## Introduction

This tool can be used to connect standards or concepts that may not have been taught to current and future grade level standards. It may be used in conjunction with the Standards Summary Tool, linked below. Math standards are dense and address a wide range of understandings, so partial mastery is to be expected.  Noting where learnings are incomplete and planning for “just in time instruction” to address missing prerequisites will help students reclaim lost learning while still accessing current standards. There are additional rows at the bottom of the table to accommodate incomplete standards that are not a prerequisite for the current grade.

To navigate to a different grade level, either scroll down the page or click on the blue headings on this page.

## 1st Grade Math

Click here to navigate to the 1st Grade Math Standards Summary Tool.

Major content of the grade is indicated by the gray shading of the standard’s coding.

 Major Content Supporting Content

## 2nd Grade Math

Click here to navigate to the 2nd Grade Math Standards Summary Tool.

 Concept/Standard not taught or incomplete Grade 2 Standards 2020-2021 Notes from Diagnostic +  Standards to Pair Operations and Algebraic Thinking   (OA) 2.OA.A.1 Add and subtract within 100 to solve one- and two-step contextual problems, with unknowns in all positions, involving situations of add to, take from, put together/take apart, and compare. Use objects, drawings, and equations with a symbol for the unknown number to represent the problem. 2.OA.B.2 Fluently add and subtract within 30 using mental strategies. By the end of 2nd grade, know from memory all sums of two one-digit numbers and related subtraction facts. 2.OA.C.3 Determine whether a group of objects (up to 20) has an odd or even number of members by pairing objects or counting them by 2s. Write an equation to express an even number as a sum of two equal addends. 2.OA.C.4 Use repeated addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends. Number and Operations in Base Ten (NBT) 2.NBT.A.1 Know that the three digits of a three-digit number represent amounts of hundreds, tens, and ones (e.g., 706 can be represented in multiple ways as 7 hundreds, 0 tens, and 6 ones; 706 ones; or 70 tens and 6 ones). 2.NBT.A.2 Count within 1000. Skip-count within 1000 by 5s, 10s, and 100s, starting from any number in its skip counting sequence. 2.NBT.A.3 Read and write numbers to 1000 using standard form, word form, and expanded form. 2.NBT.A.4 Compare two three-digit numbers based on the meanings of the digits in each place and use the symbols >, =, and < to show the relationship. 2.NBT.B.5 Fluently add and subtract within 100 using properties of operations, strategies based on place value, and/or the relationship between addition and subtraction. 2.NBT.B.6 Add up to four two-digit numbers using properties of operations and strategies based on place value. 2.NBT.B.7 Add and subtract within 1000 using concrete models, drawings, strategies based on place value, properties of operations, and/or the relationship between addition and subtraction to explain the reasoning used. 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. 2.NBT.B.9 Explain why addition and subtraction strategies work using properties of operations and place value. (Explanations may include words, drawing, or objects.) Measurement and Data (MD) 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. 2.MD.A.2 Measure the length of an object using two different units of measure and describe how the two measurements relate to the size of the unit chosen. 2.MD.A.3 Estimate lengths using units of inches, feet, yards, centimeters, and meters. 2.MD.A.4 Measure to determine how much longer one object is than another and express the difference in terms of a standard unit of length. 2.MD.B.5 Add and subtract within 100 to solve contextual problems involving lengths that are given in the same units by using drawings and equations with a symbol for the unknown to represent the problem. 2.MD.B.6 Represent whole numbers as lengths from 0 on a number line and know that the points corresponding to the numbers on the number line are equally spaced. Use a number line to represent whole number sums and differences of lengths within 100. 2.MD.C.7 Tell and write time in quarter hours and to the nearest five minutes (in a.m. and p.m.) using analog and digital clocks. 2.MD.C.8 Solve contextual problems involving dollar bills, quarters, dimes, nickels, and pennies using ¢ and $symbols appropriately. Measurement and Data (MD) 2.MD.D.9 Generate measurement data by measuring lengths of several objects to the nearest whole unit. Show the measurements by making a line plot, where the horizontal scale is marked off in whole-number units. 2.MD.D.10 Draw a pictograph and a bar graph (with intervals of one) to represent a data set with up to four categories. Solve addition and subtraction problems related to the data in a graph. 2.G.A.1 Identify triangles, quadrilaterals, pentagons, hexagons, and cubes. Draw two-dimensional shapes having specified attributes (as determined directly or visually, not by measuring), such as a given number of angles or a given number of sides of equal length. 2.G.A.2 Partition a rectangle into rows and columns of same-sized squares and find the total number of squares. 2.G.A.3 Partition circles and rectangles into two, three, and four equal shares, describe the shares using the words halves, thirds, fourths, half of, a third of, and a fourth of, and describe the whole as two halves, three thirds, four fourths. Recognize that equal shares of identical wholes need not have the same shape. Standard Grade 3 Standards 2021-2022 Grade 4 Standards 2022-2023 Nonessential prerequisite Standard not a prerequisite for 2nd Grade Standard not a prerequisite for 2nd Grade Standard not a prerequisite for 2nd Grade Concept/Standard not taught or incomplete Standard Grade 3 Standards 2021-2022 Grade 4 Standards 2022-2023 Nonessential prerequisite Standard not a prerequisite for 2nd Grade Standard not a prerequisite for 2nd Grade Major content of the grade is indicated by the gray shading of the standard’s coding.  Major Content Supporting Content ## 3rd Grade Math Click here to navigate to the 3rd Grade Math Standards Summary Tool. Grade level/Course: Grade 3  Concept/Standard not taught or incomplete Grade 3 Standards 2020-2021 Notes from Diagnostic + Standards to Pair Operations and Algebraic Thinking (OA) 3.OA.A.1 Interpret the factors and products in whole number multiplication equations (e.g., 4 x 7 is 4 groups of 7 objects with a total of 28 objects or 4 strings measuring 7 inches each with a total of 28 inches.) 3.OA.A.2 Interpret the dividend, divisor, and quotient in whole number division equations (e.g., 28 ÷ 7 can be interpreted as 28 objects divided into 7 equal groups with 4 objects in each group or 28 objects divided so there are 7 objects in each of the 4 equal groups). 3.OA.A.3 Multiply and divide within 100 to solve contextual problems, with unknowns in all positions, in situations involving equal groups, arrays, and measurement quantities using strategies based on place value, the properties of operations, and the relationship between multiplication and division (e.g., contexts including computations such as 3 x ? = 24, 6 x 16 = ?, ? ÷ 8 = 3, or 96 ÷ 6 = ?) (See Table 2 - Multiplication and Division Situations) Operations and Algebraic Thinking (OA) 3.OA.A.4 Determine the unknown whole number in a multiplication or division equation relating three whole numbers within 100. For example, determine the unknown number that makes the equation true in each of the equations: 8 x ? = 48, 5 = ? ÷ 3, 6 x 6 =? 3.OA.B.5 Apply properties of operations as strategies to multiply and divide. (Students need not use formal terms for these properties.) Examples: If 6 x 4 = 24 is known, then 4 x 6 = 24 is also known (Commutative property of multiplication). 3 x 5 x 2 can be solved by (3 x 5) x 2 or 3 x (5 x 2) (Associative property of multiplication). One way to find 8 x 7 is by using 8 x (5 + 2) = (8 x 5) + (8 x 2). By knowing that 8 x 5 = 40 and 8 x 2 = 16, then 8 x 7 = 40 + 16 = 56 (Distributive property of multiplication over addition) 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. 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 x 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By the end of 3rd grade, know from memory all products of two one-digit numbers and related division facts. 3.OA.D.8 Solve two-step contextual problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding (See Table 1 - Addition and Subtraction Situations and Table 2 - Multiplication and Division Situations). Operations and Algebraic Thinking (OA) 3.OA.D.9 Identify arithmetic patterns (including patterns in the addition and multiplication tables) and explain them using properties of operations. For example, analyze patterns in the multiplication table and observe that 4 times a number is always even (because 4 x 6 = (2 x 2) x 6 = 2 x (2 x 6), which uses the associative property of multiplication) (See Table 3 - Properties of Operations). Number and Operations in Base Ten (NBT) 3.NBT.A.1 Round whole numbers to the nearest 10 or 100 using understanding of place value. 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. 3.NBT.A.3 Multiply one-digit whole numbers by multiples of 10 in the range 10–90 (e.g., 9 x 80, 5 x 60) using strategies based on place value and properties of operations. Number and Operations - Fractions (NF) Limit denominators of fractions to 2, 3, 4, 6, and 8. 3.NF.A.1 Understand a fraction, , as the quantity formed by 1 part when a whole is partitioned into b equal parts (unit fraction); understand a fraction as the quantity formed by a parts of size . For example, represents a quantity formed by 3 parts of size . Number and Operations - Fractions (NF) Limit denominators of fractions to 2, 3, 4, 6, and 8. 3.NF.A.2.a Understand a fraction as a number on the number line. Represent fractions on a number line. a. Represent a fraction 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 and that the endpoint locates the number on the number line. For example, on a number line from 0 to 1, students can partition it into 4 equal parts and recognize that each part represents a length of and the first part has an endpoint at on the number line. 3.NF.A.2.b Represent a fraction on a number line diagram by marking off a lengths from 0. Recognize that the resulting interval has size and that its endpoint locates the number on the number line. For example, is the distance from 0 when there are 5 iterations of . 3.NF.A.3.a Explain equivalence of fractions 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. 3.NF.A.3.b Recognize and generate simple equivalent fractions (e.g., = , = ) and explain why the fractions are equivalent using a visual fraction model. 3.NF.A.3.c Express whole numbers as fractions and recognize fractions that are equivalent to whole numbers. For example, express 3 in the form 3 = ; recognize that = 6; locate and 1 at the same point on a number line diagram. 3.NF.A.3.d Compare two fractions with the same numerator or the same denominator by reasoning about their size. Recognize that comparisons are valid only when the two fractions refer to the same whole. Use the symbols >, =, or < to show the relationship and justify the conclusions. Measurement and Data (MD) 3.MD.A.1 Tell and write time to the nearest minute and measure time intervals in minutes. Solve contextual problems involving addition and subtraction of time intervals in minutes. For example, students may use a number line to determine the difference between the start time and the end time of lunch. 3.MD.A.2 Measure the mass of objects and liquid volume using standard units of grams (g), kilograms (kg), milliliters (ml), and liters (l). Estimate the mass of objects and liquid volume using benchmarks. For example, a large paper clip is about one gram, so a box of about 100 large clips is about 100 grams. 