**Write and interpret numerical expressions.**

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

Problem | Page |
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Problem 49 | 33 |

Problem 50 | 33 |

Problem 64 | 40 |

Problem 66 | 41 |

Problem 67 | 42 |

Problem 74 | 45 |

Problem 78 | 47 |

Problem 94 | 55 |

Problem 93 | 55 |

Problem 96 | 56 |

Problem 95 | 56 |

Problem 97 | 57 |

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*.

Problem | Page |
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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*.

Problem | Page |
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Problem 13 | 15 |

Problem 16 | 16 |

Problem 15 | 16 |

Problem 18 | 17 |

Problem 17 | 17 |

Problem 22 | 19 |

Problem 24 | 20 |

Problem 26 | 21 |

Problem 30 | 23 |

Problem 31 | 24 |

Problem 40 | 28 |

Problem 54 | 35 |

Problem 78 | 47 |

Problem 81 | 49 |

Problem 82 | 49 |

Problem 84 | 50 |

Problem 83 | 50 |

Problem 86 | 51 |

Problem 92 | 54 |

Problem 91 | 54 |

Problem 94 | 55 |

Problem 93 | 55 |

Problem 103 | 60 |

**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.

Problem | Page |
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Problem 21 | 19 |

Problem 25 | 21 |

Problem 57 | 37 |

Problem 59 | 38 |

**Understand the place value system.**

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

Problem | Page |
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Problem 50 | 33 |

Problem 91 | 54 |

Problem 92 | 54 |

Problem 93 | 55 |

Problem 94 | 55 |

**Understand the place value system.**

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

Problem | Page |
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Problem 68 | 42 |

Problem 70 | 43 |

Problem 90 | 53 |

Problem 92 | 54 |

Problem 91 | 54 |

Problem 102 | 59 |

Problem 101 | 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.

Problem | Page |
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Problem 2 | 9 |

Problem 9 | 13 |

Problem 13 | 15 |

Problem 15 | 16 |

Problem 16 | 16 |

Problem 17 | 17 |

Problem 24 | 20 |

Problem 25 | 21 |

Problem 29 | 23 |

Problem 30 | 23 |

Problem 34 | 25 |

Problem 42 | 29 |

Problem 43 | 30 |

Problem 47 | 32 |

Problem 48 | 32 |

Problem 50 | 33 |

Problem 49 | 33 |

Problem 63 | 40 |

Problem 74 | 45 |

Problem 76 | 46 |

Problem 75 | 46 |

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.

Problem | Page |
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Problem 14 | 15 |

Problem 18 | 17 |

Problem 21 | 19 |

Problem 23 | 20 |

Problem 44 | 30 |

Problem 45 | 31 |

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.

Problem | Page |
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Problem 26 | 21 |

Problem 32 | 24 |

Problem 31 | 24 |

Problem 35 | 26 |

Problem 59 | 38 |

Problem 61 | 39 |

Problem 69 | 43 |

Problem 79 | 48 |

Problem 89 | 53 |

**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.)*

Problem | Page |
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Problem 1 | 9 |

Problem 3 | 10 |

Problem 6 | 11 |

Problem 7 | 12 |

Problem 8 | 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*.

Problem | Page |
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Problem 1 | 9 |

Problem 3 | 10 |

Problem 6 | 11 |

Problem 7 | 12 |

Problem 8 | 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:

Problem | Page |
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Problem 6 | 11 |

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 |

**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?*

Problem | Page |
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Problem 11 | 14 |

Problem 28 | 22 |

Problem 36 | 26 |

Problem 37 | 27 |

Problem 40 | 28 |

Problem 39 | 28 |

Problem 46 | 31 |

**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.

Problem | Page |
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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 |

*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.

Problem | Page |
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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 |

**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.

Problem | Page |
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Problem 4 | 10 |

Problem 5 | 11 |

Problem 12 | 14 |

Problem 21 | 19 |

Problem 52 | 34 |

Problem 51 | 34 |

Problem 53 | 35 |

Problem 54 | 35 |

Problem 56 | 36 |

Problem 55 | 36 |

Problem 58 | 37 |

Problem 57 | 37 |

Problem 60 | 38 |

Problem 59 | 38 |

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*.

Problem | Page |
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Problem 104 | 60 |

Problem 106 | 61 |

Problem 105 | 61 |

Problem 108 | 62 |

Problem 107 | 62 |

Problem 110 | 63 |

Problem 109 | 63 |

**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.

Problem | Page |
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Problem 84 | 50 |

Problem 86 | 51 |

Problem 85 | 51 |

Problem 88 | 52 |

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.

Problem | Page |
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Problem 86 | 51 |

Problem 85 | 51 |

Problem 88 | 52 |

Problem 89 | 53 |

Common Core State Standards and Expectations© Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved.