation of a remainder depends on the context: express remainders as fractions | Grade 5 |
| WNCP | 5.1.7.1 | Create a set of equivalent fractions and explain why there are many equivalent fractions for any given fraction using concrete materials | Grade 5 |
| WNCP | 5.1.8.2 | Represent a given decimal using concrete materials or a pictorial representation | Grade 5 |
| WNCP | 5.3.6.2 | Sort a given set of quadrilaterals and explain the sorting rule. | Grade 5 |
| WNCP | 5.3.6.4 | Sort a given set of quadrilaterals according to whether or not opposite sides are parallel. | Grade 5 |
| WNCP | 5.3.7.1 | Translate a given 2-D shape horizontally, vertically or diagonally, and descrive the position and orientation of the image. | Grade 5 |
| WNCP | 5.3.7.2 | Rotate a given 2-D shape about a point, and describe the position and orientation of the image. | Grade 5 |
| WNCP | 5.3.7.3 | Reflect a given 2-D shape in a line of reflection, and describe the position and orientation of the image. | Grade 5 |
| WNCP | 5.3.7.4 | Perform a transformation ofa given 2-D shape by following instructions. | Grade 5 |
| WNCP | 5.3.7.7 | Draw a 2-D shape, reflect the shape, and identify the line of reflection and the distance of the image from the line of reflection. | Grade 5 |
| WNCP | 5.3.8.1 | Provide an example of a translation, a rotation and a reflection. | Grade 5 |
| WNCP | 5.3.8.2 | Identify a given single transformation as a translation, rotation or reflection. | Grade 5 |
| WNCP | 5.3.8.3 | Describe a given rotation by the direction of the turn (clockwise or counterclockwise). | Grade 5 |
| WNCP | 6.1.3.1 | Identify multiples for a given number and explain the strategy used to identify them | Grade 6 |
| WNCP | 6.1.3.3 | Identify the factors for a given number and explain the strategy used | Grade 6 |
| WNCP | 6.1.6.3 | Use concrete materials and pictorial representations to illustrate a given percent | Grade 6 |
| WNCP | 6.1.6.5 | Express a given percent as a fraction and a decimal | Grade 6 |
| WNCP | 6.1.6.7 | Solve a given problem involving percents | Grade 6 |
| WNCP | 6.1.7.2 | Place given integers on a number line and explain how integers are ordered | Grade 6 |
| WNCP | 6.1.7.4 | Compare two integers, represent their relationship using the symbols and =, and verify using a number line. | Grade 6 |
| WNCP | 6.1.8.5 | Solve a given problem that involves multiplication and division of decimals using multipliers from 0 to 9 and divisors from 1 to 9 | Grade 6 |
| WNCP | 6.1.9.1 | Demonstrate and explain with examples why there is a need to have a standardized order of operations. | Grade 6 |
| WNCP | 6.1.9.2 | Apply the order of operations to solve multi-step problems with or without technology, e.g., computer, calculator. | Grade 6 |
| WNCP | 6.2.1.1 | Generate values in one column of a table of values, given values in the other column and pattern rule. | Grade 6 |
| WNCP | 6.2.1.2 | State, using mathematical language, the relationship in a given table of values. | Grade 6 |
| WNCP | 6.2.1.3 | Create a concrete or pictorial representation of the relationship shown in a table of values. | Grade 6 |
| WNCP | 6.2.1.5 | Formulate a rule to describe the relationship between two columns of numbers in a table of values. | Grade 6 |
| WNCP | 6.2.1.6 | Identify missing elements in a given table of values. | Grade 6 |
| WNCP | 6.2.2.1 | Translate a pattern to a table of values and graph the table of values (limit to linear graphs with discrete elements). | Grade 6 |
| WNCP | 6.2.2.2 | Create a table of values from a given pattern or a given graph. | Grade 6 |
| WNCP | 6.3.1.4 | Estimate the measure of an angle using 45°, 90° and 180° as reference angles | Grade 6 |
| WNCP | 6.3.1.5 | Measure, using a protractor, given angles in various orientations. | Grade 6 |
| WNCP | 6.3.1.6 | Draw and label a specified angle in various orientations using a protractor | Grade 6 |
| WNCP | 6.3.1.7 | Describe the measure of an angle as the measure of rotation of one of its sides | Grade 6 |
| WNCP | 6.3.1.8 | Describe the measure of angles as the measure of an interior angle of a polygon. | Grade 6 |
| WNCP | 6.3.2.1 | Explain, using models, that the sum of the interior angles of a triangle is the same for all triangles. | Grade 6 |
| WNCP | 6.3.2.2 | Explain, using models, that the sum of the interior angles of a quadrilateral is the same for all quadrilaterals. | Grade 6 |
| WNCP | 6.3.4.2 | Sort a given set of triangles according to the measures of the interior angles. | Grade 6 |
| WNCP | 6.3.4.3 | Identify the characteristics of a given set of triangles according to their sides and/or their interior angles. | Grade 6 |
| WNCP | 6.3.4.4 | Sort a given set of triangles and explain the sorting rule. | Grade 6 |
| WNCP | 6.3.4.5 | Draw a specified triangle, e.g. scalene. | Grade 6 |
| WNCP | 6.3.4.6 | Replicate a given triangle in a different orientation and show that the two are congruent. | Grade 6 |
| WNCP | 6.3.5.3 | Demonstrate congruence (sides to sides and angles to angles) in a regular polygon by measuring. | Grade 6 |
| WNCP | 6.3.5.1 | Sort a given set of 2-D shapes into polygons and non-polygons | Grade 6 |
| WNCP | 6.3.5.4 | Demonstrate that the sides of a regular polygon are of the same length and that the angles of a regular polygon are of the same measure. | Grade 6 |
| WNCP | 6.3.6.7 | Perform and record one or more transformations of a 2-D shape that will result in a given image. | Grade 6 |
| WNCP | 6.3.8.2 | Plot a point in the first quadrant of a Cartesian plane given its ordered pair. | Grade 6 |
| WNCP | 6.3.8.3 | Match points in the first quadrant of a Cartesian plane with their corresponding ordered pair. | Grade 6 |
| WNCP | 6.3.8.4 | Plot points in the first quadrant of a Cartesian plane with intervals of 1, 2, 5 or 10 on its axes, given whole number ordered pairs. | Grade 6 |
| WNCP | 6.3.8.5 | Draw shapes or designs, given ordered pairs in the first quadrant of a Cartesian plane. | Grade 6 |
| WNCP | 6.3.8.6 | Determine the distance between points along horizontal and vertical lines in the first quadrant of a Cartesian plane. | Grade 6 |
| WNCP | 7.1.2.1 | Solve a given problem involving the addition of two or more decimal numbers | Grade 7 |
| WNCP | 7.1.2.3 | Solve a given problem involving the multiplication of decimal numbers | Grade 7 |
| WNCP | 7.1.2.4 | Solve a given problem involving the multiplication or division of decimal numbers with 2- digit multipliers or 1-digit divisors (whole numbers or decimals) | Grade 7 |
| WNCP | 7.1.3.2 | Solve a given problem that involves finding a percent | Grade 7 |
| WNCP | 7.1.5.1 | Model addition and subtraction of a given positive fraction or a given mixed number using concrete representations, and record symbolically | Grade 7 |
| WNCP | 7.1.5.2 | Determine the sum of two given positive fractions or mixed numbers with like denominators | Grade 7 |
| WNCP | 7.1.5.3 | Determine the difference of two given positive fractions or mixed numbers with like denominators | Grade 7 |
| WNCP | 7.1.6.1 | Explain, using concrete materials such as integer tiles and diagrams, that the sum of opposite integers is zero. | Grade 7 |
| WNCP | 7.1.6.2 | Illustrate, using a number line, the results of adding or subtracting negative and positive integers | Grade 7 |
| WNCP | 7.1.6.3 | Add two given integers using concrete materials or pictorial representations and record the process symbolically. | Grade 7 |
| WNCP | 7.1.6.4 | Subtract two given integers using concrete materials or pictorial representations and record the process symbolically. | Grade 7 |
| WNCP | 7.1.6.5 | Solve a given problem involving the addition and subtraction of integers. | Grade 7 |
| WNCP | 7.1.7.2 | Identify a number that would be between two given numbers in an ordered sequence or on a number line. | Grade 7 |
| WNCP | 7.2.2.1 | Create a table of values for a given linear relation by substituting values for the variable. | Grade 7 |
| WNCP | 7.2.2.2 | Create a table of values using a linear relation and graph the table of values (limited to discrete elements). | Grade 7 |
| WNCP | 7.2.2.3 | Sketch the graph from a table of values created for a given linear relation and describe the patterns found in the graph to draw conclusions, e.g., graph the relationship between n and 2n + 3. | Grade 7 |
| WNCP | 7.2.5.1 | Substitute a value for an unknown in a given expression and evaluate the expression. | Grade 7 |
| WNCP | 7.2.6.3 | Solve a given problem using a linear equation. | Grade 7 |
| WNCP | 7.2.7.3 | Solve a given problem using a linear equation and record the process. | Grade 7 |
| WNCP | 7.3.4.2 | Identify the location of a given point in any quadrant of a Cartesian plane using an integral ordered pair. | Grade 7 |
| WNCP | 7.3.4.3 | Plot the point corresponding to a given integral ordered pair on a Cartesian plane with units of 1, 2, 5 or 10 on its axes. | Grade 7 |
| WNCP | 7.3.4.4 | Draw shapes and designs, using given integral ordered pairs, in a Cartesian plane. | Grade 7 |
| WNCP | 7.3.4.5 | Create shapes and designs, and identify the points used to produce the shapes and designs in any quadrant of a Cartesian plane. | Grade 7 |
| WNCP | 7.3.5.1 | Identify the coordinates of the vertices of a given 2-D shape on a Cartesian plane. | Grade 7 |
| WNCP | 7.3.5.3 | Describe the positional change of the vertices of a given 2-D shape to the corresponding vertices of its image as a result of a transformation or successive transformations on a Cartesian plane. | Grade 7 |
| WNCP | 8.1.1.1 | Represent a given perfect square as a square region using materials, such as grid paper or square shapes. | Grade 8 |
| WNCP | 8.1.1.4 | Determine the square root of a given perfect square and record it symbolically. | Grade 8 |
| WNCP | 8.1.1.5 | Determine the square of a given number. | Grade 8 |
| WNCP | 8.1.6.8 | Model multiplication of a positive fraction by a positive fraction concretely or pictorially using an area model and record the process | Grade 8 |
| WNCP | 8.1.6.9 | Model division of a positive proper fraction by a whole number concretely or pictorially and record the process | Grade 8 |
| WNCP | 8.1.6.10 | Model division of a positive proper fraction by a positive proper fraction pictorially and record the process | Grade 8 |
| WNCP | 8.1.6.11 | Generalize and apply rules for multiplying and dividing positive fractions, including mixed numbers | Grade 8 |
| WNCP | 8.1.7.4 | Model the process of multiplying two integers using concrete materials or pictorial representations and record the process | Grade 8 |
| WNCP | 8.1.7.5 | Model the process of dividing an integer by an integer using concrete materials or pictorial representations and record the process. | Grade 8 |
| WNCP | 8.1.7.8 | Generalize and apply a rule for determining the sign of the product and quotient of integers. | Grade 8 |
| WNCP | 8.1.7.9 | Solve a given problem involving integers taking into consideration order of operations. | Grade 8 |
| WNCP | 8.2.1.1 | Determine the missing value in an ordered pair for a given equation. | Grade 8 |
| WNCP | 8.2.1.2 | Create a table of values by substituting values for a variable in the equation of a given linear relation. | Grade 8 |
| WNCP | 8.2.1.3 | Construct a graph from the equation of a given linear relation (limited to discrete data). | Grade 8 |
| WNCP | 8.2.1.4 | Describe the relationship between the variables of a given graph. | Grade 8 |
| WNCP | 8.2.2.4 | Solve a given linear equation symbolically. | Grade 8 |
| WNCP | 8.3.1.4 | Determine the measure of the third side of a right triangle, given the measures of the other two sides, to solve a given problem. | Grade 8 |
| WNCP | 8.3.1.5 | Solve a given problem that involves Pythagorean triples, e.g., 3, 4, 5 or 5, 12, 13. | Grade 8 |
| WNCP | A.1.1.7 | Evaluate powers with integral bases (excluding base 0) and whole number exponents. | Algebra |
| WNCP | A.2.1.2 | Write a linear equation to represent a given context. | Algebra |
| WNCP | A.2.1.5 | Write a linear equation representing the pattern in a given table of values and verify the equation by substituting values from the table. | Algebra |
| WNCP | A.2.2.2 | Graph a given linear relation, including horizontal and vertical lines. | Algebra |
| WNCP | A.2.2.3 | Match given equations of linear relations with their corresponding graphs. | Algebra |
| WNCP | A.2.5.2 | Write the expression for a given model of a polynomial. | Algebra |
| WNCP | A.2.5.3 | Identify the variables, degree, number of terms and coefficients, including the constant term, of a given simplified polynomial expression. | Algebra |
| WNCP | A.2.6.3 | Apply a personal strategy for addition and subtraction of given polynomial expressions, and record the process symbolically. | Algebra |
| WNCP | A.2.7.1 | Model multiplication of a given polynomial expression by a given monomial concretely or pictorially and record the process symbolically. | Algebra |
| WNCP | A.2.7.3 | Apply a personal strategy for multiplication and division of a given polynomial expression by a given monomial | Algebra |
| Wyoming | K.CC.A.1A | Count to 100 by ones and by tens. | Kindergarten |
| Wyoming | K.CC.A.2 | Count forward beginning from a given number within the known sequence (instead of having to begin at 1). | Kindergarten |
| Wyoming | K.CC.A.3 | Write numbers from 0 to 20. Represent a number of objects with a written numeral 0-20 (with 0 (Zero) representing a count of no objects). | Kindergarten |
| Wyoming | K.CC.B.4 | Understand the relationship between numbers and quantities; connect counting to cardinality. | Kindergarten |
| Wyoming | K.CC.B.5 | When counting: | Kindergarten |
| Wyoming | K.CC.C.6 | Identify whether the number of objects in one group is greater than, less than, or equal to the number of objects in another group. | Kindergarten |
| Wyoming | K.CC.C.7 | Compare two numbers between 1 and 10 presented as written numerals. | Kindergarten |
| Wyoming | K.G.H.1 | Describe objects in the environment using the names of shapes, and describe the relative positions of these objects using terms such as above, below, beside, in front of, behind, and next to. | Kindergarten |
| Wyoming | K.G.H.2 | Correctly name shapes regardless of their orientations or overall size. | Kindergarten |
| Wyoming | K.G.H.3 | Identify shapes as two-dimensional or three-dimensional. | Kindergarten |
| Wyoming | K.G.I.4 | Analyze and compare two- and three-dimensional shapes, using informal language to describe their similarities, differences, and attributes. | Kindergarten |
| Wyoming | K.G.I.6 | Use simple shapes to compose squares, rectangles, and hexagons. | Kindergarten |
| Wyoming | K.MD.F.1 | Describe several measurable attributes of one or more objects. | Kindergarten |
| Wyoming | K.MD.F.2 | Make direct comparisons of the length, capacity, weight, and temperature of objects, and recognize which object is shorter/longer, taller, lighter/heavier, warmer/cooler, and which holds more/less. | Kindergarten |
| Wyoming | K.MD.G.3 | Classify objects into given categories; count the numbers of objects in each category and sort the categories by count. | Kindergarten |
| Wyoming | K.MD.G.4 | Identify U.S. coins by name (pennies, nickels, dimes, and quarters). | Kindergarten |
| Wyoming | K.NBT.E.1 | Describe, explore, and explain how the counting numbers 11 to 19 is: composed of ten ones and more ones and decomposed into ten ones and more ones | Kindergarten |
| Wyoming | K.OA.D.1 | Model situations that involve representing addition and subtraction with objects, fingers, mental images, drawings, sounds (e.g., claps), acting out situations, verbal explanations, expressions, or equations. | Kindergarten |
