Problem solving strategies crossing the river with dogs answers

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EQUITY.

CURRICULUM. -

TEACHING. - -

LEARNING. -

ASSESSMENT.

TECHNOLOGY. -

National Council of Teachers of Mathematics Principles and Standards for School Mathematics

Principles for School Mathematics

Standards for School Mathematics

NUMBER AND OPERATIONS

-

ALGEBRA

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GEOMETRY

-

MEASUREMENT

-

DATA ANALYSIS AND PROBABILITY

-

PROBLEM SOLVING

REASONING AND PROOF

COMMUNICATION

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Curriculum Focal Points for Prekindergarten through Grade 8 Mathematics

CONNECTIONS

-

REPRESENTATION

-

-

PREKINDERGARTEN Number and Operations:

-

Geometry: -

Measurement:

KINDERGARTEN Number and Operations:

Geometry: Measurement:

GRADE 1 Number and Operations Algebra: -

-

Number and Operations:

Geometry:

GRADE 2 Number and Operations:

Number and Operations Algebra:

Measurement: -

GRADE 3 Number and Operations Algebra: -

-

Number and Operations: -

Geometry: -

GRADE 4 Number and Operations Algebra:

Number and Operations:

Measurement: -

GRADE 5 Number and Operations Algebra: -

Number and Operations:

Geometry Measurement Algebra:

GRADE 6 Number and Operations: -

Number and Operations: -

Algebra: -

GRADE 7 Number and Operations Algebra Geometry: -

Measurement Geometry Algebra: -

Number and Operations Algebra: -

GRADE 8 Algebra: -

Geometry Measurement:

Data Analysis Number and Operations Algebra: -

FMEndpaper.indd 16 7/31/2013 10:58:25 AM

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MathematicsFor Elementary Teachers TENTH EDITION A C O N T E M P O R A R Y A P P R O A C H

Gary L. Musser Blake E. Peterson William F. Burger Oregon State University Brigham Young University

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To:

Irene, my wonderful wife of 52 years who is the best mother our son could have; Greg, our son, for his inquiring mind; Maranda, our granddaughter, for her willingness to listen; my parents who have passed away, but always with me; and Mary Burger, my initial coauthor's daughter. G.L.M.

Shauna, my beautiful eternal companion and best friend, for her continual support of all my endeavors; my four children: Quinn for his creative enthusiasm for life, Joelle for her quiet yet strong confidence, Taren for her unintimidated ap- proach to life, and Riley for his good choices and his dry wit. B.E.P.

VICE PRESIDENT & EXECUTIVE PUBLISHER Laurie Rosatone PROJECT EDITOR Jennifer Brady SENIOR CONTENT MANAGER Karoline Luciano SENIOR PRODUCTION EDITOR Kerry Weinstein MARKETING MANAGER Kimberly Kanakes SENIOR PRODUCT DESIGNER Tom Kulesa OPERATIONS MANAGER Melissa Edwards ASSISTANT CONTENT EDITOR Jacqueline Sinacori SENIOR PHOTO EDITOR Lisa Gee MEDIA SPECIALIST Laura Abrams COVER & TEXT DESIGN Madelyn Lesure

This book was set by Laserwords and printed and bound by Courier Kendallville. The cover was printed by Courier Kendallville.

Copyright © 2014, 2011, 2008, 2005, John Wiley & Sons, Inc. All rights reserved. No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, electronic, me- chanical, photocopying, recording, scanning or otherwise, except as permitted under Sections 107 or 108 of the 1976 United States Copyright Act, without either the prior written permission of the Publisher, or authoriza- tion through payment of the appropriate per-copy fee to the Copyright Clearance Center, Inc. 222 Rosewood Drive, Danvers, MA 01923, website www.copyright.com. Requests to the Publisher for permission should be addressed to the Permissions Department, John Wiley & Sons, Inc., 111 River Street, Hoboken, NJ 07030-5774, (201)748-6011, fax (201)748-6008, website http://www.wiley.com/go/permissions.

Evaluation copies are provided to qualified academics and professionals for review purposes only, for use in their courses during the next academic year. These copies are licensed and may not be sold or transferred to a third party. Upon completion of the review period, please return the evaluation copy to Wiley. Return instruc- tions and a free of charge return shipping label are available at www.wiley.com/go/returnlabel. Outside of the United States, please contact your local representative.

