**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.

Problem | Page |
---|---|

Problem 13 | 15 |

Problem 56 | 36 |

Problem 57 | 37 |

Problem 58 | 37 |

Problem 60 | 38 |

Problem 63 | 40 |

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.

Problem | Page |
---|---|

Problem 24 | 20 |

Problem 26 | 21 |

Problem 25 | 21 |

Problem 28 | 22 |

Problem 27 | 22 |

Problem 30 | 23 |

Problem 29 | 23 |

Problem 31 | 24 |

Problem 32 | 24 |

Problem 34 | 25 |

Problem 33 | 25 |

Problem 36 | 26 |

Problem 35 | 26 |

Problem 38 | 27 |

Problem 37 | 27 |

Problem 40 | 28 |

Problem 39 | 28 |

Problem 42 | 29 |

Problem 41 | 29 |

Problem 43 | 30 |

Problem 44 | 30 |

Problem 46 | 31 |

Problem 45 | 31 |

Problem 48 | 32 |

Problem 47 | 32 |

Problem 50 | 33 |

Problem 49 | 33 |

Problem 51 | 34 |

Problem 52 | 34 |

Problem 55 | 36 |

Problem 61 | 39 |

Problem 62 | 39 |

Problem 64 | 40 |

Problem 63 | 40 |

Problem 66 | 41 |

Problem 65 | 41 |

Problem 67 | 42 |

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*.

Problem | Page |
---|---|

Problem 29 | 23 |

Problem 83 | 50 |

Problem 91 | 54 |

Problem 95 | 56 |

Problem 107 | 62 |

**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.

Problem | Page |
---|---|

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*.

Problem | Page |
---|---|

Problem 26 | 21 |

Problem 25 | 21 |

Problem 28 | 22 |

Problem 27 | 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.

Problem | Page |
---|---|

Problem 6 | 11 |

Problem 5 | 11 |

Problem 8 | 12 |

Problem 7 | 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.

Problem | Page |
---|---|

Problem 24 | 20 |

Problem 26 | 21 |

Problem 25 | 21 |

Problem 28 | 22 |

Problem 27 | 22 |

Problem 31 | 24 |

Problem 32 | 24 |

Problem 33 | 25 |

Problem 37 | 27 |

Problem 38 | 27 |

Problem 39 | 28 |

Problem 40 | 28 |

Problem 42 | 29 |

Problem 41 | 29 |

Problem 44 | 30 |

Problem 43 | 30 |

Problem 45 | 31 |

Problem 46 | 31 |

Problem 47 | 32 |

Problem 50 | 33 |

Problem 49 | 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.

Problem | Page |
---|---|

Problem 56 | 36 |

Problem 55 | 36 |

Problem 58 | 37 |

Problem 57 | 37 |

Problem 60 | 38 |

Problem 62 | 39 |

Problem 61 | 39 |

Problem 64 | 40 |

Problem 63 | 40 |

Problem 65 | 41 |

Problem 66 | 41 |

Problem 67 | 42 |

Problem 69 | 43 |

Problem 70 | 43 |

Problem 73 | 45 |

**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.

Problem | Page |
---|---|

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*.

Problem | Page |
---|---|

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.

Problem | Page |
---|---|

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*.

Problem | Page |
---|---|

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.

Problem | Page |
---|---|

Problem 74 | 45 |

Problem 98 | 57 |

**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), ...*

Problem | Page |
---|---|

Problem 1 | 9 |

Problem 3 | 10 |

Problem 12 | 14 |

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 |

**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.

Problem | Page |
---|---|

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 |

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.