Authors Basich Whitney • Brown • Dawson • Gonsalves • Silbey • Vielhaber Photo Credits coins: United States Mint, bills: Michael Houghton/StudiOhio; Cover Jupiter Images; iv (tl bl br) File Photo, (tc tr) The McGraw-Hill Companies, (cl c) Doug Martin, (cr) Aaron Haupt; v (1 11 12) The McGraw-Hill Companies, (5 10 13 14) File Photo; vii Dynamics Graphics Group/Creatas/Alamy; viii Digital Vision/PunchStock; ix x CORBIS; xi Digital Vision/PunchStock; xii Digital Vision/ Getty Images; 2–3 Getty Images; 15 Masterfile; 18 Photodisc/Getty Images; 58 Dynamic Graphics Value/SuperStock; 80 Getty Images; 94 Stockbyte/ SuperStock; 106–107 Getty Images; 113 Matthew Scherf/iStockphoto; 119 Burke/Triolo Productions/Getty Images; 122 Photodisc/Getty Images; 127 Brand X Pictures/PunchStock; 132 Michael Newman/PhotoEdit, Inc.; 147 Roy McMahon/CORBIS; 148 CORBIS; 150 Siede Preis/Getty Images; 161 CORBIS; 169 Getty Images; 172 Cyril Mazansky/UNEP/Peter Arnold, Inc.; 203 age fotostock/SuperStock; 204 216 218 CORBIS 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: 978-0-07-878204 MHID: 0-07-878204-X Printed in the United States of America 10 055/027 16 15 14 13 12 11 10 09 08 07 California Math Triumphs Volume 1B California Math Triumphs Volume Place Value and Basic Number Skills 1A Chapter Counting 1A Chapter Place Value 1A Chapter Addition and Subtraction 1B Chapter Multiplication 1B Chapter Division 1B Chapter Integers Volume Fractions and Decimals 2A Chapter Parts of a Whole 2A Chapter Equivalence of Fractions 2B Chapter Operations with Fractions 2B Chapter Positive and Negative Fractions and Decimals Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc Volume Ratios, Rates, and Percents 3A Chapter Ratios and Rates 3A Chapter Percents, Fractions, and Decimals 3B Chapter Using Percents 3B Chapter Rates and Proportional Reasoning Volume The Core Processes of Mathematics 4A Chapter Operations and Equality 4A Chapter Math Fundamentals 4B Chapter Math Expressions 4B Chapter Linear Equations 4B Chapter Inequalities Volume Functions and Equations 5A Chapter Patterns and Relationships 5A Chapter Graphing 5B Chapter Proportional Relationships 5B Chapter The Relationship Between Graphs and Functions Volume Measurement 6A Chapter How Measurements Are Made 6A Chapter Length and Area in the Real World 6B Chapter Exact Measures in Geometry 6B Chapter Angles and Circles iii Authors and Consultants AUTHORS Frances Basich Whitney Kathleen M Brown Dixie Dawson Project Director, Mathematics K–12 Santa Cruz County Office of Education Capitola, California Math Curriculum Staff Developer Washington Middle School Long Beach, California Math Curriculum Leader Long Beach Unified Long Beach, California Philip Gonsalves Robyn Silbey Kathy Vielhaber Mathematics Coordinator Alameda County Office of Education Hayward, California Math Specialist Montgomery County Public Schools Gaithersburg, Maryland Mathematics Consultant St Louis, Missouri Viken Hovsepian Professor of Mathematics Rio Hondo College Whittier, California Dinah Zike Educational Consultant, Dinah-Might Activities, Inc San Antonio, Texas CONSULTANTS Assessment Donna M Kopenski, Ed.D Math Coordinator K–5 City Heights Educational Collaborative San Diego, California Instructional Planning and Support ELL Support and Vocabulary Beatrice Luchin ReLeah Cossett Lent Mathematics Consultant League City, Texas Author/Educational Consultant Alford, Florida iv (tl)File Photo, (tc tr)The McGraw-Hill Companies, (cl c)Doug Martin, (cr)Aaron Haupt, (bl bc)File Photo Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc CONTRIBUTING AUTHORS California Advisory Board CALIFORNIA ADVISORY BOARD Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc 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 Study Guide, the prototype of the Teacher Wraparound Edition, and the professional development plan Linda Anderson Cheryl L Avalos Bonnie Awes