| Wyoming | K.OA.D.2 | Solve word problems using objects and drawings to find sums up to 10 and differences within 10. | Kindergarten |
| Wyoming | K.OA.D.3 | Decompose numbers less than or equal to 10 in more than one way. | Kindergarten |
| Wyoming | K.OA.D.4 | For any number from 1 to 9, find the number that makes 10 when added to the given number. | Kindergarten |
| Wyoming | K.OA.D.5 | Fluently add and subtract within 5. | Kindergarten |
| Wyoming | 1.G.K.1 | Distinguish between defining attributes (e.g., triangles are closed and three-sided) versus non-defining attributes (e.g., color, orientation, overall size); for a wide variety of shapes; build and draw shapes to possess defining attributes. | Grade 1 |
| Wyoming | 1.G.K.2 | Use two-dimensional shapes (rectangles, squares, trapezoids, rhombuses, and triangles) or three-dimensional shapes (cubes, rectangular prisms, cones, and cylinders) to create a composite figure, and create new figures from the composite figure. | Grade 1 |
| Wyoming | 1.G.K.3 | Partition circles and rectangles into two and four equal shares. | Grade 1 |
| Wyoming | 1.MD.H.1 | Order three objects by length; compare the lengths of two objects indirectly by using a third object. | Grade 1 |
| Wyoming | 1.MD.H.2 | Use nonstandard units to show the length of an object as the number of same size units of length with no gaps or overlaps. | Grade 1 |
| Wyoming | 1.MD.I.3A | Tell and write time in hours and half-hours using analog and digital clocks. | Grade 1 |
| Wyoming | 1.MD.I.3B | Identify U.S. coins by value (pennies, nickels, dimes, quarters). | Grade 1 |
| Wyoming | 1.MD.J.4 | Organize, represent, and interpret data with up to three categories; ask and answer questions about the total number of data points, how many in each category, and how many more or less are in one category than in another. | Grade 1 |
| Wyoming | 1.NBT.E.1 | Extend the number sequences to 120. | Grade 1 |
| Wyoming | 1.NBT.F.2 | Understand that the two digits of a two-digit number represent amounts of tens and ones. | Grade 1 |
| Wyoming | 1.NBT.F.3 | Compare pairs of two-digit numbers based on the values of the tens digit and the ones digits, recording the results of comparisons with the words "is greater than," "is equal to," "is less than," and with the symbols >, =, and <. | Grade 1 |
| Wyoming | 1.NBT.G.4 | Add within 100, using concrete models or drawings and strategies based on place value. | Grade 1 |
| Wyoming | 1.NBT.G.5 | Given a two-digit number, mentally find 10 more or 10 less than the number, without having to count; explain the reasoning used. | Grade 1 |
| Wyoming | 1.NBT.G.6 | Subtract multiples of 10 from an equal or larger multiple of 10 both in the range 10-90, using concrete models, drawings, and strategies based on place value. | Grade 1 |
| Wyoming | 1.OA.A.1 | Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, by using objects, drawings, or equations with a symbol for the unknown number to represent the problem. | Grade 1 |
| Wyoming | 1.OA.B.3 | Apply commutative and associative properties of addition as strategies to add and subtract. | Grade 1 |
| Wyoming | 1.OA.B.4 | Understand subtraction as an unknown-addend problem. | Grade 1 |
| Wyoming | 1.OA.C.5 | Relate counting to addition and subtraction using strategies, such as, by counting on and back. | Grade 1 |
| Wyoming | 1.OA.C.6 | Add and subtract within 20, demonstrating fluency in addition and subtraction within 10. Use strategies such as counting on; making ten using the relationship between addition and subtraction. | Grade 1 |
| Wyoming | 1.OA.D.7 | Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false. | Grade 1 |
| Wyoming | 1.OA.D.8 | Determine the unknown whole number in an addition or subtraction equation relating three whole numbers. | Grade 1 |
| Wyoming | 2.G.J.1 | Identify triangles, quadrilaterals, pentagons, hexagons, and cubes. Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces. | Grade 2 |
| Wyoming | 2.G.J.2 | Partition a rectangle into rows and columns of same-size squares and count to find the total number of them. | Grade 2 |
| Wyoming | 2.G.J.3 | Partition circles and rectangles into two, three, or four equal shares. | Grade 2 |
| Wyoming | 2.MD.F.1 | Measure the length of an object by selecting and using appropriate tools such as rulers, yardsticks, meter sticks, and measuring tapes. | Grade 2 |
| Wyoming | 2.MD.F.2 | Measure the same object or distance using a standard unit of one length and then a standard unit of a different length. Explain how the two measurements relate to the size of the unit chosen. | Grade 2 |
| Wyoming | 2.MD.F.4 | Measure in standard length units to determine how much longer one object is than another. | Grade 2 |
| Wyoming | 2.MD.G.5 | Use addition and subtraction within 100 to solve word problems involving lengths that are given in the same units. | Grade 2 |
| Wyoming | 2.MD.H.7 | Tell and write time from analog and digital clocks in five minute increments using a.m. and p.m. | Grade 2 |
| Wyoming | 2.MD.H.8 | Solve word problems up to $10 involving dollar bills, quarters, dimes, nickels, and pennies, using $ (dollars) and ¢ (cents) symbols appropriately. | Grade 2 |
| Wyoming | 2.MD.I.9 | Generate measurement data based on whole units and show data by making a line plot. | Grade 2 |
| Wyoming | 2.MD.I.10 | Use data to draw a picture graph and a bar graph (with single-unit scale) to represent a data set with up to four categories and solve simple put-together, take-apart, and compare problems using information presented in a bar graph. | Grade 2 |
| Wyoming | 2.NBT.D.1 | Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones. | Grade 2 |
| Wyoming | 2.NBT.D.2 | Skip-count by 10s and 100s within 1000 starting at any given number. | Grade 2 |
| Wyoming | 2.NBT.D.3 | Read and write numbers to 1000 using base-ten numerals, number names, and expanded form. | Grade 2 |
| Wyoming | 2.NBT.D.4 | Compare pairs of three-digit numbers based on meanings of the hundreds, tens, and ones digits, using the words "is greater than," "is equal to," "is less than," and with the symbols >, =, and < to record the results of comparisons. | Grade 2 |
| Wyoming | 2.NBT.E.5 | Add and subtract within 100 using strategies based on place value, properties of addition, and/or the relationship between addition and subtraction. | Grade 2 |
| Wyoming | 2.NBT.E.6 | Add up to four two-digit numbers using strategies based on place value and/or properties of addition. | Grade 2 |
| Wyoming | 2.NBT.E.7 | Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of addition, and/or the relationship between addition and subtraction. | Grade 2 |
| Wyoming | 2.NBT.E.8 | Add 10 or 100 to a given number 100-900, and subtract 10 or 100 from a given number 100-900. | Grade 2 |
| Wyoming | 2.OA.A.1 | Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, by using drawings and equations with a symbol for the unknown number to represent the problem. | Grade 2 |
| Wyoming | 2.OA.B.2 | Fluently add and subtract within 20 using mental strategies. By end of Grade 2, know automatically all sums of two one-digit numbers based on strategies. | Grade 2 |
| Wyoming | 2.OA.C.3 | Determine whether a group (up to 20) has an odd or even number of objects (i.e., by pairing objects or counting them by 2s). | Grade 2 |
| Wyoming | 2.OA.C.4 | Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends. | Grade 2 |
| Wyoming | 3.G.K.1 | Use attributes of quadrilaterals to classify rhombuses, rectangles, and squares. Understand that the shared attributes can define a larger category (e.g., quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories. | Grade 3 |
| Wyoming | 3.G.K.2 | Partition rectangles, regular polygons, and circles into parts with equal areas. Express the area of each part as a unit fraction of the whole. | Grade 3 |
| Wyoming | 3.MD.G.1 | Use analog clocks to tell and write time to the nearest minute and measure time intervals in minutes. Solve word problems involving addition and subtraction of time intervals in minutes. | Grade 3 |
| Wyoming | 3.MD.G.2 | Measure and estimate liquid volumes and masses of objects using grams (g), kilograms (kg), and liters (L). (Excludes compound units such as cm³ and finding the geometric volume of a container.) Add, subtract, multiply, or divide to solve one-step word problems involving masses or volumes that are given in the same units. (Excludes multiplicative comparison problems involving notions of “times as much.”) | Grade 3 |
| Wyoming | 3.MD.H.3 | Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and two-step “how many more” and “how many less” problems using information presented in scaled graphs. | Grade 3 |
| Wyoming | 3.MD.H.4 | Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Use the data to create a line plot, where the horizontal scale is marked off in appropriate units-whole numbers, halves, or quarters. | Grade 3 |
| Wyoming | 3.MD.I.5 | Understand area as an attribute of plane figures and understand concepts of area measurement, such as square units without gaps or overlaps. | Grade 3 |
| Wyoming | 3.MD.I.6 | Measure areas by counting unit squares (square cm, square m, square in., square ft, and improvised units). | Grade 3 |
| Wyoming | 3.MD.I.7 | Relate area to the operations of multiplication and addition. | Grade 3 |
| Wyoming | 3.MD.J.8 | Solve real world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different area or with the same area and different perimeter. | Grade 3 |
| Wyoming | 3.NBT.E.1 | Use place value understanding to round whole numbers to the nearest 10 or 100. | Grade 3 |
| Wyoming | 3.NBT.E.2 | Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of addition, and/or the relationship between addition and subtraction. | Grade 3 |
| Wyoming | 3.NBT.E.3 | Multiply one-digit whole numbers by multiples of 10 in the range 10-90 (e.g., 9 × 80, 5 × 60) using strategies based on place value and properties of multiplication. | Grade 3 |
| Wyoming | 3.NF.F.1 | Understand a fraction 1/𝑏 as the quantity formed by 1 part when a whole is partitioned into 𝑏 equal parts; understand a fraction 𝑎/𝑏 as the quantity formed by a parts of size 1/𝑏. | Grade 3 |
| Wyoming | 3.NF.F.2 | Understand and represent fractions on a number line diagram. | Grade 3 |
| Wyoming | 3.NF.F.3 | Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size. | Grade 3 |
| Wyoming | 3.OA.A.1 | Represent the concept of multiplication of whole numbers using models including, but not limited to, equal-sized groups ("groups of"), arrays, area models, repeated addition, and equal "jumps" on a number line. | Grade 3 |
| Wyoming | 3.OA.A.2 | Represent the concept of division of whole numbers (resulting in whole number quotients) using models including, but not limited to, partitioning, repeated subtraction, sharing, and inverse of multiplication. | Grade 3 |
| Wyoming | 3.OA.A.3 | Solve multiplication and division word problems within 100 using appropriate modeling strategies and equations. | Grade 3 |
| Wyoming | 3.OA.A.4 | Determine the unknown whole number in a multiplication or division equation relating three whole numbers when the unknown is a missing factor, product, dividend, divisor, or quotient. | Grade 3 |
| Wyoming | 3.OA.B.5 | Apply properties of multiplication as strategies to multiply and divide. | Grade 3 |
| Wyoming | 3.OA.B.6 | Understand division as an unknown-factor problem. | Grade 3 |
| Wyoming | 3.OA.C.7 | Fluently multiply and divide with factors 1-10 using mental strategies. By end of Grade 3, know automatically all products of one-digit factors based on strategies. | Grade 3 |
| Wyoming | 3.OA.D.8 | Solve two-step word problems (limited to the whole number system) using the four basic operations. Students should apply the Order of Operations when there are no parentheses to specify a particular order. | Grade 3 |
| Wyoming | 3.OA.D.9 | Identify arithmetic patterns and explain the relationships using properties of operations. | Grade 3 |
| Wyoming | 4.G.L.1 | Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures. | Grade 4 |
| Wyoming | 4.G.L.2 | Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles. | Grade 4 |
| Wyoming | 4.G.L.3 | Identify line-symmetric figures. Recognize and draw lines of symmetry for two-dimensional figures. | Grade 4 |
| Wyoming | 4.MD.I.1 | Know relative sizes of measurement units within one system of units including, but not limited to, km, m, cm; kg, g; lb, oz.; l L, ml; hr, min, sec; ft, in., gal., qt. pt., c.. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table. | Grade 4 |
| Wyoming | 4.MD.I.2 | Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. | Grade 4 |
| Wyoming | 4.MD.I.3 | Apply the area and perimeter formulas for rectangles in real world and mathematical problems. | Grade 4 |
| Wyoming | 4.MD.J.4 | Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots. | Grade 4 |
| Wyoming | 4.MD.K.5 | Regarding angles: Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint and Understand concepts of angle measurement. An angle is measured with reference to a circle with its center at the common endpoint of the rays. | Grade 4 |
| Wyoming | 4.MD.K.6 | Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure. | Grade 4 |
| Wyoming | 4.MD.K.7 | Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems. | Grade 4 |
| Wyoming | 4.NBT.D.1 | Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. | Grade 4 |
| Wyoming | 4.NBT.D.2 | Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols. | Grade 4 |
| Wyoming | 4.NBT.D.3 | Use place value understanding to round multi-digit whole numbers to any place. | Grade 4 |
| Wyoming | 4.NBT.E.4 | Add and subtract multi-digit whole numbers using place value strategies including the standard algorithm. | Grade 4 |
| Wyoming | 4.NBT.E.5 | Use strategies based on place value and the properties of multiplication to: Multiply a whole number of up to four digits by a one-digit whole number, multiply a pair of two-digit numbers, and use appropriate models to explain the calculation, such as by using equations, rectangular arrays, and/or area models. | Grade 4 |
| Wyoming | 4.NBT.E.6 | Use strategies based on place value, the properties of multiplication, and/or the relationship between multiplication and division to find quotients and remainders with up to four-digit dividends and one-digit divisors. Use appropriate models to explain the calculation, such as by using equations, rectangular arrays, and/or area models. | Grade 4 |
| Wyoming | 4.NF.F.1 | Explain why a fraction 𝑎/𝑏 is equivalent to a fraction (𝑛 × 𝑎)/(𝑛 × 𝑏) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. | Grade 4 |
| Wyoming | 4.NF.F.2 | Compare two fractions with different numerators and different denominators by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. | Grade 4 |
| Wyoming | 4.NF.G.3 | Understand a fraction 𝑎/𝑏 with 𝑎 > 1 as a sum of unit fractions (1/𝑏). | Grade 4 |
| Wyoming | 4.NF.G.4 | Apply and extend an understanding of multiplication by multiplying a whole number and a fraction. | Grade 4 |
| Wyoming | 4.NF.H.5 | Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100. | Grade 4 |
| Wyoming | 4.NF.H.6 | Use decimal notation for fractions with denominators 10 or 100. | Grade 4 |
| Wyoming | 4.NF.H.7 | Compare and order decimal numbers to hundredths and justify by using concrete and visual models. Record the results of comparisons with the words "is greater than," "is equal to," "is less than," and with the symbols >, =, and <. | Grade 4 |
| Wyoming | 4.OA.A.1 | Intentionally removed | Grade 4 |
