chapter number properties 1 and decimalsassets.pearsonschool.com/asset_mgr/current/201322/... ·...

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Check Your Readiness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1-1 Properties of Operations 6.EE.2.b, 6.EE.3 . . . . . . . . . . . . . . . . . . . . . . . . . 4 1-2 Order of Operations 6.EE.2.b, 6.EE.2.c . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 Checkpoint Quiz 1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 1-3a Activity Lab Hands On: Exploring Decimal Models . . . . . . . . . 13 1-3 Understanding Decimals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 1-4a Activity Lab Hands On: Using Models . . . . . . . . . . . . . . . . . . . 18 1-4 Adding and Subtracting Decimals 6.NS.3 . . . . . . . . . . . . . . . . . . . . . . . 19 Vocabulary Builder: High-Use Academic Words, 23 1-5a Activity Lab: Modeling Decimal Multiplication . . . . . . . . . . . . 24 1-5 Multiplying Decimals 6.NS.3, 6.EE.2.b . . . . . . . . . . . . . . . . . . . . . . . . . . 25 1-5b Activity Lab Technology: Multiplying and Dividing Decimals by 10, 100, and 1,000 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 Checkpoint Quiz 2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 1-6 Dividing Decimals 6.NS.2, 6.NS.3, 6.EE.2.b . . . . . . . . . . . . . . . . . . . . . . . . 31 1-6b Activity Lab Data Analysis: Using Decimals 6.NS.3 . . . . . . . . . . 36 Guided Problem Solving: Choosing the Right Operation, 37 Assessment and Test Prep Test-Taking Strategies: Writing Gridded Responses, 39 • Chapter Review, 40 • Chapter Test, 42 Test Prep: Reading Comprehension, 43 Number Properties and Decimals CHAPTER 1 x Contents In this chapter, you will fluently add, subtract, multiply, and divide decimals using standard algorithms. You will also identify the parts of an expression using mathematical terms and evaluate numerical expressions using the order of operations. Expressions & Equations 6.EE.2.b 6.EE.2.c 6.EE.3 The Number System 6.NS.2 6.NS.3 441190_c1_FM_TOC_px-xviii.indd 10 9/5/12 12:43 PM PEARSON LEARNING SOLUTIONS Not for resale or distribution

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Page 1: CHAPTER Number Properties 1 and Decimalsassets.pearsonschool.com/asset_mgr/current/201322/... · Check Your Readiness. . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Check Your Readiness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2

1-1 Properties of Operations 6.EE.2.b, 6.EE.3 . . . . . . . . . . . . . . . . . . . . . . . . .4

1-2 Order of Operations 6.EE.2.b, 6.EE.2.c . . . . . . . . . . . . . . . . . . . . . . . . . . .8

Checkpoint Quiz 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .12

1-3a Activity Lab Hands On: Exploring Decimal Models . . . . . . . . .13

1-3 Understanding Decimals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .14

1-4a Activity Lab Hands On: Using Models . . . . . . . . . . . . . . . . . . .18

1-4 Adding and Subtracting Decimals 6.NS.3 . . . . . . . . . . . . . . . . . . . . . . .19

• Vocabulary Builder: High-Use Academic Words, 23

1-5a Activity Lab: Modeling Decimal Multiplication . . . . . . . . . . . .24

1-5 Multiplying Decimals 6.NS.3, 6.EE.2.b . . . . . . . . . . . . . . . . . . . . . . . . . .25

1-5b Activity Lab Technology: Multiplying and Dividing Decimals by 10, 100, and 1,000 . . . . . . . . . . . . . . . . . . . . . . . . . . . .29

Checkpoint Quiz 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .30

1-6 Dividing Decimals 6.NS.2, 6.NS.3, 6.EE.2.b . . . . . . . . . . . . . . . . . . . . . . . .31

1-6b Activity Lab Data Analysis: Using Decimals 6.NS.3 . . . . . . . . . .36

• Guided Problem Solving: Choosing the Right Operation, 37

Assessment and Test Prep

• Test-Taking Strategies: Writing Gridded Responses, 39• Chapter Review, 40• Chapter Test, 42• Test Prep: Reading Comprehension, 43

Number Properties and Decimals

CHAPTER

1

x Contents

In this chapter, you will fl uently

add, subtract, multiply, and divide

decimals using standard algorithms.

You will also identify the parts of an

expression using mathematical terms

and evaluate numerical expressions

using the order of operations.

