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 |