| Wyoming | 4.OA.A.2 | Multiply or divide to solve word problems involving multiplicative comparison, by using strategies including, but not limited to, drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison. | Grade 4 |
| Wyoming | 4.OA.A.3 | Solve multi-step word problems posed with whole numbers, including problems in which remainders must be interpreted. | Grade 4 |
| Wyoming | 4.OA.B.4 | Demonstrate an understanding of factors and multiples. | Grade 4 |
| Wyoming | 4.OA.C.5 | Given a pattern, explain a rule that the pattern follows and extend the pattern. Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. | Grade 4 |
| Wyoming | 5.G.J.1 | Understand a coordinate system. | Grade 5 |
| Wyoming | 5.G.J.2 | Plot and interpret points in the first quadrant of the coordinate plane to represent real-world and mathematical situations. | Grade 5 |
| Wyoming | 5.G.K.3 | Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. | Grade 5 |
| Wyoming | 5.G.K.4 | Classify polygons in a hierarchy based on properties. | Grade 5 |
| Wyoming | 5.MD.G.1 | Solve multi-step real world problems by converting among different-sized standard measurement units within a given measurement system. | Grade 5 |
| Wyoming | 5.MD.H.2 | Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions to solve problems involving information presented in line plots. | Grade 5 |
| Wyoming | 5.MD.I.3 | Recognize volume as an attribute of three-dimensional figures and understand concepts of volume measurement such as "unit cube" and a volume of 𝑛 cubic units. | Grade 5 |
| Wyoming | 5.MD.I.4 | Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. | Grade 5 |
| Wyoming | 5.MD.I.5 | Relate volume to the operations of multiplication and solve real world and mathematical problems involving volume. | Grade 5 |
| Wyoming | 5.NBT.C.1 | Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. | Grade 5 |
| Wyoming | 5.NBT.C.2 | Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole number exponents to denote powers of 10. | Grade 5 |
| Wyoming | 5.NBT.C.3 | Read, write, and compare decimals to thousandths. | Grade 5 |
| Wyoming | 5.NBT.C.4 | Use place value understanding to round decimals to any place to a given place. | Grade 5 |
| Wyoming | 5.NBT.D.5 | Multiply multi-digit whole numbers using place value strategies including the standard algorithm. | Grade 5 |
| Wyoming | 5.NBT.D.6 | Find whole-number quotients with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of multiplication, and/or the relationship between multiplication and division, including the standard algorithm. Use appropriate models to Illustrate and explain the calculation, such as equations, rectangular arrays, and/or area models. | Grade 5 |
| Wyoming | 5.NBT.D.7 | Add, subtract, multiply, and divide decimals to hundredths using concrete models or drawings, and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; Relate the strategy to a written method and explain the reasoning used. | Grade 5 |
| Wyoming | 5.NF.E.1 | Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. | Grade 5 |
| Wyoming | 5.NF.E.2 | Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. | Grade 5 |
| Wyoming | 5.NF.F.3 | Interpret a fraction as division of the numerator by the denominator (𝑎/𝑏 = 𝑎 ÷ 𝑏). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers by using visual fraction models or equations to represent the problem. | Grade 5 |
| Wyoming | 5.NF.F.4 | Extend the concept of multiplication to multiply a fraction or whole number by a fraction. | Grade 5 |
| Wyoming | 5.NF.F.5 | Justify the reasonableness of a product when multiplying with fractions. | Grade 5 |
| Wyoming | 5.NF.F.6 | Solve real world problems involving multiplication of fractions and mixed numbers by using visual fraction models or equations to represent the problem. | Grade 5 |
| Wyoming | 5.NF.F.7 | Extend the concept of division to divide unit fractions and whole numbers by using visual fraction models and equations. | Grade 5 |
| Wyoming | 5.OA.A.1 | Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. | Grade 5 |
| Wyoming | 5.OA.A.2 | Write simple expressions requiring parentheses that record calculations with numbers, and interpret numerical expressions without evaluating them. | Grade 5 |
| Wyoming | 5.OA.B.3 | Generate two numerical patterns with each pattern having its own rule. Explain informally the relationship(s) between corresponding terms in the two patterns. | Grade 5 |
| Wyoming | 6.EE.E.1 | Write and evaluate numerical expressions involving whole-number exponents. | Grade 6 |
| Wyoming | 6.EE.E.2 | Write, read, and evaluate expressions in which letters stand for numbers. | Grade 6 |
| Wyoming | 6.EE.E.3 | Apply the properties of operations to generate equivalent expressions. | Grade 6 |
| Wyoming | 6.EE.E.4 | Identify when two expressions are equivalent. | Grade 6 |
| Wyoming | 6.EE.F.5 | Understand a solution to an equation or an inequality makes the equation or inequality true. Use substitution to determine whether a given number in a specified set makes an equation or inequality true. | Grade 6 |
| Wyoming | 6.EE.F.6 | Use variables to represent unknown numbers and write expressions when solving a real-world or mathematical problem. | Grade 6 |
| Wyoming | 6.EE.F.7 | Write and solve real-world and mathematical problems in the form of one-step, linear equations involving nonnegative rational numbers. | Grade 6 |
| Wyoming | 6.EE.F.8 | Write an inequality of the form 𝑥 > 𝑐 or 𝑥 𝑐 or 𝑥 < 𝑐 have infinitely many solutions; represent solutions of such inequalities on number line diagrams. | Grade 6 |
| Wyoming | 6.EE.G.9 | Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity (dependent variable), in terms of the other quantity (independent variable). Analyze their relationship using graphs and tables, and relate these to the equation. | Grade 6 |
| Wyoming | 6.G.H.1 | Find area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems. | Grade 6 |
| Wyoming | 6.G.H.2 | Find the volume of a right rectangular prism with fractional edge lengths in the context of solving real-world and mathematical problems by applying the formulas 𝑉 = (𝑙)(𝑤)(ℎ) and 𝑉 = (𝐵)(ℎ), and label with appropriate units. | Grade 6 |
| Wyoming | 6.G.H.3 | Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems. | Grade 6 |
| Wyoming | 6.G.H.4 | Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures in the context of solving real-world and mathematical problems. | Grade 6 |
| Wyoming | 6.RP.A.1 | Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. | Grade 6 |
| Wyoming | 6.RP.A.2 | Understand the concept of a unit rate 𝑎/𝑏 associated with a ratio 𝑎:𝑏 with 𝑏 ≠ 0, and use rate language in the context of a ratio relationship. | Grade 6 |
| Wyoming | 6.RP.A.3 | Use ratio and rate reasoning to solve real-world and mathematical problems. | Grade 6 |
| Wyoming | 6.SP.J.5 | Summarize numerical data sets in relation to their real-world context. | Grade 6 |
| Wyoming | 6.NS.B.1 | Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions by using visual fraction models and equations to represent the problem. | Grade 6 |
| Wyoming | 6.NS.C.2 | Divide multi-digit numbers using efficient and generalizable procedures including, but not limited to the standard algorithm. | Grade 6 |
| Wyoming | 6.NS.C.3 | Add, subtract, multiply, and divide manageable multi-digit decimals using efficient and generalizable procedures including, but not limited to the standard algorithm for each operation. | Grade 6 |
| Wyoming | 6.NS.D.5 | Understand that positive and negative numbers are used together to describe quantities having opposite directions or values and use them to represent quantities in real-world contexts, explaining the meaning of 0 in each situation. | Grade 6 |
| Wyoming | 6.NS.D.6 | Extend the understanding of the number line to include all rational numbers and apply this concept to the coordinate plane. | Grade 6 |
| Wyoming | 6.NS.D.7 | Understand ordering and absolute value of rational numbers. | Grade 6 |
| Wyoming | 6.NS.D.8 | Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Find distances between points with the same first coordinate or the same second coordinate; relate absolute value and distance. | Grade 6 |
| Wyoming | 7.EE.C.1 | Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients. | Grade 7 |
| Wyoming | 7.EE.C.2 | Recognize that algebraic expressions may have a variety of equivalent forms that reveal different information, and determine an appropriate form for a given real-world situation. | Grade 7 |
| Wyoming | 7.EE.D.3 | Solve multi-step real-world and mathematical problems involving rational numbers. Include fraction bars as a grouping symbol. | Grade 7 |
| Wyoming | 7.EE.D.4 | Apply the concepts of linear equations and inequalities in one variable to real-world and mathematical situations. | Grade 7 |
| Wyoming | 7.G.E.1 | Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing. | Grade 7 |
| Wyoming | 7.G.E.2 | Draw geometric shapes with given conditions using a variety of tools (e.g., ruler and protractor, or technology). Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle. | Grade 7 |
| Wyoming | 7.G.E.3 | Describe the two-dimensional figures that result from slicing three-dimensional figures parallel to the base, as in plane sections of right rectangular prisms and right rectangular pyramids. | Grade 7 |
| Wyoming | 7.G.F.4 | Investigate the concept of circles. | Grade 7 |
| Wyoming | 7.G.F.5 | Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure. | Grade 7 |
| Wyoming | 7.G.F.6 | Solve real-world and mathematical problems involving: area and surface area of objects composed of triangles and quadrilaterals; volume of objects composed only of right prisms having triangular or quadrilateral bases. | Grade 7 |
| Wyoming | 7.RP.A.1 | Compute unit rates, including those involving complex fractions, with like or different units. | Grade 7 |
| Wyoming | 7.RP.A.2 | Recognize and represent proportional relationships between quantities. | Grade 7 |
| Wyoming | 7.RP.A.3 | Solve multistep real world and mathematical problems involving ratios and percentages. | Grade 7 |
| Wyoming | 7.NS.B.1 | Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers. | Grade 7 |
| Wyoming | 7.NS.B.2 | Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers. | Grade 7 |
| Wyoming | 7.NS.B.3 | Solve real-world and mathematical problems involving the four arithmetic operations with rational numbers. | Grade 7 |
| Wyoming | 8.EE.B.1 | Understand and apply the laws of exponents (i.e., product rule, quotient rule, power to a power, product to a power, quotient to a power, zero power property, negative exponents) to generate equivalent numerical expressions limited to integer exponents. | Grade 8 |
| Wyoming | 8.EE.B.2 | Investigate concepts of square and cube roots. | Grade 8 |
| Wyoming | 8.EE.B.3 | Explore the relationship between quantities in decimal and scientific notation. | Grade 8 |
| Wyoming | 8.EE.B.4 | Apply the concepts of decimal and scientific notation to real-world and mathematical problems. | Grade 8 |
| Wyoming | 8.EE.C.5 | Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. | Grade 8 |
| Wyoming | 8.EE.C.6 | Explain why the slope 𝑚 is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation 𝑦 = 𝑚𝑥 for a line through the origin and the equation 𝑦 = 𝑚𝑥 + 𝑏 for a line intercepting the vertical axis at (0, 𝑏). | Grade 8 |
| Wyoming | 8.EE.D.7 | Extend concepts of linear equations and inequalities in one variable to more complex multi-step equations and inequalities in real-world and mathematical situations. | Grade 8 |
| Wyoming | 8.EE.D.8 | Analyze and solve pairs of simultaneous linear equations. | Grade 8 |
| Wyoming | 8.F.E.1 | Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output. | Grade 8 |
| Wyoming | 8.F.E.2 | Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). | Grade 8 |
| Wyoming | 8.F.E.3 | Interpret the equation 𝑦 = 𝑚𝑥 + 𝑏 as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. | Grade 8 |
| Wyoming | 8.F.F.4 | Apply the concepts of linear functions to real-world and mathematical situations. | Grade 8 |
| Wyoming | 8.F.F.5 | Describe qualitatively the functional relationship between two quantities by analyzing a graph where the function is increasing, decreasing, constant, linear, or nonlinear. Sketch a graph that exhibits the qualitative features of a function that has been described verbally. | Grade 8 |
| Wyoming | 8.G.G.1 | Verify experimentally the properties of rotations, reflections, and translations. | Grade 8 |
| Wyoming | 8.G.G.2 | Recognize through visual comparison that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them. | Grade 8 |
| Wyoming | 8.G.G.3 | Describe the effect of dilations, translations, rotations and reflections on two-dimensional figures using coordinates. | Grade 8 |
| Wyoming | 8.G.G.4 | Recognize through visual comparison that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two-dimensional figures, describe a sequence that exhibits the similarity between them. | Grade 8 |
| Wyoming | 8.G.G.5 | Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. | Grade 8 |
| Wyoming | 8.G.H.7 | Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems. | Grade 8 |
| Wyoming | 8.G.H.8 | Apply the Pythagorean Theorem to find the distance between two points in a coordinate system. | Grade 8 |
| Wyoming | 8.G.I.9 | Given the formulas, solve real-world and mathematical problems involving volume and surface area of cylinders. | Grade 8 |
| Wyoming | 8.SP.J.1 | Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe the association by form (linear/nonlinear), direction (positive/negative), strength (correlation), and unusual features. | Grade 8 |
| Wyoming | 8.SP.J.2 | Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line. | Grade 8 |
| Wyoming | 8.NS.A.2 | Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions. | Grade 8 |
| Wyoming | A.APR.D.3 | Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial. | High School |
| Wyoming | A.CED.G.2 | Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. | High School |
| Wyoming | A.CED.G.3 | Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context. | High School |
| Wyoming | A.REI.I.3 | Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. | High School |
| Wyoming | A.SSE.A.2 | Use the structure of an expression to identify ways to rewrite it. | High School |
| Wyoming | A.SSE.B.3 | Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression. | High School |
| Wyoming | F.BF.D.1 | Write a function that describes a relationship between two quantities. | High School |
| Wyoming | F.IF.A.2 | Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. | High School |
| Wyoming | F.IF.B.4 | For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. | High School |
| Wyoming | F.IF.C.7 | Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. | High School |
| Wyoming | S.ID.B.6 | Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. | High School |
| Knotion 2023 | 1.AS.A.1 | Unión de dos grupos de objetos para completar 10. | Grado 1 |
| Knotion 2023 | 1.AS.A.2 | Conteo de objetos para resolver sumas con hasta 10 o 20 elementos. | Grado 1 |
| Knotion 2023 | 1.AS.A.3 | Conteo del número de elementos, tangibles y dibujados, de un grupo de objetos para encontrar el total hasta 10 o 20 elementos. | Grado 1 |
| Knotion 2023 | 1.AS.A.4 | Agrupación de objetos para determinar el número de elementos en cada uno (ejemplo: 3 + 6 + __ = 14). | Grado 1 |
| Knotion 2023 | 1.AS.A.5 | Reconocimiento de cuántos elementos se quitarán de una colección con hasta 15 elementos. | Grado 1 |
| Knotion 2023 | 1.AS.A.6 | Reconocimiento de cuántos elementos faltan para completar una colección con hasta 15 elementos. | Grado 1 |
| Knotion 2023 | 1.AS.A.7 | Estrategia para sumar: descomponer uno de los sumandos para completar 10 con el otro. | Grado 1 |
