Study Guide and Intervention and Practice Workbook

[Pages:205]Study Guide and Intervention and Practice Workbook

To the Student This Study Guide and Intervention and Practice Workbook gives you additional examples and problems for the concept exercises in each lesson. The exercises are designed to aid your study of mathematics by reinforcing important mathematical skills needed to succeed in the everyday world. The materials are organized by chapter and lesson, with one Study Guide and Intervention and Practice worksheet for every lesson in Glencoe Math Connects, Course 3.

Always keep your workbook handy. Along with your textbook, daily homework, and class notes, the completed Study Guide and Intervention and Practice Workbook can help you review for quizzes and tests.

To the Teacher These worksheets are the same as those found in the Chapter Resource Masters for Glencoe Math Connects, Course 3. The answers to these worksheets are available at the end of each Chapter Resource Masters booklet as well as in your Teacher Wraparound Edition interleaf pages.

Copyright ? by The McGraw-Hill Companies, Inc. All rights reserved. Except as permitted under the United States Copyright Act, no part of this publication may be reproduced or distributed in any form or by any means, or stored in a database or retrieval system, without prior written permission of the publisher.

Send all inquiries to: Glencoe/McGraw-Hill 8787 Orion Place Columbus, OH 43240

ISBN: 978-0-07-881076-3 MHID: 0-07-881076-0

Study Guide and Intervention and Practice Workbook, Course 3

Printed in the United States of America 1 2 3 4 5 6 7 8 9 10 045 14 13 12 11 10 09 08 07

CONTENTS

Lesson/Title

Page

1-1 A Plan for Problem Solving ...................1

1-1 A Plan for Problem Solving ...................2

1-2 Variables, Expressions, and Properties ..3

1-2 Variables, Expressions, and Properties ..4

1-3 Integers and Absolute Values ...............5

1-3 Integers and Absolute Values ...............6

1-4 Adding Integers .....................................7

1-4 Adding Integers .....................................8

1-5 Subtracting Integers ..............................9

1-5 Subtracting Integers ............................10

1-6 Multiplying and Dividing Integers ........11

1-6 Multiplying and Dividing Integers ........12

1-7 Writing Equations ................................13

1-7 Writing Equations ................................14

1-8 Problem-Solving Investigation: Work

Backward.............................................15

1-8 Problem-Solving Investigation: Work

Backward.............................................16

1-9 Solving Addition and Subtraction

Equations ............................................17

1-9 Solving Addition and Subtraction

Equations ............................................18

1-10 Solving Multiplication and Division

Equations ............................................19

1-10 Solving Multiplication and Division

Equations ............................................20

2-1 Rational Numbers ...............................21

2-1 Rational Numbers............................... 22

2-2 Comparing and Ordering Rational

Numbers..............................................23

2-2 Comparing and Ordering Rational

Numbers..............................................24

2-3 Multiplying Positive and Negative

Fractions..............................................25

2-3 Multiplying Positive and Negative

Fractions..............................................26

2-4 Dividing Positive and Negative

Fractions..............................................27

2-4 Dividing Positive and Negative

Fractions..............................................28

2-5 Adding and Subtracting Like

Fractions..............................................29

2-5 Adding and Subtracting Like

Fractions..............................................30

2-6 Adding and Subtracting Unlike

Fractions..............................................31

2-6 Adding and Subtracting Unlike

Fractions..............................................32

2-7 Solving Equations with Rational

Numbers..............................................33

2-7 Solving Equations with Rational

Numbers..............................................34

2-8 Problem-Solving Investigation: Look

for a Pattern ........................................35

Lesson/Title

Page

2-8 Problem-Solving Investigation: Look

for a Pattern ........................................36

2-9 Powers and Exponents .......................37

2-9 Powers and Exponents .......................38

2-10 Scientific Notation ...............................39

2-10 Scientific Notation ...............................40

3-1 Square Roots ......................................41

3-1 Square Roots ......................................42

3-2 Estimating Square Roots ....................43

3-2 Estimating Square Roots ....................44

3-3 Problem-Solving Investigation:

Use a Venn Diagram ...........................45

3-3 Problem-Solving Investigation:

