## Common Core State Standards (CCSS) Correlations ## Mathematics

### Domain - Operations and Algebraic Thinking, Grade 5

Write and interpret numerical expressions.

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

Activity Page
Multiples and Square Numbers 30
Factors 31
Order of Operations 45
Reasoning with Numbers 51
Mixed Practice 124

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.

Activity Page
Reasoning with Numbers 51

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.

Activity Page
Number Patterns 12
Multiples and Square Numbers 30
Number Lines and Operations 42
Working with Numbers 47
Calculator Addition, Subtraction, and Multiplication 53
Geometric Patterns 92
Problem Solving 123

### Domain - Number and Operations in Base Ten, Grade 5

Understand the place value system.

Math.5.NBT.A.1: Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left.

Activity Page
Numbers to 99,999 7
Place Value 0 to 99,999 8
Ordering Numbers 9
Place Value 0.01 to 99,999 10
Numbers to 999,999 11
Expanding Numbers 13
Less Than and Greater Than 15
Division by Tens 38
Working with Numbers 47
Decimals 63
Decimal Place Value - Hundredths 64
Decimal Place Value - Thousandths 65

Understand the place value system.

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

Activity Page
Place Value 0.01 to 99,999 10
Number Patterns 12

Understand the place value system.

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

Activity Page
Estimation 24
Calculator Division 54
Rounding Decimals 72
Use of Money 75
Money Rounding 77

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.

Activity Page
Multiplication by Tens and Hundreds 26
Multiplication to 999 27
Multiplication to 9,999 28
Working with Numbers 47
Decimal Multiplication and Division 71

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.

Activity Page
Multiplication to 999 27
Multiplication to 9,999 28
Extended Multiplication 29
Multiplication and Problem Solving 32
Number Lines and Operations 42
Operations with Large Numbers 46
Missing Numbers 48
Variables 49
Multiplication and Division Practice 126

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.

Activity Page
Division 33
Division of 2-Digit Numbers 34
Division Involving Zeros 35
Divisibility 36
Division of 3-Digit Numbers 37
Division by Tens 38
Division of 4-Digit Numbers 39
Number Lines and Operations 42
Averages 43
Mean 44
Operations with Large Numbers 46
Missing Numbers 48
Variables 49
Multiplication and Division Practice 126

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.

Activity Page
Comparing Decimals 66
Decimal Subtraction 68
Decimal Multiplication 69
Decimal Division 70
Decimal Multiplication and Division 71
Rounding Decimals 72
Use of Money 75
Money Operations 76
Money Rounding 77
Digital and Analog Time 104
A.M. and P.M. Time 105
Timetables and Time Lines 106
Time Zones 107
Mixed Practice 124
Decimals Practice 128

### Domain - Number and Operations-Fractions, Grade 5

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.

Activity Page
Fraction Subtraction 61
Fractions Practice 127

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.)

Activity Page
Fraction Subtraction 61
Fractions Practice 127

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.

Activity Page
Number Patterns 12
Fraction of a Group 56
Percentages 73
Fractions, Decimals, and Percentages 74

Apply and extend previous understandings of multiplication and division to multiply and divide fractions.

Math.5.NF.B.7: Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions.

Activity Page
Number Patterns 12

Apply and extend previous understandings of multiplication and division to multiply and divide fractions.

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.

Activity Page
Number Patterns 12
Fraction of a Group 56
Percentages 73
Fractions, Decimals, and Percentages 74

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:

Activity Page
Fraction of a Group 56
Percentages 73
Fractions, Decimals, and Percentages 74

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?

Activity Page
Decimals 63
Decimal Place Value - Thousandths 65
Fractions, Decimals, and Percentages 74
Weight in Ounces and Pounds 113
Fractions Practice 127

### Domain - Measurement and Data, Grade 5

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.

Activity Page
Converting Units 50
Length in Centimeters, Inches, and Feet 108
Length in Miles 109
Weight in Ounces and Pounds 113
Weight in Pounds and Tons 114

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

Math.5.MD.C.3: Recognize volume as an attribute of solid figures and understand concepts of volume measurement.

Activity Page
Sections of Solids 94
Nets and 3D Objects 95
Shapes - General Review 96
Volume 115

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

Math.5.MD.C.5: Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume.

Activity Page
Volume 115

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

Math.5.MD.C.4: Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units.

Activity Page
Volume 115

### Domain - Geometry, Grade 5

Graph points on the coordinate plane to solve real-world and mathematical problems.

Math.5.G.A.1: Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate).

Activity Page
Coordinates 99
Coordinates and Shapes 100
Coordinates and Scale 101
Map Grid 103

Graph points on the coordinate plane to solve real-world and mathematical problems.

Math.5.G.A.2: Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation.

Activity Page
Coordinates 99
Coordinates and Shapes 100

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.

Activity Page
Angles in 2D Shapes 82
Triangles 86
Polygons 88
Parallelograms and Rhombuses 91
Geometric Patterns 92
Shapes - General Review 96
Horizontal and Vertical Lines 97
Perimeter 110
Area of Squares and Rectangles 111
Area of Triangles 112

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.

Activity Page
Triangles 86
Polygons 88
Parallelograms and Rhombuses 91
Geometric Patterns 92
Shapes - General Review 96