## Mathematics

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

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.

Activity Page
Multiplication with Modeling 35
Multiplying by 2 and 4 36
Multiplying by 0, 1, 2, and 4 37
Multiplying by 5 and 10 38
Multiplying by 9 40
Multiplying by 3, 6, and 9 41
Multiplying by 8 42
Multiplying by 2, 4, and 8 43
Multiplying by 7 44
Multiplication Tables 45
Square Numbers 46
Multiplication Review 48
Multiplication and Division 54
Using Number Lines 56
Inverse Operations 57
Which Order? 58
Missing Numbers 60
Operations Review 61
Calculator-Multiplication and Division 65

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 = ?

Activity Page
Multiplying by 2 and 4 36
Multiplying by 5 and 10 38
Multiplying by 3 and 6 39
Multiplying by 9 40
Multiplying by 3, 6, and 9 41
Multiplying by 8 42
Multiplying by 2, 4, and 8 43
Multiplying by 7 44
Multiplication Tables 45
Multiplication Review 48
Inverse Operations 57
Missing Numbers 60
Operations Review 61
Calculator-Multiplication and Division 65

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.

Activity Page
Sharing 49
Division as Repeated Subtraction 50
Division 51
Multiplication and Division 54
Division Review 55
Using Number Lines 56
Inverse Operations 57
Which Order? 58
Missing Numbers 60
Operations Review 61
Calculator-Multiplication and Division 65

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.

Activity Page
Division as Repeated Subtraction 50
Multiplication and Division 54
Division Review 55
Calculator-Multiplication and Division 65
Guided Problem Solving 129
Problem Solving 130

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.)

Activity Page
Multiplying by 0, 1, 2, and 4 37
Multiplying by 3 and 6 39
Multiplication and Division 54
Inverse Operations 57
Which Order? 58
Missing Numbers 60
Operations Review 61

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.

Activity Page
Sharing 49
Division 51
Multiplication and Division 54
Division Review 55
Using Number Lines 56
Inverse Operations 57
Bingo! 59
Missing Numbers 60
Operations Review 61
Calculator-Multiplication and Division 65

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.

Activity Page
Multiplication with Modeling 35
Multiplying by 2 and 4 36
Multiplying by 0, 1, 2, and 4 37
Multiplying by 5 and 10 38
Multiplying by 3 and 6 39
Multiplying by 9 40
Multiplying by 3, 6, and 9 41
Multiplying by 8 42
Multiplying by 2, 4, and 8 43
Multiplying by 7 44
Multiplication Tables 45
Square Numbers 46
Multiplication Review 48
Multiplication and Division 54
Using Number Lines 56
Inverse Operations 57
Which Order? 58
Bingo! 59
Missing Numbers 60
Operations Review 61

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.

Activity Page
Counting by Tens 10
Counting by Hundreds 11
Counting Forward and Backward 12
Patterns 13
Multiples 47
Rules for Patterns 62

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).

Activity Page
Guided Problem Solving 129

### 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.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
Counting by Tens 10
Multiplying by 5 and 10 38
Multiplication Tables 45

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
Counting by Hundreds 11
Expanding 3-Digit Numbers 14
Expanding 4-Digit Numbers 15
Looking for Ten When Adding 18
Adding with Regrouping to 99 19
Adding Three or More Numbers 20
Adding 3-Digit Numbers with Regrouping 21
Mental Math 22
Rounding Numbers 24
Subtraction 26
Subtraction Patterns 27
2-Digit Subtraction to 50 28
2-Digit Subtraction to 99 29
Subtraction with Regrouping 30
Subtraction with 3-Digit Numbers 31
Subtraction Strategies 32
Subtraction Review 34
Using Number Lines 56
Inverse Operations 57
Which Order? 58
Bingo! 59
Missing Numbers 60
Operations Review 61
Calculator â€“ Place Value 63
Calculator â€“ Addition and Subtraction 64
Money â€“ Coins 84
Money â€“ Bills 85
Money â€“ Addition and Subtraction 86
Money â€“ Rounding 88

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
Adding with Regrouping to 99 19
Rounding Numbers 24
Estimating 25
Money â€“ Rounding 88
Money â€“ Estimating 89

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

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.

Activity Page
Fraction Names 66
Naming Fractions 67
Comparing Fractions 68
Fractions of a Collection 69
Equivalent Fractions 70
Fractions Review 71
Hundredths 72
Fractions to Decimals 76
Decimals and Fractions 77
Less Than and Greater Than 78
Decimals Review 82

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.

Activity Page
Comparing Fractions 68
Counting Forward and Backward with Decimals 74
Decimals and Fractions 77
Less Than and Greater Than 78
Decimals Review 82

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.

Activity Page
Comparing Fractions 68
Equivalent Fractions 70
Fractions Review 71
Hundredths 72
Tenths 73
Less Than and Greater Than 78

### 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.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.

Activity Page
Digital and Analog Time 110
Calendars 111
Timelines and Timetables 112

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").

Activity Page
Capacity in Liters 120
Capacity - Formal 121
Cubic Inches 122
Cubic Centimeters 123

Represent and interpret data.

Math.3.MD.B.4: Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Show the data by making a line plot, where the horizontal scale is marked off in appropriate units— whole numbers, halves, or quarters.

Activity Page
Length in Inches 113
Length in Inches and Feet 115
Perimeter 118

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
Picture Graphs 126
Bar Graphs 128

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).

Activity Page
Area 119

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 119

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 119

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.

Activity Page
Perimeter 118

### 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.

Activity Page
Two-Dimensional Shapes 91
Pentagons and Octagons 92
Trapezoids and Parallelograms 93
Shape Designs 94
Regular and Irregular Shapes 95