Library of Congress Cataloging-in-Publication Data

Musser, Gary L. Mathematics for elementary teachers : a contemporary approach / Gary L. Musser, Oregon State University,

William F. Burger, Blake E. Peterson, Brigham Young University. -- 10th edition. pages cm

Includes index. ISBN 978-1-118-45744-3 (hardback)

1. Mathematics. 2. Mathematics–Study and teaching (Elementary) I. Title. QA39.3.M87 2014 510.2’4372–dc23 2013019907

Printed in the United States of America

10 9 8 7 6 5 4 3 2 1

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Gary L. Musser is Professor Emeritus from Oregon State University. He earned both his B.S. in Mathematics Education in 1961 and his M.S. in Mathematics in 1963 at the University of Michigan and his Ph.D. in Mathematics (Radical Theory) in 1970 at the University of Miami in Florida. He taught at the junior and senior high, junior college college, and university levels for more than 30 years. He spent his final 24 years teaching prospective teachers in the Department of Mathematics at Oregon State University. While at OSU, Dr. Musser developed the mathematics component of the elementary teacher program. Soon after Profesor William F. Burger joined the OSU Department of Mathematics in a similar capacity, the two of them began to write the first edtion of this book. Professor Burger passed away during the preparation of the second edition, and Professor Blake E. Peterson was hired at OSU as his replacement. Professor Peter- son joined Professor Musser as a coauthor beginning with the fifth edition.

Professor Musser has published 40 papers in many journals, including the Pacific Journal of Mathematics, Canadian Journal of Mathematics, The Mathematics Association of America Monthly, the NCTM’s The Mathematics Teacher, the NCTM’s The Arithmetic Teacher, School Science and Mathematics, The Oregon Mathematics Teacher, and The Computing Teacher. In addition, he is a coauthor of two other college mathematics books: College Geometry—A Problem-Solving Approach with Applications (2008) and A Mathematical View of Our World (2007). He also coauthored the K-8 series Mathematics in Action. He has given more than 65 invited lectures/ workshops at a variety of conferences, including NCTM and MAA conferences, and was awarded 15 federal, state, and local grants to improve the teaching of mathematics.

While Professor Musser was at OSU, he was awarded the university’s prestigious College of Science Carter Award for Teaching. He is currently living in sunny Las Vegas, were he continues to write, ponder the mysteries of the stock market, enjoy living with his wife and his faithful yellow lab, Zoey.

Blake E. Peterson is currently a Professor in the Department of Mathematics Educa- tion at Brigham Young University. He was born and raised in Logan, Utah, where he graduated from Logan High School. Before completing his BA in secondary mathe- matics education at Utah State University, he spent two years in Japan as a missionary for The Church of Jesus Christ of Latter Day Saints. After graduation, he took his new wife, Shauna, to southern California, where he taught and coached at Chino High School for two years. In 1988, he began graduate school at Washington State Univer- sity, where he later completed a M.S. and Ph.D. in pure mathematics.

After completing his Ph.D., Dr. Peterson was hired as a mathematics educator in the Department of Mathematics at Oregon State University in Corvallis, Oregon, where he taught for three years. It was at OSU where he met Gary Musser. He has since moved his wife and four children to Provo, Utah, to assume his position at Brigham Young University where he is currently a full professor.

Dr. Peterson has published papers in Rocky Mountain Mathematics Journal, The American Mathematical Monthly, The Mathematical Gazette, Mathematics Magazine, The New England Mathematics Journal, School Science and Mathematics, The Journal of Mathematics Teacher Education, and The Journal for Research in Mathematics as well as chapters in several books. He has also published in NCTM’s Mathematics Teacher, and Mathematics Teaching in the Middle School. His research interests are teacher education in Japan and productive use of student mathematical thinking during instruction, which is the basis of an NSF grant that he and 3 of his colleagues were recently awarded. In addition to teaching, research, and writing, Dr. Peterson has done consulting for the College Board, founded the Utah Association of Mathematics Teacher Educators, and has been the chair of the editorial panel for the Mathematics Teacher.

Aside from his academic interests, Dr. Peterson enjoys spending time with his family, fulfilling his church responsi- bilities, playing basketball, mountain biking, water skiing, and working in the yard.

v

ABOUT THE AUTHORS

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vi

Are you puzzled by the numbers on the cover? They are 25 different randomly selected counting numbers from 1 to 100. In that set of numbers, two different arithmetic pro- gressions are highlighted. (An arithmetic progression is a sequence of numbers with a common difference between consecutive pairs.) For example, the sequence highlighted in green, namely 7, 15, 23, 31, is an arithmetic progression because the difference between 7 and 15 is 8, between 15 and 23 is 8, and between 23 and 31 is 8. Thus, the sequence 7, 15, 23, 31 forms an arithmetic progression of length 4 (there are 4 numbers in the sequence) with a common difference of 8. Similarly, the numbers highlighted in red, namely 45, 69, 93, form another arithmetic progression. This progression is of length 3 which has a common difference of 24.