Expressions & Equations6.EE.2.b6.EE.2.c6.EE.3

The Number System6.NS.26.NS.3

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PEARSON LEARNING SOLUTIONS Not for resale or distribution

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Contents xi

Check Your Readiness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .44

2-1a Activity Lab Hands On: Patterns and Expressions 6.EE.2 . . . . .46

2-1 Variables and Expressions 6.EE.2, 6.EE.2.c, 6.EE.6 . . . . . . . . . . . . . . . . . .47

2-2a Activity Lab Algebra Thinking: Modeling Expressions 6.EE.2, 6.EE.2.a, 6.EE.2.b . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .51

2-2 Writing Algebraic Expressions 6.EE.2, 6.EE.2.a, 6.EE.2.b, 6.EE.6 . . . . . . . .52

Checkpoint Quiz 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .57

2-3 Using Number Sense to Solve One-Step Equations 6.EE.5, 6.EE.6, 6.EE.7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .58

• Vocabulary Builder: High-Use Academic Words, 62

2-4a Activity Lab Hands On: Modeling Equations 6.EE.5, 6.EE.6, 6.EE.7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .63

2-4 Solving Addition Equations 6.EE.5, 6.EE.6, 6.EE.7 . . . . . . . . . . . . . . . . . .64

2-5 Solving Subtraction Equations 6.EE.5, 6.EE.6, 6.EE.7 . . . . . . . . . . . . . . .68

Checkpoint Quiz 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .71

2-6a Activity Lab Hands On: Modeling Division Equations 6.EE.5, 6.EE.6, 6.EE.7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .71

2-6 Solving Multiplication and Division Equations 6.EE.5, 6.EE.6, 6.EE.7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .72

• Guided Problem Solving: Writing Equations to Solve Problems, 77

Assessment and Test Prep

• Test-Taking Strategies: Writing Short Responses, 79

• Chapter Review, 80• Chapter Test, 82• Test Prep: Cumulative Review, 83

Expressions and Equations

CHAPTER

2

In this chapter, you will extend

your understanding of arithmetic to

algebraic expressions and equations.

You will use letters as variables to

represent unknown numerical values

and write expressions and solve

equations of the form x + p = q and px = q.

Expressions & Equations6.EE.26.EE.2.a6.EE.2.b6.EE.2.c6.EE.56.EE.66.EE.7

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Check Your Readiness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .84

3-1 Divisibility and Mental Math . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .86

3-2 Exponents 6.EE.1, 6.EE.2, 6.EE.2.c . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .90

3-3 Prime Numbers and Prime Factorization . . . . . . . . . . . . . . . . . . . . . .94

Checkpoint Quiz 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .98

3-4 Greatest Common Factor 6.NS.4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .99

3-5 Least Common Multiple 6.NS.4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .103

3-6 The Distributive Property 6.EE.2.b, 6.EE.3, 6.EE.4 . . . . . . . . . . . . . . . . .107

• Vocabulary Builder: Making Word Lists, 112

Checkpoint Quiz 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .112

3-7 Simplifying Algebraic Expressions 6.EE.2.b, 6.EE.3, 6.EE.4 . . . . . . . . . .113

• Guided Problem Solving: Practice Solving Problems, 117

Assessment and Test Prep

• Test-Taking Strategies: Writing Extended Responses, 119• Chapter Review, 120• Chapter Test, 122• Test Prep: Reading Comprehension, 123

Number TheoryCHAPTER

3

In this chapter, you will apply

your understanding of place value,

operations, and inverse properties

of operations to explore algebraic

number theory. You will fi nd the

greatest common factor and least

common multiple of two whole

numbers. You will also use the

distributive property and identify

when two expressions are equivalent.

The Number System6.NS.4

Expressions & Equations6.EE.16.EE.26.EE.2.b6.EE.2.c6.EE.36.EE.4

xii Contents

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Contents xiii

Check Your Readiness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .124

4-1a Activity Lab Hands On: Modeling Fraction Multiplication . . .126

4-1 Multiplying Fractions and Mixed Numbers . . . . . . . . . . . . . . . . . . .127

4-2 Modeling Fraction Division 6.NS.1 . . . . . . . . . . . . . . . . . . . . . . . . . . .132

4-3 Dividing Fractions 6.NS.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .136

4-4 Dividing Mixed Numbers 6.NS.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . .140

4-4b Activity Lab Technology: Using a Calculator for Fractions 6.NS.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .144

Checkpoint Quiz 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .145

4-5 Equations with Fractions 6.EE.6, 6.EE.7 . . . . . . . . . . . . . . . . . . . . . . .146

• Guided Problem Solving: Practice Solving Problems, 151

Assessment and Test Prep

• Test-Taking Strategies: Eliminating Answers, 153• Chapter Review, 154• Chapter Test, 156• Test Prep: Reading Comprehension, 157

Fraction OperationsCHAPTER

4

In this chapter, you will apply and

extend previous understandings

of multiplication and division of

fractions. You will draw on your

knowledge of operations, fractions,

multiples, and factors to multiply

and divide fractions and mixed

numbers. You will apply these skills

as you write and solve equations

involving multiplication and division

of fractions.

