TEACHER GUIDE

FOR TH H E COMMON N CO CORE ORE S ST TAT E STANDAR TA S TANDARD R D S FO F O R M AT T H E M ATICS

3 2 1 INCLUDES Tier 1 – Tier 2 – Tier 3 Correlations Diagnostic Interviews for Every Common Core Cluster Tier 1 Lessons, Tier 2 Prerequisite Skills, and Tier 3 Scaffolded Examples with Answers

G RADE E 6

TEACHER GUIDE

Response to FOR THE COMMON CORE STATE STANDARDS FOR MATHEMATICS

GRADE 6

3 2

© Houghton Mifflin Harcourt Publishing Company

1

Includes Tier 1 – Tier 2 – Tier 3 Correlations Diagnostic Interviews for Every Common Core Cluster Tier 1 Lessons, Tier 2 Prerequisite Skills, and Tier 3 Scaffolded Examples with Answers

G REAT S OURCE • H EINEMANN • H OLT MCD OUGAL • R IGBY RIVERDEEP • R IVERSIDE PUBLISHING • S AXON • S TECK-VAUGHN

Math Expressions ©2013

3 2 1

UNIT

1

Rates, Ratios, and Proportions BIG IDEA 1

Tier 1 Lesson

Lesson 1

Factor Puzzles and the Multiplication Table

4

Lesson 2

Solving Factor Puzzles

4

Lesson 3

Rate Situations and Rate Tables

1, 3

Lesson 4

Rate Situations and Unit Rate Language

1, 3

Lesson 5

Unit Rates, Products, and Rate Tables

1, 3

BIG IDEA 2

Special Rate Situations and Graphing

Tier 1 Lesson

Lesson 6

Unit Pricing

7

Lesson 7

Constant Speed

7

BIG IDEA 3

Solve Problems with Ratio and Proportion

Tier 1 Lesson

Lesson 8

Ratio as Linked Rates

5

Lesson 9

Finding Linked Values in Ratio Tables

2

Lesson 10

Seeing Proportions in Ratio Tables

6

Lesson 11

Identify and Solve Proportion Situations

BIG IDEA 4 © Houghton Mifflin Harcourt Publishing Company

Multiplication and Rates

Identify, Solve, and Write Proportion Situations

Lesson 12

Solve Numeric Proportion Problems

Lesson 13

Basic Ratio Solution Strategies

Lesson 14

Write and Solve Proportion Problems

Lesson 15

Focus on Mathematical Practices

MATH EXPRESSIONS ©2013 CORRELATION

6, 8

Tier 1 Lesson 5, 6 8 6, 8 3, 7, 8

1

Math Expressions ©2013

3 2 1

UNIT

Area of Polygons BIG IDEA 1

3

Units of Area

53, 73

Lesson 2

Area of Any Right Triangle

53, 74

Lesson 3

Area of Any Parallelogram

53, 73

Lesson 4

Area of Any Triangle

53, 75

Lesson 5

Select the Needed Measurements

73, 75

Derive Area Formulas and Solve Problems: Trapezoids and Other Polygons

Tier 1 Lesson

Lesson 6

Area of Any Trapezoid

Lesson 7

Area of a Complex Figure

79

Lesson 8

Area of Any Regular Polygon

78

Lesson 9

Graph Polygons in the Coordinate Plane

83

Lesson 10

Focus on Mathematical Practices

53

76, 77

Operations with Whole Numbers, Fractions, and Decimals BIG IDEA 1

2

Tier 1 Lesson

Lesson 1

BIG IDEA 2

UNIT

Derive Area Formulas and Solve Problems: Parallelograms and Triangles

Multiplication and Division of Whole Numbers and Decimals

Tier 1 Lesson

Lesson 1

Place Value and Whole Number Division

26

Lesson 2

Estimated Multipliers in Division

26

Lesson 3

Multiplying by a Decimal

28

Lesson 4

Decimal Divisors

30

Lesson 5

Multiplication or Division

26, 28, 30

MATH EXPRESSIONS ©2013 CORRELATION

© Houghton Mifflin Harcourt Publishing Company