Kathleen M Brown 4th/5th Grade Teacher Oliveira Elementary School, Fremont, California Mathematics Consultant Retired Teacher Hacienda Heights, California Teacher, 6th Grade Math Monroe Clark Middle School San Diego, California Math Curriculum Staff Developer Washington Middle School Long Beach, California Carol Cronk Audrey M Day Jill Fetters Grant A Fraser, Ph.D Mathematics Program Specialist San Bernardino City Unified School District San Bernardino, California Classroom Teacher Rosa Parks Elementary School San Diego, California Math Teacher Tevis Jr High School Bakersfield, California Professor of Mathematics California State University, Los Angeles Los Angeles, California Eric Kimmel Donna M Kopenski, Ed.D Michael A Pease Chuck Podhorsky, Ph.D Mathematics Department Chair Frontier High School Bakersfield, California Math Coordinator K–5 City Heights Educational Collaborative San Diego, California Instructional Math Coach Aspire Public Schools Oakland, California Math Director City Heights Educational Collaborative San Diego, California Arthur K Wayman, Ph.D Frances Basich Whitney Mario Borrayo Melissa Bray Professor Emeritus California State University, Long Beach Long Beach, California Project Director, Mathematics K–12 Santa Cruz County Office of Education Capitola, CA Teacher Rosa Parks Elementary San Diego, California K–8 Math Resource Teacher Modesto City Schools Modesto, California v (L to R 11 12)The McGraw-Hill Companies, (5 10 13 14)File Photo California Reviewers CALIFORNIA REVIEWERS Each California Reviewer reviewed at least two chapters of the Student Study Guides, providing feedback and suggestions for improving the effectiveness of the mathematics instruction Melody McGuire Math Teacher California College Preparatory Academy Oakland, California 6th and 7th Grade Math Teacher McKinleyville Middle School McKinleyville, California Eppie Leamy Chung Monica S Patterson Teacher Modesto City Schools Modesto, California Educator Aspire Public Schools Modesto, California Judy Descoteaux Rechelle Pearlman Mathematics Teacher Thornton Junior High School Fremont, California 4th Grade Teacher Wanda Hirsch Elementary School Tracy, California Paul J Fogarty Armida Picon Mathematics Lead Aspire Public Schools Modesto, California 5th Grade Teacher Mineral King School Visalia, California Lisa Majarian Anthony J Solina Classroom Teacher Cottonwood Creek Elementary Visalia, California Lead Educator Aspire Public Schools Stockton, California vi Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc Bobbi Anne Barnowsky Volume 1A Place Value and Basic Number Skills Chapter Counting Chapters 1, 2, and are contained in Volume 1A Chapters 4, 5, and are contained in Volume 1B 1-1 Counting Numbers Less Than 100 1NS1.1 1-2 Whole Numbers Less Than 100 11 Standards Addressed in This Chapter 1NS1.1 Count, read, and write whole numbers to 100 1NS1.1 Progress Check 18 1-3 Equal Expressions 19 1NS1.3 1-4 Number Patterns .25 1NS1.2 Progress Check 32 1-5 Numbers That Make Ten .33 1NS1.4 1-6 Expanded Form for Two-Digit Numbers 39 1NS1.2 Compare and order whole numbers to 100 by using the symbols for less than, equal to, or greater than () 1NS1.3 Represent equivalent forms of the same number through the use of physical models, diagrams, and number expressions (to 20) (e.g., may be represented as + 4, + 3, + + + 2, 10 - 2, 11 - 3) 1NS1.4 Count and group objects in ones and tens (e.g., three groups of 10 and equals 34, or 30 + 4) 1NS1.4 Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc Progress Check 46 1-7 Use Symbols to Compare Numbers 47 1NS1.2 1-8 Order Whole Numbers Less Than 100 53 1NS1.2 Progress Check 59 Assessment Study Guide .60 Chapter Test .64 Bridal Veil Falls, El Capitan, and Half Dome, Yosemite National Park Standards Practice 66 vii Dynamics Graphics Group/Creatas/Alamy Contents Chapter Place Value Standards Addressed in This Chapter 2-1 Whole Numbers