| Knotion 2023 | 1.AS.B.10 | Estrategia de cálculo mental: restar unidades a un número de dos dígitos. | Grado 1 |
| Knotion 2023 | 1.AS.B.8 | Estrategias de cálculo mental para completar 10. | Grado 1 |
| Knotion 2023 | 1.AS.B.9 | Conteo de elementos (hasta 20) utilizando marcos de diez para encontrar el sumando faltante. | Grado 1 |
| Knotion 2023 | 1.AS.C.11 | Descomposición de números del 11 al 15 para representarlos con decenas y unidades. | Grado 1 |
| Knotion 2023 | 1.AS.C.12 | Descomposición de números menores a 30 para expresarlos con decenas y unidades. | Grado 1 |
| Knotion 2023 | 1.AS.D.13 | Resolución de problemas que implican quitar elementos de una colección de hasta 15 elementos. | Grado 1 |
| Knotion 2023 | 1.AS.D.14 | Identificación del símbolo (+ o -) que completa una operación. | Grado 1 |
| Knotion 2023 | 1.AS.E.15 | Estrategia escrita y de cálculo mental: calcular complementos de múltiplos de diez: 24 + __ = 30. | Grado 1 |
| Knotion 2023 | 1.AS.E.16 | Estrategias de cálculo mental para completar 100 (encontrar complementos y suma de números). | Grado 1 |
| Knotion 2023 | 1.AS.E.17 | Estrategia de cálculo mental: encontrar el número de dos dígitos que falta para completar 100. | Grado 1 |
| Knotion 2023 | 1.AS.F.18 | Descomposición del 100 para expresarlo como una suma de decenas. | Grado 1 |
| Knotion 2023 | 1.AS.F.19 | Descomposición de números en dos sumandos para comparar y encontrar equivalencias (hasta 100). | Grado 1 |
| Knotion 2023 | 1.AS.F.20 | Resolución de problemas que implican utilizar estrategias de suma, como descomponer un número en decenas y unidades. | Grado 1 |
| Knotion 2023 | 1.AS.F.21 | Resolución de problemas utilizando sumas repetidas. | Grado 1 |
| Knotion 2023 | 1.AS.G.22 | Uso de marcos de diez para sumar dos cantidades (hasta 50). | Grado 1 |
| Knotion 2023 | 1.AS.G.23 | Uso de marcos de diez para sumar números de dos dígitos (hasta 100) sin reagrupar. | Grado 1 |
| Knotion 2023 | 1.AS.G.25 | Resolución de problemas que implican calcular una cantidad inicial o final cuyo total es menor o igual a 100. | Grado 1 |
| Knotion 2023 | 1.AS.H.29 | Resolución de sumas utilizando la recta numérica. | Grado 1 |
| Knotion 2023 | 1.AS.H.30 | Resolución de sumas utilizando la recta numérica: primero contando de 10 en 10 y luego sumando el resto de los números de uno en uno. | Grado 1 |
| Knotion 2023 | 1.AS.I.31 | Resolución de problemas que implican utilizar la recta numérica para restar. | Grado 1 |
| Knotion 2023 | 1.AS.J.32 | Aplicación del algoritmo convencional para sumar números de dos dígitos con números de un dígito sin reagrupar. | Grado 1 |
| Knotion 2023 | 1.AS.J.33 | Aplicación del algoritmo convencional para sumar números de hasta dos dígitos (sin reagrupar). | Grado 1 |
| Knotion 2023 | 1.AS.J.34 | Aplicación del algoritmo convencional para sumar números de tres dígitos (sin reagrupar). | Grado 1 |
| Knotion 2023 | 1.MM.A.1 | Establecimiento de relaciones temporales utilizando los términos antes y después. | Grado 1 |
| Knotion 2023 | 1.MM.B.10 | Comparación y ordenamiento de objetos de diferentes longitudes utilizando un intermediario. | Grado 1 |
| Knotion 2023 | 1.MM.B.11 | Descripción de objetos en función de su longitud, utilizando los términos: corto, largo, más corto que y más largo que. | Grado 1 |
| Knotion 2023 | 1.MM.B.12 | Comparación de longitudes no lineales utilizando un intermediario. | Grado 1 |
| Knotion 2023 | 1.MM.B.13 | Comparación de objetos considerando dos dimensiones: longitud y altura. | Grado 1 |
| Knotion 2023 | 1.MM.B.14 | Medición de trayectorias con ayuda de un intermediario. | Grado 1 |
| Knotion 2023 | 1.MM.B.15 | Uso de intermediarios para medir longitudes que no pueden compararse directamente. | Grado 1 |
| Knotion 2023 | 1.MM.B.7 | Comparación directa de segmentos (tiras de papel) con objetos de la misma longitud. | Grado 1 |
| Knotion 2023 | 1.MM.B.8 | Comparación del largo y ancho de dos figuras para establecer relaciones entre ellas. | Grado 1 |
| Knotion 2023 | 1.MM.B.9 | Ordenamiento de longitudes. | Grado 1 |
| Knotion 2023 | 1.MM.C.16 | Peso de objetos. | Grado 1 |
| Knotion 2023 | 1.MM.C.17 | Uso de términos para comparar pesos: pesado, ligero, más pesado que, más ligero que. | Grado 1 |
| Knotion 2023 | 1.MM.C.18 | Reconocimiento de que el peso de un objeto no depende de su tamaño. | Grado 1 |
| Knotion 2023 | 1.MM.C.19 | Interpretación de una balanza. | Grado 1 |
| Knotion 2023 | 1.MM.C.20 | Comparación del peso de varios objetos utilizando una balanza. | Grado 1 |
| Knotion 2023 | 1.MM.C.21 | Ordenamiento de objetos de acuerdo con su peso. | Grado 1 |
| Knotion 2023 | 1.MM.C.22 | Equilibrio del peso de dos objetos en una balanza. | Grado 1 |
| Knotion 2023 | 1.MM.D.23 | Comparación de la capacidad de recipientes. | Grado 1 |
| Knotion 2023 | 1.MM.D.24 | Identificación de recipientes con la misma capacidad, sin importar su forma o tamaño. | Grado 1 |
| Knotion 2023 | 1.MM.D.25 | Clasificación de recipientes de acuerdo con su capacidad. | Grado 1 |
| Knotion 2023 | 1.MM.D.26 | Uso de diferentes procedimientos para vaciar la misma cantidad de líquido en dos recipientes distintos. | Grado 1 |
| Knotion 2023 | 1.MM.D.27 | Reconocimiento de que la capacidad de un recipiente no depende de su forma. | Grado 1 |
| Knotion 2023 | 1.N.A.1 | Comunicación y comparación de la cardinalidad de una colección de no más de diez elementos. | Grado 1 |
| Knotion 2023 | 1.N.A.2 | Ordenamiento de colecciones agrupadas de distintas formas para representar el mismo número. | Grado 1 |
| Knotion 2023 | 1.N.A.3 | Uso de la forma escrita de un número (con palabras) para contar, comparar y representar la cantidad de elementos en una colección de objetos. | Grado 1 |
| Knotion 2023 | 1.N.A.4 | Comparación de colecciones con procedimientos propios (con determinados materiales o dibujos). | Grado 1 |
| Knotion 2023 | 1.N.A.5 | Reconocimiento de colecciones con el mismo número de objetos. | Grado 1 |
| Knotion 2023 | 1.N.A.6 | Conteo para formar colecciones con el mismo número de elementos. | Grado 1 |
| Knotion 2023 | 1.N.A.7 | Estrategias para contar los elementos de una colección: formar grupos de cinco o diez elementos y contar de dos en dos y de cinco en cinco. | Grado 1 |
| Knotion 2023 | 1.N.A.8 | Uso de la forma escrita de un número (con palabras) para indicar la cantidad de objetos en una colección con hasta 30 elementos. | Grado 1 |
| Knotion 2023 | 1.N.B.10 | Lectura y escritura de números del 1 al 30. | Grado 1 |
| Knotion 2023 | 1.N.B.9 | Conteo del uno al 30, hacia delante y hacia atrás, en voz alta. | Grado 1 |
| Knotion 2023 | 1.N.C.11 | Cardinalidad de un conjunto con hasta cincuenta elementos. | Grado 1 |
| Knotion 2023 | 1.N.C.12 | Lectura y escritura de números del 1 al 50. | Grado 1 |
| Knotion 2023 | 1.N.D.13 | Uso de números ordinales hasta el décimo. | Grado 1 |
| Knotion 2023 | 1.N.E.14 | Lectura y escritura de números del 1 al 80. | Grado 1 |
| Knotion 2023 | 1.N.E.15 | Descubrimiento de patrones al escribir una secuencia numérica hasta el 80. | Grado 1 |
| Knotion 2023 | 1.N.E.16 | Representación de números hasta 80 con decenas y unidades. | Grado 1 |
| Knotion 2023 | 1.N.F.17 | Secuencias numéricas hasta el 100. | Grado 1 |
| Knotion 2023 | 1.N.F.18 | Composición y descomposición de números en decenas y unidades hasta el 100. | Grado 1 |
| Knotion 2023 | 1.N.F.19 | Descubrimiento de patrones al escribir una secuencia numérica hasta el 100. | Grado 1 |
| Knotion 2023 | 1.N.G.20 | Identificación del valor de billetes y monedas de $100, $20, $10, $5, $2 y $1 para establecer comparaciones y equivalencias entre ellos. | Grado 1 |
| Knotion 2023 | 1.N.H.21 | Uso de la recta numérica para representar números hasta 100. | Grado 1 |
| Knotion 2023 | 1.N.I.22 | Comparación de números de dos dígitos, para determinar si uno es igual, mayor o menor que el otro, utilizando los símbolos >, <, =. | Grado 1 |
| Knotion 2023 | 1.N.I.23 | Ordenamiento de números en orden ascendente y descendente. | Grado 1 |
| Knotion 2023 | 1.N.I.24 | Ordenamiento de secuencias numéricas en orden ascendente y descendente hasta el 100. | Grado 1 |
| Knotion 2023 | 1.N.I.25 | Ordenamiento de la secuencia numérica del 1 al 100 en orden ascendente y descendente. | Grado 1 |
| Knotion 2023 | 1.N.I.26 | Cálculo del doble de un número hasta 20. | Grado 1 |
| Knotion 2023 | 1.N.I.27 | Cálculo del doble de un número más uno, hasta 50. | Grado 1 |
| Knotion 2023 | 1.N.J.28 | Relación entre un número y una colección que lo representa, así como su antecesor y su sucesor. | Grado 1 |
| Knotion 2023 | 1.N.J.29 | Reconocimiento del antecesor y el sucesor de números hasta 100. | Grado 1 |
| Knotion 2023 | 1.N.J.30 | Identificación del antecesor y el sucesor en una secuencia numérica (con números hasta 100). | Grado 1 |
| Knotion 2023 | 1.N.J.31 | Identificación del antecesor y el sucesor del doble de un número. | Grado 1 |
| Knotion 2023 | 1.N.K.32 | Representación de números de dos dígitos en decenas y unidades. | Grado 1 |
| Knotion 2023 | 1.N.K.33 | Identificación de centenas utilizando el valor posicional de sus dígitos. | Grado 1 |
| Knotion 2023 | 1.N.K.34 | Representación de números hasta 100 agrupándolos en decenas y unidades. | Grado 1 |
| Knotion 2023 | 1.N.K.35 | Descomposición, en decenas y unidades, de números de dos dígitos. | Grado 1 |
| Knotion 2023 | 1.SSF.A.1 | Identificación de figuras geométricas y de cómo se colocan en una configuración de figuras. | Grado 1 |
| Knotion 2023 | 1.SSF.A.2 | Identificación de diferentes maneras de realizar una composición de figuras utilizando distintas figuras geométricas. | Grado 1 |
| Knotion 2023 | 1.SSF.A.3 | Reconocimiento de la forma, el tamaño y la posición de las figuras que forman una configuración de figuras. | Grado 1 |
| Knotion 2023 | 1.SSF.A.4 | Identificación de figuras geométricas: triángulos, cuadrados, rectángulos, rombos y romboides. | Grado 1 |
| Knotion 2023 | 1.SSF.B.5 | Reconocimiento de distintas formas de realizar la composición de una figura utilizando figuras geométricas. | Grado 1 |
| Knotion 2023 | 1.SSF.B.6 | Construcción de un rectángulo utilizando figuras geométricas. | Grado 1 |
| Knotion 2023 | 1.SSF.B.7 | Composición y descomposición de figuras al cortarlas y doblarlas. | Grado 1 |
| Knotion 2023 | 1.SSF.B.8 | Composición y descomposición de figuras geométricas, como rombos, trapecios y hexágonos, en triángulos. | Grado 1 |
| Knotion 2023 | 1.SSF.C.10 | Clasificación de figuras de acuerdo con su número de lados, número de vértices y el tipo de lados que tiene. | Grado 1 |
| Knotion 2023 | 1.SSF.C.11 | Identificación de figuras geométricas (círculo, cuadrado, triángulo y rectángulo) al doblar y cortar hojas de papel tamaño carta. | Grado 1 |
| Knotion 2023 | 1.SSF.C.12 | Identificación de figuras siguiendo e interpretando instrucciones para realizar una construcción geométrica. | Grado 1 |
| Knotion 2023 | 1.SSF.C.13 | Identificación de figuras geométricas en entramados de puntos. | Grado 1 |
| Knotion 2023 | 1.SSF.C.14 | Reproducción y comparación de patrones geométricos en una retícula triangular. | Grado 1 |
| Knotion 2023 | 1.SSF.C.15 | Copia y creación de diseños en una cuadrícula cuadrada. | Grado 1 |
| Knotion 2023 | 1.SSF.C.16 | Uso de bloques geométricos para diseñar una figura en una retícula triangular. | Grado 1 |
| Knotion 2023 | 1.SSF.C.17 | Nombres y características de polígonos. | Grado 1 |
| Knotion 2023 | 1.SSF.C.9 | Identificación de características de las figuras geométricas (cuadrado, rectángulo, triángulo, rombo, pentágono, hexágono, trapecio isósceles, círculo): número de lados, lados curvos, lados rectos, lados cortos y largos. | Grado 1 |
| Knotion 2023 | 1.SSF.D.18 | Diferenciación de cuerpos geométricos estableciendo las diferencias entre cuerpos que ruedan y que no ruedan. | Grado 1 |
| Knotion 2023 | 1.SSF.D.19 | Reconocimiento de las caras de un cuerpo geométrico como figuras planas. | Grado 1 |
| Knotion 2023 | 1.SSF.D.20 | Construcción de maquetas utilizando cuerpos geométricos e identificación de las figuras que componen sus caras. | Grado 1 |
| Knotion 2023 | 1.ST.A.1 | Uso de tablas para registrar los datos mostrados en una imagen. | Grado 1 |
| Knotion 2023 | 1.ST.A.2 | Uso de la información registrada en una tabla para responder preguntas o extraer datos. | Grado 1 |
| Knotion 2023 | 1.ST.A.3 | Análisis de los datos de una tabla para responder preguntas. | Grado 1 |
| Knotion 2023 | 1.ST.A.4 | Registro de información en tablas para obtener conclusiones. | Grado 1 |
| Knotion 2023 | 1.ST.A.5 | Obtención de conclusiones a partir de la información de una tabla. | Grado 1 |
| Knotion 2023 | 1.ST.B.6 | Aplicación de una encuesta para obtener datos. | Grado 1 |
| Knotion 2023 | 1.ST.B.7 | Recolección y análisis de datos para responder preguntas. | Grado 1 |
| Knotion 2023 | 2.AS.A.1 | Formación de colecciones utilizando objetos que representan decenas y unidades, y comparación de las mismas con cantidades escritas con numerales. | Grado 2 |
| Knotion 2023 | 2.AS.B.2 | Descomposición en dos sumandos de una cantidad menor que 100. | Grado 2 |
| Knotion 2023 | 2.AS.B.3 | Resolución de problemas en los cuales se identifica el valor de un sumando. | Grado 2 |
| Knotion 2023 | 2.AS.C.10 | Uso de agrupamientos en decenas y centenas para sumar números de tres cifras. | Grado 2 |
| Knotion 2023 | 2.AS.C.11 | Descomposición de números en centenas, decenas y unidades para sumar cantidades de tres cifras. | Grado 2 |
| Knotion 2023 | 2.AS.C.4 | Resolución de sumas con estrategias propias en diferentes situaciones. | Grado 2 |
| Knotion 2023 | 2.AS.C.5 | Identificación, en una narración, de los números que forman parte de una suma y creación de narraciones a partir de una suma. | Grado 2 |
| Knotion 2023 | 2.AS.C.6 | Uso del algoritmo de la suma de números del orden de las centenas. | Grado 2 |
| Knotion 2023 | 2.AS.C.7 | Suma de decenas completas para practicar la suma de números con dos cifras. | Grado 2 |
| Knotion 2023 | 2.AS.C.8 | Algoritmo de las sumas de transformación y su procedimiento de resolución. | Grado 2 |
| Knotion 2023 | 2.AS.C.9 | Suma de cantidades menores a 100 con estrategias propias. | Grado 2 |
| Knotion 2023 | 2.AS.D.12 | Solución de problemas en los que se usa la suma para resolver la resta. | Grado 2 |
| Knotion 2023 | 2.AS.D.13 | Uso de diferentes estrategias para sumar, restar y descomponer números hasta 100. | Grado 2 |
| Knotion 2023 | 2.AS.D.14 | Suma de cantidades menores a 100 con estrategias propias. | Grado 2 |
| Knotion 2023 | 2.AS.D.15 | Uso de estrategias para resolver problemas de suma y resta. | Grado 2 |
| Knotion 2023 | 2.AS.E.16 | Resolución de problemas que implican restas de números del orden de las centenas para determinar valores en diferentes contextos, como el del dinero. | Grado 2 |
| Knotion 2023 | 2.AS.E.17 | Deducción del algoritmo convencional de la resta al comprender los elementos que la componen. | Grado 2 |
| Knotion 2023 | 2.AS.H.21 | Uso de estrategias propias para resolver problemas de suma y resta. | Grado 2 |
| Knotion 2023 | 2.AS.H.22 | Resolución de problemas en los que se aumenta o disminuye a una cantidad inicial de un número de tres cifras. | Grado 2 |
| Knotion 2023 | 2.AS.I.23 | Suma de decenas y unidades por separado para sumar números de dos cifras. | Grado 2 |
| Knotion 2023 | 2.AS.I.24 | Descomposición de la suma en números dobles + 1. | Grado 2 |
| Knotion 2023 | 2.AS.I.25 | Estrategias de cálculo mental: Completar el número 10 para realizar sumas con más de dos sumandos. | Grado 2 |
| Knotion 2023 | 2.AS.I.26 | Uso de la estrategia de completar decenas al sumar. | Grado 2 |