3.MD.B.3 Draw a scaled pictograph and a scaled bar graph to represent a data set with several categories. Solve one- and two-step "how many more" and "how many less" problems using information presented in scaled graphs. 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. Measurement and Data (MD) 3.MD.C.5.a Recognize that plane figures have an area and understand concepts of area measurement. a. Understand that a square with side length 1 unit, called "a unit square," is said to have "one square unit" of area and can be used to measure area. 3.MD.C.5.b Understand that a plane figure which can be covered without gaps or overlaps by n unit squares is said to have an area of n square units. 3.MD.C.6 Measure areas by counting unit squares (square centimeters, square meters, square inches, square feet, and improvised units). 3.MD.C.7.a Relate area of rectangles to the operations of multiplication and addition. Find the area of a rectangle with whole-number side lengths by tiling it and show that the area is the same as would be found by multiplying the side lengths. 3.MD.C.7.b Multiply side lengths to find areas of rectangles with whole number side lengths in the context of solving real-world and mathematical problems and represent whole-number products as rectangular areas in mathematical reasoning. 3.MD.C.7.c Use tiling to show in a concrete case that the area of a rectangle with whole-number side lengths a and b + c is the sum of a x b and a x c. Use area models to represent the distributive property in mathematical reasoning. For example, in a rectangle with dimensions 4 by 6, students can decompose the rectangle into 4 x 3 and 4 x 3 to find the total area of 4 x 6. (See Table 3 - Properties of Operations) Measurement and Data (MD) 3.MD.C.7.d Recognize area as additive. Find areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas of the non-overlapping parts, applying this technique to solve real-world problems. 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. Geometry (G) 3.G.A.1 Understand that shapes in different categories may share attributes and that the shared attributes can define a larger category. Recognize rhombuses, rectangles, and squares as examples of quadrilaterals and draw examples of quadrilaterals that do not belong to any of these subcategories. 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. 3.G.A.3 Determine if a figure is a polygon. Concept/Standard not taught or incomplete Standard Grade 4 Standards 2021-2022 Grade 5 Standards 2022-2023 Nonessential prerequisite Standard is not a prerequisite for 3rd Grade Standard is not a prerequisite for 3rd Grade Concept/Standard not taught or incomplete Standard Grade 4 Standards 2021-2022 Grade 5 Standards 2022-2023 Nonessential prerequisite Standard is not a prerequisite for 3rd Grade Standard is not a prerequisite for 3rd Grade Major content of the grade is indicated by the gray shading of the standard’s coding.  Major Content Supporting Content ## 4th Grade Math Click here to navigate to the 4th Grade Math Standards Summary Tool. Grade level/Course: Grade 4  Concept/Standard not taught or incomplete Grade 4 Standards 2020-2021 Notes from Diagnostic + Standards to Pair Operations and Algebraic Thinking (OA) 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. 4.OA.A.2 Multiply or divide to solve contextual problems involving multiplicative comparison, and distinguish multiplicative comparison from additive comparison. For example, school A has 300 students and school B has 600 students: to say that school B has two times as many students is an example of multiplicative comparison; to say that school B has 300 more students is an example of additive comparison. Operations and Algebraic Thinking (OA) 4.OA.A.3 Solve multi-step contextual problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. 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. 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. Number and Operations in Base Ten (NBT) 4.NBT.A.1 Recognize that in a multi-digit whole number (less than or equal to 1,000,000), a digit in one place represents 10 times as much as it represents in the place to its right. For example, recognize that 7 in 700 is 10 times bigger than the 7 in 70 because 700 ÷ 70 = 10 and 70 x 10 = 700. Number and Operations in Base Ten (NBT) 4.NBT.A.2 Read and write multi-digit whole numbers (less than or equal to 1,000,000) using standard form, word form, and expanded form (e.g. the expanded form of 4256 is written as 4 x 1000 + 2 x 100 + 5 x 10 + 6 x 1). Compare two multi-digit numbers based on meanings of the digits in each place and use the symbols >, =, and < to show the relationship. 4.NBT.A.3 Round multi-digit whole numbers to any place (up to and including the hundred-thousand place) using understanding of place value. 4.NBT.B.4 Fluently add and subtract within 1,000,000 using appropriate strategies and algorithms. 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. 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. Number and Operations - Fractions (NF) Limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100. 4.NF.A.1 Explain why a fraction is equivalent to a fraction or 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. For example, = = . 4.NF.A.2 Compare two fractions with different numerators and different denominators by creating common denominators or common numerators or by comparing to a benchmark fraction such as . Recognize that comparisons are valid only when the two fractions refer to the same whole. Use the symbols >, =, or < to show the relationship and justify the conclusions. 4.NF.B.3.a Understand a fraction with a > 1 as a sum of fractions . For example, = + + + . Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. 4.NF.B.3.b Decompose a fraction into a sum of fractions with the same denominator in more than one way (e.g., = + + ; = + ; 2 = 1 + 1 + = + + ), recording each decomposition by an equation. Justify decompositions by using a visual fraction model. 4.NF.B.3.c Add and subtract mixed numbers with like denominators by replacing each mixed number with an equivalent fraction and/or by using properties of operations and the relationship between addition and subtraction. Number and Operations - Fractions (NF) Limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100. 4.NF.B.3.d Solve contextual problems involving addition and subtraction of fractions referring to the same whole and having like denominators. 4.NF.B.4.a Apply and extend previous understandings of multiplication as repeated addition to multiply a whole numberby a fraction. Understand a fraction as a multiple of . For example, use a visual fraction model to represent as the product 5 × , recording the conclusion by the equation = 5 x . 4.NF.B.4.b Understand a multiple of as a multiple of and use this understanding to multiply a whole number by a fraction. For example, use a visual fraction model to express 3 × as 6 × , recognizing this product as . (In general, 𝑛 x = = (𝑛 x 𝑎) x .) 4.NF.B.4.c Solve contextual problems involving multiplication of a whole number by a fraction (e.g., by using visual fraction models and equations to represent the problem). For example, if each person at a party will eat of a pound of roast beef, and there will be 4 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie? 4.NF.C.5 Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100. For example, express as and add + = . Number and Operations - Fractions (NF) Limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100. 4.NF.C.6 Read and write decimal notation for fractions with denominators 10 or 100. Locate these decimals on a number line. 4.NF.C.7 Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Use the symbols >, =, or < to show the relationship and justify the conclusions. Measurement and Data (MD) 4.MD.A.1 Measure and estimate to determine relative sizes of measurement units within a single system of measurement involving length, liquid volume, and mass/weight of objects using customary and metric units. 4.MD.A.2 Solve one- or two-step real-world problems involving whole number measurements with all four operations within a single system of measurement including problems involving simple fractions. 4.MD.A.3 Know and 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. 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). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, from a line plot find and interpret the difference in length between the longest and shortest specimens in an insect collection. Measurement and Data (MD) 4.MD.C.5.a Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement. Understand that an angle is measured with reference to a circle with its center at the common endpoint of the rays, by considering the fraction of the circular arc between the points where the two rays intersect the circle. 4.MD.C.5.b Understand that an angle that turns through 1/360 of a circle is called a "one-degree angle," and can be used to measure angles. An angle that turns through n one-degree angles is said to have an angle measure of n degrees and represents a fractional portion of the circle. 4.MD.C.6 Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure. 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). 4.G.A.1 Draw points, lines, line segments, rays, angles (right, acute, obtuse, straight, reflex), and perpendicular and parallel lines. Identify these in two-dimensional figures. 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. Measurement and Data (MD) 4.G.A.3 Recognize and draw lines of symmetry for two-dimensional figures. Concept/Standard not taught or incomplete Standard Grade 5 Standards 2021-2022 Grade 6 Standards 2022-2023 Nonessential prerequisite Standard is not a prerequisite for 4th Grade Standard is not a prerequisite for 4th Grade Standard is not a prerequisite for 4th Grade Standard is not a prerequisite for 4th Grade Major content of the grade is indicated by the gray shading of the standard’s coding.  Major Content Supporting Content ## 5th Grade Math Click here to navigate to the 5th Grade Math Standards Summary Tool. Grade level/Course: Grade 5  Concept/Standard not taught or incomplete Grade 5 Standards 2020-2021 Notes from Diagnostic + Standards to Pair Operations and Algebraic Thinking (OA) 5.OA.A.1 Use parentheses and/or brackets in numerical expressions and evaluate expressions having these symbols using the conventional order (Order of Operations). 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 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. 5.OA.B.3.a Generate two numerical patterns using two given rules. For example, given the rule "Add 3" and the starting number 0, and given the rule "Add 6" and the starting number 0, generate terms in the resulting sequences. Identify relationships between corresponding terms in two numerical patterns. For example, observe that the terms in one sequence are twice the corresponding terms in the other sequence. Operations and Algebraic Thinking (OA) 5.OA.B.3.b Form ordered pairs consisting of corresponding terms from two numerical patterns and graph the ordered pairs on a coordinate plane. Number and Operations in Base Ten (NBT) 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. 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. 5.NBT.A.3 Read and write decimals to thousandths using standard form, word form, and expanded form (e.g., the expanded form of 347.392 is written as 3 x 100 + 4 x 10 + 7 x 1 + 3 x (1/10) + 9 x (1/100) + 2 x (1/1000)). Compare two decimals to thousandths based on meanings of the digits in each place and use the symbols >, =, and < to show the relationship. 5.NBT.A.4 Round decimals to the nearest hundredth, tenth, or whole number using understanding of place value. 