Authors Basich Whitney • Brown • Dawson • Gonsalves • Silbey • Vielhaber Thinkstock/Alamy Photo Credits Cover, i Thinkstock/Alamy; iv (tl)File Photo, (tc tr)The McGraw-Hill Companies, (cl c)Doug Martin, (cr)Aaron Haupt, (bl bc)File Photo; v (L to R 11 12)The McGraw-Hill Companies, (5 10 13 14) File Photo; vii Ian Grant/Alamy; viii Medioimages/PunchStock; ix Digital Vision/PunchStock; x, xi, CORBIS; 2–3 Brian Pieters/Masterfile; 10 Mike Powell/Getty Images; 14 Michael Houghton/StudiOhio; 16 The McGraw-Hill Companies; 40–41 F Lukasseck/ Masterfile 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: 978-0-07-878209-1 MHID: 0-07-878209-0 Printed in the United States of America 10 055/027 16 15 14 13 12 11 10 09 08 07 California Math Triumphs Volume 4A 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 4A The Core Processes of Mathematics Chapter Operations and Equality 1-1 Addition and Subtraction Operations 3AF1.0 1-2 Multiplication and Division Operations .11 3AF1.0 Progress Check .18 1-3 Equality 19 4AF2.1, 4AF2.2 1-4 Operations with Unknown Quantities 25 4AF1.1 Progress Check .31 Assessment Chapters and are contained in Volume 4A Chapters 3, 4, and are contained in Volume 4B Standards Addressed in This Chapter 3AF1.0 Students select appropriate symbols, operations, and properties to represent, describe, simplify, and solve simple number relationships 4AF1.1 Use letters, boxes, or other symbols to stand for any number in simple expressions or equations (e.g., demonstrate an understanding and the use of the concept of a variable) 4AF2.1 Know and understand that equals added to equals are equal 4AF2.2 Know and understand that equals multiplied by equals are equal Study Guide .32 Chapter Test .36 Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc Standards Practice 38 Point Lobos State Park vii Ian Grant/Alamy Contents Chapter Math Fundamentals Standards Addressed in This Chapter 2-1 Commutative Property 42 2AF1.1, 3AF1.5 2-2 Associative Property .49 2AF1.1, 3AF1.5 Progress Check .56 2-3 Distributive Property 57 5AF1.3 2-4 Order of Operations 63 7AF1.2 Progress Check .69 2AF1.1 Use the commutative and associative rules to simplify mental calculations and to check results 3AF1.5 Recognize and use the commutative and associative properties of multiplication (e.g., if × = 35, then what is × 5? and if × × = 105, then what is × × 5?) 5AF1.3 Know and use the distributive property in equations and expressions with variables 7AF1.2 Use the correct order of operations to evaluate algebraic expressions such as 3(2x + 5)2 Assessment Study Guide .70 Chapter Test .74 Standards Practice 76 Mustard plants in Napa Valley Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc viii Medioimages/PunchStock Contents Chapter Math Expressions 3-1 Algebraic Expressions .4 7AF1.1 3-2 Translating Verbal Phrases into Mathematical Symbols 11 5AF1.2, 7AF1.1 Progress Check .20 3-3 Simplify Expressions 21 7AF1.3 3-4 Evaluate Variable Expressions 29 5AF1.2, 6AF1.2, 7AF1.3 Progress Check .35 Assessment Study Guide .36 Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc Chapter Test .40 Chapters and are contained in Volume 4A Chapters 3, 4, and are contained in Volume 4B Standards Addressed in This Chapter 5AF1.2 Use a letter to represent an unknown number; write and evaluate simple algebraic expressions in one variable by substitution 6AF1.2 Write and evaluate an algebraic expression for a given situation, using up to three variables 7AF1.1 Use variables and appropriate operations to write an expression, an equation, an inequality, or a system of equations or inequalities that represents a verbal description (e.g., three less than a number, half