Sadlier-Oxford A Division of William H. Sadlier, Inc. New York, NY 10005- 1002 AUDIO LEARNING VISUAL LEARNING HEAR THE MATH! SEE THE MATH! SHARED LEARNING SHARE THE MATH! INTERACTIVE LEARNING DO THE MATH! SGT 1 www.progressinmathematics.com For Progress in Mathematics Grades 3-6 Sadlier-Oxford 001_008_3603_2_PE3-6.indd 1 7/25/08 12:12:18 PM AUDIO GLOSSARY From A to Z Find the meanings and hear the pronunciations of math words and phrases. ALTERNATIVE TEACHING MODELS Tutorials Watch and listen to these animated math lessons. VIRTUAL MANIPULATIVES Manipulatives Practice and model math concepts with virtual manipulatives. PRACTICE Problem of the Day Tackle a new problem every day! Skills Update Review your skills with Lesson and Practice pages. Math Minutes Race against the clock with timed activities! Practice Activities Practice makes perfect with these fun activities! Vocabulary Activities Review your math vocabulary while playing Hangman or Word Scramble. ENRICHMENT Activities Challenge yourself with these interactive activities. MATH ALIVE AT HOME Take-Home Activities Share your math experience at home! Technology Resources: www.progressinmathematics.com Introduction At www.progressinmathematics.com, you will fi nd a lot of technology resources that you can use at home, and your teacher may make them available when you are at school. SGT 2 001_008_3603_2_PE3-6.indd 2 7/25/08 12:12:27 PM # A B C D E F G H I J K L M N O P Q R S T U V W X Y Z Grade home Glossary home www.progressinmathematics.com Choose the fi rst letter of a term you want to review. 1 Click on the term. 2 Listen as the glossary pronounces the word. 3 GRADE 3 AUDIO GLOSSARY SGT 3 Click From A to Z. If you are not sure what a certain word means or how to pronounce it, use your online Audio Glossary. The glossary is easy to use. Just choose your grade level and the fi rst letter of the term you want to review. INTERACTIVE COMPATIBLE AUDIO LEARNING 001_008_3603_2_PE3-6.indd 3 7/25/08 12:12:32 PM Red Team Blue Team Green Team Red Team Blue Team GRADE 3 www.progressinmathematics.com SGT 4 ALTERNATIVE TEACHING MODELS Click Tutorials. If there is a skill or concept that you need help with or do not understand, review the animated Alternative Teaching Models (there are 2 for each chapter). Each Alternative Teaching Model gives a step- by-step explanation of one of the skills or concepts in the chapter. www.progressinmathematics.com INTERACTIVE COMPATIBLE VISUAL LEARNING 001_008_3603_2_PE3-6.indd 4 7/25/08 12:12:40 PM www.progressinmathematics.com www.progressinmathematics.com GRADE 6 GRADE 5 Click Manipulatives. Virtual Manipulatives are visual models that you can actually move or manipulate to show what is happening. You can use these tools to build numbers, rotate shapes, and even jump on a number line. Select your grade and the chapter you are working on. The manipulatives that are listed will be ones that you can use to visualize the concepts of the chapter. VIRTUAL MANIPULATIVES SGT 5 INTERACTIVE COMPATIBLE 001_008_3603_2_PE3-6.indd 5 7/25/08 12:12:49 PM www.progressinmathematics.com GRADE 5 PRACTICE Click Practice Activities. There is an interactive activity for each chapter in your textbook. The activity practices the most important skills of the chapter. Use the activity while you are learning the skills, or come back to it later to review. Click Math Minutes. You can practice your basic facts as well as compute with larger numbers to see how accurately you can compute if you are given a time limit. Click Vocabulary Activities. In each chapter, you will be learning new math terms that you will need to know. A good way to review these terms is to play either the Hangman game or Word Scramble in your online vocabulary activities. SGT 6 www.progressinmathematics.com www.progressinmathematics.com GRADE 4 GRADE 4 www.progressinmathematics.com www.progressinmathematics.com INTERACTIVE COMPATIBLE INTERACTIVE LEARNING 001_008_3603_2_PE3-6.indd 6 7/25/08 12:12:53 PM GRADE 6 GRADE 3 *Whiteboard projectable only. GRADE 3 ENRICHMENT Click Skills Update.