The Number System6.NS.1

Expressions & Equations6.EE.66.EE.7

Contents

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xiv Contents

Check Your Readiness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .158

5-1 Ratios 6.RP.1, 6.RP.3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .160

5-1b Activity Lab Hands On: Modeling Ratios 6.RP.3 . . . . . . . . . . .164

• Vocabulary Builder: Making Word Lists, 165

5-2 Unit Rates 6.RP.2, 6.RP.3, 6.RP.3.b . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .166

5-3 Equivalent Ratios and Rates 6.RP.3, 6.RP.3.a . . . . . . . . . . . . . . . . . . . .170

5-4 Using Ratios to Convert Measurement Units 6.RP.3.d . . . . . . . . . . . .174

Checkpoint Quiz 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .178

5-5 Understanding Percents 6.RP.3.c . . . . . . . . . . . . . . . . . . . . . . . . . . . . .179

5-6a Activity Lab Hands On: Modeling Percents 6.RP.3.c . . . . . . . .183

5-6 Percents, Fractions, and Decimals . . . . . . . . . . . . . . . . . . . . . . . . . .184

5-7 Finding the Percent of a Number 6.RP.3.c . . . . . . . . . . . . . . . . . . . . .188

Checkpoint Quiz 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .192

5-8 Finding the Whole 6.RP.3.c . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .193

• Guided Problem Solving: Practice Solving Problems, 197

Assessment and Test Prep

• Test-Taking Strategies: Working Backward, 199• Chapter Review, 200• Chapter Test, 202• Test Prep: Cumulative Review, 203

Ratios and PercentsCHAPTER

5

In this chapter, you will extend

your knowledge of simplifying and

computing with fractions as you

explore the concept of ratios and unit

rates. You will use ratios and rates to

solve real-world and mathematical

problems.

Ratios & Proportional Relationships

6.RP.16.RP.26.RP.36.RP.3.a 6.RP.3.b6.RP.3.c6.RP.3.d

• Chapter Test, 202 Cumulative Review, 203

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Contents xv

Check Your Readiness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .204

6-1 Exploring Integers 6.NS.5, 6.NS.6, 6.NS.6.a, 6.NS.6.c, 6.NS.7.c . . . . . . . . .206

6-2 Comparing and Ordering Integers 6.NS.7.a . . . . . . . . . . . . . . . . . . . .210

6-3 Rational Numbers 6.NS.5, 6.NS.6, 6.NS.6.c, 6.NS.7.b . . . . . . . . . . . . . . . .213

Checkpoint Quiz 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .217

6-4 Comparing and Ordering Rational Numbers 6.NS.5, 6.NS.6, 6.NS.6.c, 6.NS.7.a, 6.NS.7.b . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .218

6-5 Inequalities 6.EE.5, 6.EE.6, 6.EE.8, 6.NS.7.d . . . . . . . . . . . . . . . . . . . . . . .223

Checkpoint Quiz 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .227

6-6 Solving One-Step Inequalities 6.EE.5 . . . . . . . . . . . . . . . . . . . . . . . . .228

• Guided Problem Solving: Practice Solving Problems, 231

Assessment and Test Prep

• Test-Taking Strategies: Using a Variable, 233• Chapter Review, 234• Chapter Test, 236• Test Prep: Cumulative Review, 237

Integers and Rational Numbers

CHAPTER

6

In this chapter, you will apply and

extend previous understandings of

numbers to the system of rational

numbers. You will use number lines

to order and compare integers and

models to represent addition and

subtraction of integers with same or

different signs. You will also reason

about and develop strategies for

solving one-variable inequalities.

The Number System6.NS.56.NS.66.NS.6.a6.NS.6.c6.NS.7.a6.NS.7.b6.NS.7.c6.NS.7.d

Expressions & Equations6.EE.56.EE.66.EE.8

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xvi Contents

Check Your Readiness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .238

7-1a Activity Lab Technology: Graphing Points 6.NS.6, 6.NS.6.c . . .240

7-1 Points in the Coordinate Plane 6.NS.6, 6.NS.6.c, 6.NS.8 . . . . . . . . . . . .241

7-2a Activity Lab: Refl ections in the Coordinate Plane 6.NS.6.b . .245

7-2 Polygons in the Coordinate Plane 6.NS.6.b, 6.NS.8, 6.G.3 . . . . . . . . . . .246

Checkpoint Quiz 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .250

7-3 Functions 6.EE.9 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .251

7-4 Graphing Functions 6.EE.9 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .255

Checkpoint Quiz 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .260

7-5 Functions in the Real World 6.EE.9 . . . . . . . . . . . . . . . . . . . . . . . . . . .261

• Guided Problem Solving: Practice Solving Problems, 265

Assessment and Test Prep

• Test-Taking Strategies: Drawing a Picture, 267• Chapter Review, 268• Chapter Test, 270• Test Prep: Cumulative Review, 271

The Coordinate PlaneCHAPTER

7

In this chapter, you will extend

your understanding of ordered pairs

by graphing integers and functions

containing integers on the coordinate

plane. You will also represent and

analyze quantitative relationships

between dependent and independent

variables. You will write functions

with unknown variables to model and

solve real-world problems.