as large as area A) 7AF1.3 Simplify numerical expressions by applying properties of rational numbers (e.g., identity, inverse, distributive, associative, commutative) and justify the process used Standards Practice 42 Burney Falls ix Digital Vision/PunchStock Contents Chapter Linear Equations Standards Addressed in This Chapter 4-1 Translate Word Phrases into Equations .46 7AF1.1 4-2 Solve Equations Using Addition and Subtraction .53 4AF2.1, 7AF4.0 Progress Check 60 4-3 Solve Equations Using Multiplication and Division 61 4AF2.2, 7AF4.0 4-4 Multi-Step Equations 67 7AF4.0 Progress Check 74 4-5 Symbolic Computation 75 4AF2.1 Know and understand that equals added to equals are equal 4AF2.2 Know and understand that equals multiplied by equals are equal 7NS1.3 Convert fractions to decimals and percents and use these representations in estimations, computations, and applications 7AF1.1 Use variables and appropriate operations to write an expression, an equation, an inequality, or a system of equations or inequalities that represents a verbal description (e.g., three less than a number, half as large as area A) 7AF4.0 Students solve simple linear equations and inequalities over the rational numbers 7NS1.3 Assessment Chapter Test 86 Standards Practice 88 x CORBIS Alabama Hills, Owens Valley Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc Study Guide 82 Step by Step Practice Find the value of 14 - · (2 - 1)2 - + Step Use the order of operations Simplify the grouping symbols )2 - + 14 - · (2 - 1)2 - + = 14 - · ( Step Simplify the exponent 14 - · 12 - + = 14 - · -5+2 Step Multiply and divide 14 - · - + = 14 Step Add and subtract 14 - - + = = = -5+2 -5+2 +2 Find the value of each expression Copyright © by The McGraw-Hill Companies, Inc - (1 + 8) + · 32 = - + · 32 =9- +3· =9- + = + = ÷ + (5 · 2)2 - = ÷ + ( =8÷2+ = + = -7 )2 - -7 -7 = 20 - 42 ÷ · + (7 - 4) = (4 - 3)2 · 50 ÷ - (3 + 6) = 10 21 + 30 ÷ ÷ · 12 = 6-1 11 50 ÷ (7 + 3) · ÷ = 12 (122 - 22) ÷ (6 + 1) - = 13 [152 - 32 - (2 · 8)] ÷ 25 = GO ON Lesson 2-4 Order of Operations 65 Step by Step Problem-Solving Practice 14 NUTRITION Marcos has baskets that hold 12 oranges each He has more baskets of 10 oranges each Write and simplify an expression to find how many oranges Marcos has in all Problem-Solving Strategies Draw a diagram Guess and check Act it out ✓ Solve a simpler problem Work backward Understand Read the problem Write what you know There are baskets with oranges each and baskets with oranges each Plan Pick a strategy One strategy is to solve a simpler problem In this case, solving a simpler problem means to work on smaller parts of the expression, one at a time Solve Write an expression for the total number of oranges · 12 + baskets of 12 · 10 baskets of 10 Simplify the expression using the order of operations · 12 + · 10 = = Marcos has + Multiply Add oranges Write and simplify an expression to solve each problem 15 NATURE Brandy likes to watch birds She saw a wren make nests Three wrens each made nests Five nests were damaged during a storm How many nests were left? Check off each step Understand Plan Solve Check 66 Chapter Math Fundamentals Copyright © by The McGraw-Hill Companies, Inc You can use addition to check 12 + 12 + 10 + 10 + 10 + 10 + 10 + 10 = Check 16 COLLECTIONS Tyler bought packs of comic books Each pack had comic books He gave comic books to his brother Then he bought more packs of comic books with 18 books in each How many comic books does Tyler have now? 17 PHOTOGRAPHY Marlene was looking through her photo album She looked at pages with photos each She removed photos Then she looked at 10 pages with photos each She removed photos Finally she looked at pages with photos each How many photos were left in the album? 