* Print Skills Update lessons and practice pages to review previously taught math skills and concepts. Click Activities. The Enrichment activities online are topics that go beyond what you are learning in class. Each activity starts with a page that explains the concept and then gives you time to practice the concept. www.progressinmathematics.com SGT 7 Name Date Count by 2s. Count by 2s, 5s, 10s 14 16 18 22 24 26 28 17 19 21 25 27 29 31 20 30 35 40 45 50 55 35 45 50 55 60 65 70 20 30 40 50 60 70 80 90 30 40 50 60 70 80 90 100 16 18 28 32 1. 12, ______, ______, ______, 20, ______, ______, ______, ______ 2. 15, ______, ______, ______, 23, ______, ______, ______, ______ Count by 5s. 3. 15, ______, 25, ______, ______, ______, ______, ______, ______ 4. 30, ______, 40, ______, ______, ______, ______, ______, ______ Count by 10s. 5. 10, ______, ______, ______, ______, ______, ______, ______, ______ 6. 20, ______, ______, ______, ______, ______, ______, ______, ______ Write the missing numbers. 7. 10, 12, 14, ______, ______, 20 8. 22, 24, 26, ______, 30, ______ www.progressinmathematics.com www.progressinmathematics.com Click Problem of the Day.* Sharpen your problem- solving skills every day. Print and solve one problem each day! INTERACTIVE COMPATIBLE 001_008_3603_2_PE3-6.indd 7 7/25/08 12:13:01 PM Dear Family, Today our class began Chapter 1. We will learn about place value. Let’s do the activity below together so I can review the skills I will need in order to understand the math in this chapter. Then we can read some of the new vocabulary I will learn in Chapter 1. Love, ____________________ How Many Tens, How Many Ones? With your child, list the age of everyone in your family on a sheet of paper. Ask your child to say how many tens and how many ones there are in each age. Draw a frame like the one at the right for each family member. Tell your child to write in each frame the number of tens and ones for each age. Then have her/him write an addition with the number of tens and the number of ones for each age, and find the sum. expanded form shows the place value of the digits in a number 600 � 40 � 7 standard form 647 thousand nearest ten the number achieved after rounding to the nearest ten 251 250 nearest hundred the number achieved after rounding to the nearest hundred tens ones + = m quantities granted to users of Progress in Mathematics. Chapter 1 www.progressinmathematics.com GRADE 3 - ENGLISH users of Progress in Mathematics. Dear Family, Today our class completed Chapter 1. We learned how to read, write, compare, and order numbers to hundred thousands. These skills are needed to work with numbers and to understand place value. We explored patterns of skip counting with 2s, 3s, 4s, 5s, and 10s, which will help us to learn multiplication facts. We practiced rounding 3- and 4-digit numbers to the nearest ten, hundred, or thousand. This skill is necessary for estimating with numbers. We also worked with money, which will help us make and count change. Love, ________________________ Key Skills and Concepts Students’ learning in Chapter 1 was guided by giving particular emphasis to the following key skills and concepts: NS 2.3 • Identify the place value for each digit in numbers to 10,000. • Use expanded notation to represent numbers. GRADE 3 - ENGLISH tics, para reproducir esta página para sus estudiantes. Querida familia: Hoy nuestra clase terminó el capítulo 1. Aprendimos a leer, escribir, comparar y ordenar números hasta los cientos de miles. Este conocimiento es necesario para trabajar con números y para entender el valor posicional. Aprendimos a contar de 2 en 2, de 3 en 3, de 4 en 4, de 5 en 5 y de 10 en 10, lo que nos servirá para aprender operaciones de multiplicación. Aprendimos a redondear números de 3 y 4 dígitos hasta la decena, centena o millar más cercano. Este conocimiento es necesario para hacer estimaciones con números. También practicamos con dinero, lo cual nos ayudará a la hora de dar o recibir cambio. Con cariño, _____________________________ Destrezas y