**Represent and solve problems involving multiplication and division.**

*Math.3.OA.A.4*: Determine the unknown whole number in a multiplication or division equation relating three whole numbers. *For example, determine the unknown number that makes the equation true in each of the equations 8 × ? = 48, 5 = _ ÷ 3, 6 × 6 = ?*

Problem | Page |
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Problem 2 | 9 |

Problem 49 | 33 |

Problem 54 | 35 |

Problem 57 | 37 |

Problem 58 | 37 |

Problem 60 | 38 |

Problem 61 | 39 |

Problem 62 | 39 |

Problem 64 | 40 |

Problem 63 | 40 |

Problem 65 | 41 |

Problem 67 | 42 |

**Represent and solve problems involving multiplication and division.**

*Math.3.OA.A.3*: Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.

Problem | Page |
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Problem 2 | 9 |

Problem 7 | 12 |

Problem 33 | 25 |

Problem 34 | 25 |

Problem 35 | 26 |

Problem 39 | 28 |

Problem 40 | 28 |

Problem 41 | 29 |

Problem 46 | 31 |

Problem 48 | 32 |

Problem 47 | 32 |

Problem 49 | 33 |

Problem 51 | 34 |

Problem 54 | 35 |

Problem 56 | 36 |

Problem 55 | 36 |

Problem 57 | 37 |

Problem 58 | 37 |

Problem 60 | 38 |

Problem 61 | 39 |

Problem 62 | 39 |

Problem 63 | 40 |

Problem 64 | 40 |

Problem 65 | 41 |

Problem 67 | 42 |

**Represent and solve problems involving multiplication and division.**

*Math.3.OA.A.1*: Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each. *For example, describe a context in which a total number of objects can be expressed as 5 × 7*.

Problem | Page |
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Problem 34 | 25 |

Problem 33 | 25 |

Problem 35 | 26 |

Problem 38 | 27 |

Problem 37 | 27 |

Problem 39 | 28 |

Problem 40 | 28 |

Problem 41 | 29 |

Problem 44 | 30 |

Problem 46 | 31 |

Problem 47 | 32 |

Problem 48 | 32 |

Problem 50 | 33 |

Problem 49 | 33 |

Problem 51 | 34 |

Problem 54 | 35 |

Problem 56 | 36 |

**Represent and solve problems involving multiplication and division.**

*Math.3.OA.A.2*: Interpret whole-number quotients of whole numbers, e.g., interpret 56 ÷ 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each. *For example, describe a context in which a number of shares or a number of groups can be expressed as 56 ÷ 8*.

Problem | Page |
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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 67 | 42 |

Problem 70 | 43 |

Problem 71 | 44 |

**Understand properties of multiplication and the relationship between multiplication and division.**

*Math.3.OA.B.5*: Apply properties of operations as strategies to multiply and divide. *Examples: If 6 × 4 = 24 is known, then 4 × 6 = 24 is also known. (Commutative property of multiplication.) 3 × 5 × 2 can be found by 3 × 5 = 15, then 15 × 2 = 30, or by 5 × 2 = 10, then 3 × 10 = 30. (Associative property of multiplication.) Knowing that 8 × 5 = 40 and 8 × 2 = 16, one can find 8 × 7 as 8 × (5 + 2) = (8 × 5) + (8 × 2) = 40 + 16 = 56. (Distributive property.)*

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

Problem 2 | 9 |

Problem 7 | 12 |

Problem 34 | 25 |

Problem 33 | 25 |

Problem 35 | 26 |

Problem 40 | 28 |

Problem 39 | 28 |

Problem 41 | 29 |

Problem 46 | 31 |

Problem 47 | 32 |

Problem 48 | 32 |

Problem 49 | 33 |

Problem 51 | 34 |

Problem 54 | 35 |

Problem 55 | 36 |

Problem 56 | 36 |

Problem 58 | 37 |

Problem 57 | 37 |

Problem 60 | 38 |

Problem 61 | 39 |

Problem 62 | 39 |

Problem 64 | 40 |

Problem 63 | 40 |

Problem 65 | 41 |

Problem 67 | 42 |

Problem 70 | 43 |

Problem 71 | 44 |

**Understand properties of multiplication and the relationship between multiplication and division.**

*Math.3.OA.B.6*: Understand division as an unknown-factor problem. *For example, find 32 ÷ 8 by finding the number that makes 32 when multiplied by 8*.

Problem | Page |
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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 67 | 42 |

Problem 70 | 43 |

Problem 71 | 44 |

**Multiply and divide within 100.**

*Math.3.OA.C.7*: Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 × 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers.

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

Problem 2 | 9 |

Problem 7 | 12 |

Problem 33 | 25 |

Problem 34 | 25 |

Problem 35 | 26 |

Problem 39 | 28 |

Problem 40 | 28 |

Problem 41 | 29 |

Problem 46 | 31 |

Problem 47 | 32 |

Problem 48 | 32 |

Problem 49 | 33 |

Problem 51 | 34 |

Problem 54 | 35 |

Problem 55 | 36 |

Problem 56 | 36 |

Problem 58 | 37 |

Problem 57 | 37 |

Problem 60 | 38 |

Problem 61 | 39 |

Problem 62 | 39 |

Problem 64 | 40 |

Problem 63 | 40 |

Problem 65 | 41 |

Problem 67 | 42 |

Problem 70 | 43 |

Problem 71 | 44 |

**Solve problems involving the four operations, and identify and explain patterns in arithmetic.**

*Math.3.OA.D.8*: Solve two-step word problems using the four operations. 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.(This standard is limited to problems posed with whole numbers and having whole-number answers; students should know how to perform operations in the conventional order when there are no parentheses to specify a particular order).