Use a Venn Diagram ...........................46

3-4 The Real Number System...................47

3-4 The Real Number System...................48

3-5 The Pythagorean Theorem .................49

3-5 The Pythagorean Theorem .................50

3-6 Using the Pythagorean Theorem ........51

3-6 Using the Pythagorean Theorem ........52

3-7 Distance on the Coordinate Plane ......53

3-7 Distance on the Coordinate Plane ......54

4-1 Ratios and Rates ................................55

4-1 Ratios and Rates ................................56

4-2 Proportional and Nonproportional

Relationships.......................................57

4-2 Proportional and Nonproportional

Relationships.......................................58

4-3 Rate of Change ...................................59

4-3 Rate of Change ...................................60

4-4 Constant Rate of Change ...................61

4-4 Constant Rate of Change ...................62

4-5 Solving Proportions.............................63

4-5 Solving Proportions.............................64

4-6 Problem-Solving Investigation: Draw a

Diagram ...............................................65

4-6 Problem-Solving Investigation: Draw a

Diagram ...............................................66

4-7 Similar Polygons..................................67

4-7 Similar Polygons..................................68

4-8 Dilations .............................................69

4-8 Dilations .............................................70

4-9 Indirect Measurement .........................71

4-9 Indirect Measurement .........................72

4-10 Scale Drawings and Models ...............73

4-10 Scale Drawings and Models ...............74

5-1 Ratios and Percents ............................75

5-1 Ratios and Percents ............................76

5-2 Comparing Fractions, Decimals, and

Percents ..............................................77

5-2 Comparing Fractions, Decimals, and

Percents ..............................................78

5-3 Algebra: The Percent Proportion.........79

5-3 Algebra: The Percent Proportion.........80

iii

Lesson/Title

Page

5-4 Finding Percents Mentally ...................81

5-4 Finding Percents Mentally ...................82

5-5 Problem-Solving Investigation:

Reasonable Answers ..........................83

5-5 Problem-Solving Investigation:

Reasonable Answers ..........................84

5-6 Percent and Estimation .......................85

5-6 Percent and Estimation .......................86

5-7 Algebra: The Percent Equation ...........87

5-7 Algebra: The Percent Equation ...........88

5-8 Percent of Change ..............................89

5-8 Percent of Change ..............................90

5-9 Simple Interest ....................................91

5-9 Simple Interest ....................................92

6-1 Line and Angle Relationships .............93

6-1 Line and Angle Relationships .............94

6-2 Problem-Solving Investigation:

Use Logical Reasoning .......................95

6-2 Problem-Solving Investigation:

Use Logical Reasoning .......................96

6-3 Polygons and Angles ..........................97

6-3 Polygons and Angles ..........................98

6-4 Congruent Polygons............................99

6-4 Congruent Polygons..........................100

6-5 Symmetry ..........................................101

6-5 Symmetry ..........................................102

6-6 Reflections ........................................103

6-6 Reflections ........................................104

6-7 Translations .......................................105

6-7 Translations .......................................106

7-1 Circumference and Area of Circles ...107

7-1 Circumference and Area of Circles ...108

7-2 Problem-Solving Investigation: Solve a

Simpler Program ...............................109

7-2 Problem-Solving Investigation: Solve a

Simpler Program ...............................110

7-3 Area of Composite Figures ...............111

7-3 Area of Composite Figures ...............112

7-4 Three-Dimensional Figures...............113

7-4 Three-Dimensional Figures...............114

7-5 Volume of Prisms and Cylinders .......115

7-5 Volume of Prisms and Cylinders .......116

7-6 Volume of Pyramids and Cones........117

7-6 Volume of Pyramids and Cones........118

7-7 Surface Area of Prisms and

Cylinders ...........................................119

7-7 Surface Area of Prisms and

Cylinders ...........................................120

7-8 Surface Area of Pyramids .................121

7-8 Surface Area of Pyramids .................122

7-9 Similar Solids ....................................123

7-9 Similar Solids ....................................124

8-1 Simplifying Algebraic Expressions ....125

8-1 Simplifying Algebraic Expressions ....126

8-2 Solving Two-Step Equations..............127

8-2 Solving Two-Step Equations..............128

8-3 Writing Two-Step Equations ..............129

Lesson/Title

Page

8-3 Writing Two-Step Equations ..............130

8-4 Solving Equations with Variables on

Each Side..........................................131

8-4 Solving Equations with Variables on

Each Side..........................................132

8-5 Problem-Solving Investigation:

