 ## Common Core State Standards (CCSS) Correlations ## N/A

### 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 56 36
Problem 57 37
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Problem 69 43
Problem 76 46
Problem 78 47
Problem 80 48
Problem 79 48
Problem 84 50
Problem 94 55
Problem 93 55
Problem 97 57
Problem 106 61

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 24 20
Problem 26 21
Problem 25 21
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Problem 27 22
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Problem 31 24
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Problem 40 28
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Problem 48 32
Problem 47 32
Problem 50 33
Problem 49 33
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Problem 52 34
Problem 55 36
Problem 62 39
Problem 61 39
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Problem 63 40
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Problem 65 41
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Problem 70 43
Problem 73 45
Problem 78 47
Problem 80 48
Problem 79 48
Problem 84 50
Problem 89 53
Problem 93 55
Problem 94 55
Problem 97 57
Problem 106 61

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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Problem 29 23
Problem 83 50
Problem 91 54
Problem 95 56
Problem 107 62

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

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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Problem 2 9
Problem 106 61
Problem 107 62
Problem 108 62

Generalize place value understanding for multi-digit whole numbers.

Math.4.NBT.A.1: Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. For example, recognize that 700 ÷ 70 = 10 by applying concepts of place value and division.

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Problem 26 21
Problem 25 21
Problem 27 22
Problem 28 22
Problem 32 24
Problem 33 25
Problem 49 33
Problem 53 35
Problem 65 41
Problem 67 42
Problem 87 52

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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Problem 5 11
Problem 6 11
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Problem 8 12
Problem 10 13
Problem 18 17
Problem 17 17
Problem 21 19

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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Problem 24 20
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Problem 28 22
Problem 31 24
Problem 32 24
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Problem 37 27
Problem 38 27
Problem 40 28
Problem 39 28
Problem 42 29
Problem 41 29
Problem 43 30
Problem 44 30
Problem 45 31
Problem 46 31
Problem 47 32
Problem 49 33
Problem 50 33
Problem 51 34
Problem 53 35

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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Problem 55 36
Problem 56 36
Problem 57 37
Problem 58 37
Problem 60 38
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Problem 62 39
Problem 63 40
Problem 64 40
Problem 66 41
Problem 65 41
Problem 67 42
Problem 70 43
Problem 69 43
Problem 73 45

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

Extend understanding of fraction equivalence and ordering.

Math.4.NF.A.1: Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions.

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Problem 14 15
Problem 54 35

Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers.

Math.4.NF.B.3: Understand a fraction a/b with a > 1 as a sum of fractions 1/b.

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Problem 54 35

Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers.

Math.4.NF.B.4: Apply and extend previous understandings of multiplication to multiply a fraction by a whole number.

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Problem 59 38

Understand decimal notation for fractions, and compare decimal fractions.

Math.4.NF.C.5: Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100.2 For example, express 3/10 as 30/100, and add 3/10 + 4/100 = 34/100.

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Problem 14 15

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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Problem 74 45
Problem 98 57

### Domain - Measurement and Data, Grade 4

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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Problem 2 9
Problem 9 13
Problem 18 17
Problem 19 18
Problem 20 18
Problem 23 20
Problem 68 42
Problem 71 44
Problem 72 44
Problem 74 45
Problem 75 46
Problem 82 49
Problem 81 49
Problem 83 50
Problem 86 51
Problem 85 51
Problem 87 52
Problem 90 53
Problem 92 54
Problem 93 55
Problem 95 56
Problem 98 57
Problem 109 63

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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Problem 1 9
Problem 3 10
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Problem 11 14
Problem 15 16
Problem 32 24
Problem 45 31
Problem 49 33
Problem 67 42
Problem 91 54
Problem 96 56
Problem 107 62