California algebra readiness: concepts, skills, and problem solving

574 Pages·2007·30.92 MB·English

by  Jack Price

About the Cover
Reaching a dizzying height of 146 feet and a top speed of 55 miles
per hour, the Knott’s Silver Bullet at Knott’s Berry Farm in Buena Park,
California, is one of the most exciting roller coasters in the world.
Riders of the Silver Bullet zoom through six inversions, including the
cobra roll you see on the cover. In Chapter 6, you will learn about
rates of change, such as speeds.
About the Graphics
Twisted torus. Created with Mathematica.
A torus with rose-shaped cross section is constructed. Then the
cross section is rotated around its center as it moves along a circle
to form a twisted torus, For more information, and for programs to
construct such graphics, see: www.wolfram.com/r/textbook.
Copyright © 2008 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 permission of the publisher.
Send all inquiries to:
Glencoe/McGraw-Hill
8787 Orion Place
Columbus, OH 43240-4027
ISBN: 9870078777370
MHID: 0-07-0877737-2
Printed in the United States of America.
1 2 3 4 5 6 7 8 9 10 043/079 16 15 14 13 12 11 10 09 08 07
Prerequisite Skills
Chapter Variables, Expressions, and Properties

Chapter Integers and Equations

Chapter Fractions

Chapter Decimals

Chapter Exponents and Roots

Chapter Ratios, Rates, Proportion, and Percent

Chapter Algebra on the Coordinate Plane

Chapter Geometry Basics

iii
Authors
Contributing Authors
Viken Hovsepian
Professor of Mathematics
Rio Hondo College
Whittier, California
Jack Price, Ed.D.
Professor Emeritus
California State
Polytechnic University
Pomona, California
Dinah Zike
Educational Consultant
Dinah-Might Activities, Inc.
San Antonio, Texas
Consultants
Content ELL Support and Vocabulary
Leo Winters ReLeah Cossett Lent
Instructor Author/Educational Consultant
California State University, Northridge Alford, Florida
Northridge, California
Assessment
Donna M. Kopenski, Ed.D.
K–5 Math Coordinator
Rosa Parks Elementary
San Diego, California
iv Meet the Author at ca.algebrareadiness.com
California Advisory Board
Glencoe wishes to thank the following professionals for their invaluable
feedback during the development of the program. They reviewed the
table of contents, the prototype of the Student Edition, the prototype of
the Teacher Wraparound Edition, and the professional development plan.
Linda Anderson Cheryl L. Avalos Bonnie Awes
4th/5th Grade Teacher Mathematics Consultant Teacher, 6th Grade Math
Oliveira Elementary School Retired Teacher Monroe Clark Middle School
Fremont, California Hacienda Heights, California San Diego, California
Mario Borrayo Melissa Bray Kathleen M. Brown
Teacher K–8 Math Resource Teacher Math Curriculum Staff
Rosa Parks Elementary Modesto City Schools Developer
San Diego, California Modesto, California Washington Middle School
Long Beach, California
Carol Cronk Audrey M. Day Jill Fetters
Mathematics Program Classroom Teacher Math Teacher
Specialist Rosa Parks Elementary Tevis Jr. High School
San Bernardino City Unified School Bakersfield, California
School District San Diego, California
San Bernardino, California
v
Grant A. Fraser, Ph.D. Eric Kimmel Donna M. Kopenski, Ed.D.
Professor of Mathematics Mathematics Department K–5 Math Coordinator
California State University, Chair Rosa Parks Elementary
Los Angeles Frontier High School San Diego, California
Los Angeles, California Bakersfield, California
Michael A. Pease Chuck Podhorsky, Ph.D. Vicki A. Vierra
Instructional Math Coach Math Director K–12 Math Specialist
Aspire Public Schools City Heights Educational Ventura County Office of
Oakland, California Collaborative Education
San Diego, California Camarillo, California
Arthur K. Wayman, Ph.D. Frances Basich Whitney
Professor Emeritus Project Director,
California State University, Mathematics K–12
Long Beach Santa Cruz County Office of
Long Beach, California Education
Capitola, California
vi
CCaalliiffoorrnniiaa RReevviieewweerrss
Each California Reviewer reviewed at least two chapters of the
Student Edition, providing feedback and suggestions for
improving the effectiveness of the mathematics instruction.
Alma Casey Allen Lee W. Ault Dr. Donald R. Price
Retired Mathematics Instructor Teacher, Adjunct Professor,
ABC Unified School District Selma High School Motivational Speaker
Cerritos, California Selma, California Rowland Unified School District
Rowland Heights, California
Marilyn Armas Allotta Stella Kumagai
Mathematics Teacher Mathematics Coach James D. Sherman
Rancho Bernardo High School Monterey Peninsula Unified Assistant Principal/Math Academies
San Diego, California School District Coordinator
Monterey, California Quimby Oak Middle School
Dr. Hal Anderson
San Jose, California
Professor Mathematics Education Rebecca Newburn
California State University, Long Beach Mathematics Teacher Larry R. Waters
Long Beach, California Mill Valley Middle School Mathematics Teacher
Mill Valley, California Eastlake High School
Chula Vista, California