| Knotion 2023 | 2.AS.I.27 | Obtención de complementos del tipo a + __ = 100. | Grado 2 |
| Knotion 2023 | 2.AS.I.28 | Obtención de complementos de 10. | Grado 2 |
| Knotion 2023 | 2.AS.I.29 | Obtención de complementos de 100 para números terminados en 0 o en 5. | Grado 2 |
| Knotion 2023 | 2.AS.I.30 | Cálculo mental de sumas de dos cifras, descomponiendo uno de los sumandos. | Grado 2 |
| Knotion 2023 | 2.AS.I.31 | Estrategias de cálculo mental: Sumar 100 a un número menor a 100. | Grado 2 |
| Knotion 2023 | 2.AS.I.32 | Suma de decenas completas para practicar la suma de números con dos cifras. | Grado 2 |
| Knotion 2023 | 2.AS.I.33 | Suma de decenas y unidades por separado para sumar números de dos cifras. | Grado 2 |
| Knotion 2023 | 2.AS.I.34 | Estrategias de cálculo mental: Completar decenas para sumar números de dos cifras. | Grado 2 |
| Knotion 2023 | 2.AS.I.35 | Suma de centenas completas. | Grado 2 |
| Knotion 2023 | 2.AS.I.36 | Completación a centenas y un millar agregando decenas a un número dado. | Grado 2 |
| Knotion 2023 | 2.AS.I.37 | Agrupamiento de unidades, decenas y centenas completas para sumar cantidades hasta 1 000. | Grado 2 |
| Knotion 2023 | 2.AS.I.38 | Estrategias de cálculo mental: Completar centenas al sumar números de dos y tres cifras. | Grado 2 |
| Knotion 2023 | 2.AS.I.39 | Obtención de complementos de 1 000 para números que son múltiplos de 10. | Grado 2 |
| Knotion 2023 | 2.AS.J.40 | Estrategias de cálculo mental: Sumar y restar mentalmente una unidad o una decena a una cantidad dada. | Grado 2 |
| Knotion 2023 | 2.AS.J.41 | Descomposición de un número utilizando sumas y restas. | Grado 2 |
| Knotion 2023 | 2.AS.J.42 | Estrategias de cálculo mental: Sumar y restar una cifra por 10. | Grado 2 |
| Knotion 2023 | 2.AS.J.43 | Uso de decenas completas como un paso intermedio al restar. | Grado 2 |
| Knotion 2023 | 2.AS.J.44 | Descomposición de un número utilizando sumas y restas. | Grado 2 |
| Knotion 2023 | 2.AS.J.45 | Suma y resta de números de uno o dos dígitos a un múltiplo de 10. | Grado 2 |
| Knotion 2023 | 2.AS.J.46 | Suma y resta de números de dos dígitos a números que terminan en el mismo número que el primero (67 - 17). | Grado 2 |
| Knotion 2023 | 2.AS.K.47 | Resta de una decena a una centena. | Grado 2 |
| Knotion 2023 | 2.AS.K.48 | Resta de un número de dos dígitos a 100 y de dos o tres dígitos a 1 000. | Grado 2 |
| Knotion 2023 | 2.AS.K.49 | Estrategias de cálculo mental: Restas de 100 menos un número. | Grado 2 |
| Knotion 2023 | 2.AS.K.50 | Vinculación entre la descomposición y reagrupación para resolver operaciones. | Grado 2 |
| Knotion 2023 | 2.MD.A.1 | Construcción y regularidades de series numéricas de 2 en 2, de 3 en 3, de 4 en 4,... hasta de 9 en 9. | Grado 2 |
| Knotion 2023 | 2.MD.A.2 | Resolución de problemas que implican el uso de las series de 2 en 2, de 3 en 3,... hasta de 9 en 9. | Grado 2 |
| Knotion 2023 | 2.MD.B.3 | Resolución de problemas, con apoyo de material gráfico, que implican sumas de sumandos iguales. | Grado 2 |
| Knotion 2023 | 2.MD.B.4 | Resolución de problemas que implican adiciones de sumandos iguales con procedimientos propios. | Grado 2 |
| Knotion 2023 | 2.MD.B.5 | Identificación de la suma con la que se resuelve un problema. | Grado 2 |
| Knotion 2023 | 2.MD.C.6 | Cálculo de la cantidad total de elementos en arreglos rectangulares. | Grado 2 |
| Knotion 2023 | 2.MD.C.7 | Búsqueda de estrategias de conteo en arreglos rectangulares en las que no son perceptibles todos los elementos. | Grado 2 |
| Knotion 2023 | 2.MD.C.8 | Resolución de problemas que implican calcular la cantidad total de elementos en arreglos rectangulares. | Grado 2 |
| Knotion 2023 | 2.MD.C.9 | Descomposición de cantidades que puedan representarse por medio de arreglos rectangulares. | Grado 2 |
| Knotion 2023 | 2.MD.D.10 | Uso de un arreglo rectangular para calcular una multiplicación. | Grado 2 |
| Knotion 2023 | 2.MD.D.11 | Uso de la multiplicación para la simplificación del cálculo de elementos de un arreglo rectangular. | Grado 2 |
| Knotion 2023 | 2.MD.E.12 | Resolución de situaciones de reparto a partir de sumas iteradas, arreglos rectangulares y aplicación de los productos de dígitos. | Grado 2 |
| Knotion 2023 | 2.MD.F.13 | Reconocimiento de que una suma de cantidades iguales puede escribirse como una multiplicación usando el signo ×. | Grado 2 |
| Knotion 2023 | 2.MD.F.14 | Resolución de multiplicaciones usando procedimientos propios. | Grado 2 |
| Knotion 2023 | 2.MD.F.15 | Identificación de situaciones que pueden o no resolverse con una multiplicación. | Grado 2 |
| Knotion 2023 | 2.MD.F.16 | Identificación de la multiplicación que permite encontrar el resultado de un problema y resolverla con procedimientos propios. | Grado 2 |
| Knotion 2023 | 2.MD.F.17 | Resolución de problemas que requieren la explicitación de la multiplicación. | Grado 2 |
| Knotion 2023 | 2.MD.F.18 | Relación entre una suma iterada y una multiplicación (tablas). | Grado 2 |
| Knotion 2023 | 2.MD.F.19 | Conmutatividad en la multiplicación. | Grado 2 |
| Knotion 2023 | 2.MD.F.20 | Identificación de problemas verbales que se resuelven con una multiplicación o con una suma. | Grado 2 |
| Knotion 2023 | 2.MD.F.21 | Cálculo mental de multiplicaciones por cuatro. | Grado 2 |
| Knotion 2023 | 2.MD.F.22 | Comprensión del significado de multiplicar dos números de una cifra en el cuadro de multiplicaciones. | Grado 2 |
| Knotion 2023 | 2.MD.F.23 | Reconocimiento de la relación que existe en los resultados de diversas multiplicaciones (2, 4 y 8; 3 y 2; 10 y 5; 6 y 3; 9 y 10). | Grado 2 |
| Knotion 2023 | 2.MD.F.24 | Construcción de estrategias para calcular el producto de un número por 7. | Grado 2 |
| Knotion 2023 | 2.MD.F.25 | Resolución de situaciones de reparto a partir de sumas iteradas, arreglos rectangulares y aplicación de los productos de dígitos. | Grado 2 |
| Knotion 2023 | 2.MD.F.26 | Cálculo de diversas cantidades empleando multiplicaciones. | Grado 2 |
| Knotion 2023 | 2.MM.A.10 | Uso del metro como la unidad de medida convencional para medir longitudes. | Grado 2 |
| Knotion 2023 | 2.MM.A.11 | Afinación de los procedimientos para ordenar diferentes unidades de medida de acuerdo con su longitud. | Grado 2 |
| Knotion 2023 | 2.MM.A.12 | Reconocimiento de que se puede expresar la longitud utilizando distintas unidades de medida. | Grado 2 |
| Knotion 2023 | 2.MM.A.3 | Reconocimiento de que el tamaño del intermediario arroja diferentes medidas. | Grado 2 |
| Knotion 2023 | 2.MM.A.4 | Construcción y uso de una unidad de medida única para medir distancias. | Grado 2 |
| Knotion 2023 | 2.MM.A.5 | Reconocimiento de que la medida depende del tamaño de la unidad de medida utilizada. | Grado 2 |
| Knotion 2023 | 2.MM.A.8 | Reconocimiento de las ventajas de tener varias unidades de medida establecidas para medir longitudes. | Grado 2 |
| Knotion 2023 | 2.MM.B.17 | Introducción del kilogramo como medida de peso. | Grado 2 |
| Knotion 2023 | 2.MM.C.23 | Identificación de unidades de medida no convencionales para comparar la capacidad de dos recipientes. | Grado 2 |
| Knotion 2023 | 2.MM.C.28 | Uso del litro como unidad de medida convencional. | Grado 2 |
| Knotion 2023 | 2.MM.D.29 | Relación del kilogramo, el litro y el metro con su magnitud de referencia. | Grado 2 |
| Knotion 2023 | 2.MM.D.30 | Vinculación entre la magnitud, la medición y la unidad de medida correspondiente. | Grado 2 |
| Knotion 2023 | 2.N.A.1 | Expresión oral y escrita de números del 0 al 100. | Grado 2 |
| Knotion 2023 | 2.N.A.2 | Conceptualización de la centena. | Grado 2 |
| Knotion 2023 | 2.N.A.3 | Uso de decenas y unidades para completar 100. | Grado 2 |
| Knotion 2023 | 2.N.A.4 | Identificación de regularidades en el tablero de 100 y su uso para encontrar números en el tablero. | Grado 2 |
| Knotion 2023 | 2.N.B.10 | Representación, de diferentes maneras, de números hasta 1 000. | Grado 2 |
| Knotion 2023 | 2.N.B.11 | Representación de un millar en centenas, decenas y unidades. | Grado 2 |
| Knotion 2023 | 2.N.B.12 | Ordenamiento de cantidades hasta 1 000. | Grado 2 |
| Knotion 2023 | 2.N.B.13 | Conteo hasta 1 000 de manera ascendente y descendente de 1 en 1, de 10 en 10 o de 100 en 100. | Grado 2 |
| Knotion 2023 | 2.N.B.5 | Regularidades en la serie numérica hasta el 1 000. | Grado 2 |
| Knotion 2023 | 2.N.B.6 | Agrupamiento y desagrupamiento de cantidades hasta 1 000. | Grado 2 |
| Knotion 2023 | 2.N.B.8 | Uso de grupos de 100 y 10, representados con dibujos y numerales, para formar cantidades. | Grado 2 |
| Knotion 2023 | 2.N.B.9 | Representación de números utilizando objetos que simbolizan centenas, decenas y unidades y con numerales. | Grado 2 |
| Knotion 2023 | 2.N.C.14 | Complementos a centenas inmediatas. | Grado 2 |
| Knotion 2023 | 2.N.D.15 | Regularidades en la escritura de los nombres de los números. | Grado 2 |
| Knotion 2023 | 2.N.E.16 | Composición y descomposición de un número a partir de su nombre. | Grado 2 |
| Knotion 2023 | 2.N.E.17 | Composición y descomposición de números de dos cifras en decenas y unidades y a partir de su nombre. | Grado 2 |
| Knotion 2023 | 2.N.F.18 | Comparación de números utilizando decenas y unidades. | Grado 2 |
| Knotion 2023 | 2.N.F.19 | Comparación de cantidades de dos cifras, con base en el número que ocupa el lugar de las decenas. | Grado 2 |
| Knotion 2023 | 2.N.F.20 | Comparación de números de tres cifras formados con tarjetas de centenas, decenas y unidades. | Grado 2 |
| Knotion 2023 | 2.N.F.21 | Comparación de números de tres cifras formados a partir de objetos que representan centenas, decenas y unidades. | Grado 2 |
| Knotion 2023 | 2.N.F.22 | Comparación de números de tres cifras. | Grado 2 |
| Knotion 2023 | 2.N.G.23 | Agrupación y desagrupación de objetos que representan decenas y unidades. | Grado 2 |
| Knotion 2023 | 2.N.H.24 | Uso de estrategias de conteo para cuantificar y comparar colecciones concretas de alrededor de 100 elementos: agrupamientos de 5 en 5, de 10 en 10, de 20 en 20. | Grado 2 |
| Knotion 2023 | 2.N.H.25 | Comparación de colecciones de dos y tres cifras para establecer cuál es mayor, menor o igual, empleando los signos correspondientes: >, <, =. | Grado 2 |
| Knotion 2023 | 2.N.I.26 | Escritura de números como la suma de los valores posicionales de cada cifra y viceversa (notación desarrollada). | Grado 2 |
| Knotion 2023 | 2.N.I.27 | Análisis del valor posicional del cero en números de tres cifras. | Grado 2 |
| Knotion 2023 | 2.N.I.28 | Identificación del valor posicional para la comparación y el ordenamiento de números. | Grado 2 |
| Knotion 2023 | 2.N.I.29 | Representación de cantidades formadas por unidades, decenas y centenas por medio de diversos agrupamientos. | Grado 2 |
| Knotion 2023 | 2.N.I.30 | Valor posicional para identificar el millar. | Grado 2 |
| Knotion 2023 | 2.N.J.31 | Lectura de números escritos y, a partir de ellos, creación de colecciones de objetos con agrupamientos en decenas y centenas. | Grado 2 |
| Knotion 2023 | 2.N.J.32 | Uso de monedas de $10 y $1 y de billetes de $100 para profundizar en el conocimiento de la serie numérica hasta el 1 000. | Grado 2 |
| Knotion 2023 | 2.N.J.33 | Identificación del valor posicional de los dígitos en números hasta 1 000 con billetes de $100 y monedas de $10 y $1. | Grado 2 |
| Knotion 2023 | 2.SSF.A.1 | Construcción de triángulos y cuadrados a partir de rectángulos, y de rectángulos y triángulos a partir de cuadrados. | Grado 2 |
| Knotion 2023 | 2.SSF.A.10 | Reproducción de figuras empleando una retícula cuadriculada. | Grado 2 |
| Knotion 2023 | 2.SSF.A.11 | Reconocimiento del círculo. | Grado 2 |
| Knotion 2023 | 2.SSF.A.12 | Reconocimiento de los cuadriláteros: rombo, romboide y trapecio. | Grado 2 |
| Knotion 2023 | 2.SSF.A.13 | Distinción del rombo del romboide al descomponerlos en otras figuras geométricas. | Grado 2 |
| Knotion 2023 | 2.SSF.A.2 | Reconocimiento de las características geométricas de las figuras. | Grado 2 |
| Knotion 2023 | 2.SSF.A.3 | Reconocimiento de una figura geométrica por su número de lados y las relaciones entre sus longitudes. | Grado 2 |
| Knotion 2023 | 2.SSF.A.4 | Características y posición de figuras. | Grado 2 |
| Knotion 2023 | 2.SSF.A.5 | Identificación de figuras con características comunes. | Grado 2 |
| Knotion 2023 | 2.SSF.A.6 | Identificación de los triángulos como figuras de tres lados rectos. | Grado 2 |
| Knotion 2023 | 2.SSF.A.7 | Identificación de cuadriláteros como figuras de cuatro lados rectos. | Grado 2 |
| Knotion 2023 | 2.SSF.A.8 | Exploración de la idea de ángulo recto como característica de cualquier cuadrado o rectángulo. | Grado 2 |
| Knotion 2023 | 2.SSF.A.9 | Identificación de triángulos, trapecios, rombos y hexágonos regulares en un mosaico. | Grado 2 |
| Knotion 2023 | 2.SSF.B.14 | Reconocimiento de figuras geométricas en las caras de diversos prismas. | Grado 2 |
| Knotion 2023 | 2.SSF.C.15 | Construcción de modelos de prismas y descripción de los mismos usando características como caras, aristas y vértices. | Grado 2 |
| Knotion 2023 | 2.SSF.C.16 | Descripción oral de los cuerpos geométricos. | Grado 2 |
| Knotion 2023 | 2.SSF.C.17 | Representación de un cuerpo geométrico a partir de su descripción. | Grado 2 |
| Knotion 2023 | 2.SSF.C.18 | Relación de características de un cuerpo geométrico con sus representaciones. | Grado 2 |
| Knotion 2023 | 2.SSF.C.19 | Desarrollo de la percepción geométrica y espacial con la descripción de configuraciones geométricas. | Grado 2 |
| Knotion 2023 | 2.SSF.C.20 | Descripción de construcciones con cuerpos geométricos. | Grado 2 |
| Knotion 2023 | 2.SSF.D.21 | Reconocimiento de la relación entre figuras y cuerpos geométricos en diversos prismas. | Grado 2 |
| Knotion 2023 | 2.SSF.E.22 | Exploración de triángulos isósceles para generar diferentes polígonos (triángulos, cuadriláteros, pentágonos y hexágonos). | Grado 2 |
| Knotion 2023 | 2.SSF.E.23 | Descomposición del hexágono en diferentes figuras. | Grado 2 |
| Knotion 2023 | 2.SSF.F.24 | Construcción y descripción de configuraciones geométricas usando cubos. | Grado 2 |
| Knotion 2023 | 2.ST.A.1 | Identificación de un tema de interés para realizar una encuesta. | Grado 2 |
| Knotion 2023 | 2.ST.A.2 | Elaboración de un formato de encuesta. | Grado 2 |
| Knotion 2023 | 2.ST.A.3 | Recolección de datos y su análisis para responder preguntas de interés de un grupo. | Grado 2 |
| Knotion 2023 | 2.ST.B.4 | Uso de tablas sencillas para organizar y comunicar datos obtenidos de una encuesta. | Grado 2 |
| Knotion 2023 | 2.ST.B.5 | Uso de una tabla para organizar la información recolectada y para presentar resultados. | Grado 2 |
| Knotion 2023 | 2.ST.C.6 | Elaboración de preguntas para obtener conclusiones al interpretar los datos de una tabla. | Grado 2 |
| Knotion 2023 | 3.AS.A.1 | Ampliación del rango de los números que usará para resolver problemas que impliquen juntar dos o tres cantidades en una sola. | Grado 3 |
| Knotion 2023 | 3.AS.A.2 | Solución de problemas de sumas con números naturales hasta 10 000. | Grado 3 |
| Knotion 2023 | 3.AS.B.3 | Descomposición de números para aproximar el resultado de sumas o restas de números con hasta tres cifras. | Grado 3 |
| Knotion 2023 | 3.AS.C.4 | Ampliación del rango de los números que usará para resolver problemas que impliquen quitar una cantidad a otra. | Grado 3 |
| Knotion 2023 | 3.AS.C.5 | Solución de problemas de restas con números naturales hasta 10 000. | Grado 3 |
| Knotion 2023 | 3.AS.C.6 | Algoritmo convencional para la resta sin reagrupar. | Grado 3 |
| Knotion 2023 | 3.AS.E.8 | Escritura de sumas con fracciones para comparar y expresar el resultado de un reparto equitativo. | Grado 3 |
