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

### Domain - Operations and Algebraic Thinking, Grade 5

Write and interpret numerical expressions.

Math.5.OA.A.1: Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols.

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Problem 94 55
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Problem 102 59

Write and interpret numerical expressions.

Math.5.OA.A.2: Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, express the calculation “add 8 and 7, then multiply by 2” as 2 × (8 + 7). Recognize that 3 × (18932 + 921) is three times as large as 18932 + 921, without having to calculate the indicated sum or product.

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Problem 65 41
Problem 80 48

Analyze patterns and relationships.

Math.5.OA.B.3: Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. For example, given the rule “Add 3” and the starting number 0, and given the rule “Add 6” and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so.

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Problem 54 35
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### Domain - Number and Operations in Base Ten, Grade 5

Understand the place value system.

Math.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.

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Problem 21 19
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Problem 59 38

Understand the place value system.

Math.5.NBT.A.3: Read, write, and compare decimals to thousandths.

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Problem 50 33
Problem 92 54
Problem 91 54
Problem 94 55
Problem 93 55

Understand the place value system.

Math.5.NBT.A.4: Use place value understanding to round decimals to any place.

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Problem 68 42
Problem 70 43
Problem 90 53
Problem 91 54
Problem 92 54
Problem 101 59
Problem 102 59

Perform operations with multi-digit whole numbers and with decimals to hundredths.

Math.5.NBT.B.7: Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.

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Problem 48 32
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Problem 49 33
Problem 50 33
Problem 63 40
Problem 74 45
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Problem 77 47
Problem 90 53

Perform operations with multi-digit whole numbers and with decimals to hundredths.

Math.5.NBT.B.5: Fluently multiply multi-digit whole numbers using the standard algorithm.

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Problem 54 35
Problem 78 47

Perform operations with multi-digit whole numbers and with decimals to hundredths.

Math.5.NBT.B.6: Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

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Problem 59 38
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Problem 69 43
Problem 79 48
Problem 89 53

### Domain - Number and Operations-Fractions, Grade 5

Use equivalent fractions as a strategy to add and subtract fractions.

Math.5.NF.A.1: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.)

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Problem 7 12

Use equivalent fractions as a strategy to add and subtract fractions.

Math.5.NF.A.2: Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2.

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Problem 1 9
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Problem 7 12

Apply and extend previous understandings of multiplication and division to multiply and divide fractions.

Math.5.NF.B.5: Interpret multiplication as scaling (resizing), by:

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Problem 41 29
Problem 48 32
Problem 71 44
Problem 76 46

Apply and extend previous understandings of multiplication and division to multiply and divide fractions.

Math.5.NF.B.3: Interpret a fraction as division of the numerator by the denominator (a/b = a : b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie?

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Apply and extend previous understandings of multiplication and division to multiply and divide fractions.

Math.5.NF.B.6: Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem.

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Problem 24 20
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Problem 33 25
Problem 38 27
Problem 41 29
Problem 48 32
Problem 71 44
Problem 76 46

Apply and extend previous understandings of multiplication and division to multiply and divide fractions.

Math.5.NF.B.4: Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.

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Problem 24 20
Problem 25 21
Problem 27 22
Problem 33 25
Problem 38 27
Problem 41 29
Problem 48 32
Problem 71 44
Problem 76 46

### Domain - Measurement and Data, Grade 5

Convert like measurement units within a given measurement system.

Math.5.MD.A.1: Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems.

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Problem 69 43

Represent and interpret data.

Math.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.

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### Domain - Geometry, Grade 5

Classify two-dimensional figures into categories based on their properties.

Math.5.G.B.3: Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles.

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Problem 89 53

Classify two-dimensional figures into categories based on their properties.

Math.5.G.B.4: Classify two-dimensional figures in a hierarchy based on properties.

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Problem 86 51
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Problem 89 53