2

Math Expressions ©2013

3 2 1

BIG IDEA 2

Tier 1 Lesson

Lesson 6

Comparing, Adding, and Subtracting with the Same Unit

27, 41

Lesson 7

Equivalent Fractions or Decimals

40, 41

Lesson 8

Finding a Common Unit Fraction

32

Lesson 9

Mixed Problem Solving

BIG IDEA 3

Multiplying Fractions and Dividing with Fractions and Whole Numbers

27, 32

Tier 1 Lesson

Lesson 10

Multiplying with Fractions

35

Lesson 11

Dividing with Fractions and Whole Numbers

20

Lesson 12

Is It Multiplying or Dividing?

BIG IDEA 4

© Houghton Mifflin Harcourt Publishing Company

Relating, Composing, and Decomposing Decimals and Fractions

Dividing a Fraction by a Fraction

20, 35

Tier 1 Lesson

Lesson 13

Dividing Numerators and Denominators

20, 22

Lesson 14

Dividing by Unsimplifying

22, 35

Lesson 15

Dividing by Multiplying by the Reciprocal

22, 35

Lesson 16

Is it Multiplying or Dividing?

22, 35

Lesson 17

Mixed Practice with Decimals and Fractions

22, 27, 35

Lesson 18

Focus on Mathematical Practices

27, 28, 35

UNIT

4

Surface Area of Prisms and Pyramids BIG IDEA 1

Nets and Surface Area of Prisms

Tier 1 Lesson

Lesson 1

Nets and Surface Area for Rectangular Prisms

85

Lesson 2

Nets and Surface Area for Nonrectangular Prisms

84

Lesson 3

Surface Area of Prisms

86

BIG IDEA 2

Nets and Surface Area of Pyramids

Tier 1 Lesson

Lesson 4

Nets for Pyramids

84

Lesson 5

Surface Area of Pyramids

87

Lesson 6

Focus on Mathematical Practices

MATH EXPRESSIONS ©2013 CORRELATION

84, 85, 86

3

Math Expressions ©2013

3 2 1

UNIT

Expressions and Equations BIG IDEA 1

Tier 1 Lesson

Lesson 1

Expressions and Order of Operations

52, 53

Lesson 2

Expressions with Exponents

49, 50

Lesson 3

Interpreting and Analyzing Expressions

51, 52

Lesson 4

Modeling and Simplifying Expressions

51, 53

Lesson 5

Expressions for Area and Surface Area

51, 79, 86

BIG IDEA 2

Equivalent Expressions

Tier 1 Lesson

Lesson 6

Equivalent Expressions

55, 56

Lesson 7

The Commutative and Associative Properties

55, 56

Lesson 8

The Distributive Property

55, 56

Lesson 9

Practice with Expressions

59

BIG IDEA 3

Representing and Describing Quantitative Relationships

Tier 1 Lesson

Lesson 10

Relating Two Quantities

Lesson 11

Motion at a Constant Speed

70

Lesson 12

Relating Equations, Tables, and Graphs

72

Lesson 13

Writing Equations

60

BIG IDEA 4

4

Writing, Interpreting, and Analyzing Expressions

68, 69

Solving Equations and Inequalities

Tier 1 Lesson

Lesson 14

Inequalities

58, 66, 67

Lesson 15

Solutions of Equations and Inequalities

Lesson 16

Addition and Subtraction Equations

61, 62

Lesson 17

Multiplication and Division Equations

63, 64

Lesson 18

Focus on Mathematical Practices

69, 72

57

MATH EXPRESSIONS ©2013 CORRELATION

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5

Math Expressions ©2013

3 2 1

UNIT

6

UNIT

7

Volume of a Rectangular Prism BIG IDEA

Volume of Formulas for Rectangular Prisms

Lesson 1

What Is Volume?