5.NBT.B.5 Fluently multiply multi-digit whole numbers (up to three-digit by four-digit factors) using appropriate strategies and algorithms. Number and Operations in Base Ten (NBT) 5.NBT.B.6 Find whole-number quotients and remainders of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. 5.NBT.B.7 Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between operations; assess the reasonableness of answers using estimation strategies. (Limit division problems so that either the dividend or the divisor is a whole number.) Number and Operations - Fractions (NF) 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, + = + = . (In general + = .) 5.NF.A.2 Solve contextual problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result + = , by observing that < . Number and Operations - Fractions (NF) 5.NF.B.3 Interpret a fraction as division of the numerator by the denominator ( = a ÷ b). For example, ¾ = 3 ÷ 4 so when 3 wholes are shared equally among 4 people, each person has a share of size 3/4. Solve contextual problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers by using visual fraction models or equations to represent the problem. For example, if 8 people want to share 49 sheets of construction paper equally, how many sheets will each person receive? Between what two whole numbers does your answer lie? 5.NF.B.4.a Apply and extend previous understandings of multiplication to multiply a fraction by a whole number or a fraction by a fraction. a. Interpret the product x q as a x (q ÷ b) (partition the quantity q into b equal parts and then multiply by a). Interpret the product x q as (a x q) ÷ b (multiply a times the quantity q and then partition the product into b equal parts). For example, use a visual fraction model or write a story context to show that x 6 can be interpreted as 2 x (6 ÷ 3) or (2 x 6) ÷ 3. Do the same with x = . (In general, x = .) 5.NF.B.4.b Apply and extend previous understandings of multiplication to multiply a fraction by a whole number or a fraction by a fraction. B. Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles and represent fraction products as rectangular areas. Number and Operations - Fractions (NF) 5.NF.B.5.a Interpret multiplication as scaling (resizing). a. Compare the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication. For example, know if the product will be greater than, less than, or equal to the factors. 5.NF.B.5.b Interpret multiplication as scaling (resizing). b. Explain why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explain why multiplying a given number by a fraction less than 1 results in a product less than the given number; and relate the principle of fraction equivalence= to the effect of multiplying by 1. 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. 5.NF.B.7.a Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. Interpret division of a unit fraction by a non-zero whole number and compute such quotients. For example, use visual models and the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) x 4 = 1/3 Number and Operations - Fractions (NF) 5.NF.B.7.b Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. Interpret division of a whole number by a unit fraction and compute such quotients. For example, use visual models and the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 x (1/5) = 4. 5.NF.B.7.c Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. Solve real-world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3 cup servings are in 2 cups of raisins? Measurement and Data (MD) 5.MD.A.1 Convert customary and metric measurement units within a single system by expressing measurements of a larger unit in terms of a smaller unit. Use these conversions to solve multi-step real-world problems involving distances, intervals of time, liquid volumes, masses of objects, and money (including problems involving simple fractions or decimals). For example, 3.6 liters and 4.1 liters can be combined as 7.7 liters or 7700 milliliters. 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. Measurement and Data (MD) 5.MD.C.3.a Recognize volume as an attribute of solid figures and understand concepts of volume measurement. Understand that a cube with side length 1 unit, called a "unit cube," is said to have "one cubic unit" of volume and can be used to measure volume. 5.MD.C.3.b Recognize volume as an attribute of solid figures and understand concepts of volume measurement. Understand that a solid figure which can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units. 5.MD.C.4 Measure volume by counting unit cubes, using cubic centimeters, cubic inches, cubic feet, and improvised units. 5.MD.C.5.a Relate volume to the operations of multiplication and addition and solve real-world and mathematical problems involving volume of right rectangular prisms. Find the volume of a right rectangular prism with whole-number side lengths by packing it with unit cubes and show that the volume is the same as would be found by multiplying the edge lengths, equivalently by multiplying the height by the area of the base. Represent whole-number products of three factors as volumes (e.g., to represent the associative property of multiplication). 5.MD.C.5.b Relate volume to the operations of multiplication and addition and solve real-world and mathematical problems involving volume of right rectangular prisms. Know and apply the formulas V = l x w x h and V = B x h (where B represents the area of the base) for rectangular prisms to find volumes of right rectangular prisms with whole number edge lengths in the context of solving real-world and mathematical problems. Measurement and Data (MD) 5.MD.C.5.c Relate volume to the operations of multiplication and addition and solve real-world and mathematical problems involving volume of right rectangular prisms. Recognize volume as additive. Find volumes of solid figures composed of two non-overlapping right rectangular prisms by adding the volumes of the non-overlapping parts, applying this technique to solve real-world problems. Geometry (G) 5.G.A.1 Graph ordered pairs and label points using the first quadrant of the coordinate plane. Understand in the ordered pair that the first number indicates the horizontal distance traveled along the x-axis from the origin and the second number indicates the vertical distance traveled along the y-axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate). 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. 5.G.B.3 Classify two-dimensional figures in a hierarchy based on properties. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Standard Grade 6 Standards 2021-2022 Grade 7 Standards 2022-2023 Nonessential prerequisite Standard not a prerequisite for 5th Grade Standard Grade 6 Standards 2021-2022 Grade 7 Standards 2022-2023 Nonessential prerequisite Standard not a prerequisite for 5th Grade Standard not a prerequisite for 5th Grade Standard not a prerequisite for 5th Grade Standard not a prerequisite for 5th Grade Major content of the grade is indicated by the gray shading of the standard’s coding.  Major Content Supporting Content ## 6th Grade Math Click here to navigate to the 6th Grade Math Standards Summary Tool.  Concept/Standard not taught or incomplete Grade 6 Standards 2020-2021 Notes from Diagnostic + Standards to Pair Ratios and Proportional Relationships (RP) 6.RP.A.1 Understand 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 a bird house at the zoo was 2:1, because for every 2 wings there was 1 beak. Another example could be for every vote candidate A received, candidate C received nearly three votes. 6.RP.A.2 Understand the concept of a unit rate ab associated with a ratio a: b with b ≠ 0. Use rate language in the context of a ratio relationship. For example, this recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar. Also, we paid$75 for 15 hamburgers, which is a rate of $5 per hamburger. (Expectations for unit rates in 6th grade are limited to non-complex fractions). Ratios and Proportional Relationships (RP) 6.RP.A.3.a 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). Make tables of equivalent ratios relating quantities with whole number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios. 6.RP.A.3.b Solve unit rate problems including those involving unit pricing and constant speed. For example, if a runner ran 10 miles in 90 minutes, running at that speed, how long will it take him to run 6 miles? How fast is he running in miles per hour? 6.RP.A.3.c Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent. 6.RP.A.3.d Use ratio reasoning to convert customary and metric measurement units (within the same system); manipulate and transform units appropriately when multiplying or dividing quantities. The Number System (NS) 6.NS.A.1 Interpret and compute quotients of fractions, and solve contextual problems involving division of fractions by fractions (e.g., using visual fraction models and equations to represent the problem is suggested). For example, create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 times 8/9 is 2/3 ((a/b) ÷ (c/d) = ad/bc.) Further example: How much chocolate will each person get if 3 people share ½ lb of chocolate equally? How wide is a rectangular strip of land with length ¾ miles and area ½ square mile? The Number System (NS) 6.NS.B.2 Fluently divide multi-digit numbers using a standard algorithm. 6.NS.B.3 Fluently add, subtract, multiply, and divide multi-digit decimals using a standard algorithm for each operation. 6.NS.B.4 Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1–100 with a common factor as a multiple of a sum of two whole numbers with no common factor. For example, express 36 + 8 as 4 (9 + 2). 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. 6.NS.C.6.a 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. Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line; recognize that the opposite of the opposite of a number is the number itself. For example, – (–3) = 3, and that 0 is its own opposite. The Number System (NS) 6.NS.C.6.b Understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane; recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes. 6.NS.C.6.c Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. 6.NS.C.7.a Understand ordering and absolute value of rational numbers. Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram. For example, interpret –3 > –7 as a statement that –3 is located to the right of –7 on a number line oriented from left to right. 6.NS.C.7.b Write, interpret, and explain statements of order for rational numbers in real-world contexts. For example, write –3 > –7 to express the fact that –3 is warmer than –7. 6.NS.C.7.c Understand the absolute value of a rational number as its distance from 0 on the number line and distinguish comparisons of absolute value from statements about order in a real-world context. For example, an account balance of -24 dollars represents a greater debt than an account balance - 14 dollars because -24 is located to the left of -14 on the number line The Number System (NS) 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. Expressions and Equations (EE) 6.EE.A.1 Write and evaluate numerical expressions involving whole-number exponents. 6.EE.A.2.a Write, read, and evaluate expressions in which variables stand for numbers. Write expressions that record operations with numbers and with variables. For example, express the calculation "Subtract y from 5" as 5 – y. 6.EE.A.2.b Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, and coefficient); view one or more parts of an expression as a single entity. For example, describe the expression 2 (8 + 7) as a product of two factors; view (8 + 7) as both a single entity and a sum of two terms. 