to 1,000 .70 2NS1.1, 2NS1.2 2-2 Round and Compare Whole Numbers Less Than 1,000 77 2NS1.3, 4NS1.3 Progress Check .84 2-3 Whole Numbers Less Than 10,000 .85 3NS1.3, 3NS1.5 2-4 Round and Compare Whole Numbers Less Than 10,000 91 4NS1.2, 4NS1.3 Progress Check .98 2-5 Read and Write Whole Numbers in the Millions .99 4NS1.1 4NS1.2, 4NS1.3 2-7 Order and Compare Numbers to Two Decimal Places 111 4NS1.2, 4NS1.6 Progress Check 119 Assessment 2NS1.2 Use words, models, and expanded forms (e.g., 45 = tens + 5) to represent numbers (to 1,000) 2NS1.3 Order and compare whole numbers to 1,000 by using the symbols 3NS1.3 Identify the place value for each digit in numbers to 10,000 3NS1.5 Use expanded notation to represent numbers (e.g., 3,206 = 3,000 + 200 + 6) 4NS1.1 Read and write whole numbers in the millions 4NS1.2 Order and compare whole numbers and decimals to two decimal places 4NS1.3 Round whole numbers through the millions to the nearest ten, hundred, thousand, ten thousand, or hundred thousand 4NS1.6 Write tenths and hundredths in decimal and fraction notations and know the fraction and decimal equivalents for halves and fourths (e.g., = 0.5 or 0.50; = = 1.75) 4 Study Guide 120 Chapter Test 124 Standards Practice 126 viii Digital Digital Vision/PunchStock Vision/PunchStock Giant Redwoods, Sequoia National Park Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc 2-6 Round and Compare Whole Numbers in the Millions 105 2NS1.1 Count, read, and write whole numbers to 1,000 and identify the place value for each digit Contents Chapter Addition and Subtraction Standards Addressed in This Chapter 3-1 Addition Facts for to 130 1NS2.1, 1NS2.6, 2NS2.2 3-2 Addition Facts for and 137 1NS2.1, 1NS2.6, 2NS2.2 Progress Check 144 3-3 Addition Facts for and 145 1NS2.1, 1NS2.5, 1NS2.7 3-4 Estimate and Add Greater Numbers 151 2NS2.3, 3NS1.3, 4NS1.3, 4NS3.1 Progress Check 158 3-5 Subtraction Facts for to 159 1NS2.1, 1NS2.5, 1NS2.6 3-6 Subtraction Facts for to 165 1NS2.1, 1NS2.5, 1NS2.6 Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc Progress Check 172 3-7 Subtract with Zeros .173 2NS1.2, 2NS2.3, 3NS2.1 3-8 Estimate and Subtract Greater Numbers 181 3NS2.1, 4NS3.1 Progress Check 189 Assessment Study Guide 190 Chapter Test 194 1NS2.1 Know the addition facts (sums to 20) and the corresponding subtraction facts and commit them to memory 1NS2.5 Show the meaning of addition (putting together, increasing) and subtraction (taking away, comparing, finding the difference) 1NS2.6 Solve addition and subtraction problems with one- or two-digit numbers (e.g., + 58 = ) 1NS2.7 Find the sum of three one-digit numbers 2NS2.2 Find the sum or difference of two whole numbers up to three digits long 2NS2.3 Use mental arithmetic to find the sum or difference of two two-digit numbers 3NS1.3 Identify the place value for each digit in numbers to 10,000 3NS2.1 Find the sum or difference of two whole numbers between and 10,000 4NS1.3 Round whole numbers through the millions to the nearest ten, hundred, thousand, ten thousand, or hundred thousand 4NS3.1 Demonstrate an understanding of, and the ability to use, standard algorithms for the addition and subtraction of multidigit numbers Standards Practice 196 Cacti growing in Baja California Peninsula ix CORBIS Contents Chapter Multiplication 4-1 Introduction to Multiplication 3NS2.2, 4NS4.1 4-2 Multiply with 0, 1, and 10 3NS2.2, 3NS2.4, 3NS2.6 11 Progress Check 18 4-3 Multiply by 3NS2.2, 3NS2.4 19 4-4 Multiply by 3NS2.2, 3NS2.4 25 Progress Check 32 4-5 Multiply by 3NS2.2, 3NS2.4, 4NS3.2 33 4-6 Multiply by 3NS2.2, 3NS2.4, 4NS3.2, 4NS4.1 39 Progress Check 46 4-7 Multiply by 3NS2.2, 3NS2.4, 4NS3.2, 4NS4.1 .47 4-8 Multiply by 3NS2.2, 3NS2.4, 4NS3.2, 4NS4.1 53 Progress Check 60 4-9 Multiply by 3NS2.2, 3NS2.4, 4NS3.2, 4NS4.1 61 Progress Check 74 4-11 Multiply by 11 and 12 3NS2.2, 3NS2.4, 4NS3.2, 4NS4.1 75 4-12 Perfect Squares 3NS2.2, 4NS4.1 81 Progress