## Mathematics

### Domain - Operations and Algebraic Thinking, Grade 3

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.

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Multiplication Within 100 13
Division Within 100 14
Multiplication and Division Within 100 16
Word Problems with Mixed Operations 17
Multiplication Within 100 38
Division Within 100 39
Multiplication and Division Within 100 41
Word Problems with Mixed Operations 42
Multiplication Within 100 63
Division Within 100 64
Multiplication and Division Within 100 66
Word Problems with Mixed Operations 67

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.)

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Relating Multiplication and Division Within 100 15
Relating Multiplication and Division Within 100 40
Relating Multiplication and Division Within 100 65

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).

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Word Problems with Mixed Operations 17
Multiple-step Problems with Two Questions 18
Multiple-step Problems with a Hidden Question 19
Estimate Sums 21
Estimate Products 22
Word Problems with Mixed Operations 42
Multiple-step Problems with Two Questions 43
Multiple-step Problems with a Hidden Question 44
Estimate Sums 46
Estimate Products 47
Word Problems with Mixed Operations 67
Multiple-step Problems with Two Questions 68
Multiple-step Problems with a Hidden Question 69
Estimate Sums 71
Estimate Products 72

### Domain - Number and Operations in Base Ten, Grade 3

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.

Activity Page

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.

Activity Page
Estimation and Rounding 20
Estimate Sums 21
Estimation and Rounding 45
Estimate Sums 46
Estimation and Rounding 70
Estimate Sums 71

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.

Activity Page
Estimate Products 22
Estimate Products 47
Estimate Products 72

### Domain - Number and Operations-Fractions, Grade 3

Develop understanding of fractions as numbers.

Math.3.NF.A.2: Understand a fraction as a number on the number line; represent fractions on a number line diagram.

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Fractions 23
Fractions 48
Fractions 73

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.

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Comparing Fractions 24
Comparing Fractions 49
Comparing Fractions 74

### Domain - Develop understanding of fractions as numbers., Grade 3

Understand a fraction as a number on the number line; represent fractions on a number line diagram.

Math.3.NF.A.2a: Represent a fraction 1/b on a number line diagram by defining the interval from 0 to 1 as the whole and partitioning it into b equal parts. Recognize that each part has size 1/b and that the endpoint of the part based at 0 locates the number 1/b on the number line.

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Fractions 23
Fractions 48
Fractions 73

Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size.

Math.3.NF.A.3b: Recognize and generate simple equivalent fractions, e.g., 1/2 = 2/4, 4/6 = 2/3). Explain why the fractions are equivalent, e.g., by using a visual fraction model.

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Comparing Fractions 24
Comparing Fractions 49
Comparing Fractions 74

Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size.

Math.3.NF.A.3a: Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line.

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Comparing Fractions 24
Comparing Fractions 49
Comparing Fractions 74

Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size.

Math.3.NF.A.3c: Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers. Examples: Express 3 in the form 3 = 3/1; recognize that 6/1 = 6; locate 4/4 and 1 at the same point of a number line diagram.

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More Fractions 25
More Fractions 50
More Fractions 75

### Domain - Measurement and Data, Grade 3

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

Math.3.MD.A.2: Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l).(Excludes compound units such as cm3 and finding the geometric volume of a container) Add, subtract, multiply, or divide to solve one-step word problems involving masses or volumes that are given in the same units, e.g., by using drawings (such as a beaker with a measurement scale) to represent the problem.(Excludes multiplicative comparison problems (problems involving notions of "times as much").

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Metric Units 26
Metric Units 51
Metric Units 76

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.

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Time to the Half Hour and Quarter Hour 28
Time to the Minute 29
Elapsed Time 30
Units of Time 31
Time to the Half Hour and Quarter Hour 53
Time to the Minute 54
Elapsed Time 55
Units of Time 56
Time to the Half Hour and Quarter Hour 78
Time to the Minute 79
Elapsed Time 80
Units of Time 81

Represent and interpret data.

Math.3.MD.B.3: Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and two-step “how many more” and “how many less” problems using information presented in scaled bar graphs. For example, draw a bar graph in which each square in the bar graph might represent 5 pets.

Activity Page
Addition and Subtraction with Bar Graphs 11
Addition and Subtraction with Pictographs 12
Addition and Subtraction with Bar Graphs 36
Addition and Subtraction with Pictographs 37
Addition and Subtraction with Bar Graphs 61
Addition and Subtraction with Pictographs 62

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.

Activity Page
Area 33
Area 58
Area 83

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.

Activity Page
Area 33
Area 58
Area 83

Geometric measurement: recognize perimeter as an attribute of plane figures and distinguish between linear and area measures.

Math.3.MD.D.8: Solve real world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters.

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Perimeter 32
Perimeter and Area 34
Perimeter 57
Perimeter and Area 59
Perimeter 82
Perimeter and Area 84

### Domain - Geometry, Grade 3

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.

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Two-dimensional Shapes 27
Two-dimensional Shapes 52
Two-dimensional Shapes 77