6.EE.A.2.c Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations). Expressions and Equations (EE) 6.EE.A.3 Apply the properties of operations (including, but not limited to, commutative, associative, and distributive properties) to generate equivalent expressions. The distributive property is prominent here. For example, apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y. 6.EE.A.4 Identify when expressions are equivalent (i.e., when the expressions name the same number regardless of which value is substituted into them). For example, the expression 5b + 3b is equivalent to (5 +3) b, which is equivalent to 8b. 6.EE.B.5 Understand solving an equation or inequality is carried out by determining if any of the values from a given set make the equation or inequality true. Use substitution to determine whether a given number in a specified set makes an equation or inequality true. 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. 6.EE.B.7 Solve real-world and mathematical problems by writing and solving one-step equations of the form x + p = q and px = q for cases in which p, q, and x are all nonnegative rational numbers. Expressions and Equations (EE) 6.EE.B.8 Interpret and write an inequality of the form x > c or x < c which represents a condition or constraint in a real-world or mathematical problem. Recognize that inequalities have infinitely many solutions; represent solutions of inequalities on number line diagrams. 6.EE.C.9.a Use variables to represent two quantities in a real-world problem that change in relationship to one another. For example, Susan is putting money in her savings account by depositing a set amount each week (50). Represent her savings account balance with respect to the number of weekly deposits (s = 50w, illustrating the relationship between balance amount s and number of weeks w). 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. 6.EE.C.9.b Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation Geometry (G) 6.G.A.1 Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; know and apply these techniques in the context of solving real-world and mathematical problems. 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. Know and apply the formulas V = lwh and V = Bh where B is the area of the base to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems. Geometry (G) 6.G.A.3 Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side that joins two vertices (vertical or horizontal segments only). Know and apply these techniques in the context of solving real-world and mathematical problems. 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. Statistics and Probability (SP) 6.SP.A.1 Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. For example, “How old am I?” is not a statistical question, but “How old are the students in my school?” is a statistical question because one anticipates variability in students’ ages. 6.SP.A.2 Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center (mean, median, mode), spread (range), and overall shape. 6.SP.A.3 Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number. 6.SP.B.4 Display a single set of numerical data using dot plots (line plots), box plots, pie charts, and stem plots. 6.SP.B.5.a Summarize numerical data sets in relation to their context. Report the number of observations. Statistics and Probability (SP) 6.SP.B.5.b Describe the nature of the attribute under investigation, including how it was measured and its units of measurement. 6.SP.B.5.c Give quantitative measures of center (median and/or mean) and variability (range) as well as describing any overall pattern with reference to the context in which the data were gathered. 6.SP.B.5.d Relate the choice of measures of center to the shape of the data distribution and the context in which the data were gathered. Standard Grade 7 Standards 2021-2022 Grade 8 Standards 2022-2023 Nonessential prerequisite Standard not a prerequisite for 6th Grade Standard not a prerequisite for 6th Grade Standard not a prerequisite for 6th Grade Standard not a prerequisite for 6th Grade Standard not a prerequisite for 6th Grade Major content of the grade is indicated by the gray shading of the standard’s coding.  Major Content Supporting Content ## 7th Grade Math Click here to navigate to the 7th Grade Math Standards Summary Tool. Grade level/Course: Grade 7  Concept/Standard not taught or incomplete Grade 7 Standards 2020-2021 Notes from Diagnostic + Standards to Pair Ratios and Proportional Relationships (RP) 7.RP.A.1 Compute unit rates associated with ratios of fractions, including ratios of lengths, areas, and other quantities measured in like or different units. For example, if a person walks 1/2 mile in each 1/4 hour, compute the unit rate as the complex fraction 1/2/1/4 miles per hour, equivalently 2 miles per hour. 7.RP.A.2.a Recognize and represent proportional relationships between quantities. Decide whether two quantities are in a proportional relationship (e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin). 7.RP.A.2.b Recognize and represent proportional relationships between quantities. Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships. Ratios and Proportional Relationships (RP) 7.RP.A.2.c Recognize and represent proportional relationships between quantities. Represent proportional relationships by equations. For example, if total cost t is proportional to the number n of items purchased at a constant price p, the relationship between the total cost and the number of items can be expressed as t = pn. 7.RP.A.2.d Recognize and represent proportional relationships between quantities. Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r) where r is the unit rate. 7.RP.A.3 Use proportional relationships to solve multi-step ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error. The Number System (NS) 7.NS.A.1.a 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. Describe situations in which opposite quantities combine to make 0. 7.NS.A.1.b Understand p + q as the number located a distance |q| from p, in the positive or negative direction depending on whether q is positive or negative. Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing real-world contexts. 7.NS.A.1.c Understand subtraction of rational numbers as adding the additive inverse, p – q = p + (–q). Show that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in real-world contexts. The Number System (NS) 7.NS.A.1.d Apply properties of operations as strategies to add and subtract rational numbers. 7.NS.A.2.a Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers. 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. 7.NS.A.2.b Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with non-zero divisor) is a rational number. If p and q are integers, then – (p/q) = (–p)/q = p/(–q). Interpret quotients of rational numbers by describing real-world contexts. 7.NS.A.2.c Apply properties of operations as strategies to multiply and divide rational numbers. 7.NS.A.2.d Convert a rational number to a decimal using long division; know that the decimal form of a rational number terminates in 0s or eventually repeats. 7.NS.A.3 Solve real-world and mathematical problems involving the four operations with rational numbers. (Computations with rational numbers extend the rules for manipulating fractions to complex fractions.) Expressions and Equations (EE) 7.EE.A.1 Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients. Expressions and Equations (EE) 7.EE.A.2 Understand that rewriting an expression in different forms in a contextual problem can provide multiple ways of interpreting the problem and how the quantities in it are related. For example, shoes are on sale at a 25% discount. How is the discounted price P related to the original cost C of the shoes? C - .25C = P. In other words, P is 75% of the original cost for C - .25C can be written as .75C. 7.EE.B.3.a Solve multi-step real-world and mathematical problems posed with positive and negative rational numbers presented in any form (whole numbers, fractions, and decimals). Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate. 7.EE.B.3.b Assess the reasonableness of answers using mental computation and estimation strategies. 7.EE.B.4.a 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. Solve contextual problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. For example, the perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width? 7.EE.B.4.b Solve contextual problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality on a number line and interpret it in the context of the problem. For example: As a salesperson, you are paid$50 per week plus $3 per sale. This week you want your pay to be at least$100. Write an inequality for the number of sales you need to make, and describe the solutions. (Note that inequalities using >, <, ≤, ≥ are included in this standard). Geometry (G) 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. 7.G.A.2  Draw 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. 7.G.B.3  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. 7.G.B.4  Know and use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure. 7.G.B.5  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. Statistics and Probability (SP) 7.SP.A.1  Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences. Statistics and Probability (SP) 7.SP.A.2   Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions. For example, estimate the mean word length in a book by randomly sampling words from the book; predict the winner of a school election based on randomly sampled survey data. Gauge how far off the estimate or prediction might be. 7.SP.B.3  Informally assess the degree of visual overlap of two numerical data distributions with similar variabilities, measuring the difference between the centers by expressing it as a multiple of a measure of variability. For example, the mean height of players on the basketball team is 10 cm greater than the mean height of players on the soccer team; on a dot plot or box plot, the separation between the two distributions of heights is noticeable. 7.SP.B.4  Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations. For example, decide whether the words in a chapter of a 7th grade science book are generally longer than the words in a chapter of a 4th grade science book. 7.SP.C.5  Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around 1/2 indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event. Statistics and Probability (SP) 7.SP.C.6  Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its long-run relative frequency, and predict the approximate relative frequency given the probability. For example, when rolling a number cube 600 times, predict that a 3 or 6 would be rolled roughly 200 times, but probably not exactly 200 times. 7.SP.C.7.a  Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy.   Develop a uniform probability model by assigning equal probability to all outcomes, and use the model to determine probabilities of events. For example, if a student is selected at random from a class, find the probability that Jane will be selected and the probability that a girl will be selected. 7.SP.C.7.b  Develop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process. For example, find the approximate probability that a spinning penny will land heads up or that a tossed paper cup will land open end down. Do the outcomes for the spinning penny appear to be equally likely based on the observed frequencies? 7.SP.D.8.a  Summarize numerical data sets in relation to their context.  Give quantitative measures of center (median and/or mean) and variability (range and/or interquartile range), as well as describe any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered. 7.SP.D.8.b  Know and relate the choice of measures of center (median and/or mean) and variability (range and/or interquartile range) to the shape of the data distribution and the context in which the data were gathered. Concept/Standard not taught or incomplete Standard Grade 8 Standards 2021-2022 Algebra I Standards 2022-2023 Nonessential prerequisite Standard not a prerequisite for 7th Grade Standard not a prerequisite for 7th Grade Standard not a prerequisite for 7th Grade Standard not a prerequisite for 7th Grade Standard not a prerequisite for 7th Grade