The Number System6.NS.66.NS.6.b6.NS.6.c6.NS.8

Expressions & Equations6.EE.9

Geometry6.G.3

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Contents xvii

Check Your Readiness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .272

8-1a Activity Lab Hands On: Comparing Areas 6.G.1 . . . . . . . . . . .274

8-1 Areas of Parallelograms and Triangles 6.G.1 . . . . . . . . . . . . . . . . . . .275

• Vocabulary Builder: Using Concept Maps, 279

8-2 Areas of Polygons 6.G.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .280

Checkpoint Quiz 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .284

8-3a Activity Lab Hands On: Three-Dimensional Views . . . . . . . .285

8-3 Three-Dimensional Figures and Spatial Reasoning . . . . . . . . . . . . .286

• Guided Problem Solving: Practice Solving Problems, 290

8-4 Surface Area of Prisms and Pyramids 6.G.4 . . . . . . . . . . . . . . . . . . . .292

Checkpoint Quiz 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .296

8-5a Activity Lab Hands On: Exploring Volume 6.G.2 . . . . . . . . . .297

8-5 Volumes of Rectangular Prisms 6.G.2 . . . . . . . . . . . . . . . . . . . . . . . . .299

Assessment and Test Prep

• Test-Taking Strategies: Measuring to Solve, 303• Chapter Review, 304• Chapter Test, 306• Test Prep: Reading Comprehension, 307

Geometry and Measurement

CHAPTER

8

In this chapter, you will reason

about the relationships among shapes

as you use formulas to determine

area, surface area, and volume of

two- and three-dimensional shapes.

You will fi nd the area of triangles,

special quadrilaterals, and polygons,

and the volume of right rectangular

prisms. You will also represent three-

dimensional fi gures using nets made

up of rectangles and triangles, and

use the nets to fi nd the surface area

of these fi gures.

Geometry6.G.16.G.26.G.4

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xviii Contents

Check Your Readiness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .308

9-1a Activity Lab Hands On: Exploring the Mean 6.SP.3, 6.SP.5, 6.SP.5.c . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .310

9-1 Finding the Mean 6.SP.3, 6.SP.5, 6.SP.5.c . . . . . . . . . . . . . . . . . . . . . . . .311

• Vocabulary Builder: High-Use Academic Words, 313

9-2 Median and Mode 6.SP.3, 6.SP.5, 6.SP.5.c. . . . . . . . . . . . . . . . . . . . . . . .316

9-3 Frequency Tables and Dot Plots 6.SP.4 . . . . . . . . . . . . . . . . . . . . . . . .320

9-4 Box and Whisker Plots 6.SP.4, 6.SP.5.a, 6.SP.5.b . . . . . . . . . . . . . . . . . . .324

Checkpoint Quiz 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .328

9-5 Histograms 6.SP.4, 6.SP.5, 6.SP.5.b, 6.SP.5.c . . . . . . . . . . . . . . . . . . . . . . .329

• Guided Problem Solving: Solving Multiple-Step Problems, 333

9-6 Variability of Data 6.SP.2, 6.SP.3, 6.SP.5.c . . . . . . . . . . . . . . . . . . . . . . . .335

9-7 Shape of Distributions 6.SP.2, 6.SP.5.d . . . . . . . . . . . . . . . . . . . . . . . . .340

Checkpoint Quiz 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .345

9-8 Statistical Questions 6.SP.1, 6.SP.2 . . . . . . . . . . . . . . . . . . . . . . . . . . . .346

Assessment and Test Prep

• Test-Taking Strategies: Answering the Question Asked, 350• Chapter Review, 351• Chapter Test, 353• Test Prep: Cumulative Review, 354

Data and GraphsCHAPTER

9

In this chapter, you will develop an

understanding of statistical variability

and distributions. You will also display

numerical data in plots and graphs,

look for and use patterns in the data,

and summarize numerical data sets

based on their contexts.

Statistics & Probability6.SP.16.SP.26.SP.36.SP.46.SP.56.SP.5.a6.SP.5.b6.SP.5.c6.SP.5.d

441190_c1_FM_TOC_px-xviii.indd 18 9/5/12 12:43 PM

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