| Knotion 2023 | 3.AS.F.9 | Uso de la recta numérica y representaciones gráficas para representar fracciones y su suma. | Grado 3 |
| Knotion 2023 | 3.AS.G.10 | Elaboración de estrategias para sumar o restar fracciones con el mismo denominador. | Grado 3 |
| Knotion 2023 | 3.AS.G.11 | Solución de problemas de suma y resta con fracciones que tienen el mismo denominador. | Grado 3 |
| Knotion 2023 | 3.MD.A.1 | Reconocimiento de situaciones aditivas y situaciones multiplicativas. | Grado 3 |
| Knotion 2023 | 3.MD.A.2 | Uso de la multiplicación para representar problemas resueltos con sumas repetidas y arreglos rectangulares. | Grado 3 |
| Knotion 2023 | 3.MD.A.3 | Solución de problemas con un factor constante y utilizando tablas (relaciones entre los números de la tabla para calcular otros resultados). | Grado 3 |
| Knotion 2023 | 3.MD.B.4 | Cálculo del producto al multiplicar un número por un múltiplo de 10. | Grado 3 |
| Knotion 2023 | 3.MD.B.5 | Cálculo del producto al multiplicar dos dígitos. | Grado 3 |
| Knotion 2023 | 3.MD.C.6 | División como reparto equitativo y agrupamiento. | Grado 3 |
| Knotion 2023 | 3.MD.C.7 | Solución de divisiones: repartos uno a uno con apoyo gráfico, formando grupos con la misma cantidad de elementos y contando el número de grupos, sumando varias veces una cantidad y contando los sumandos. | Grado 3 |
| Knotion 2023 | 3.MD.C.8 | Verificación de problemas de reparto equitativo con ayuda de objetos tangibles. | Grado 3 |
| Knotion 2023 | 3.MD.C.9 | Representaciones usuales de la división (a ÷ b = c) para resolver problemas de reparto equitativo o de agrupamiento. | Grado 3 |
| Knotion 2023 | 3.MD.D.10 | Cálculo de productos de un dígito por un número de una o dos cifras. | Grado 3 |
| Knotion 2023 | 3.MD.D.11 | Solución de multiplicaciones con números mayores que 10. | Grado 3 |
| Knotion 2023 | 3.MD.E.12 | Determinación del factor faltante en una multiplicación. | Grado 3 |
| Knotion 2023 | 3.MD.F.13 | Relación de los elementos de la división y de la multiplicación; es decir, si a x b = c, entonces c/a = b y c/b = a. | Grado 3 |
| Knotion 2023 | 3.MD.F.14 | Uso de una multiplicación para obtener el cociente de una división. | Grado 3 |
| Knotion 2023 | 3.MD.G.15 | Relación entre el cociente, el divisor y el residuo de una división para verificar un reparto equitativo. | Grado 3 |
| Knotion 2023 | 3.MD.G.16 | Análisis e interpretación del residuo de una división en situaciones de reparto, equitativo o no. | Grado 3 |
| Knotion 2023 | 3.MD.H.17 | Aproximación del cociente de una división. | Grado 3 |
| Knotion 2023 | 3.MD.H.18 | Relación del dividendo con el producto de dos dígitos. | Grado 3 |
| Knotion 2023 | 3.MD.I.19 | Construcción de un algoritmo para resolver divisiones con números de una cifra. | Grado 3 |
| Knotion 2023 | 3.MD.I.20 | Introducción al algoritmo convencional de la división. | Grado 3 |
| Knotion 2023 | 3.MD.I.21 | Solución de divisiones con números con hasta dos cifras, utilizando la división larga. | Grado 3 |
| Knotion 2023 | 3.MD.J.22 | Reconocimiento de patrones en productos y la propiedad asociativa de la multiplicación a partir de arreglos rectangulares. | Grado 3 |
| Knotion 2023 | 3.MD.K.23 | Algoritmo convencional para la división con y sin residuo. | Grado 3 |
| Knotion 2023 | 3.MM.A.1 | Noción de cuánto duran una hora, un minuto y un segundo. | Grado 3 |
| Knotion 2023 | 3.MM.A.2 | Comparación del tiempo necesario para completar tareas específicas, utilizando unidades convencionales y no convencionales. | Grado 3 |
| Knotion 2023 | 3.MM.B.3 | Expresión del tiempo en diferentes tipos de relojes: analógico, digital y de arena. | Grado 3 |
| Knotion 2023 | 3.MM.C.4 | Mediciones en centímetros utilizando un metro o una regla. | Grado 3 |
| Knotion 2023 | 3.MM.D.5 | Introducción de la noción de mitades y cuartos de unidades de capacidad. | Grado 3 |
| Knotion 2023 | 3.MM.E.6 | Comparación del peso de dos objetos y verificarlo utilizando una balanza. | Grado 3 |
| Knotion 2023 | 3.MM.E.7 | Introducción de la noción de mitades y cuartos de unidades de peso. | Grado 3 |
| Knotion 2023 | 3.MM.F.10 | Expresión de medidas en medios y cuartos de metro, kilogramo y litro. | Grado 3 |
| Knotion 2023 | 3.MM.F.8 | Introducción de la noción de mitades y cuartos de unidades de peso, capacidad y longitud. | Grado 3 |
| Knotion 2023 | 3.MM.F.9 | Verificación de estimaciones fraccionarias de medidas de longitud, peso y capacidad utilizando instrumentos de medición graduados. | Grado 3 |
| Knotion 2023 | 3.N.A.1 | Reconocimiento del valor posicional de los dígitos de un número de cinco cifras. | Grado 3 |
| Knotion 2023 | 3.N.A.2 | Composición y descomposición de números en millares, centenas, decenas y unidades. | Grado 3 |
| Knotion 2023 | 3.N.B.3 | Representación de un millar utilizando centenas, decenas y unidades. | Grado 3 |
| Knotion 2023 | 3.N.C.4 | Expresiones equivalentes de una misma cantidad utilizando billetes y monedas. | Grado 3 |
| Knotion 2023 | 3.N.D.5 | Lectura, escritura y orden de números de cinco cifras. | Grado 3 |
| Knotion 2023 | 3.N.E.6 | Descomposición de números para aproximar el resultado de sumas o restas de números con hasta tres cifras. | Grado 3 |
| Knotion 2023 | 3.N.F.10 | Análisis de relaciones parte-todo utilizando mediciones y reparto equitativo. | Grado 3 |
| Knotion 2023 | 3.N.F.7 | Noción de fracciones en situaciones de reparto equitativo. | Grado 3 |
| Knotion 2023 | 3.N.F.8 | La relación parte-todo como concepto. | Grado 3 |
| Knotion 2023 | 3.N.F.9 | Reflexión acerca de la unidad de referencia en fracciones. | Grado 3 |
| Knotion 2023 | 3.N.G.11 | Representación gráfica de una fracción. | Grado 3 |
| Knotion 2023 | 3.N.G.12 | Representación numérica de una fracción. | Grado 3 |
| Knotion 2023 | 3.N.G.13 | Creación e interpretación de la representación gráfica de fracciones. | Grado 3 |
| Knotion 2023 | 3.N.H.14 | Fracciones mixtas. | Grado 3 |
| Knotion 2023 | 3.N.I.15 | Reparto equitativo con resultados mayores o menores a un entero. | Grado 3 |
| Knotion 2023 | 3.N.I.16 | Identificación de distintas formas de escribir sumas equivalentes con fracciones. | Grado 3 |
| Knotion 2023 | 3.N.J.17 | Ordenamiento de fracciones en casos sencillos (cuando tienen el mismo numerador o denominador). | Grado 3 |
| Knotion 2023 | 3.N.J.18 | Representación de fracciones en la recta numérica. | Grado 3 |
| Knotion 2023 | 3.PGFEE.A.1 | Identificación de ejes de simetría en diversas figuras, en particular en triángulos. | Grado 3 |
| Knotion 2023 | 3.PGFEE.A.2 | Análisis de la simetría de diferentes figuras geométricas. | Grado 3 |
| Knotion 2023 | 3.PGFEE.B.3 | Descomposición de figuras para obtener triángulos: hexágonos, octágonos, trapecios, cuadrados, rectángulos y rombos. | Grado 3 |
| Knotion 2023 | 3.PGFEE.C.4 | Construcción de figuras geométricas utilizando retículas, moldes y otros recursos. | Grado 3 |
| Knotion 2023 | 3.SL.A.1 | Interpretación de pictogramas para contestar preguntas específicas. | Grado 3 |
| Knotion 2023 | 3.SL.A.2 | Elaboración de pictogramas con base en la información de una encuesta. | Grado 3 |
| Knotion 2023 | 3.SL.A.3 | Elaboración de pictogramas a partir de la información de una tabla de datos. | Grado 3 |
| Knotion 2023 | 3.SSF.A.1 | Análisis de triángulos al resolver problemas que implican comparar sus lados. | Grado 3 |
| Knotion 2023 | 3.SSF.A.2 | Descripción de las características de los triángulos. | Grado 3 |
| Knotion 2023 | 3.SSF.A.3 | Nombres de los triángulos de acuerdo con la relación de sus lados. | Grado 3 |
| Knotion 2023 | 3.ST.B.4 | Presentación y lectura de tablas de datos. | Grado 3 |
| Knotion 2023 | 3.ST.B.5 | Análisis e interpretación de una tabla de datos. | Grado 3 |
| Knotion 2023 | 3.ST.B.6 | Uso de la información en tablas de datos para responder preguntas específicas. | Grado 3 |
| Knotion 2023 | 4.AS.A.2 | Realización de operaciones utilizando el algoritmo convencional para sumar. | Grado 4 |
| Knotion 2023 | 4.AS.B.3 | Identificación del minuendo y del sustraendo al restar números de hasta cinco dígitos. | Grado 4 |
| Knotion 2023 | 4.AS.C.4 | Aplicación del algoritmo convencional para restar y sumar números enteros (operaciones con transformación). | Grado 4 |
| Knotion 2023 | 4.AS.C.5 | Resolución de problemas que involucran sumar o restar números de hasta cinco dígitos. | Grado 4 |
| Knotion 2023 | 4.AS.D.6 | Aplicación de estrategias de cálculo mental para sumar números de hasta cuatro dígitos (redondeo). | Grado 4 |
| Knotion 2023 | 4.AS.D.7 | Uso de estrategias de cálculo mental para restar números de hasta cuatro dígitos (descomposición de uno o dos números). | Grado 4 |
| Knotion 2023 | 4.AS.D.8 | Simplificación o descomposición de sumas y restas con múltiplos de 100 para resolverlos mentalmente. | Grado 4 |
| Knotion 2023 | 4.AS.E.10 | Uso de procedimientos informales para sumar y restar fracciones que tienen distintos denominadores en casos simples (medios, cuartos, tercios, etcétera). | Grado 4 |
| Knotion 2023 | 4.AS.E.11 | Identificación del total de fracciones necesarias para obtener números enteros. | Grado 4 |
| Knotion 2023 | 4.AS.E.12 | Resolución de sumas y restas con fracciones que tienen el mismo denominador. | Grado 4 |
| Knotion 2023 | 4.AS.E.13 | Solución de problemas que implican sumar o restar una fracción. | Grado 4 |
| Knotion 2023 | 4.AS.E.14 | Uso de fracciones mixtas para representar fracciones impropias en diferentes contextos y situaciones que implican juntar, añadir y quitar. | Grado 4 |
| Knotion 2023 | 4.AS.E.9 | Representación gráfica del número de partes usadas para sumar dos o más fracciones (hasta doceavos). | Grado 4 |
| Knotion 2023 | 4.MD.A.1 | Relación entre la multiplicación, la suma iterada y los arreglos rectangulares. | Grado 4 |
| Knotion 2023 | 4.MD.B.2 | Análisis de la relación entre dos cantidades y su valor unitario. | Grado 4 |
| Knotion 2023 | 4.MD.C.3 | Identificación del factor faltante en una multiplicación de la cual se conoce el producto. | Grado 4 |
| Knotion 2023 | 4.MD.D.4 | Memorización de productos (tablas de multiplicar) al utilizar estrategias diferentes o mediante productos conocidos que se usan para calcular otros. | Grado 4 |
| Knotion 2023 | 4.MD.E.5 | Resolución de multiplicaciones con factorización. | Grado 4 |
| Knotion 2023 | 4.MD.E.6 | Uso de procedimientos propios para resolver problemas de multiplicaciones con medidas. | Grado 4 |
| Knotion 2023 | 4.MD.F.15 | Relación del algoritmo convencional con la descomposición de factores. | Grado 4 |
| Knotion 2023 | 4.MD.F.16 | Uso del algoritmo convencional para multiplicar números de hasta tres dígitos por uno de dos o tres dígitos. | Grado 4 |
| Knotion 2023 | 4.MD.G.7 | Obtención de un cociente de dos dígitos o más por aproximación. | Grado 4 |
| Knotion 2023 | 4.MD.G.8 | Obtención de un cociente de dos o más dígitos, encontrando cocientes parciales. | Grado 4 |
| Knotion 2023 | 4.MD.H.9 | Reconocimiento de la división como la operación opuesta a la multiplicación. | Grado 4 |
| Knotion 2023 | 4.MD.I.10 | Algoritmo para la división. | Grado 4 |
| Knotion 2023 | 4.MD.I.11 | Algoritmo para la división con cocientes de dos dígitos. | Grado 4 |
| Knotion 2023 | 4.MD.J.12 | Obtención del cociente redondeando o descomponiendo el dividendo. | Grado 4 |
| Knotion 2023 | 4.MD.J.13 | Aproximación del valor de un cociente entre potencias de 10. | Grado 4 |
| Knotion 2023 | 4.MD.K.14 | Divisiones con residuo. | Grado 4 |
| Knotion 2023 | 4.MM.A.1 | Relación entre el metro, el decímetro, el centímetro y el milímetro. | Grado 4 |
| Knotion 2023 | 4.MM.A.2 | Uso del milímetro como unidad de medida para expresar longitudes cortas. | Grado 4 |
| Knotion 2023 | 4.MM.A.3 | Solución de problemas de medición utilizando unidades y sus submúltiplos de longitud, peso y capacidad. | Grado 4 |
| Knotion 2023 | 4.MM.B.4 | Comparación de superficies por descomposición, superposición o reproduciéndolas con o sin retícula. | Grado 4 |
| Knotion 2023 | 4.MM.B.5 | Aproximación del área de una superficie utilizando retículas cuadradas y triangulares. | Grado 4 |
| Knotion 2023 | 4.MM.B.6 | Expresión de la medida de una superficie en metros cuadrados. | Grado 4 |
| Knotion 2023 | 4.MM.B.7 | Solución de problemas que implican el cálculo del área de rectángulos expresados en unidades específicas. | Grado 4 |
| Knotion 2023 | 4.MM.C.10 | Solución de problemas de medición utilizando unidades y sus submúltiplos de longitud, peso y capacidad. | Grado 4 |
| Knotion 2023 | 4.MM.C.8 | Uso del gramo como unidad de peso. | Grado 4 |
| Knotion 2023 | 4.MM.C.9 | Comparación de pesos en gramos y kilogramos. | Grado 4 |
| Knotion 2023 | 4.MM.D.11 | Expresión de capacidades en litros y mililitros. | Grado 4 |
| Knotion 2023 | 4.MM.D.12 | Solución de problemas de medición utilizando unidades y sus submúltiplos de longitud, peso y capacidad. | Grado 4 |
| Knotion 2023 | 4.N.A.1 | Lectura y escritura de números enteros de hasta cinco cifras (mayores a 10 000). | Grado 4 |
| Knotion 2023 | 4.N.B.2 | Identificación del valor posicional de las cifras de números enteros de hasta cinco cifras. | Grado 4 |
| Knotion 2023 | 4.N.C.3 | Expresión de un número entero de hasta cinco cifras utilizando la notación desarrollada, notación estándar, expresión escrita o el valor posicional. | Grado 4 |
| Knotion 2023 | 4.N.D.4 | Comparación de números enteros de hasta cinco dígitos, escritos en notación estándar o expresión escrita, utilizando los símbolos > y <. | Grado 4 |
| Knotion 2023 | 4.N.D.5 | Ordenamiento de números naturales de cinco cifras. | Grado 4 |
| Knotion 2023 | 4.N.E.6 | Identificación de la parte de un entero que representa una fracción. | Grado 4 |
| Knotion 2023 | 4.N.E.7 | Identificación de la fracción de un número entero. | Grado 4 |
| Knotion 2023 | 4.N.G.10 | Anticipación, argumentación y verificación de la fracción mayor en un conjunto de fracciones con el mismo numerador o denominador. | Grado 4 |
| Knotion 2023 | 4.N.G.11 | Resolución de problemas, que implican reparto equitativo, utilizando y comparando fracciones (medios, cuartos, octavos; tercios, sextos, doceavos; quintos, décimos). | Grado 4 |
| Knotion 2023 | 4.N.G.8 | Comparación visual de fracciones. | Grado 4 |
| Knotion 2023 | 4.N.G.9 | Comparación de fracciones con el mismo denominador y numerador. | Grado 4 |
| Knotion 2023 | 4.N.H.12 | Clasificación de fracciones en propias, impropias y mixtas. | Grado 4 |
| Knotion 2023 | 4.N.I.13 | Equivalencias entre las representaciones gráficas de fracciones. | Grado 4 |
| Knotion 2023 | 4.N.I.14 | Identificación de expresiones equivalentes a una fracción al resolver problemas que incluyen reparto equitativo y medición. | Grado 4 |
| Knotion 2023 | 4.SSF.A.1 | Identificación de ángulos rectos y comparación de ángulos mayores o menores a 90º. | Grado 4 |
| Knotion 2023 | 4.SSF.A.2 | Clasificación de ángulos en rectos, agudos y obtusos. | Grado 4 |
| Knotion 2023 | 4.SSF.A.3 | Uso del grado como unidad de medida de los ángulos. | Grado 4 |
| Knotion 2023 | 4.SSF.B.4 | Uso de escuadras para trazar rectas paralelas y perpendiculares. | Grado 4 |
| Knotion 2023 | 4.SSF.B.5 | Estudio de rectas paralelas y perpendiculares en cuadriláteros. | Grado 4 |
| Knotion 2023 | 4.SSF.C.7 | Identificación de ángulos rectos en figuras geométricas. | Grado 4 |
| Knotion 2023 | 4.SSF.C.8 | Relación entre el nombre del triángulo y sus ángulos interiores. | Grado 4 |
| Knotion 2023 | 4.SSF.D.10 | Clasificación de cuadriláteros de acuerdo con sus características, como sus ángulos y las longitudes de sus lados. | Grado 4 |
| Knotion 2023 | 4.SSF.D.9 | Estudio de cuadriláteros al medir sus lados, comparar sus ángulos y analizar su simetría respecto a un eje. | Grado 4 |