82

Lesson 2

Fractional Unit Cubes

81

Lesson 3

Compose Rectangular Prisms with Fractional Edge Lengths

81

Lesson 4

Volume of Prisms with Fractional Edge Lengths

81, 82

Lesson 5

Write and Solve Equations About Volume

53, 82

Lesson 6

Focus on Mathematical Practices

88

Ratios and Rates with Fractions, Decimals, and Percents BIG IDEA 1

© Houghton Mifflin Harcourt Publishing Company

Tier 1 Lesson

Ratios, Fractions, Unit Rates, and Cross-Multiplying

Tier 1 Lesson

Lesson 1

Comparing Ratios

5, 7

Lesson 2

Unit Rates

8

Lesson 3

Ratios, Fractions, and Fraction Notation

4

Lesson 4

Understanding Cross-Multiplication

6

BIG IDEA 2

Ratios with Tape Diagrams and Equations

Tier 1 Lesson

Lesson 5

Describing Ratios with Tape Diagrams

1, 6

Lesson 6

Ratios and Multiplicative Comparisons

3

Lesson 7

Solve Ratio and Rate Problems

5

BIG IDEA 3

Percent

Tier 1 Lesson

Lesson 8

The Meaning of Percent

Lesson 9

Percent of a Number

12

Lesson 10

Percent Calculations

12, 14

Lesson 11

Solve Percent Problems

MATH EXPRESSIONS ©2013 CORRELATION

9, 10, 11

13

5

Math Expressions ©2013

3 2 1

BIG IDEA 4

Relate Different Measurement Units

Tier 1 Lesson

Lesson 12

Convert Units of Length

15

Lesson 13

Convert Units of Liquid Volume, Mass, and Weight

16, 17

Lesson 14

Focus on Mathematical Practices

2, 12

UNIT

Analyzing Statistics BIG IDEA 1

Displaying Data

Tier 1 Lesson

Lesson 1

Making Sense of Data

89, 93

Lesson 2

Dot Plots and Histograms

BIG IDEA 2

Tier 1 Lesson

Lesson 3

Making Data Groups Equal

Lesson 4

Use the Mean

Lesson 5

The Mean as a Balance Point

98

Lesson 6

Find and Use the Median

99

BIG IDEA 3

6

Summarizing Data: The Mean, the Median

93, 94, 95

Describing Variability in Data

98, 99 92, 98, 99

Tier 1 Lesson

Lesson 7

Variability in Data

92, 102

Lesson 8

Box Plots

96

Lesson 9

Mean Absolute Deviation

101

Lesson 10

Clusters, Peaks, Gaps, and Outliers

90, 103

Lesson 11

Collect, Display, and Interpret Data

95

Lesson 12

Focus on Mathematical Practices

90, 92

MATH EXPRESSIONS ©2013 CORRELATION

© Houghton Mifflin Harcourt Publishing Company

8

Math Expressions ©2013

3 2 1

UNIT

9

Rational Numbers and the Coordinate Plane BIG IDEA 1

Discuss, Compare, and Graph Integers

Tier 1 Lesson

Lesson 1

Negative Numbers in the Real World

37

Lesson 2

Integers on a Number Line

38

Lesson 3

Compare and Order Integers

43, 45

Lesson 4

Integers and the Coordinate Plane

39, 48

BIG IDEA 2

Discuss, Compare, and Graph Rational Numbers

Tier 1 Lesson

Lesson 5

Rational Numbers on a Number Line

38

Lesson 6

Compare and Order Rational Numbers

44

Lesson 7

Rational Numbers and the Coordinate Plane

Lesson 8

Focus on Mathematical Practices

42, 47

© Houghton Mifflin Harcourt Publishing Company

37, 39, 48

MATH EXPRESSIONS ©2013 CORRELATION

7