conceptos claves U l it i i i t d l id l d iñ t d Lo que aprendieron los estudiantes en el capítulo 1 se hizo poniendo énfasis en las siguientes destrezas y conceptos claves: NS 2.3 • Identificar el valor posicional de cada dígito de números hasta el 10,000. • Usar la forma desarrollada de representar números. GRADE 3 - SPANISH Click Take-Home Activities. Keep your family involved in what you are learning. For each chapter, there are two letters to your family. Use the fi rst letter at the beginning of the chapter, to review previously learned skills with a family activity, and read about the new skills you will learn. The second letter tells your family about the skills you learned in the chapter and has another fun activity that you and your family members can do together. Both letters are in English and in Spanish. MATH ALIVE AT HOME SGT 8 SHARED LEARNING 001_008_3603_2_PE3-6.indd 8 7/25/08 12:13:05 PM  Sadlier-Oxford A Division of William H. Sadlier, Inc. www.sadlier-oxford.com Catherine D. LeTourneau Alfred S. Posamentier with Elinor R. Ford Frank Lucido Associate Professor in Bilingual/Multicultural Education Texas A&M University Corpus Christi, TX R. James Milgram Professor of Mathematics Stanford University Palo Alto, CA Madelaine Gallin Former Math Coordinator Community School District #6 New York, NY Tim Mason Title 1 Specialist Palm Beach County School District West Palm Beach, FL Lucy Lugones Math Coordinator St. Luke’s School Whitestone, NY Rosalie Pedalino Porter Consultant Bilingual/ESL Programs Amherst, MA 8205-4_Proto_i 10/5/05 4:20 PM Page i Copyright © 2009 by William H. Sadlier, Inc. All rights reserved. This publication, or any part thereof, may not be reproduced in any form, or by any means, including electronic, photographic, or mechanical, or by any sound recording system, or by any device for storage and retrieval of information, without the written permission of the publisher. Address inquiries to Permissions Department, William H. Sadlier, Inc., 9 Pine Street, New York, NY 10005-1002. is a registered trademark of William H. Sadlier, Inc. Printed in the United States of America ISBN: 978-0-8215-3605-6 The publisher gratefully acknowledges Rose Anita McDonnell (1905–2003) and her colleagues for the important role they played in the development of Progress in Mathematics for more than sixty years. The publisher wishes to thank the following teachers and administrators, who read portions of the series prior to publication, for their valuable contributions. Madonna Atwood Teacher St. Louis, MO Debra Wright Principal Winter Haven, FL John Palladino Professor at Eastern Michigan University Ypsilanti, MI Marie Bicsak Math Coordinator Mt. Clemens, MI Suzanne Ryan Grade 4 Teacher Orono, MN Brandy Roth Grade 3 Teacher Kissimmee, FL Barbara Murphy Grade 4 Teacher Chesterfield, MO Sr. Maristella Dunlavy, O.P. Principal Springfield, IL Sara Kobylarz Grade 3 Teacher Bronx, NY Candace Govin Grades 4– 8 Math Teacher/Coordinator Plantation, FL Elizabeth M. Johnson Grade 5 Teacher Bettendorf, IA Sr. Martha Carmody, O.P. Grade 4 Teacher Springfield, IL Jeannine Frey Grade 3 Teacher Chesterfield, MO Br. Ralph Darmento, F.S.C. Deputy Superintendent of Schools Newark, NJ Sr. Adriana Cernoch Grade 6 Teacher Dallas, TX Linda Hamby Grade 5 Teacher DesPeres, MO Jacqueline A. Byrd Grade 5 Teacher Chesterfield, MO Mary E. Stokes Grade 5 Teacher Oak Forest, IL Grades 3–6 Reviewers Grade-Level Reviewers Judith A. Devine Educational Consultant Springfield, PA Stephanie D. Garland Educational Consultant St. Louis, MO 3605-6_PE5_ii_Copyright:8205-4_Proto_22-23PSintro copy 7/31/08 10:03 AM Page ii 456789 RRDW 13 12 11 10 iii Progress in Mathematics, now in its sixth decade of user-proven success, is a complete basal mathematics program. Written by experienced teacher- authors, it integrates a traditional course of study and today’s academic Standards with the most up-to-date methods of teaching. Progress in Mathematics is designed to meet the individual needs of all learners. Teachers who use Progress