Guess and Check..............................133

8-5 Problem-Solving Investigation:

Guess and Check..............................134

8-6 Inequalities ........................................135

8-6 Inequalities ........................................136

8-7 Solving Inequalities by Adding and

Subtracting ........................................137

8-7 Solving Inequalities by Adding and

Subtracting ........................................138

8-8 Solving Inequalities by Multiplying or

Dividing .............................................139

8-8 Solving Inequalities by Multiplying or

Dividing .............................................140

9-1 Sequences ........................................141

9-1 Sequences ........................................142

9-2 Functions...........................................143

9-2 Functions...........................................144

9-3 Representing Linear Functions .........145

9-3 Representing Linear Functions .........146

9-4 Slope .................................................147

9-4 Slope .................................................148

9-5 Direct Variation ..................................149

9-5 Direct Variation ..................................150

9-6 Slope-Intercept Form ........................151

9-6 Slope-Intercept Form ........................152

9-7 Systems of Equations .......................153

9-7 Systems of Equations .......................154

9-8 Problem-Solving Investigation:

Use a Graph......................................155

9-8 Problem-Solving Investigation:

Use a Graph......................................156

9-9 Scatter Plots......................................157

9-9 Scatter Plots......................................158

10-1 Linear and Nonlinear Functions ........159

10-1 Linear and Nonlinear Functions ........160

10-2 Graphing Quadratic Functions ..........161

10-2 Graphing Quadratic Functions ..........162

10-3 Problem-Solving Investigation:

Make a Model....................................163

10-3 Problem-Solving Investigation:

Make a Model....................................164

10-4 Graphing Cubic Functions.................165

10-4 Graphing Cubic Functions.................166

10-5 Multiplying Monomials.......................167

10-5 Multiplying Monomials.......................168

10-6 Dividing Monomials ...........................169

10-6 Dividing Monomials ...........................170

10-7 Powers of Monomials .........................171

10-7 Powers of Monomials .........................172

10-8 Roots of Monomials ...........................173

10-8 Roots of Monomials ...........................174

iv

Lesson/Title

Page

11-1 Problem-Solving Investigation: Make

a Table ...............................................175

11-1 Problem-Solving Investigation: Make

a Table ...............................................176

11-2 Histograms ........................................177

11-2 Histograms ........................................178

11-3 Circle Graphs ....................................179

11-3 Circle Graphs ....................................180

11-4 Measures of Central Tendency and

Range................................................181

11-4 Measures of Central Tendency and

Range................................................182

11-5 Measures of Variation .......................183

11-5 Measures of Variation .......................184

11-6 Box-and-Whisker Plots......................185

11-6 Box-and-Whisker Plots......................186

11-7 Stem-and-Leaf Plots ..........................187

11-7 Stem-and-Leaf Plots ..........................188

11-8 Select an Appropriate Display...........189

11-8 Select an Appropriate Display...........190

12-1 Counting Outcomes ..........................191

12-1 Counting Outcomes ..........................192

12-2 Probability of Compound Events.......193

12-2 Probability of Compound Events.......194

12-3 Experimental and Theoretical

Probability .........................................195

12-3 Experimental and Theoretical

Probability .........................................196

12-4 Problem-Solving Investigation:

Act it Out ...........................................197

12-4 Problem-Solving Investigation:

Act it Out ...........................................198

12-5 Using Sampling to Predict.................199

12-5 Using Sampling to Predict.................200

v

Copyright ? Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.

Lesson 1-1

1-1

NAME ________________________________________ DATE ______________ PERIOD _____

Study Guide and Intervention

A Plan for Problem Solving

You can always use the four-step plan to solve a problem.

Understand Determine what information is given in the problem and what you need to find.

Plan

Select a strategy including a possible estimate.

Solve

Solve the problem by carrying out your plan.

Check

Examine your answer to see if it seems reasonable.

Example 1

Plant A and Plant B are two new experimental apple trees being grown in a laboratory. The table displays their heights, in millimeters, when they are 5 to 10 days old.

Day

5

6

7

8

9

10

Plant A

36

39

42

45

48

51

Plant B

32

36

40

44

48

52

Estimate the height of each plant on day 12.