18 Explain why 16 ÷ + has a different value than 16 ÷ (2 + 6) Skills, Concepts, and Problem Solving Copyright © by The McGraw-Hill Companies, Inc Name the step that should be performed first in each expression 19 · + (4 ÷ 2) - 22 20 · (3 - 6)2 + ÷ 21 (7 - 22 · 4) - ÷ 22 + (6 - · 7) ÷ 22 23 3[(100 + 25) × 2] - 25 24 18 + 66 _ 35 - 14 Find the value of each expression 25 50 ÷ + · 22 - (8 - 2) = 26 32 + ÷ - (10 + 2) = 27 16 - 42 · + 18 - 15 = 28 (9 - 6)2 + ÷ + · = 29 15 + 35 _ ×5= 21 + 30 2(14 - 6) _ = 22 31 10[8(15 - 7) - (4 × 3)] = 32 5[(12 + 5) - 3(19 - 14)] = GO ON Lesson 2-4 Order of Operations 67 Write and simplify an expression to solve each problem 33 BOOKS Ramona borrowed stacks of books with books each She then returned books Then Ramona borrowed stacks of books each How many books does Ramona have now? 34 COLLECTIONS Don had 100 collector cards He sold packs of baseball cards with 10 cards each He then bought packs of football cards with 12 cards each Then Don sold 25 hockey cards How many cards does Don have left? Vocabulary Check sentence Write the vocabulary word that completes each 35 A(n) multiplied by itself is the number of times a base is 36 The is a set of rules that tells what order to follow when evaluating an expression 37 Writing in Math Does 30 - (10 - 5) equal (30 - 10) - 5? Explain Solve Explain your reasoning 38 (Lesson 2-2, p 49) SPORTS Amy bought the boxes of softballs shown Each softball cost $4 How much did Amy spend? Contains softballs Use the Commutative and Associative Properties fo fill in each blank Check your answer (Lesson 2-1, p 42) 39 68 + 16 = + = 68 Chapter Math Fundamentals 40 + = 12 + 17 = Contains softballs Copyright © by The McGraw-Hill Companies, Inc Spiral Review Chapter Progress Check (Lessons 2-3 and 2-4) Use the Distributive Property and a model to find each product · 13 = · 16 = Name each operation that should be performed first - · (7 + 4)2 ÷ 32 · - (12 ÷ 4) + Use the Distributive Property to find each product Show your work 7(3 + 2) = 6(8 - 2) = 3(k + 5) = -6(p - 7) = Copyright © by The McGraw-Hill Companies, Inc Find the value of each expression 18 + 22 ÷ · (5 - 2) + = 10 10 - (2 - 1)2 + 16 ÷ · (1 + 1) = 11 28 ÷ 22 · + ÷ = 12 64 ÷ 42 · 25 - (30 - 18) ÷ = Solve Explain your reasoning 13 BASKETBALL Tamar made six 2-point field goals and two 3-point field goals How many points did Tamar score? 14 SHOPPING Payton had 50 pencils He sold bags of pencils with pencils each He then bought packs of pencils with 10 pencils each Then Payton gave 20 pencils to his sister How many pencils does Payton have left? Chapter Math Fundamentals 69 Chapter Study Guide Vocabulary and Concept Check Associative Property of Addition, p 49 Write the vocabulary word that completes each sentence The property that states that the order in which two numbers are multiplied does not change the product is the The property that states that the grouping of the factors does not change the product is the (2 + 4) + = + (4 + 7) shows the Associative Property of Multiplication, p 49 base (of a power), p 63 Commutative Property of Addition, p 42 Commutative Property of Multiplication, p 42 Distributive Property, p 57 exponent, p 63 order of operations, p 63 a(b + c) = ab + ac or a(b – c) = ab – ac is the + = + shows the The is a set of rules that tells what order to use when evaluating an expression 1) Simplify within parentheses 2) Simplify exponents 3) Multiply and divide from left to right 4) Add and subtract from left to right 70 Chapter Study Guide Copyright © by The McGraw-Hill Companies, Inc Write the correct vocabulary term in each