come to understand that students may progress as quickly as they can or as slowly as they must. In Grade 5, the concepts of fractions and decimals will be further developed, and your fifth grader will use all four operations with these number types. There will also be an increased emphasis on algebraic thinking. Other topics that are studied include: statistics, geometry, measurement, probability, percents, and proportions. Special attention is given to critical thinking, problem solving, mental math, and journalizing. But overall success in achieving the goals of this program depends on ongoing teacher-family-student interaction. It is important for you to encourage your fifth grader to achieve success in mathematics and enjoy it as well.You can help your student see math as useful and practical by relating it to everyday situations. It is also helpful to provide a quiet space and time for homework, and to reinforce the idea that by practicing math concepts and skills in your home environment, your student can have fun while learning mathematics. Throughout the school year, you and your student can access Math Alive At Home pages at www.sadlier-oxford.com. These pages include the math vocabulary of each chapter plus fun-filled activities that will help you relate the math your student is learning in school to the real world. We know that by using Progress in Mathematics your fifth grader will not only learn to value math, but become a confident problem solver and learn to reason and communicate mathematically as well. 8205-4_iii 4/26/06 9:40 AM Page iii iv Introduction to Problem Solving Problem-Solving Model . . . . . . . . . . . . . . 22 Problem-Solving Strategy: Logical Reasoning . . . . . . . . . . . . . . . . 24 Problem-Solving Strategy: Interpret the Remainder . . . . . . . . . . . . 25 Problem-Solving Strategy: Use More Than One Step . . . . . . . . . . 26 Problem-Solving Strategy: Make a Table . . . . . . . . . . . . . . . . . . . . 27 Problem-Solving Applications: Mixed Review . . . . . . . . . . . . . . . . . . . . 28 Letter to the Family . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii Skills Update A handbook for reviewing essential and previously taught skills An Introduction to Skills Update. . . . . . . . xii Numeration I Place Value to Thousands. . . . . . . . 1 II Compare and Order Whole Numbers . . . . . . . . 2 III Round Whole Numbers. . . . . . . . . . 3 Whole Number Operations I Add and Subtract Whole Numbers . . . . . . . . . . . . . 4 II Multiply One Digit . . . . . . . . . . . . . . 5 III One-Digit Quotients . . . . . . . . . . . . 6 IV Two-Digit Quotients. . . . . . . . . . . . . 7 Fractions I Fractions . . . . . . . . . . . . . . . . . . . . . 8 II Equivalent Fractions . . . . . . 9 III Add and Subtract Fractions: Like Denominators . . . . . . . . . . 10 Decimals Tenths and Hundredths. . . . . . . . . 11 Geometry I Geometric Concepts . . . . . . . . . . . 12 II Identify Polygons. . . . . . . . . . . . . . 13 Measurement I Customary Units of Length . . . . . . 14 II Customary Units of Capacity and Weight . . . . . . . . . . . . . . . . 15 III Metric Units of Length. . . . . . . . . . 16 IV Metric Units of Capacity and Mass. . . . . . . . . . . . . . . . . . 17 Statistics I Make Pictographs . . . . . . . . . . . . . 18 II Make Bar Graphs . . . . . . . . . . . . . 19 Probability I Equally/Not Equally Likely Outcomes . . . . . . . . . . . . . . . . . 20 II List Outcomes . . . . . . . . . . . . . . . . 21 *Develops concept or skill with manipulatives. Lesson promotes algebraic reasoning. 8205-4_iv-xi 10/3/05 12:54 AM Page iv Chapter Multiplication Chapter Opener . . . . . . . . . . . . . . . . . . . . 65 2-1 Factors and Products . . . . 66 2-2 Properties of Multiplication . . . . . . . . . 68 2-3 Mental Math: Special Factors . . . . 70 2-4 Patterns in Multiplication . . 72 2-5 Estimate Products. . . . . . . . . . . . . 74 2-6 Zeros in the Multiplicand . . . . . . . . 76 2-7 Multiply Two Digits. . . . . . . . . . . . . 78 2-8 Multiply Three Digits . . . . . . . . . . . 