| Knotion 2023 | 4.SSF.E.11 | Análisis de las características de los paralelogramos. | Grado 4 |
| Knotion 2023 | 4.SSF.F.12 | Construcción de cuadriláteros al doblar, recortar o dibujar desarrollos planos de figuras. | Grado 4 |
| Knotion 2023 | 4.SSF.F.13 | Aplicación de herramientas de geometría dinámica para construir cuadriláteros (GeoGebra). | Grado 4 |
| Knotion 2023 | 4.SSF.G.14 | Descripción de las características de los triángulos utilizados para construir un cuadrilátero. | Grado 4 |
| Knotion 2023 | 4.ST.B.3 | Identificación de los elementos de una gráfica de barras. | Grado 4 |
| Knotion 2023 | 4.ST.B.4 | Elaboración de gráficas de barras a partir de la información obtenida en encuestas y experimentos. | Grado 4 |
| Knotion 2023 | 4.ST.B.5 | Identificación de la información que representa cada barra y la frecuencia absoluta de un valor en una gráfica de barras. | Grado 4 |
| Knotion 2023 | 4.ST.B.6 | Interpretación de la información en una gráfica de barras para responder preguntas o resolver operaciones. | Grado 4 |
| Knotion 2023 | 4.ST.C.7 | Comparación de la información en pictogramas con la información en gráficas de barras. | Grado 4 |
| Knotion 2023 | 4.ST.D.8 | Relación entre la información que se presenta en una tabla y la de una gráfica de barras. | Grado 4 |
| Knotion 2023 | 5.AS.A.1 | Solución de sumas y restas de múltiplos de 100, que tengan hasta cinco cifras, por medio de cálculo mental. | Grado 5 |
| Knotion 2023 | 5.AS.A.2 | Aproximación del resultado de sumas y restas de múltiplos de 100, hasta de cinco cifras, por medio del cálculo mental. | Grado 5 |
| Knotion 2023 | 5.AS.B.3 | Uso del cálculo mental para resolver problemas de suma con decimales. | Grado 5 |
| Knotion 2023 | 5.AS.C.4 | Uso del cálculo mental para resolver problemas de resta con decimales. | Grado 5 |
| Knotion 2023 | 5.AS.D.5 | Solución de sumas con decimales utilizando el algoritmo convencional. | Grado 5 |
| Knotion 2023 | 5.AS.E.6 | Solución de restas con decimales utilizando el algoritmo convencional. | Grado 5 |
| Knotion 2023 | 5.AS.F.7 | Uso del cálculo mental para resolver sumas y restas con fracciones que tienen el mismo denominador. | Grado 5 |
| Knotion 2023 | 5.AS.G.8 | Uso de fracciones equivalentes para resolver sumas de fracciones que tienen denominadores múltiplos entre sí. | Grado 5 |
| Knotion 2023 | 5.AS.H.9 | Uso de fracciones equivalentes para resolver restas de fracciones que tienen denominadores múltiplos entre sí. | Grado 5 |
| Knotion 2023 | 5.AS.I.10 | Sucesiones aritméticas crecientes y decrecientes con fracciones. | Grado 5 |
| Knotion 2023 | 5.MD.A.1 | Identificación de patrones al multiplicar números enteros por 10, 100 y 1 000 como estrategia de cálculo mental. | Grado 5 |
| Knotion 2023 | 5.MD.B.2 | Aproximación del producto de multiplicaciones de números naturales de dos y tres cifras, redondeándolos a múltiplos de 10, 100 o 1 000. | Grado 5 |
| Knotion 2023 | 5.MD.C.3 | Análisis de los elementos de la división al usar el algoritmo convencional para resolver diferentes problemas. | Grado 5 |
| Knotion 2023 | 5.MD.D.4 | Aplicación de estrategias de cálculo mental para dividir números de hasta tres cifras entre números de hasta dos cifras. | Grado 5 |
| Knotion 2023 | 5.MD.E.5 | Uso del algoritmo convencional de la división para resolver divisiones con dividendos de hasta tres cifras. | Grado 5 |
| Knotion 2023 | 5.MD.E.6 | Extensión del algoritmo convencional de la división de números enteros para obtener cocientes decimales. | Grado 5 |
| Knotion 2023 | 5.MD.F.7 | Resolución de problemas de reparto al expresar el cociente de una división como una fracción. | Grado 5 |
| Knotion 2023 | 5.MD.G.10 | Multiplicación de un número natural por uno decimal al convertirlo en fracción decimal. | Grado 5 |
| Knotion 2023 | 5.MD.G.8 | Multiplicación de fracciones por números naturales: multiplicando el numerador por el número natural, justificado por la suma iterada. | Grado 5 |
| Knotion 2023 | 5.MD.G.9 | Deducción de estrategias para multiplicar un número decimal por un número natural (suma iterada). | Grado 5 |
| Knotion 2023 | 5.MD.H.11 | Multiplicación de números decimales por números naturales por medio del algoritmo convencional. | Grado 5 |
| Knotion 2023 | 5.MD.I.12 | Identificación de patrones al multiplicar decimales por 10, 100 y 1 000 como estrategia de cálculo mental. | Grado 5 |
| Knotion 2023 | 5.MM.A.1 | Solución de problemas, que involucran longitudes y distancias, utilizando metros, centímetros, milímetros y kilómetros como unidades de medida. | Grado 5 |
| Knotion 2023 | 5.MM.A.2 | Identificación de equivalencias entre distintas unidades de longitud. | Grado 5 |
| Knotion 2023 | 5.MM.A.3 | Solución a problemas de conversión entre los múltiplos y submúltiplos del metro. | Grado 5 |
| Knotion 2023 | 5.MM.B.4 | Solución a problemas relacionados con el peso, utilizando kilogramos y toneladas como unidades de medida. | Grado 5 |
| Knotion 2023 | 5.MM.C.5 | Solución a problemas relacionados con la capacidad, utilizando litros como unidad de medida. | Grado 5 |
| Knotion 2023 | 5.N.A.1 | Lectura y escritura de números de hasta nueve cifras. | Grado 5 |
| Knotion 2023 | 5.N.B.2 | Ordenamiento de números naturales de hasta nueve cifras. | Grado 5 |
| Knotion 2023 | 5.N.C.3 | Representación de fracciones por medio de superficies. | Grado 5 |
| Knotion 2023 | 5.N.D.4 | Uso de varias estrategias para obtener fracciones equivalentes. | Grado 5 |
| Knotion 2023 | 5.N.E.5 | Localización, en la recta numérica, de fracciones con distintos denominadores. | Grado 5 |
| Knotion 2023 | 5.N.F.6 | Representación de números decimales usando modelos de área. | Grado 5 |
| Knotion 2023 | 5.N.G.7 | Expresión de la parte decimal de un número utilizando décimas, centésimas y milésimas. | Grado 5 |
| Knotion 2023 | 5.N.H.8 | Lectura y escritura de números decimales al expresar, con notación desarrollada, la parte decimal. | Grado 5 |
| Knotion 2023 | 5.N.I.9 | Escritura de números decimales basándose en el valor posicional de sus dígitos. | Grado 5 |
| Knotion 2023 | 5.N.J.10 | Representación de números decimales ubicándolos en la recta numérica. | Grado 5 |
| Knotion 2023 | 5.N.K.11 | Comparación de números decimales. | Grado 5 |
| Knotion 2023 | 5.N.L.12 | Ordenamiento de números decimales. | Grado 5 |
| Knotion 2023 | 5.N.M.13 | Comparación y análisis gráfico de fracciones con el mismo denominador. | Grado 5 |
| Knotion 2023 | 5.N.M.14 | Comparación de fracciones utilizando fracciones equivalentes. | Grado 5 |
| Knotion 2023 | 5.PGFEE.A.1 | Análisis de las características de los prismas y sus desarrollos planos. | Grado 5 |
| Knotion 2023 | 5.PGFEE.A.2 | Construcción de prismas rectangulares rectos. | Grado 5 |
| Knotion 2023 | 5.PROP.A.1 | Obtención del valor unitario en situaciones de proporcionalidad directa. | Grado 5 |
| Knotion 2023 | 5.PROP.B.2 | Cálculo de valores faltantes en situaciones de proporcionalidad en las que se da o se pide obtener el valor unitario. | Grado 5 |
| Knotion 2023 | 5.PROP.B.3 | Identificación y uso del factor constante de proporcionalidad para calcular valores faltantes en situaciones de proporcionalidad directa. | Grado 5 |
| Knotion 2023 | 5.PROP.C.4 | Resolución de problemas de razones (n por cada m) utilizando equivalencias. | Grado 5 |
| Knotion 2023 | 5.SL.D.4 | Uso de coordenadas y pares ordenados para ubicar puntos. | Grado 5 |
| Knotion 2023 | 5.SSF.A.1 | Clasificación de los prismas según la forma de sus bases. | Grado 5 |
| Knotion 2023 | 5.SSF.A.2 | Análisis del número de caras, aristas y vértices de un prisma. | Grado 5 |
| Knotion 2023 | 5.SSF.B.3 | Uso de retículas para reproducir figuras. | Grado 5 |
| Knotion 2023 | 5.SSF.B.4 | Uso de puntos de referencia en la reproducción de figuras. | Grado 5 |
| Knotion 2023 | 5.SSF.C.5 | Identificación de la diferencia entre círculo y circunferencia. | Grado 5 |
| Knotion 2023 | 5.SSF.D.6 | Identificación de los elementos de un círculo. | Grado 5 |
| Knotion 2023 | 5.SSF.F.10 | Obtención de las áreas de rectángulos utilizando metros y centímetros cuadrados como unidades de medida. | Grado 5 |
| Knotion 2023 | 5.SSF.F.11 | Deducción de la fórmula para calcular el área de rectángulos y expresarla de manera oral (área = base x altura). | Grado 5 |
| Knotion 2023 | 5.SSF.F.8 | Comparación de las áreas de rectángulos por medio de superposición. | Grado 5 |
| Knotion 2023 | 5.SSF.F.9 | Comparación de las áreas de rectángulos utilizando unidades de referencia y expresando el área con unidades cuadradas (cm^2 y m^2). | Grado 5 |
| Knotion 2023 | 5.SSF.G.12 | Cálculo de los perímetros de polígonos regulares e irregulares utilizando diferentes estrategias. | Grado 5 |
| Knotion 2023 | 5.SSF.H.13 | Cálculo de los perímetros de círculos utilizando diferentes estrategias. | Grado 5 |
| Knotion 2023 | 5.SSF.I.14 | Identificación de la razón constante (pi) entre el perímetro y el diámetro de círculos. | Grado 5 |
| Knotion 2023 | 5.ST.C.5 | Análisis del concepto de moda. | Grado 5 |
| Knotion 2023 | 5.ST.C.6 | Cálculo de la media en situaciones de reparto equitativo y uso de las medidas de tendencia central como aproximaciones cuando los datos representan valores repetidos. | Grado 5 |
| Knotion 2023 | 5.ST.D.7 | Comparación de la media y la mediana como medidas representativas en un conjunto de datos. | Grado 5 |
| Knotion 2023 | 5.ST.D.8 | Comparación de la moda, la media y la mediana como medidas representativas en un conjunto de datos. | Grado 5 |
| Knotion 2023 | 6.AS.A.1 | Solución de sumas de fracciones que tienen denominadores múltiplos entre sí. | Grado 6 |
| Knotion 2023 | 6.AS.A.2 | Solución de sumas de fracciones que tienen denominadores que no son múltiplos entre sí. | Grado 6 |
| Knotion 2023 | 6.AS.B.3 | Solución de restas de fracciones que tienen denominadores múltiplos entre sí | Grado 6 |
| Knotion 2023 | 6.AS.B.4 | Solución de restas de fracciones que tienen denominadores que no son múltiplos entre sí. | Grado 6 |
| Knotion 2023 | 6.AS.C.5 | Sumas de números decimales utilizando valor posicional. | Grado 6 |
| Knotion 2023 | 6.AS.C.6 | Uso del algoritmo convencional para sumar números decimales. | Grado 6 |
| Knotion 2023 | 6.AS.D.7 | Restas de números decimales utilizando valor posicional. | Grado 6 |
| Knotion 2023 | 6.AS.D.8 | Uso del algoritmo convencional para restar números decimales. | Grado 6 |
| Knotion 2023 | 6.AS.E.10 | Uso de estrategias de cálculo mental para aproximar el resultado de sumas y restas con números decimales. | Grado 6 |
| Knotion 2023 | 6.AS.E.9 | Solución de sumas y restas con números decimales y revisión de los resultados utilizando el algoritmo convencional. | Grado 6 |
| Knotion 2023 | 6.MD.A.1 | Multiplicación de números decimales por un número natural utilizando la suma iterada. | Grado 6 |
| Knotion 2023 | 6.MD.B.2 | Multiplicación de fracciones por un número natural. | Grado 6 |
| Knotion 2023 | 6.MD.B.3 | Multiplicación de fracciones en las que se desconoce uno de los factores. | Grado 6 |
| Knotion 2023 | 6.MD.C.4 | Multiplicación de números decimales por potencias de 10 de forma rápida. | Grado 6 |
| Knotion 2023 | 6.MD.C.5 | Solución de multiplicaciones con números decimales en las que se desconoce uno de los factores. | Grado 6 |
| Knotion 2023 | 6.MD.D.6 | Aproximación del cociente de una división con números decimales utilizando la suma iterada. | Grado 6 |
| Knotion 2023 | 6.MD.E.7 | Solución de problemas de reparto en los que se requiere dividir un número decimal entre un número natural mediante diversos procedimientos (cocientes estimados, algoritmo convencional y cocientes parciales). | Grado 6 |
| Knotion 2023 | 6.MD.J.12 | Solución de problemas de reparto en los que se requiere dividir una fracción entre un número natural mediante diversos recursos (numerador múltiplo, representación gráfica y multiplicación del denominador por el divisor). | Grado 6 |
| Knotion 2023 | 6.MM.A.1 | Deducción de la fórmula para calcular el área de un triángulo a partir de un rectángulo. | Grado 6 |
| Knotion 2023 | 6.MM.B.2 | Cálculo del área de rombos. | Grado 6 |
| Knotion 2023 | 6.MM.C.3 | Cálculo del área de romboides al transformarlos en un rectángulo. | Grado 6 |
| Knotion 2023 | 6.MM.D.4 | Cálculo del volumen de un prisma utilizando distintas unidades no convencionales. | Grado 6 |
| Knotion 2023 | 6.MM.E.5 | Clasificación y comparación del volumen de dos o más prismas utilizando cubos o paralelepípedos. | Grado 6 |
| Knotion 2023 | 6.MM.F.6 | Cálculo del área de trapecios al transformarlos en un rectángulo. | Grado 6 |
| Knotion 2023 | 6.MM.G.7 | Diferenciación del área y el perímetro e identificación del hecho de que a mayor perímetro no necesariamente corresponde mayor área. | Grado 6 |
| Knotion 2023 | 6.N.A.1 | Lectura y escritura de números naturales de cualquier cantidad de cifras. | Grado 6 |
| Knotion 2023 | 6.N.B.2 | Notación desarrollada de un número natural. | Grado 6 |
| Knotion 2023 | 6.N.C.3 | Comparación de números naturales de cualquier cantidad de cifras. | Grado 6 |
| Knotion 2023 | 6.N.D.4 | Significado e interpretación de la parte decimal de un número (valor posicional). | Grado 6 |
| Knotion 2023 | 6.N.E.5 | Comparación del significado de la parte decimal al usar unidades de medida de tiempo, longitud y peso. | Grado 6 |
| Knotion 2023 | 6.N.F.6 | Ordenamiento de fracciones utilizando distintos recursos como la recta numérica (con o sin un número de referencia como el cero u otro número). | Grado 6 |
| Knotion 2023 | 6.N.G.7 | Ordenamiento de números decimales utilizando distintos recursos como la recta numérica (con o sin un número de referencia como el cero u otro número). | Grado 6 |
| Knotion 2023 | 6.N.I.9 | Localización de números positivos y negativos en una recta numérica. | Grado 6 |
| Knotion 2023 | 6.N.J.10 | Comparación y ordenamiento de números enteros. | Grado 6 |
| Knotion 2023 | 6.N.K.11 | Identificación del opuesto de un número entero (simétrico). | Grado 6 |
| Knotion 2023 | 6.PGFEE.A.1 | Cálculo de términos faltantes en sucesiones con progresión aritmética. | Grado 6 |
| Knotion 2023 | 6.PGFEE.A.2 | Descripción de las características y comportamiento de sucesiones con progresión aritmética mediante una regla descrita con sus palabras. | Grado 6 |
| Knotion 2023 | 6.PGFEE.A.3 | Completación de sucesiones de figuras con progresión aritmética y reconocimiento de sus regularidades. | Grado 6 |
| Knotion 2023 | 6.PGFEE.B.4 | Cálculo de términos faltantes en una sucesión numérica con progresión geométrica. | Grado 6 |
| Knotion 2023 | 6.PGFEE.B.5 | Descripción de las características y comportamiento de las sucesiones numéricas con progresión geométrica mediante una regla descrita con sus palabras. | Grado 6 |
| Knotion 2023 | 6.PGFEE.B.6 | Completación de sucesiones de figuras con progresión geométrica y reconocimiento de sus regularidades. | Grado 6 |
| Knotion 2023 | 6.PROP.A.1 | Representación gráfica de porcentajes simples (50 %, 25 %, 20 %, 10 % y 1 %). | Grado 6 |
| Knotion 2023 | 6.PROP.B.2 | Identificación de porcentajes como fracciones. | Grado 6 |
| Knotion 2023 | 6.PROP.C.3 | Aplicación de porcentajes (50 %, 25 %, 20 %, 10 % y 1 %) para obtener la fracción de las cantidades correspondientes. | Grado 6 |
| Knotion 2023 | 6.PROP.D.4 | Obtención de porcentajes usando diversas estrategias. | Grado 6 |
| Knotion 2023 | 6.PROP.D.5 | Obtención de un porcentaje utilizando porcentajes fáciles, como 50 %, 10 % y 1 %. | Grado 6 |
| Knotion 2023 | 6.PROP.E.6 | Identificación de situaciones que implican proporcionalidad. | Grado 6 |