blank Lesson Review 2-1 Commutative Property (pp 42–48) Use the Commutative Properties to fill in each blank Check your answer 10 2·8= Example Draw a model to show + = + Which property did you show? ·2 Create a model for each side of the equation 16 = 1 1 + = + 15 11 = + Copyright © by The McGraw-Hill Companies, Inc Associative Property (pp 49–55) Use the Associative Properties to fill in each blank Check your answer 13 · (4 · 3) = (8 · = 1 + 1 = + 1 1 1 1 = 1 = The order of the numbers changed, but the sum did not This is the Commutative Property of Addition = 22 2-2 + +4= 12 + Example Use the Associative Property to fill in each blank Check your answer )·3 (6 · 3) · = · ( · 2) Use the Associative Property of Multiplication (6 · 3) · = · ( · 2) 14 (5 + 9) + = + ( 15 + (13 + 15) = ( 2+ Check by multiplying the numbers on each side of the equation (6 · 3) · = · (3 · 2) 18 · = · 36 = 36 + 3) + )+ = 15 + = Chapter Study Guide 71 Draw a model to show each equation Example 16 (2 · 3) · = · (3 · 5) Which property did you show? Draw a model to show (1 · 3) · = · (3 · 4) Which property did you show? Create a model for each side of the equation 1 1 1 1·3 1·3 1 1 1 1·3 1·3 1 1 1 = 1 1 = 1 1 1 = 1 1 1 1 3·4 1 1 1 1 (1 · 3) · = · (3 · 4) 17 (2 + 3) + = + (3 + 4) Which property did you show? 18 4·7·5=4· =( ·7 · 5) · = ·7 11 + (9 + 4) = ( = = 72 Chapter Study Guide Example Use the Commutative and Associative Properties to find the sum mentally 15 + + Determine which grouping would help you find the sum using mental math Group 15 and Then find the sum = 19 Associative Property of Multiplication + 9) + +4 15 + + = 15 + + = (15 + 5) + = 20 + or 29 Copyright © by The McGraw-Hill Companies, Inc Use the Commutative and Associative Properties to find each sum or product mentally The grouping of the factors did not change the product 2-3 Distributive Property (pp 57–62) Use the Distributive Property to find each product 20 9(5 - 3) = ( · 5) - ( = Use the Distributive Property to find 7(8 + 3) · 3) - 5(x + 8) = ( · x) + ( = 7(8 + 3) = (7 · 8) + (7 · 3) Simplify within the parentheses Then add (7 · 8) + (7 · 3) = 56 + 21 = 21 Example = 77 · 8) + = 2-4 Order of Operations (pp 63–68) Find the value of each expression Copyright © by The McGraw-Hill Companies, Inc 22 Find the value of - + 15 ÷ × 10 + ÷ - × = 23 11 - + × = 24 125 ÷ 52 · = Use the order of operations There are no grouping symbols or exponents Multiply and divide - + 15 ÷ × = - + × = - + 20 Add and subtract - + 20 = + 20 = 24 Find the value of each expression 25 Example Example 3 × - (4 - 2) + ÷ = Find the value of 18 ÷ + (2 + 1)2 · - 26 32 - + (1 + 2)3 ÷ = 27 62 + ÷ (8 - 6) × = Use the order of operations Simplify the grouping symbols 18 ÷ + (2 + 1)2 · - = 18 ÷ + 32 · - Simplify the exponent 18 ÷ + 32 · - = 18 ÷ + · - Multiply and divide 18 ÷ + · - = + 36 - Add and subtract + 36 - = 42 - = 37 Chapter Study Guide 73 Chapter Chapter Test Use the Commutative Properties to fill in each blank Check your answer 4·6= ·4 + = + 11 24 = = 7+9= + = · 12 = · = Give an example of the Commutative Property of Addition Check your example Use the Associative Properties to fill in each blank Check your answer · (4 · 10) = ( · 4) · 10 = + (1 + 15) = ( · 10 = = + 15 = + (16 + 13) = ( = + )+ (7 · 2) · = + = ·( · ) · Copyright © by The McGraw-Hill Companies, Inc = 10 + 1) + 15 = Give an example of the Associative Property of Multiplication Check your answer Use the Distributive Property to find each product Show your work 11 9(2 + 5) = 12 2(20 - y) = 14 (7 - 3)2 · ÷ + (11 + 8) = Find the value of each expression 13 16 + 23 ÷ · - (16 - 10) = GO ON 74 Chapter Test Solve Explain your reasoning 15 COOKING