Understand Plan Solve

Check

You know their heights for days 5 to 10. You need to determine their heights in two more days.

Determine whether there is a pattern and extend that pattern to day 12.

Comparing each plant's heights on consecutive days, we see that Plant A's height increases by 3 millimeters each day, while Plant B's height increases by 4 millimeters each day. To estimate Plant A's height on day 12, assume that it will grow 3 millimeters each day past day 10, so it will be 51 3 3 or 57 millimeters. To estimate Plant B's height on day 12, assume that it will grow 4 millimeters each day past day 10, so it will be 52 4 4 or 60 millimeters.

Given what we know about each plant's height and how plants grow in general, both estimates seem reasonable.

Exercises

Use the four-step plan to solve each problem.

1. MOVIES A movie ticket costs $3.50. A large popcorn costs $3.75 and a large soda costs $3.00. How much will it cost two friends to go to a movie if they share a popcorn and each has a large soda?

2. FLOUR BEETLES The population of a flour beetle doubles in about a week. How long would it take for the population to grow to eight times its original size?

Chapter 1

1

Course 3

1-1

NAME ________________________________________ DATE ______________ PERIOD _____

Practice

A Plan for Problem Solving

Use the four-step plan to solve each problem.

1. FOOD The table shows a portion of the price list for a local pizzeria. Tony has $17 that he can spend to buy one large pizza. If the pattern in the prices continues, what is the greatest number of toppings that Tony can order on his pizza? What is the cost of that pizza?

Toppings 1 2 3 4

Price $12.99 $13.79 $14.59 $15.39

2. MOVIES Mr. Sedgwick paid $13 for one adult ticket and one child ticket for a movie. Mrs. Wong paid $18 for one adult ticket and two child tickets to see the same movie, and Mr. Gomez paid $23 for one adult ticket and three child tickets. If the pattern continues, how much should Mrs. Beauregard expect to pay for one adult ticket and four child tickets?

3. SPORTS The track coach must buy at least two bottles of water for each participant in a track meet. One team has 35 members, and the other team has 28 members. If each case of water contains 24 bottles, what is the fewest number of full cases that the coach can buy?

4. GEOGRAPHY The land area of Washington, D.C., is 61 square miles. In a recent year, the population of Washington, D.C., was 563,384. If one square mile is equal to 640 acres, about how many people per acre were there in Washington, D.C.?

5. ART SUPPLIES At the craft store, a paint brush costs $0.79, and a small bottle of paint costs $0.89. What combination of paint brushes and bottles of paint could you buy for exactly $4.15?

6. GEOMETRY Draw the next two figures in the pattern.

Copyright ? Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.

Chapter 1

2

Course 3

Copyright ? Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.

Lesson 1-2

1-2

NAME ________________________________________ DATE ______________ PERIOD _____

Study Guide and Intervention

Variables, Expressions, and Properties

When finding the value of an expression with more than one operation, perform the operations in the order specified by the order of operations.

Order of Operations

1. Perform all operations within grouping symbols first; start with the innermost grouping symbols. 2. Evaluate all powers before other operations. 3. Multiply and divide in order from left to right. 4. Add and subtract in order from left to right.

Example 1 Evaluate the expression (5 7) 2 3 (8 1).

(5 7) 2 3 (8 1) 12 2 3 (8 1) Add inside the left parentheses.

12 2 3 9

Add inside the remaining parentheses.

6 3 9

Divide.

18 9

Multiply.

9

Subtract.

Example 2 Evaluate the expression 3x2 4y if x 3 and y 2.

3x2 4y 3(3)2 4(2) Replace x with 3 and y with 2.

3(9) 4(2) Evaluate the power first.

27 8

Do all multiplications.

19

Subtract.

Exercises

Evaluate each expression.

1. 4 5 8

2. 16 12 4

3. 14 2 3(5)

4. 5 6 2 3

5. 2 32 10 14

6. 22 32 8 5

7. (10 5) 3

8. 52 (8 6)

9. (17 5)(6 5) 11. 5[24 (6 8)]

10. 3 7(14 8 2) 12. 32142

Evaluate each expression if a 3, b 5, and c 6.

13. a 3b

14. 4b 3c

15. 2a b 5c

16. (ab)2

17. a(b c)

18. 3(bc 8) a

Chapter 1

3

Course 3

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