| Knotion 2023 | 6.PROP.E.7 | Cálculo de valores faltantes en situaciones de proporcionalidad directa aplicando la multiplicación o división de los valores de las filas por un número natural o al sumar los valores correspondientes de dos filas (suma término a término). | Grado 6 |
| Knotion 2023 | 6.PROP.E.8 | Cálculo de valores faltantes en situaciones de proporcionalidad usando el valor unitario, ya sea que esté dado o que lo calculen. | Grado 6 |
| Knotion 2023 | 6.PROP.E.9 | Cálculo de valores faltantes usando la constante de proporcionalidad. | Grado 6 |
| Knotion 2023 | 6.PROP.F.10 | Comparación de razones al igualar uno de los términos. | Grado 6 |
| Knotion 2023 | 6.PROP.G.11 | Comparación de razones con las fracciones que las representan. | Grado 6 |
| Knotion 2023 | 6.SL.B.3 | Lectura y elaboración de planos con una escala establecida. | Grado 6 |
| Knotion 2023 | 6.SL.B.4 | Interpretación de planos simples e identificación de medidas reales basándose en las del plano. | Grado 6 |
| Knotion 2023 | 6.SL.C.5 | Creación de un sistema de referencia para ubicar puntos en un plano (uso de letras o números). | Grado 6 |
| Knotion 2023 | 6.SL.C.6 | Descripción y construcción de figuras geométricas y segmentos de recta en un plano cartesiano. | Grado 6 |
| Knotion 2023 | 6.SSF.A.1 | Medición y trazo de ángulos. | Grado 6 |
| Knotion 2023 | 6.SSF.B.2 | Clasificación de triángulos por la medida de sus ángulos y lados. | Grado 6 |
| Knotion 2023 | 6.SSF.C.3 | Construcción de triángulos y medición de sus ángulos internos. | Grado 6 |
| Knotion 2023 | 6.SSF.E.5 | Análisis de las características de prismas y pirámides. | Grado 6 |
| Knotion 2023 | 6.SSF.E.6 | Análisis de los desarrollos planos de prismas y pirámides. | Grado 6 |
| Knotion 2023 | 6.SSF.E.7 | Construcción de cuerpos geométricos al trazar su desarrollo plano. | Grado 6 |
| Knotion 2023 | 6.ST.B.2 | Creación de encuestas. | Grado 6 |
| Knotion 2023 | 6.ST.D.5 | Cálculo de la moda y la media aritmética de un conjunto de datos. | Grado 6 |
| Knotion 2023 | 7.AS.A.1 | Sumas con dos números del mismo signo para concluir que los valores absolutos de ambos se suman y el resultado conserva el mismo signo. | Grado 7 |
| Knotion 2023 | 7.AS.A.2 | Sumas de dos números de distinto signo para concluir que el resultado es la diferencia del valor absoluto mayor y el valor absoluto menor con el signo del número con mayor valor absoluto. | Grado 7 |
| Knotion 2023 | 7.AS.A.3 | Identificación de la conmutatividad de la suma y los números simétricos. | Grado 7 |
| Knotion 2023 | 7.AS.A.4 | Generalización de los resultados obtenidos en situaciones y contextos específicos, como a – b = a + (–b), y presentación de algunas regularidades como reglas y propiedades; por ejemplo: x + (–x) = 0, x + 0 = x, x – 0 = x | Grado 7 |
| Knotion 2023 | 7.E.A.1 | Identificación de cantidades conocidas y desconocidas a partir de enunciados. | Grado 7 |
| Knotion 2023 | 7.E.A.2 | Representación de situaciones mediante la construcción de una ecuación con una literal. | Grado 7 |
| Knotion 2023 | 7.E.A.3 | Interpretación de la igualdad como la equivalencia entre expresiones tanto algebraicas como numéricas. | Grado 7 |
| Knotion 2023 | 7.E.A.4 | Resolución algebraica de ecuaciones lineales del tipo Ax + B = C. | Grado 7 |
| Knotion 2023 | 7.E.A.5 | Verificación de la solución de una ecuación lineal. | Grado 7 |
| Knotion 2023 | 7.E.B.6 | Transición del lenguaje verbal a simbólico y viceversa, en el contexto de operaciones relacionadas con ecuaciones lineales. | Grado 7 |
| Knotion 2023 | 7.F.A.1 | Identificación y uso de constantes de proporcionalidad, que son fracciones o decimales. | Grado 7 |
| Knotion 2023 | 7.F.A.2 | Integración de proporcionalidad y multiplicación de fracciones. | Grado 7 |
| Knotion 2023 | 7.F.B.3 | Identificación de una relación funcional con tablas de variación, gráficas y expresiones algebraicas. | Grado 7 |
| Knotion 2023 | 7.F.B.4 | Interpretación de tablas y gráficas mostrando relaciones de variación lineal. | Grado 7 |
| Knotion 2023 | 7.F.B.5 | Construcción de gráficas aproximadas de situaciones, descritas verbalmente, en las que la variación sea constante. | Grado 7 |
| Knotion 2023 | 7.F.B.6 | Pendiente o razón de cambio constante en la gráfica de una línea recta. | Grado 7 |
| Knotion 2023 | 7.F.B.7 | Relación entre la inclinación de la línea recta con la noción de razón de cambio. | Grado 7 |
| Knotion 2023 | 7.F.B.8 | Deducción de una expresión algebraica a partir de pares de datos sobre la recta o en la tabla e interpretación del significado de los parámetros a y b en la ecuación y = ax + b. | Grado 7 |
| Knotion 2023 | 7.MD.A.1 | Resolución de operaciones que involucran suma, resta, multiplicación y división de números con signo. | Grado 7 |
| Knotion 2023 | 7.MD.B.3 | Aplicación del factor fraccionario o decimal a cantidades que también estén expresadas con fracciones o decimales. | Grado 7 |
| Knotion 2023 | 7.MD.C.4 | Resolución de divisiones entre decimales. | Grado 7 |
| Knotion 2023 | 7.MD.D.5 | Introducción a la multiplicación por a/b como una constante de proporcionalidad. | Grado 7 |
| Knotion 2023 | 7.MD.E.6 | Establecimiento de la propiedad según la cual un cociente no se altera cuando se multiplican el dividendo y el divisor por un mismo número (a ÷ b = ka ÷ kb). | Grado 7 |
| Knotion 2023 | 7.MM.A.1 | Desarrollo y aplicación de fórmulas de perímetros y áreas usando literales. | Grado 7 |
| Knotion 2023 | 7.MM.C.3 | Obtención de fórmulas para calcular el volumen de prismas rectos. | Grado 7 |
| Knotion 2023 | 7.MM.C.4 | Cálculo de cualquiera de las dimensiones involucradas en la fórmula del volumen de un prisma. | Grado 7 |
| Knotion 2023 | 7.N.A.1 | Distinción entre fracciones equivalentes, fracciones decimales y decimales cuando se presentan en un mismo ejercicio. | Grado 7 |
| Knotion 2023 | 7.N.A.2 | Expresiones con notación decimal de fracciones que no tienen como denominador una potencia de 10, pero que sí son equivalentes a una fracción decimal. | Grado 7 |
| Knotion 2023 | 7.N.A.3 | Expresión de fracciones no decimales mediante aproximaciones con números decimales finitos y mediante números decimales periódicos. | Grado 7 |
| Knotion 2023 | 7.N.A.4 | Uso de la recta numérica para ilustrar la propiedad de la densidad del conjunto de las fracciones y del conjunto de los decimales. | Grado 7 |
| Knotion 2023 | 7.PGFEE.A.1 | Descripción de regularidades de una sucesión por medio de una expresión algebraica. | Grado 7 |
| Knotion 2023 | 7.PGFEE.A.2 | Construcción de la expresión algebraica de la regla de asociación de una sucesión. | Grado 7 |
| Knotion 2023 | 7.PGFEE.A.3 | Planteamiento de problemas que serían más complicados al resolverlos con métodos aritméticos. | Grado 7 |
| Knotion 2023 | 7.PGFEE.A.4 | Introducción de las leyes de los signos. | Grado 7 |
| Knotion 2023 | 7.PGFEE.A.5 | Planteamiento y resolución de problemas de sucesiones cuyas expresiones algebraicas tienen la forma ax + b. | Grado 7 |
| Knotion 2023 | 7.PGFEE.A.6 | Identificación de las reglas generales para la obtención de cualquier término de una sucesión con progresión aritmética. | Grado 7 |
| Knotion 2023 | 7.PGFEE.A.7 | Planteamiento de diferentes reglas generales de una sucesión. | Grado 7 |
| Knotion 2023 | 7.PROP.A.1 | Uso del tanto por ciento bajo la forma de una razón expresada con dos números ""n por cada 100"". | Grado 7 |
| Knotion 2023 | 7.PROP.A.2 | Expresión del tanto por ciento mediante números con punto decimal. | Grado 7 |
| Knotion 2023 | 7.PROP.A.3 | Cálculo mental exacto y aproximado de porcentajes. | Grado 7 |
| Knotion 2023 | 7.PROP.A.4 | Planteamiento de situaciones en las que el tanto por ciento es a veces mayor que 100. | Grado 7 |
| Knotion 2023 | 7.PROP.A.5 | Aplicación de porcentajes a superficies en forma de fracción. | Grado 7 |
| Knotion 2023 | 7.PROP.A.6 | Planteamiento de situaciones en las que haya variación proporcional y la constante se exprese con un porcentaje. | Grado 7 |
| Knotion 2023 | 7.SSF.A.1 | Introducción del término congruencia y construcción de triángulos con datos mínimos. | Grado 7 |
| Knotion 2023 | 7.SSF.B.2 | Uso del término congruencia para referirse a los ángulos entre paralelas cortadas por una transversal. | Grado 7 |
| Knotion 2023 | 7.SSF.C.3 | Suma de ángulos interiores de triángulos y cuadriláteros. | Grado 7 |
| Knotion 2023 | 7.SSF.D.4 | Uso de los criterios de congruencia de triángulos para probar propiedades de cuadriláteros y paralelogramos. | Grado 7 |
| Knotion 2023 | 8.E.A.1 | Solución de sistemas de dos ecuaciones lineales con dos incognitas (sistemas de 2 × 2) utilizando el método gráfico. | Grado 8 |
| Knotion 2023 | 8.E.A.2 | Solución de sistemas de dos ecuaciones lineales con dos incognitas (sistemas 2 × 2) utilizando el método de sustitución. | Grado 8 |
| Knotion 2023 | 8.E.A.3 | Solución de sistemas de dos ecuaciones lineales con dos incognitas (sistemas 2 × 2) utilizando el método de igualación. | Grado 8 |
| Knotion 2023 | 8.E.A.4 | Solución de sistemas de dos ecuaciones lineales con dos incognitas (sistemas 2 × 2) utilizando el método de eliminación. | Grado 8 |
| Knotion 2023 | 8.F.A.1 | Identificación y estudio de la variación de proporcionalidad directa (lineal) en temas aplicados a la física. | Grado 8 |
| Knotion 2023 | 8.MD.A.1 | Multiplicaciones que combinan números decimales y fracciones. | Grado 8 |
| Knotion 2023 | 8.MD.A.2 | Divisiones que combinan números decimales y fracciones. | Grado 8 |
| Knotion 2023 | 8.MD.A.3 | Aplicación sucesiva de factores de proporcionalidad como introducción a la división entre fracciones. | Grado 8 |
| Knotion 2023 | 8.MD.B.4 | Multiplicación y división con números enteros, fracciones y decimales positivos y negativos. | Grado 8 |
| Knotion 2023 | 8.MD.B.5 | Uso de sucesiones para mostrar la ley de los signos. | Grado 8 |
| Knotion 2023 | 8.MD.B.6 | Generalización de las reglas para multiplicar y dividir números con signo. | Grado 8 |
| Knotion 2023 | 8.MD.C.7 | Introducción a las operaciones potencia y raíz cuadrada como operaciones inversas. | Grado 8 |
| Knotion 2023 | 8.MD.D.8 | Deducción de la potencia de una misma base. | Grado 8 |
| Knotion 2023 | 8.MD.D.9 | Deducción de la potencia de potencias y el cociente de potencias. | Grado 8 |
| Knotion 2023 | 8.MD.E.10 | Análisis y aplicación de la jerarquía de operaciones de números con signo. | Grado 8 |
| Knotion 2023 | 8.MM.A.1 | Cálculo del área del círculo a partir de un polígono regular. | Grado 8 |
| Knotion 2023 | 8.MM.B.2 | Construcción de cuerpos geométricos a partir de su desarrollo plano. | Grado 8 |
| Knotion 2023 | 8.MM.B.3 | Solución de problemas que implican el cálculo del volumen de prismas rectos cuya base es un polígono regular. | Grado 8 |
| Knotion 2023 | 8.MM.D.5 | Conversiones de unidades en el Sistema Internacional de Unidades. | Grado 8 |
| Knotion 2023 | 8.MM.D.6 | Conversión de unidades del Sistema Internacional de Unidades al sistema inglés y viceversa. | Grado 8 |
| Knotion 2023 | 8.MM.E.7 | Solución de problemas que implican el cálculo del volumen del cilindro. | Grado 8 |
| Knotion 2023 | 8.MM.E.8 | Generalización de la fórmula de los prismas para el cilindro, considerándolo como un prisma con base circular. | Grado 8 |
| Knotion 2023 | 8.PGFEE.A.1 | Equivalencia de expresiones cuando estas representan la regla de una misma sucesión. | Grado 8 |
| Knotion 2023 | 8.PGFEE.B.2 | Expresión de áreas y perímetros utilizando lenguaje algebraico. | Grado 8 |
| Knotion 2023 | 8.PGFEE.B.3 | Uso de variables para representar dimensiones y relacionar la representación geométrica con la algebraica. | Grado 8 |
| Knotion 2023 | 8.PGFEE.B.4 | Evaluación de las expresiones para distintos valores de las dimensiones de áreas y perímetros de figuras, y verificación de la igualdad de los resultados obtenidos. | Grado 8 |
| Knotion 2023 | 8.PGFEE.B.5 | Obtención de las fórmulas para el cálculo del perímetro de polígonos usando literales para representar las dimensiones. | Grado 8 |
| Knotion 2023 | 8.PGFEE.C.6 | Jerarquía de operaciones con expresiones algebraicas. | Grado 8 |
| Knotion 2023 | 8.PGFEE.C.7 | Operaciones con monomios y polinomios. | Grado 8 |
| Knotion 2023 | 8.PGFEE.C.8 | Operaciones con polinomios. | Grado 8 |
| Knotion 2023 | 8.PROP.A.1 | Solución de problemas de reparto proporcional. | Grado 8 |
| Knotion 2023 | 8.PROP.A.2 | Identificación de la gráfica de una relación de proporcionalidad directa. | Grado 8 |
| Knotion 2023 | 8.PROP.A.3 | Solución de problemas que implican calcular el valor unitario, razones y la constante de proporcionalidad directa. | Grado 8 |
| Knotion 2023 | 8.PROP.B.4 | Solución de problemas de proporcionalidad inversa. | Grado 8 |
| Knotion 2023 | 8.PROP.B.5 | Resolución de problemas de proporcionalidad inversa. | Grado 8 |
| Knotion 2023 | 8.PROP.B.6 | Obtención de la expresión algebraica de la variación de proporcionalidad inversa (y = a/x). | Grado 8 |
| Knotion 2023 | 8.SSF.A.1 | Deducción de las medidas de los ángulos interior, exterior y central de los polígonos regulares. | Grado 8 |
| Knotion 2023 | 8.SSF.B.4 | Suma de los ángulos interiores de un polígono. | Grado 8 |
| Knotion 2023 | 8.SSF.C.5 | Resolución de problemas de construcción de polígonos regulares con instrumentos geométricos a partir de varios datos. | Grado 8 |
| Knotion 2023 | 8.ST.A.1 | Cálculo de las medidas de tendencia central. | Grado 8 |
| Knotion 2023 | 8.ST.A.2 | Cálculo del rango de un conjunto de datos. | Grado 8 |
| Knotion 2023 | 8.ST.A.3 | Cálculo de las medidas de tendencia central, el rango y la desviación media de un conjunto de datos. | Grado 8 |
| Knotion 2023 | 9.E.A.2 | Factorización de expresiones algebraicas. | Grado 9 |
| Knotion 2023 | 9.E.A.3 | Factorización de términos semejantes. | Grado 9 |
| Knotion 2023 | 9.E.A.5 | Factorización de trinomios y trinomios cuadrados perfectos. | Grado 9 |
| Knotion 2023 | 9.F.B.3 | Elaboración de gráficas por pedazos. | Grado 9 |
| Knotion 2023 | 9.F.B.5 | Elaboración de gráficas por pedazos que describen un problema o situación dada. | Grado 9 |
| Knotion 2023 | 9.F.B.6 | Obtención de las ecuaciones lineales representadas en una gráfica por pedazos. | Grado 9 |
| Knotion 2023 | 9.PGFEE.A.1 | Formulación de expresiones algebraicas equivalentes para calcular el área de figuras geométricas. | Grado 9 |
| Knotion 2023 | 9.PGFEE.B.4 | Análisis de ejemplos de ecuaciones cuadráticas, que no son funciones, utilizando sus gráficas. | Grado 9 |
| Knotion 2023 | 9.PGFEE.C.5 | Obtención de expresiones cuadráticas equivalentes para calcular el enésimo término de una sucesión. | Grado 9 |
| Knotion 2023 | 9.SSF.D.6 | Cálculo de longitudes utilizando el teorema de Pitágoras. | Grado 9 |
| Knotion 2023 | 9.SSF.D.7 | Solución de problemas aplicando el teorema de Pitágoras. | Grado 9 |
| Knotion 2023 | 9.ST.A.4 | Realización de gráficas de barras y representación de la moda, la mediana y la desviación media en ellas. | Grado 9 |
| State | Standards | Grade Level |
Real-time access to district and school progress and data helps you better support teachers.
Adaptive content, sequencing, and assessment truly individualize learning with real-time scaffolding.
It's not just about whether an answer is right or wrong—it’s also about how a student solves the problem.
The DreamBox dashboard enables educators to immediately understand where students are and what they need to grow.
Access students’ progress and proficiency against standards at the classroom, school, or district level.
With visible thinking that shows students’ work, DreamBox goes far beyond video lectures and digitized worksheets.
Effective PD provides meaningful opportunities for teachers to continue to improve their knowledge and skills.