Hoshi needs gallons of stew for a potluck dinner Each gallon of stew requires cans of beef gravy Each can of beef gravy costs $1.20 How much will the gravy for the stew cost? gallon Copyright © by The McGraw-Hill Companies, Inc 16 gallon gallon SHOPPING Devin bought boxes of markers with markers in each box Jennifer purchased boxes with markers in each box Compare the number of markers 17 FITNESS Sofia participated in two 50-minute aerobics sessions last week and three 50-minute aerobics sessions this week How many minutes did she work out during both weeks? 18 POPULATION An apartment complex has units Four people lived in each unit Then people moved away The next month families of moved into the complex What is the total number of people living in the apartment complex now? Correct the mistakes 19 ART Terri purchased boxes of acrylic paint tubes, each containing tubes of paint Raul purchased boxes, each containing acrylic paint tubes Raul told Terri that he bought more tubes of paint than she did because he bought more boxes What mistake did Raul make? 20 FOOD At the school cafeteria, the cook had sandwiches Two students purchased each The cook then sold two teachers each Her assistant made 11 more sandwiches She dropped of them on the floor so it had to be thrown away The assistant said, “Now you only have 10 sandwiches to sell.” What mistake did she make? Chapter Test 75 Chapter Standards Practice Choose the best answer and fill in the corresponding circle on the sheet at right If × × = 504, then what is × × 8? Which property is shown in the sentence below? A 567 C 448 (21 × 8) + (21 × 5) = 21 × (8 + 5) B 504 D 343 A Associative Property of Addition B Distributive Property of Multiplication over Addition C Commutative Property of Addition 49 × (130 × 62) = D Identity Property of Multiplication F (48 × 130) × 26 G (49 × 130) × 62 H (49 × 103) × 62 J (47 × 130) × 62 Which property is shown in the sentence below? (346 × 751) × 203 = 346 × (751 × 203) F Associative Property of Multiplication G Distributive Property of Multiplication over Addition H Commutative Property of Multiplication J Identity Property of Multiplication 10 ft 14 ft A 2(10 × 14) C 2(14) × 2(10) B 2(14) + 10 D + (14 × 10) Which property is shown in the sentence below? 33.7 × 1.8 = 1.8 × 33.7 A Associative Property of Addition B Distributive Property of Multiplication over Addition 76 234 ÷ × [52 - (4 × 3)] = F 1,014 H 27 G 954 J Chapter Standards Practice C Commutative Property of Multiplication D Identity Property of Multiplication GO ON Copyright © by The McGraw-Hill Companies, Inc Olivia wants to paint the two opposite walls in her bedroom If she knows the dimensions of one wall, which expression can help her figure out the square footage of both walls? Gabriel buys books at a back-toschool sale Which expression has a value equal to the cost of books? 12 How many pounds of bananas can Andre buy with $3.00? Bananas Item Cost CD $15 Book $24 T-shirt $19 39¢ per lb F pounds H pounds G pounds J 10 pounds F (2 × 24) + (3 × 24) ANSWER SHEET G (2 × 15) + (4 × 15) Directions: Fill in the circle of each correct answer H (2 × 19) + (3 × 19) J (2 × 24) + (4 × 24) Which symbol makes the sentence true? Copyright © by The McGraw-Hill Companies, Inc 216 □ = 54 10 A B C D F G H J A B C D F G H J A B C D A + C × F G H J B - D ÷ A B C D F G H J A B C D 10 F G H J 11 A B C D 12 F G H J Which shows the difference of a number and 46 is 108? F x + 46 = 108 H x × 46 = 108 G x - 46 = 108 J x ÷ 46 = 108 Success Strategy 11 Which is the answer to a division statement? A difference C quotient B product D sum If two answers seem correct, compare them for differences Reread the