Major content of the grade is indicated by the gray shading of the standard’s coding.

 Major Content Supporting Content

## 8th Grade Math

Click here to navigate to the 8th Grade Math Standards Summary Tool.

 Concept/Standard not taught or incomplete Grade 8 Standards 2020-2021 Notes from Diagnostic +  Standards to Pair The Number System (NS) 8.NS.A.1  Know that numbers that are not rational are called irrational.  Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually or terminates, and convert a decimal expansion which repeats eventually or terminates into a rational number. 8.NS.A.2  Use rational approximations of irrational numbers to compare the size of irrational numbers locating them approximately on a number line diagram.  Estimate the value of irrational expressions such as . For example, by truncating the decimal expansion of , show that  is between 1 and 2, then between 1.4 and 1.5, and explain how to continue on to get better approximations. Expressions and Equations (EE) 8.EE.A.1  Know and apply the properties of integer exponents to generate equivalent numerical expressions.   For example,   x   =  = = . Expressions and Equations (EE) 8.EE.A.2  Use square root and cube root symbols to represent solutions to equations of the form  = p and   = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that  is irrational. 8.EE.A.3  Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities and to express how many times as much one is than the other. For example, estimate the population of the United States as 3 x  and the population of the world as 7 x , and determine that the world population is more than 20 times larger. 8.EE.A.4  Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology. 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. 8.EE.B.6  Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; know and 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. Expressions and Equations (EE) 8.EE.C.7.a  Solve linear equations in one variable. 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). 8.EE.C.7.b  Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms. 8.EE.C.8.a  Analyze and solve systems of two linear equations. 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 8.EE.C.8.b  Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection. For example, 3x + 2y = 5 and 3x + 2y = 6 have no solution because 3x + 2y cannot simultaneously be 5 and 6. 8.EE.C.8.c  Solve real-world and mathematical problems leading to two linear equations in two variables. For example, given coordinates for two pairs of points, determine whether the line through the first pair of points intersects the line through the second pair. Functions (F) 8.F.A.1  Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output. (Function notation is not required in 8th grade.) 8.F.A.2  Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a linear function represented by a table of values and another linear function represented by an algebraic expression, determine which function has the greater rate of change. 8.F.A.3  Know and interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. For example, the function A = 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. 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. 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. Geometry (G) 8.G.A.1.a   Verify experimentally the properties of rotations, reflections, and translations:  Lines are taken to lines, and line segments to line segments of the same length. 8.G.A.1.b  Verify experimentally the properties of rotations, reflections, and translations: Angles are taken to angles of the same measure. 8.G.A.1.c  Verify experimentally the properties of rotations, reflections, and translations: Parallel lines are taken to parallel lines. 8.G.A.2  Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates. 8.G.A.3  Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. For example, arrange three copies of the same triangle so that the sum of the three angles appears to form a line, and give an argument in terms of transversals why this is so. 8.G.B.4  Explain a proof of the Pythagorean Theorem and its converse. 8.G.B.5  Know and apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions. 8.G.B.6  Apply the Pythagorean Theorem to find the distance between two points in a coordinate system. 8.G.C.7 Know and understand the formulas for the volumes of cones, cylinders, and spheres, and use them to solve real-world and mathematical problems. Statistics and Probability (SP) 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. 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. 8.SP.A.3  Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept. For example, in a linear model for a biology experiment, interpret a slope of 1.5 cm/hr as meaning that an additional hour of sunlight each day is associated with an additional 1.5 cm in mature plant height. 8.SP.B.4  Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation. Understand that, just as with simple events, the probability of a compound event is the fraction of outcomes in the sample space for which the compound event occurs. Represent sample spaces for compound events using methods such as organized lists, tables, and tree diagrams. For an event described in everyday language (e.g., "rolling double sixes"), identify the outcomes in the sample space which compose the event. Standard Algebra I Standards 2021-2022 Geometry Standards 2022-2023 Nonessential prerequisite Standard not a prerequisite for 8th Grade Standard not a prerequisite for 8th Grade Standard not a prerequisite for 8th Grade Standard not a prerequisite for 8th Grade Standard not a prerequisite for 8th Grade

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 Major Content Supporting Content

## Algebra 1

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Grade level/Course: Algebra I