Check 88 Standards Addressed in This Chapter 2NS3.1 Use repeated addition, arrays, and counting by multiples to multiplication 2NS3.3 Know the multiplication tables of 2s, 5s, and 10s (to “times 10”) and commit them to memory 3NS2.2 Memorize to automaticity the multiplication table for numbers between and 10 3NS2.4 Solve simple problems involving multiplication of multidigit numbers by one-digit numbers (3,671 × = ) 3NS2.6 Understand the special properties of and in multiplication and division 4NS3.2 Demonstrate an understanding of, and the ability to use, standard algorithms for multiplying a multidigit number by a two-digit number and for dividing a multidigit number by a one-digit number; use relationships between them to simplify computations and to check results 4NS4.1 Understand that many whole numbers break down in different ways (e.g., 12 = × = × = × × 3) 4-13 Multiply Large Numbers 3NS2.4, 3NS2.6, 4NS3.2 89 Assessment Study Guide 95 Chapter Test 102 Standards Practice .104 x CORBIS Poppy meadow in the Santa Ynez Mountains Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc 4-10 Multiply by 3NS2.2, 3NS2.4, 4NS3.2, 4NS4.1 67 Chapters 1, 2, and are contained in Volume 1A Chapters 4, 5, and are contained in Volume 1B 9 9 9 GO ON Lesson 6-2 Add Integers 183 Step by Step Practice Find the sum of -6 and -3 Use the number line Step Graph the first number Step From the first number, move left Step Where are you on the number line? -9 Step Write the sum -6 + (-3) = -9 Find each sum Use the number line –6 + = -1 –3 + = -6 Start at and move places -3 right –4 + (–2) = -6 + (–3) = 10 + (–3) = 11 –6 + (–1) = -7 12 –3 + (–4) = 13 + (–7) = 14 + (–9) = -2 -1 -7 -1 What is the opposite of each number? Use it to show the Inverse Property of Addition 15 14 17 -92 184 -14; 14 + (-14) = 16 -48 92; -92 + 92 = 18 Chapter Integers 48; -48 + 48 = -5; + (-5) = Copyright © by The McGraw-Hill Companies, Inc Find each sum Step by Step Problem-Solving Practice Solve 19 20 Problem-Solving Strategies ✓ Draw a picture Use logical reasoning Make a table Solve a simpler problem Work backward HIKING Two friends start out on a day-long hike on a hill They begin at an elevation of 500 feet Their hike takes them to an altitude that is 200 feet lower than where they began What is their current altitude? Understand Read the problem Write what you know The hikers begin at an altitude of 500 ft They walk down 200 ft feet in altitude Plan Pick a strategy One strategy is to draw a picture Solve Begin at 500 feet and go down 200 feet 500 + (–200) = 300 ft Check Does the answer make sense? Look over your solution Did you answer the question? IJLFCFHJOT GFFU IJLFFOET GFFU GAMES Tammy puts 10 quarters into a video game She uses $1 of her credit How much credit does she have left? $2.50 + (-$1.00) = $1.50 Copyright © by The McGraw-Hill Companies, Inc Check off each step 21 ✔ Understand ✔ Plan ✔ Solve ✔ Check HEALTH Julio had a fever of 102ºF At the end of the day, his temperature had gone down degrees What was his temperature at the end of the day? 100°F 22 Give examples of the Inverse Property and Commutative Property of Addition Explain each property See TWE margin GO ON Lesson 6-2 Add Integers 185 Skills, Concepts, and Problem Solving Find each sum Use counters 23 -1 + (–6) = ĕ 24 ĕ ĕ ĕ ĕ ... California Math Triumphs Volume Place Value and Basic Number Skills 1A Chapter Counting 1A Chapter Place Value 1A Chapter Addition and Subtraction 1B Chapter Multiplication 1B Chapter Division 1B Chapter... Value and Basic Number Skills Chapter Counting Chapters 1, 2, and are contained in Volume 1A Chapters 4, 5, and are contained in Volume 1B 1-1 Counting Numbers Less Than 100 1NS1.1 1-2 Whole Numbers... thousand, ten thousand, or hundred thousand 4NS3.1 Demonstrate an understanding of, and the ability to use, standard algorithms for the addition and subtraction of multidigit numbers Standards