Problem | Page |
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Problem 7 | 12 |

Problem 12 | 14 |

Problem 13 | 15 |

Problem 25 | 21 |

Problem 59 | 38 |

Problem 80 | 48 |

Problem 82 | 49 |

Problem 81 | 49 |

Problem 83 | 50 |

Problem 84 | 50 |

Problem 85 | 51 |

Problem 86 | 51 |

Problem 88 | 52 |

Problem 87 | 52 |

Problem 90 | 53 |

**Solve problems involving the four operations, and identify and explain patterns in arithmetic.**

*Math.3.OA.D.9*: Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations. *For example, observe that 4 times a number is always even, and explain why 4 times a number can be decomposed into two equal addends*.

Problem | Page |
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Problem 7 | 12 |

Problem 20 | 18 |

Problem 50 | 33 |

Problem 53 | 35 |

Problem 59 | 38 |

Problem 73 | 45 |

Problem 80 | 48 |

Problem 81 | 49 |

Problem 86 | 51 |

Problem 85 | 51 |

Problem 87 | 52 |

Problem 90 | 53 |

**Use place value understanding and properties of operations to perform multi-digit arithmetic.4**

*Math.3.NBT.A.2*: Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction.

Problem | Page |
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Problem 1 | 9 |

Problem 3 | 10 |

Problem 4 | 10 |

Problem 6 | 11 |

Problem 14 | 15 |

Problem 16 | 16 |

Problem 15 | 16 |

Problem 18 | 17 |

Problem 17 | 17 |

Problem 19 | 18 |

Problem 22 | 19 |

Problem 21 | 19 |

Problem 24 | 20 |

Problem 23 | 20 |

Problem 29 | 23 |

Problem 30 | 23 |

Problem 77 | 47 |

Problem 78 | 47 |

Problem 79 | 48 |

**Use place value understanding and properties of operations to perform multi-digit arithmetic.4**

*Math.3.NBT.A.1*: Use place value understanding to round whole numbers to the nearest 10 or 100.

Problem | Page |
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Problem 5 | 11 |

Problem 12 | 14 |

Problem 13 | 15 |

Problem 25 | 21 |

Problem 88 | 52 |

**Use place value understanding and properties of operations to perform multi-digit arithmetic.4**

*Math.3.NBT.A.3*: Multiply one-digit whole numbers by multiples of 10 in the range 10–90 (e.g., 9 × 80, 5 × 60) using strategies based on place value and properties of operations.

Problem | Page |
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Problem 41 | 29 |

Problem 53 | 35 |

Problem 58 | 37 |

Problem 82 | 49 |

Problem 85 | 51 |

**Develop understanding of fractions as numbers.**

*Math.3.NF.A.3*: Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size.

Problem | Page |
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Problem 76 | 46 |

Problem 75 | 46 |

Problem 99 | 58 |

Problem 100 | 58 |

**Develop understanding of fractions as numbers.**

*Math.3.NF.A.1*: Understand a fraction 1/*b* as the quantity formed by 1 part when *a* whole is partitioned into *b* equal parts; understand a fraction *a*/*b* as the quantity formed by a parts of size 1/*b*.

Problem | Page |
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Problem 98 | 57 |

**Solve problems involving measurement and estimation of intervals of time, liquid volumes, and masses of objects.**

*Math.3.MD.A.1*: Tell and write time to the nearest minute and measure time intervals in minutes. Solve word problems involving addition and subtraction of time intervals in minutes, e.g., by representing the problem on a number line diagram.

Problem | Page |
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Problem 8 | 12 |

Problem 9 | 13 |

Problem 10 | 13 |

Problem 11 | 14 |

Problem 26 | 21 |

Problem 28 | 22 |

Problem 27 | 22 |

Problem 89 | 53 |

**Geometric measurement: understand concepts of area and relate area to multiplication and to addition.**

*Math.3.MD.C.7*: Relate area to the operations of multiplication and addition.

Problem | Page |
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Problem 42 | 29 |

Problem 104 | 60 |

Problem 103 | 60 |

**Geometric measurement: understand concepts of area and relate area to multiplication and to addition.**

*Math.3.MD.C.6*: Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units).

Problem | Page |
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Problem 42 | 29 |

Problem 104 | 60 |

Problem 103 | 60 |

**Geometric measurement: understand concepts of area and relate area to multiplication and to addition.**

*Math.3.MD.C.5*: Recognize area as an attribute of plane figures and understand concepts of area measurement.

Problem | Page |
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Problem 42 | 29 |

Problem 104 | 60 |

Problem 103 | 60 |

**Reason with shapes and their attributes.**

*Math.3.G.A.2*: Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole. *For example, partition a shape into 4 parts with equal area, and describe the area of each part as 1/4 of the area of the shape*.

Problem | Page |
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Problem 100 | 58 |

**Reason with shapes and their attributes.**

*Math.3.G.A.1*: Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories.

Problem | Page |
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Problem 102 | 59 |

Problem 101 | 59 |

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.