 Concept/ Standard not taught or incomplete Algebra I  Standards 2020-2021 Notes from Diagnostic +  Standards to Pair Quantities* (N.Q) A1.N.Q.A.1 Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays. A1.N.Q.A.2 Identify, interpret, and justify appropriate quantities for the purpose of descriptive modeling. A1.N.Q.A.3 Choose a level of accuracy appropriate to limitations on measurement when reporting quantities. Seeing Structure in Expressions (A.SSE) A1.A.SSE.A.1.a  Interpret expressions that represent a quantity in terms of its context.★   Interpret parts of an expression, such as terms, factors, and coefficients. A1.A.SSE.A.1.b  Interpret expressions that represent a quantity in terms of its context.★   Interpret complicated expressions by viewing one or more of their parts as a single entity. A1.A.SSE.A.2 Use the structure of an expression to identify ways to rewrite it. Seeing Structure in Expressions (A.SSE) A1.A.SSE.B.3.a  Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.★ Factor a quadratic expression to reveal the zeros of the function it defines. A1.A.SSE.B.3.b   Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.★ Complete the square in a quadratic expression in the form + Bx + C to reveal the maximum or minimum value of the function it defines. A1.A.SSE.B.3.c   Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.★ Use the properties of exponents to rewrite exponential expressions. Arithmetic with Polynomials and Rational Expressions (A.APR) A1.A.APR.A.1 Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. A1.A.APR.B.2 Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial. Creating Equations★ (A.CED) A1.A.CED.A.1 Create equations and inequalities in one variable and use them to solve problems. A1.A.CED.A.2 Create equations in two or more variables to represent relationships between quantities; graph equations with two variables on coordinate axes with labels and scales. A1.A.CED.A.3 Represent constraints by equations or inequalities and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. Creating Equations★ (A.CED) A1.A.CED.A.4 Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. Reasoning with Equations and Inequalities (A.REI) A1.A.REI.A.1 Explain each step in solving an equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method. A1.A.REI.B.2 Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters A1.A.REI.B.3.a Solve quadratic equations and inequalities in one variable. Use the method of completing the square to rewrite any quadratic equation in x into an equation of the form  = q that has the same solutions. Derive the quadratic formula from this form. A1.A.REI.B.3.b   Solve quadratic equations by inspection (e.g., for  = 49), taking square roots, completing the square, knowing and applying the quadratic formula, and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions. A1.A.REI.C.4 Write and solve a system of linear equations in context. A1.A.REI.D.5 Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line). A1.A.REI.D.6 Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the approximate solutions using technology. ★ Reasoning with Equations and Inequalities (A.REI) A1.A.REI.D.7 Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes. Interpreting Functions (F.IF) A1.F.IF.A.1 Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x). A1.F.IF.A.2 Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. A1.F.IF.B.3 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. ★ A1.F.IF.B.4 Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. ★ A1.F.IF.B.5 Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.★ A1.F.IF.C.6.a Graph functions expressed symbolically and show key features of the graph, by hand and using technology. Graph linear and quadratic functions and show intercepts, maxima, and minima. Interpreting Functions (F.IF) A1.F.IF.C.6.b Graph functions expressed symbolically and show key features of the graph, by hand and using technology.  Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. A1.F.IF.C.7 Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.  a. Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context. A1.F.IF.C.8 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). Building Functions (F.BF) A1.F.BF.A.1 Write a function that describes a relationship between two quantities.★ Determine an explicit expression, a recursive process, or steps for calculation from a context. A1.F.BF.B.2 Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Linear, Quadratic, and Exponential Models★ (F.LE) A1.F.LE.A.1.a Distinguish between situations that can be modeled with linear functions and with exponential functions.  Recognize that linear functions grow by equal differences over equal intervals and that exponential functions grow by equal factors over equal intervals. Linear, Quadratic, and Exponential Models★ (F.LE) A1.F.LE.A.1.b Distinguish between situations that can be modeled with linear functions and with exponential functions.  Recognize situations in which one quantity changes at a constant rate per unit interval relative to another. A1.F.LE.A.1.c Distinguish between situations that can be modeled with linear functions and with exponential functions.  Recognize situations in which a quantity grows or decays by a constant factor per unit interval relative to another. A1.F.LE.A.2 Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a table, a description of a relationship, or input-output pairs. A1.F.LE.A.3 Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function. A1.F.LE.B.4 Interpret the parameters in a linear or exponential function in terms of a context. Interpreting Categorical and Quantitative Data (S.ID) A1.S.ID.A.1 Represent single or multiple data sets with dot plots, histograms, stem plots (stem and leaf), and box plots. A1.S.ID.A.2 Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. Interpreting Categorical and Quantitative Data (S.ID A1.S.ID.A.3 Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers). A1.S.ID.B.4.a Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.  Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. A1.S.ID.B.4.b Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.  Fit a linear function for a scatter plot that suggests a linear association. A1.S.ID.C.5 Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data. A1.S.ID.C.6 Use technology to compute and interpret the correlation coefficient of a linear fit. A1.S.ID.C.7 Distinguish between correlation and causation. Standard Geometry Standards 2021-2022 Algebra II 2022-2023 Nonessential prerequisite Standard not a prerequisite for Algebra I Standard not a prerequisite for Algebra I Standard not a prerequisite for Algebra I Standard not a prerequisite for Algebra I Standard Geometry Standards 2021-2022 Algebra II 2022-2023 Nonessential prerequisite Standard not a prerequisite for Algebra I Standard not a prerequisite for Algebra I Standard not a prerequisite for Algebra I

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 Major Content Supporting Content

## Algebra 2

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Grade level/Course:  Algebra II

 Concept/ Standard not taught or incomplete Algebra II  Standards 2020-2021 Notes from Diagnostic +  Standards to Pair The Real Number System  (N,RN) A2.N.RN.A.1 Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents. A2.N.RN.A.2 Rewrite expressions involving radicals and rational exponents using the properties of exponents. Quantities* (N.Q) A2.N.Q.A.1 Identify, interpret, and justify appropriate quantities for the purpose of descriptive modeling. The Complex Number System (N.CN) A2.N.CN.A.1   Know there is a complex number i such that  = –1, and every complex number has the form a + bi with a and b real. A2.N.CN.A.2 Know and use the relation  = –1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers. A2.N.CN.B.3   Solve quadratic equations with real coefficients that have complex solutions. Seeing Structure in Expressions (A.SSE) A2.A.SSE.A.1 Use the structure of an expression to identify ways to rewrite it. A2.A.SSE.B.2 Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.★ a. Use the properties of exponents to rewrite expressions for exponential functions. A2.A.SSE.B.3 Recognize a finite geometric series (when the common ratio is not 1), and use the sum formula to solve problems in context. Arithmetic with Polynomials and Rational Expressions (A.APR) A2.A.APR.A.1 Know and apply the Remainder Theorem: For a polynomial p(x) and a number a, the remainder on division by x – a is p(a), so p(a) = 0 if and only if (x – a) is a factor of p(x). A2.A.APR.A.2 Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial. A2.A.APR.B.3 Know and use polynomial identities to describe numerical relationships. A2.A.APR.C.4 Rewrite rational expressions in different forms. Creating Equations* (A.CED) A2.A.CED.A.1 Create equations and inequalities in one variable and use them to solve problems. A2.A.CED.A.2 Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. Reasoning with Equations and Inequalities (A.REI) A2.A.REI.A.1 Explain each step in solving an equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method. A2.A.REI.A.2 Solve rational and radical equations in one variable, and identify extraneous solutions when they exist. A2.A.REI.B.3 Solve quadratic equations and inequalities in one variable. a. Solve quadratic equations by inspection (e.g., for  = 49), taking square roots, completing the square, knowing and applying the quadratic formula, and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as a ± bi for real numbers a and b. A2.A.REI.C.4 Write and solve a system of linear equations in context. A2.A.REI.C.5 Solve a system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. A2.A.REI.D.6 Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the approximate solutions using technology. ★ Interpreting Functions (F.IF) A2.F.IF.A.1 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. ★ A2.F.IF.A.2 Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.★ A2.F.IF.B.3.a Graph functions expressed symbolically and show key features of the graph, by hand and using technology.★ Graph square root, cube root, and piecewise defined functions, including step functions and absolute value functions. A2.F.IF.B.3.b Graph functions expressed symbolically and show key features of the graph, by hand and using technology.★ Graph polynomial functions, identifying zeros when suitable factorizations are available and showing end behavior. A2.F.IF.B.3.c Graph functions expressed symbolically and show key features of the graph, by hand and using technology.★ Graph exponential and logarithmic functions, showing intercepts and end behavior. A2.F.IF.B.4 Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function. a. Know and use the properties of exponents to interpret expressions for exponential functions. A2.F.IF.B.5 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). Building Functions   (F.BF) A2.F.BF.A.1.a Write a function that describes a relationship between two quantities.★ Determine an explicit expression, a recursive process, or steps for calculation from a context. A2.F.BF.A.1.b Write a function that describes a relationship between two quantities.★ Combine standard function types using arithmetic operations. A2.F.BF.A.2 Write arithmetic and geometric sequences with an explicit formula and use them to model situations.★ A2.F.BF.B.3 Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. A2.F.BF.B.4 Find inverse functions. a. Find the inverse of a function when the given function is one-to-one. Linear, Quadratic, and Exponential Models*  (F.LE) A2.F.LE.A.1 Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a table, a description of a relationship, or input-output pairs. A2.F.LE.A.2 For exponential models, express as a logarithm the solution to = d where a, c, and d are numbers and the base b is 2, 10, or e; evaluate the logarithm using technology. A2.F.LE.B.3 Interpret the parameters in a linear or exponential function in terms of a context. Trigonometric Functions   (T.TF) A2.F.TF.A.1.a Understand and use radian measure of an angle.  Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle. A2.F.TF.A.1.b Understand and use radian measure of an angle.  Use the unit circle to find sin θ, cos θ, and tan θ when θ is a commonly recognized angle between 0 and 2π. A2.F.TF.A.2 Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian measures of angles traversed counterclockwise around the unit circle. A2.F.TF.B.3.a Know and use trigonometric identities to find values of trig functions. a. Given a point on a circle centered at the origin, recognize and use the right triangle ratio definitions of sin θ, cos θ, and tan θ to evaluate the trigonometric functions. A2.F.TF.B.3.b Know and use trigonometric identities to find values of trig functions.  Given the quadrant of the angle, use the identity  θ +  θ = 1 to find sin θ given cos θ, or vice versa. Interpreting Categorical and Quantitative Data   (S.ID) A2.S.ID.A.1 Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages using the Empirical Rule. A2.S.ID.B.2 Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. a. Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Making Inferences and Justifying Conclusions  (S.IC) A2.S.IC.A.1 Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each. A2.S.IC.A.2 Use data from a sample survey to estimate a population mean or proportion; use a given margin of error to solve a problem in context. Conditional Probability and the Rules of Probability   (S.CP) A2.S.CP.A.1 Describe events as subsets of a sample space (the set of outcomes) using characteristics (or categories) of the outcomes, or as unions, intersections, or complements of other events (“or,” “and,” “not”). A2.S.CP.A.2 Understand that two events A and B are independent if the probability of A and B occurring together is the product of their probabilities, and use this characterization to determine if they are independent. A2.S.CP.A.3  Know and understand the conditional probability of A given B as P(A and B)/P(B), and interpret independence of A and B as saying that the conditional probability of A given B is the same as the probability of A, and the conditional probability of B given A is the same as the probability of B. A2.S.CP.A.4 Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations. A2.S.CP.B.5 Find the conditional probability of A given B as the fraction of B’s outcomes that also belong to A and interpret the answer in terms of the model. A2.S.CP.B.6 Know and apply the Addition Rule, P(A or B) = P(A) + P(B) – P(A and B), and interpret the answer in terms of the model. Concept/ Standard not taught or incomplete Standard 4th  Year Math Standards 2021-2022 Nonessential Prerequisite Standard not a prerequisite for Algebra II Standard not a prerequisite for Algebra II Standard not a prerequisite for Algebra II Standard not a prerequisite for Algebra II Standard not a prerequisite for Algebra II