80 2-9 Zeros in the Multiplier . . . . . . . . . . 82 2-10 Multiplication with Money . . . . . . . 84 2-11 Problem-Solving Strategy: Use More Than One Step . . . . . . . 86 2-12 Problem-Solving Applications: Mixed Review . . . . . . . . . . . . . . . . 88 End of Chapter Check Your Progress (Lessons 1–12) . . 90 Enrichment: Exponents . . . . . . . . 91 Chapter 2 Test. . . . . . . . . . . . . . . . . . . . . 92 Cumulative Review. . . . . . . . . . . . . . . . . 93 v Chapter Place Value, Addition, and Subtraction Chapter Opener . . . . . . . . . . . . . . . . . . . . 29 1-1 What Is a Billion? . . . . . . . . . . . . . 30 1-2 Place Value to Billions. . . . . . . . . . 32 1-3 Expanded Form . . . . . . . . . . . . . . 34 1-4 Thousandths . . . . . . . . . . . . . . . . . 36 1-5 Decimals Greater Than One . . . . . 38 1-6 Compare and Order Numbers . . . . . . . 40 1-7 Rounding Numbers . . . . . . . . . . . . 42 1-8 Addition Properties/ Subtraction Rules . . . . . 44 1-9 Estimate Sums and Differences . . . . . . . . . . . . . . . . 46 1-10 Addition: Three or More Addends . . . . . . . . . . . . 48 1-11 Subtraction with Zeros . . . . . . . . . 50 1-12 Larger Sums and Differences . . . . 52 1-13 Roman Numerals . . . . . . . . . . . . . 54 1-14 Problem-Solving Strategy: Guess and Test . . . . . . . . . 56 1-15 Problem-Solving Applications: Mixed Review . . . . . . . . . . . . . . . . 58 End of Chapter Check Your Progress (Lessons 1–15) . . 60 Enrichment: Logic and Venn Diagrams . . 61 Chapter 1 Test. . . . . . . . . . . . . . . . . . . . . 62 Cumulative Review. . . . . . . . . . . . . . . . . 63 * *Develops concept or skill with manipulatives. Lesson promotes algebraic reasoning. 8205-4_iv-xi 10/3/05 12:56 AM Page v vi Chapter Division Chapter Opener . . . . . . . . . . . . . . . . . . . . 95 3-1 Understanding Division . . . . . . . . . 96 3-2 Division Patterns . . . . . . . . 98 3-3 Three-Digit Quotients . . . . . . . . . 100 3-4 Larger Quotients . . . . . . . . . . . . . 102 3-5 Zeros in the Quotient . . . . . . . . . 104 3-6 Short Division . . . . . . . . . . . . . . . 106 3-7 Explore Divisibility . . . . . . . . . . . . 108 3-8 Divisibility and Mental Math . . . . 110 3-9 Estimation: Compatible Numbers . . . . . . . . . . . . . . . . . 112 3-10 Teens as Divisors . . . . . . . . . . . . 114 3-11 Two-Digit Divisors . . . . . . . . . . . . 116 3-12 Divide Larger Numbers . . . . . . . . 118 3-13 Divide Money . . . . . . . . . . . . . . . 120 3-14 Order of Operations . . . . . 122 3-15 Problem-Solving Strategy: Make a Table/Find a Pattern . . . . . . . . . . . . . 124 3-16 Problem-Solving Applications: Mixed Review . . . . . . . . . . . . . . . 126 End of Chapter Check Your Progress (Lessons 1–16) . 128 Enrichment: Translate Algebraic Expressions . . . . . . . . . . . . . . 129 Chapter 3 Test. . . . . . . . . . . . . . . . . . . . 130 Cumulative Review. . . . . . . . . . . . . . . . 131 * * Chapter Number Theory and Fractions Chapter Opener . . . . . . . . . . . . . . . . . . . 133 4-1 Explore Prime and Composite Numbers . . . . . . . . 134 4-2 Factors, Primes, and Composites . . . . . . . . . . . . . . . 136 4-3 Greatest Common Factor . . . . . . 138 4-4 Fraction Sense . . . . . . . . . . . . . . 140 4-5 Fractions in Lowest Terms. . . . . . 142 4-6 Fractions in Greater Terms . . . . . . . 144 4-7 Multiples: LCM and LCD . . . . . . . 146 4-8 Mixed Numbers. . . . . . . . . . . . . . 148 4-9 Fractions Greater Than or Equal to One . . . . . . . . . . . . . . 150 4-10 Compare and Order Fractions . . . . . . . . . . . 152 4-11 Problem-Solving Strategy: Make an Organized List . . . . . . . 154 4-12 Problem-Solving Applications: Mixed Review . . . . . . . . . . . . . . . 156 End of Chapter Check Your Progress (Lessons 1–12) . 158 Enrichment: Density of Fractions . . . . . . 159 Chapter 4 Test. . . . . . . . . . . . . . . . . . . . 160 Cumulative Review. . . . . . . . . . . . . . . . 161 *Develops concept or skill with manipulatives. Lesson promotes algebraic reasoning. 8205-4_iv-xi 10/3/05 12:58 AM Page vi