California Content Standards for Mathematics vii
PPrreerreeqquuiissiittee SSkkiillllss
ASSESSMENT Prerequisite Skills Pretest . . . . . . . . . . . . . 2
1 Whole Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .6
Progress Check 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .9
2 Place Value . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .10
Progress Check 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .13
3 Addition and Subtraction . . . . . . . . . . . . . . . . . . . . . . . . . . .14
Progress Check 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .17
4 Multiplication and Division . . . . . . . . . . . . . . . . . . . . . . . . . .18
Progress Check 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .21
5 Exponents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .22
Progress Check 5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .25
6 Prime Factorization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .26
Progress Check 6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .29
7 Fractions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .30
Progress Check 7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .33
8 Decimals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .34
Progress Check 8 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .37
9 Least Common Multiple . . . . . . . . . . . . . . . . . . . . . . . . . . . .38
Progress Check 9 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .41
10 Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .42
Progress Check 10 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .45
11 Angles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .46
H.O.T. Problems Progress Check 11 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .49
Higher Order Thinking
12 Probability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .50
• Talk Math
8, 12, 16, 20, 24, 27, 28, 31, 32, Progress Check 12 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .53
35, 36, 40, 44, 47, 48
ASSESSMENT: Prerequisite Skills Posttest. . . . . . . . . . . . .54
• Writing in Math
8, 12, 16, 20, 24, 28, 32, 36, 40,
44, 48, 52
vviiiiii
C H APTER VVaarriiaabblleess,, EExxpprreessssiioonnss,,
1
aanndd PPrrooppeerrttiieess
1-1 A Plan for Problem Solving . . . . . . . . . . . . . . . . . . . . . . . .60
1-2 Expressions and Equations . . . . . . . . . . . . . . . . . . . . . . . .65
1-3 Order of Operations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .70
Progress Check 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .76
1-4 Commutative and Associative Properties . . . . . . . . . . . . .77
1-5 Distributive Property . . . . . . . . . . . . . . . . . . . . . . . . . . . . .84
Progress Check 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .90
1-6 Problem-Solving Strategy: Guess and Check . . . . . . . . . .91
1-7 Additional Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . .93
Explore 1-8 Math Lab: Simplify Expressions
Using Tiles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .98
1-8 Simplifying Expressions . . . . . . . . . . . . . . . . . . . . . . . . . .100 T
a
b
l
e
ASSESSMENT
o
f
Chapter 1 Study Guide and Review . . . . . . . . . . . . .106 C
o
n
Chapter 1 Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .109 t
e
n
Standards Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . .110 t
s
Note-Taking Tips 59
Standards Practice
• Multiple Choice
64, 69, 75, 83, 89, 97, 105, 110
• Short Answer 111
• Extended Response 111
H.O.T. Problems
Higher Order Thinking
• Talk Math 61, 65, 68, 72, 78, 86,
94, 96, 101, 103, 105
• Writing in Math
64, 69, 74, 81, 82, 88, 92, 97
iixx
C H APTE
R
2
IInntteeggeerrss aanndd EEqquuaattiioonnss
2-1 Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .114
2-2 Integers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .119
Progress Check 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .125
Explore 2-3 Math Lab: Model Integer Operations
Using Cubes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .126
2-3 Adding and Subtracting Integers . . . . . . . . . . . . . . . . . . .128
Progress Check 2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .134
2-4 Multiplying Integers . . . . . . . . . . . . . . . . . . . . . . . . . . . . .135
2-5 Dividing Integers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .141
Progress Check 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .146
2-6 Problem-Solving Strategy: Look for a Pattern . . . . . . . .147
2-7 Solving Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .149
ASSESSMENT
Chapter 2 Study Guide and Review . . . . . . . . . . . . .154
Chapter 2 Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .157
Standards Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . .158
Note-Taking Tips 113
Standards Practice
• Multiple Choice
118, 124, 133, 140, 145, 153, 158
• Short Answer 159
• Extended Response 159
H.O.T. Problems
Higher Order Thinking
• Talk Math
115, 119, 122, 129, 132, 137, 139,
142, 144, 149
• Writing in Math
118, 124, 133, 140, 145, 148, 153
x