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 Major Content Supporting Content

## Geometry

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 Concept/ Standard not taught or incomplete Geometry Standards 2020-2021 Notes from Diagnostic +  Standards to Pair Congruence (G.CO) G.CO.A.1 Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, plane, distance along a line, and distance around a circular arc. G.CO.A.2 Represent transformations in the plane in multiple ways, including technology. Describe transformations as functions that take points in the plane (pre-image) as inputs and give other points (image) as outputs. Compare transformations that preserve distance and angle measure to those that do not (e.g., translation versus horizontal stretch). G.CO.A.3 Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry the shape onto itself. G.CO.A.4 Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments. Congruence (G.CO) G.CO.A.5 Given a geometric figure and a rigid motion, draw the image of the figure in multiple ways, including technology. Specify a sequence of rigid motions that will carry a given figure onto another. G.CO.B.6 Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure; given two figures, use the definition of congruence in terms of rigid motions to determine informally if they are congruent. G.CO.B.7 Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent. G.CO.B.8 Explain how the criteria for triangle congruence (ASA, SAS, AAS, and SSS) follow from the definition of congruence in terms of rigid motions. G.CO.C.9 Prove theorems about lines and angles. G.CO.C.10 Prove theorems about triangles. G.CO.C.11 Prove theorems about parallelograms. G.CO.D.12 Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). Similarity, Right Triangles, and Trigonometry (G.SRT) G.SRT.A.1 Verify informally the properties of dilations given by a center and a scale factor. G.SRT.A.2 Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides. G.SRT.A.3 Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar. G.SRT.B.4 Prove theorems about similar triangles. G.SRT.B.5 Use congruence and similarity criteria for triangles to solve problems and to justify relationships in geometric figures. G.SRT.C.6 Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles. G.SRT.C.7 Explain and use the relationship between the sine and cosine of complementary angles. G.SRT.C.8.a  Solve triangles. ★    Know and use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems G.SRT.C.8.b  Solve triangles. ★   Know and use the Law of Sines and Law of Cosines to solve problems in real life situations. Recognize when it is appropriate to use each. Circles (G.C) G.C.A.1 Recognize that all circles are similar. G.C.A.2 Identify and describe relationships among inscribed angles, radii, and chords. G.C.A.3 Construct the incenter and circumcenter of a triangle and use their properties to solve problems in context. Circles (G.C) G.C.B.4 Know the formula and find the area of a sector of a circle in a real-world context. Expressing Geometric Properties with Equations (G.GPE) G.GPE.A.1 Know and write the equation of a circle of given center and radius using the Pythagorean Theorem. G.GPE.B.2 Use coordinates to prove simple geometric theorems algebraically. G.GPE.B.3 Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems. G.GPE.B.4 Find the point on a directed line segment between two given points that partitions the segment in a given ratio. G.GPE.B.5 Know and use coordinates to compute perimeters of polygons and areas of triangles and rectangles.★ Geometric Measurement and Dimension (G.GMD) G.GMD.A.1 Give an informal argument for the formulas for the circumference of a circle and the volume and surface area of a cylinder, cone, prism, and pyramid. G.GMD.A.2 Know and use volume and surface area formulas for cylinders, cones, prisms, pyramids, and spheres to solve problems.★ Modeling with Geometry (G.MG) G.MG.A.1 Use geometric shapes, their measures, and their properties to describe objects.★ G.MG.A.2 Apply geometric methods to solve real-world problems.★
 Concept/ Standard not taught or incomplete Standard Algebra II Standards 2021-2022 4th Year Math 2022-2023 Nonessential prerequisite Standard not a prerequisite for Geometry Standard not a prerequisite for Geometry Standard not a prerequisite for Geometry Standard not a prerequisite for Geometry Standard not a prerequisite for Geometry Standard not a prerequisite for Geometry

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 Major Content Supporting Content

## Integrated Math 1

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Grade level/Course:  Integrated Math 1

 Concept/ Standard not taught or incomplete Integrated Math I  Standards 2020-2021 Notes from Diagnostic +  Standards to Pair Quantities* (N.Q) M1.N.Q.A.1 Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays. M1.N.Q.A.2 Identify, interpret, and justify appropriate quantities for the purpose of descriptive modeling. M1.N.Q.A.3 Choose a level of accuracy appropriate to limitations on measurement when reporting quantities. Seeing Structure in Expressions   (A.SSE) M1.A.SSE.A.1.a Interpret expressions that represent a quantity in terms of its context.★ Interpret parts of an expression, such as terms, factors, and coefficients. M1.A.SSE.A.1.b Interpret expressions that represent a quantity in terms of its context.★  Interpret complicated expressions by viewing one or more of their parts as a single entity. Seeing Structure in Expressions (A.SSE) M1.A.SSE.B.2 Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.★ a. Use the properties of exponents to rewrite exponential expressions. Creating Equations★   (A.CED) M1.A.CED.A.1 Create equations and inequalities in one variable and use them to solve problems. M1.A.CED.A.2 Create equations in two or more variables to represent relationships between quantities; graph equations with two variables on coordinate axes with labels and scales. M1.A.CED.A.3 Represent constraints by equations or inequalities and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. M1.A.CED.A.4 Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. Reasoning with Equations and Inequalities   (A.REI) M1.A.REI.A.1 Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. M1.A.REI.B.2 Write and solve a system of linear equations in context. M1.A.REI.C.3 Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line). Reasoning with Equations and Inequalities   (A.REI) M1.A.REI.C.4 Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the approximate solutions using technology. ★ M1.A.REI.C.5 Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes. Interpreting Functions (F.IF) M1.F.IF.A.1 Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x). M1.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. M1.F.IF.B.3 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. ★ M1.F.IF.B.4 Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. ★ Interpreting Functions (F.IF) M1.F.IF.B.5 Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.★ M1.F.IF.C.6 Graph functions expressed symbolically and show key features of the graph, by hand and using technology. a. Graph linear functions and show its intercepts. M1.F.IF.C.7 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). Building Functions   (F.BF) M1.F.BF.A.1 Write a function that describes a relationship between two quantities.★ a. Determine an explicit expression, a recursive process, or steps for calculation from a context. M1.F.BF.A.2 Write arithmetic and geometric sequences with an explicit formula and use them to model situations.★ Linear and Exponential Models★   (F.LE) M1.F.LE.A.1.a Distinguish between situations that can be modeled with linear functions and with exponential functions.  Recognize that linear functions grow by equal differences over equal intervals and that exponential functions grow by equal factors over equal intervals. Linear and Exponential Models★   (F.LE) M1.F.LE.A.1.b Distinguish between situations that can be modeled with linear functions and with exponential functions.  Recognize situations in which one quantity changes at a constant rate per unit interval relative to another. M1.F.LE.A.1.c Distinguish between situations that can be modeled with linear functions and with exponential functions.  Recognize situations in which a quantity grows or decays by a constant factor per unit interval relative to another. M1.F.LE.A.2 Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a table, a description of a relationship, or input-output pairs. M1.F.LE.A.3 Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly. M1.F.LE.B.4 Interpret the parameters in a linear or exponential function in terms of a context. Congruence   (G.CO) M1.G.CO.A.1 Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, plane, distance along a line, and distance around a circular arc. Congruence   (G.CO) M1.G.CO.A.2 Represent transformations in the plane in multiple ways, including technology. Describe transformations as functions that take points in the plane (pre-image) as inputs and give other points (image) as outputs. Compare transformations that preserve distance and angle measure to those that do not (e.g., translation versus horizontal stretch). M1.G.CO.A.3 Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry the shape onto itself. M1.G.CO.A.4 Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments. M1.G.CO.A.5 Given a geometric figure and a rigid motion, draw the image of the figure in multiple ways, including technology. Specify a sequence of rigid motions that will carry a given figure onto another. M1.G.CO.B.6 Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure; given two figures, use the definition of congruence in terms of rigid motions to determine informally if they are congruent. M1.G.CO.B.7 Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent. M1.G.CO.B.8 Explain how the criteria for triangle congruence (ASA, SAS, AAS, and SSS) follow from the definition of congruence in terms of rigid motions. Congruence   (G.CO) M1.G.CO.C.9 Prove theorems about lines and angles. M1.G.CO.C.10 Prove theorems about triangles. M1.G.CO.C.11 Prove theorems about parallelograms. Interpreting Categorical and Quantitative Data   (S.ID) M1.S.ID.A.1 Represent single or multiple data sets with dot plots, histograms, stem plots (stem and leaf), and box plots. M1.S.ID.A.2 Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. M1.S.ID.A.3 Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers). M1.S.ID.B.4.a Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.   Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. M1.S.ID.B.4.b Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.  Fit a linear function for a scatter plot that suggests a linear association. M1.S.ID.C.5 Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data. M1.S.ID.C.6 Compute (using technology) and interpret the correlation coefficient of a linear fit M1.S.ID.C.7 Distinguish between correlation and causation. Concept/ Standard not taught or incomplete Standard Integrated Math II Standard 2021-2022 Integrated Math III Standard 2022-2023 Nonessential prerequisite Standard not a prerequisite for Integrated Math I Standard not a prerequisite for Integrated Math I Standard not a prerequisite for Integrated Math I Standard not a prerequisite for Integrated Math I Standard not a prerequisite for Integrated Math I

