 ## Common Core State Standards (CCSS) Correlations ## Mathematics

### Domain - Operations and Algebraic Thinking, Grade 4

Use the four operations with whole numbers to solve problems.

Math.4.OA.A.3: Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.

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Problem Solving with Mixed Operations: Missing or Extra Information 17
Multiple-step Problems with Mixed Operations 18
Problem Solving with Mixed Operations: Missing or Extra Information 42
Multiple-step Problems with Mixed Operations 43
Problem Solving with Mixed Operations: Missing or Extra Information 67
Multiple-step Problems with Mixed Operations 68

Use the four operations with whole numbers to solve problems.

Math.4.OA.A.2: Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison.

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Problem Solving with Mixed Operations: Missing or Extra Information 17
Problem Solving with Mixed Operations: Missing or Extra Information 42
Problem Solving with Mixed Operations: Missing or Extra Information 67

Gain familiarity with factors and multiples.

Math.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.

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Factors and Multiples 19
Prime and Composite Numbers 20
Factors and Multiples 44
Prime and Composite Numbers 45
Factors and Multiples 69
Prime and Composite Numbers 70

Generate and analyze patterns.

Math.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.

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Input/Output and Function Tables 21
Input/Output and Function Tables 46
Input/Output and Function Tables 71

### Domain - Number and Operations in Base Ten, Grade 4

Generalize place value understanding for multi-digit whole numbers.

Math.4.NBT.A.3: Use place value understanding to round multi-digit whole numbers to any place.

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Estimating Sums and Differences of Whole Numbers 11
Estimating Products and Quotients 16
Estimating Sums and Differences of Whole Numbers 36
Estimating Products and Quotients 41
Estimating Sums and Differences of Whole Numbers 61
Estimating Products and Quotients 66

Generalize place value understanding for multi-digit whole numbers.

Math.4.NBT.A.2: Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.

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Comparing Numbers to Hundred Thousands 12
Comparing Numbers to Hundred Thousands 37
Comparing Numbers to Hundred Thousands 62

Use place value understanding and properties of operations to perform multi-digit arithmetic.

Math.4.NBT.B.4: Fluently add and subtract multi-digit whole numbers using the standard algorithm.

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Addition and Subtraction to One Million 10
Addition and Subtraction to One Million 35
Addition and Subtraction to One Million 60

Use place value understanding and properties of operations to perform multi-digit arithmetic.

Math.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.

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Multiplication and Division Using Basic Facts 13
Multiplying by One-digit and Two-digit Numbers 14
Multiplication and Division Using Basic Facts 38
Multiplying by One-digit and Two-digit Numbers 39
Multiplication and Division Using Basic Facts 63
Multiplying by One-digit and Two-digit Numbers 64

Use place value understanding and properties of operations to perform multi-digit arithmetic.

Math.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.

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Dividing by One-digit Numbers 15
Dividing by One-digit Numbers 40
Dividing by One-digit Numbers 65

### Domain - Number and Operations-Fractions, Grade 4

Extend understanding of fraction equivalence and ordering.

Math.4.NF.A.2: Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.

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Comparing Fractions 22
Comparing Fractions 47
Comparing Fractions 72

Understand decimal notation for fractions, and compare decimal fractions.

Math.4.NF.C.7: Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual model.

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Comparing Decimals 28
Comparing Decimals 53
Comparing Decimals 78

### Domain - Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers., Grade 4

Understand a fraction <i>a</i>/<i>b</i> with <i>a</i> &gt; 1 as a sum of fractions 1/<i>b</i>.

Math.4.NF.B.3d: Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators, e.g., by using visual fraction models and equations to represent the problem.

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Adding and Subtracting Fractions with Like and Unlike Denominators 23
Adding and Subtracting Fractions with Like and Unlike Denominators 48
Adding and Subtracting Fractions with Like and Unlike Denominators 73

Understand a fraction <i>a</i>/<i>b</i> with <i>a</i> &gt; 1 as a sum of fractions 1/<i>b</i>.

Math.4.NF.B.3a: Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.

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Adding and Subtracting Fractions with Like and Unlike Denominators 23
Adding and Subtracting Fractions with Like and Unlike Denominators 48
Adding and Subtracting Fractions with Like and Unlike Denominators 73

Understand a fraction <i>a</i>/<i>b</i> with <i>a</i> &gt; 1 as a sum of fractions 1/<i>b</i>.

Math.4.NF.B.3c: Add and subtract mixed numbers with like denominators, e.g., by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction.

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Improper Fractions and Mixed Numbers 24
Adding and Subtracting Mixed Numbers 25
Improper Fractions and Mixed Numbers 49
Adding and Subtracting Mixed Numbers 50
Improper Fractions and Mixed Numbers 74
Adding and Subtracting Mixed Numbers 75

Apply and extend previous understandings of multiplication to multiply a fraction by a whole number.

Math.4.NF.B.4c: Solve word problems involving multiplication of a fraction by a whole number, e.g., by using visual fraction models and equations to represent the problem. For example, if each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?

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Multiplying Fractions by Whole Numbers 26
Word Problems with Whole Numbers and Fractions 27
Multiplying Fractions by Whole Numbers 51
Word Problems with Whole Numbers and Fractions 52
Multiplying Fractions by Whole Numbers 76
Word Problems with Whole Numbers and Fractions 77

Apply and extend previous understandings of multiplication to multiply a fraction by a whole number.

Math.4.NF.B.4a: Understand a fraction a/b as a multiple of 1/b. For example, use a visual fraction model to represent 5/4 as the product 5 × (1/4), recording the conclusion by the equation 5/4 = 5 × (1/4).

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Multiplying Fractions by Whole Numbers 26
Multiplying Fractions by Whole Numbers 51
Multiplying Fractions by Whole Numbers 76

### Domain - Measurement and Data, Grade 4

Solve problems involving measurement and conversion of measurements.

Math.4.MD.A.1: Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table. For example, know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), ...

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Converting Customary and Metric Units 29
Converting Units of Time 30
Converting Customary and Metric Units 54
Converting Units of Time 55
Converting Customary and Metric Units 79
Converting Units of Time 80

Solve problems involving measurement and conversion of measurements.

Math.4.MD.A.2: Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale.

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Converting Units of Time 30
Elapsed Time 31
Converting Units of Time 55
Elapsed Time 56
Converting Units of Time 80
Elapsed Time 81

Solve problems involving measurement and conversion of measurements.

Math.4.MD.A.3: Apply the area and perimeter formulas for rectangles in real world and mathematical problems. For example, find the width of a rectangular room given the area of the flooring and the length, by viewing the area formula as a multiplication equation with an unknown factor.

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Perimeter and Area 32
Perimeter and Area 57
Perimeter and Area 82

Geometric measurement: understand concepts of angle and measure angles.

Math.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.

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Angles 34
Angles 59
Angles 84

### Domain - Geometry, Grade 4

Draw and identify lines and angles, and classify shapes by properties of their lines and angles.

Math.4.G.A.1: Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures.

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Lines and Angles 33
Lines and Angles 58
Lines and Angles 83