problem to find the best answer between the two Chapter Standards Practice 77 Index A division whole numbers, 11–17 addend, 4, 49 addition whole numbers, 4–10 Addition Property of Equality, 19 Algebra and Functions, 4, 11, 19, 25, 42, 49, 57, 63 E P equation, 19 product, 11, 42 exponent, 63 F Answer Sheet, 39, 77 Associative Property of Multiplication, 49 B I inverse operations, 25 K Key Concept, 4, 11, 19, 25, 42, 49, 57, 63 Chapter Preview, 3, 41 Chapter Test, 36–37, 74–75 coefficient, Commutative Property of Addition, 42 Commutative Property of Multiplication, 42 constant, 11 Correct the Mistakes, 37, 75 D difference, Distributive Property of Multiplication, 57 78 Index L like terms, 21 M manipulatives balance scale (bucket), 19, 20, 21, 22, 23, 25, 26, 27, 29, 31, 34, 35, 57 base-ten blocks, 6, 8, 13, 15, 18, 19, 20, 21, 22, 23, 25, 26, 27, 29, 31, 34, 35, 42, 43, 44, 46, 49, 55, 57, 58, 59, 71, 72 money, 14 Math Reasoning See Step-byStep Problem Solving multiplication whole numbers, 11–17 Multiplication Property of Equality, 19 quotient, 11 R Real-World Applications advertising, 24 ages, 31 art, 9, 33, 75 bake sale, 32 baking, 12, 36, 37 basketball, 59, 60, 69 books, 62, 68 cards, 33 carnival, chemistry, 37 club, 15 coin collecting, 46 coins, 16 collections, 9, 67, 68 comic books, 16 construction, 54 cooking, 53, 75 crafts, design, 32 elections, 29 entertainment, 29 farming, 32 field trips, 37 fitness, 9, 16, 56, 75 food, 17, 29, 33, 37, 54, 75 football, 37, 61 fossils, 18 four wheeling, 10 fund-raising, 30 Copyright © by The McGraw-Hill Companies, Inc California Mathematics Content Standards, 4, 11, 19, 25, 42, 49, 57, 63 Progress Check, 8, 31, 56, 69 Q base (of a power), 63 C Problem Solving See Step-byStep Problem Solving factor, 49 Assessment, 36–37, 74–75 Associative Property of Addition, 49 order of operations, 63 equal, 19 algebraic expression, 4, 11 array, 11, 16, 33, 42, 43, 44, 45, 46, 49, 50, 51, 53, 56, 57, 60, 69, 72 O stores, 46 taste test, 15 temperature, 18 travel, 18, 37 trips, 61 volunteering, 48 weather, 17, 24 Reflect, 8, 15, 23, 29, 46, 53, 60, 67 S Success Strategy, 39, 77 sum, 4, 42 T term, 4, 21 V variable, 4, 25 simplify, 21–28 Vocabulary, 4, 11, 19, 25, 42, 49, 57, 63 Spiral Review, 17, 24, 30, 48, 55, 68 Vocabulary and Concept Check, 32, 70 Standards Practice, 38–39, 76–77 Vocabulary Check, 9–10, 17, 24, 30, 48, 55, 62, 68 Step-by-Step Practice, 6, 13, 21, 27, 44, 51, 59, 65 Step-by-Step Problem Solving Practice Act it out, 45–46 Solve a simpler problem, 7–8, 22–23, 52, 66 Use a model, 14–15, 59–60 Work backward, 28–29 W Who is Correct?, 5, 13, 21, 26, 43, 50, 58, 64 whole numbers, 4–10, 11–17 Writing in Math, 10, 17, 24, 30, 48, 55, 62, 68 Study Guide, 32–35, 70–73 subtraction whole numbers, 4–10 Copyright © by The McGraw-Hill Companies, Inc games, 47 gardening, 11 hobbies, 10, 15, 16, 23, 47 homework, 36 jewelry, 46 jobs, 30, 36 landscaping, 14, 16 money, 7, 12, 22, 31, 60, 61 movies, 9, 24 music, 10, 47 nature, 66 numbers, 47, 48, 55 packaging, 14, 16, 33 part-time job, 14 parties, 61 photography, 48, 67 photos, 14, 17 population, 24, 75 projects, reading, 18 safety, 55 sales, 10 school, 5, 13, 17, 18, 30, 60 school days, 52 school supplies, shopping, 16, 23, 33, 36, 45, 54, 56, 62, 69, 75 snacks, 28 soccer, softball, sports, 5, 12, 18, 53, 68 stamp collecting, 52 Index 79 ... 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... 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. .. MHID: 0-07-878209-0 Printed in the United States of America 10 055/027 16 15 14 13 12 11 10 09 08 07 California Math Triumphs Volume 4A California Math Triumphs Volume Place Value and Basic Number