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## Integrated Math 2

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Grade level/Course:  Integrated Math 2

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## Integrated Math 3

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Grade level/Course:  Integrated Math 3

 Concept/ Standard not taught or incomplete Integrated Math III  Standards 2020-2021 Notes from Diagnostic +  Standards to Pair Quantities*   (N.Q) M3.N.Q.A.1 Identify, interpret, and justify appropriate quantities for the purpose of descriptive modeling. Seeing Structure in Expressions (A.SSE) M3.A.SSE.A.1 Use the structure of an expression to identify ways to rewrite it. M3.A.SSE.B.2 Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression. ★ a. Use the properties of exponents to rewrite expressions for exponential functions. M3.A.SSE.B.3 Recognize a finite geometric series (when the common ratio is not 1), and use the sum formula to solve problems in context. Arithmetic with Polynomials and Rational Expressions   (A.APR) M3.A.APR.A.1 Know and apply the Remainder Theorem: For a polynomial p(x) and a number a, the remainder on division by x – a is p(a), so p(a) = 0 if and only if (x – a) is a factor of p(x). Arithmetic with Polynomials and Rational Expressions   (A.APR) M3.A.APR.A.2 Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial. M3.A.APR.B.3 Know and use polynomial identities to describe numerical relationships. M3.A.APR.C.4 Rewrite rational expressions in different forms. Creating Equations★  (A–CED) M3.A.CED.A.1 Create equations and inequalities in one variable and use them to solve problems. M3.A.CED.A.2 Create equations in two or more variables to represent relationships between quantities; graph equations with two variables on coordinate axes with labels and scales. M3.A.CED.A.3 Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. Reasoning with Equations and Inequalities   (A.REI) M3.A.REI.A.1 Explain each step in solving an equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method. M3.A.REI.A.2 Solve rational and radical equations in one variable, and identify extraneous solutions when they exist. M3.A.REI.B.3 Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the approximate solutions using technology. ★ Interpreting Functions (F.IF) M3.F.IF.A.1 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. ★ M3.F.IF.A.2 Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. ★ M3.F.IF.B.3.a Graph functions expressed symbolically and show key features of the graph, by hand and using technology.★ Graph linear and quadratic functions and show intercepts, maxima, and minima. M3.F.IF.B.3.b Graph functions expressed symbolically and show key features of the graph, by hand and using technology.★ Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. M3.F.IF.B.3.c Graph functions expressed symbolically and show key features of the graph, by hand and using technology.★ Graph polynomial functions, identifying zeros when suitable factorizations are available and showing end behavior. M3.F.IF.B.3.d Graph functions expressed symbolically and show key features of the graph, by hand and using technology.★ Graph exponential and logarithmic functions, showing intercepts and end behavior. Interpreting Functions (F.IF) M3.F.IF.B.4 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). Building Functions   (F.BF) M3.F.BF.A.1 Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. M3.F.BF.A.2 Find inverse functions. a. Find the inverse of a function when the given function is one-to-one.. Linear, Quadratic, and Exponential Models★   (F.LE) M3.F.LE.A.1 Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function. M3.F.LE.A.2 For exponential models, express as a logarithm the solution to = d where a, c, and d are numbers and the base b is 2, 10, or e; evaluate the logarithm using technology. Trigonometric Functions  (F.TF) M3.F.TF.A.1.a Understand and use radian measure of an angle. Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle. M3.F.TF.A.1.b Understand and use radian measure of an angle. Use the unit circle to find sin θ, cos θ, and tan θ when θ is a commonly recognized angle between 0 and 2π. M3.F.TF.A.2 Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian measures of angles traversed counterclockwise around the unit circle. Trigonometric Functions  (F.TF) M3.F.TF.B.3.a Know and use trigonometric identities to find values of trig functions. Given a point on a circle centered at the origin, recognize and use the right triangle ratio definitions of sin θ, cos θ, and tan θ to evaluate the trigonometric functions. M3.F.TF.B.3.b Know and use trigonometric identities to find values of trig functions. Given the quadrant of the angle, use the identity  θ +   θ = 1 to find sin θ given cos θ, or vice versa. Congruence (G.CO) M3.G.CO.A.1 Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). Circles (G.C) M3.G.C.A.1 Recognize that all circles are similar. M3.G.C.A.2 Identify and describe relationships among inscribed angles, radii, and chords. M3.G.C.A.3 Construct the incenter and circumcenter of a triangle and use their properties to solve problems in context. M3.G.C.B.4 Know the formula and find the area of a sector of a circle in a real-world context. Expressing Geometric Properties with Equations  (G.GPE) M3.G.GPE.A.1 Know and write the equation of a circle of given center and radius using the Pythagorean Theorem. M3.G.GPE.B.2 Use coordinates to prove simple geometric theorems algebraically. Expressing Geometric Properties with Equations  (G.GPE) M3.G.GPE.B.3 Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems. M3.G.GPE.B.4 Find the point on a directed line segment between two given points that partitions the segment in a given ratio. M3.G.GPE.B.5 Know and use coordinates to compute perimeters of polygons and areas of triangles and rectangles.★ Modeling with Geometry   (G.MG) M3.G.MG.A.1 Use geometric shapes, their measures, and their properties to describe objects.★ M3.G.MG.A.2 Apply geometric methods to solve real-world problems.★ Interpreting Categorical and Quantitative Data (S.ID) M3.S.ID.A.1 Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages using the Empirical Rule. M3.S.ID.B.2.a Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.  Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. M3.S.ID.B.2.b Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.  Fit a linear function for a scatter plot that suggests a linear association. Making Inferences and Justifying Conclusions (S.IC) M3.S.IC.A.1 Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each. M3.S.IC.A.2 Use data from a sample survey to estimate a population mean or proportion; use a given margin of error to solve a problem in context. Concept/Standard not taught or incomplete Standard 4th Year Math Standards 2021-2022 Not an essential prerequisite Standard not a prerequisite for Integrated Math III Standard not a prerequisite for Integrated Math III Standard not a prerequisite for Integrated Math III Standard not a prerequisite for Integrated Math III Standard not a prerequisite for Integrated Math III Standard not a prerequisite for Integrated Math III

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