You may be wondering why these arithmetic progressions are on the cover. It is to acknowledge the work of the mathematician Endre Szemerédi. On May 22, 2012, he was awarded the $1,000,000 Abel prize from the Norwegian Academy of Science and Letters for his analysis of such progressions. This award recognizes mathematicians for their contributions to mathematics that have a far reaching impact. One of Pro- fessor Szemerédi’s significant proofs is found in a paper he wrote in 1975. This paper proved a famous conjecture that had been posed by Paul Erdös and Paul Turán in 1936. Szemerédi’s 1975 paper and the Erdös/Turán conjecture are about finding arith- metic progressions in random sets of counting numbers (or integers). Namely, if one randomly selects half of the counting numbers from 1 and 100, what lengths of arith- metic progressions can one expect to find? What if one picks one-tenth of the numbers from 1 to 100 or if one picks half of the numbers between 1 and 1000, what lengths of arithmetic progressions is one assured to find in each of those situations? While the result of Szemerédi’s paper was interesting, his greater contribution was that the tech- nique used in the proof has been subsequently used by many other mathematicians.

Now let’s go back to the cover. Two progressions that were discussed above, one of length 4 and one of length 3, are shown in color. Are there others of length 3? Of length 4? Are there longer ones? It turns out that there are a total of 28 different arithmetic progressions of length three, 3 arithmetic progressions of length four and 1 progression of length five. See how many different progressions you can find on the cover. Perhaps you and your classmates can find all of them.

ABOUT THE COVER

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viivii

1 Introduction to Problem Solving 2

2 Sets, Whole Numbers, and Numeration 42

3 Whole Numbers: Operations and Properties 84

4 Whole Number Computation—Mental, Electronic, and Written 128

5 Number Theory 174

6 Fractions 206

7 Decimals, Ratio, Proportion, and Percent 250

8 Integers 302

9 Rational Numbers, Real Numbers, and Algebra 338

10 Statistics 412

11 Probability 484

12 Geometric Shapes 546

13 Measurement 644

14 Geometry Using Triangle Congruence and Similarity 716

15 Geometry Using Coordinates 780

16 Geometry Using Transformations 820

Epilogue: An Eclectic Approach to Geometry 877

Topic 1 Elementary Logic 881

Topic 2 Clock Arithmetic: A Mathematical System 891

Answers to Exercise/Problem Sets A and B, Chapter Reviews, Chapter Tests, and Topics Section A1

Index I1

Contents of Book Companion Web Site

Resources for Technology Problems

Technology Tutorials

Webmodules

Additional Resources

Videos

BRIEF CONTENTS

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viii

Preface xi

1 Introduction to Problem Solving 2 1.1 The Problem-Solving Process and Strategies 5 1.2 Three Additional Strategies 21

2 Sets, Whole Numbers, and Numeration 42 2.1 Sets as a Basis for Whole Numbers 45 2.2 Whole Numbers and Numeration 57 2.3 The Hindu–Arabic System 67

3 Whole Numbers: Operations and Properties 84 3.1 Addition and Subtraction 87 3.2 Multiplication and Division 101 3.3 Ordering and Exponents 116

4 Whole Number Computation—Mental, Electronic, and Written 128 4.1 Mental Math, Estimation, and Calculators 131 4.2 Written Algorithms for Whole-Number Operations 145 4.3 Algorithms in Other Bases 162

5 Number Theory 174 5.1 Primes, Composites, and Tests for Divisibility 177 5.2 Counting Factors, Greatest Common Factor, and Least

Common Multiple 190

6 Fractions 206 6.1 The Set of Fractions 209 6.2 Fractions: Addition and Subtraction 223 6.3 Fractions: Multiplication and Division 233

7 Decimals, Ratio, Proportion, and Percent 250 7.1 Decimals 253 7.2 Operations with Decimals 262 7.3 Ratio and Proportion 274 7.4 Percent 283

8 Integers 302 8.1 Addition and Subtraction 305 8.2 Multiplication, Division, and Order 318

CONTENTS

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ix

9 Rational Numbers, Real Numbers, and Algebra 338 9.1 The Rational Numbers 341 9.2 The Real Numbers 358 9.3 Relations and Functions 375 9.4 Functions and Their Graphs 391

10 Statistics 412 10.1 Statistical Problem Solving 415 10.2 Analyze and Interpret Data 440 10.3 Misleading Graphs and Statistics 460

11 Probability 484 11.1 Probability and Simple Experiments 487 11.2 Probability and Complex Experiments 502 11.3 Additional Counting Techniques 518 11.4 Simulation, Expected Value, Odds, and Conditional

Probability 528

12 Geometric Shapes 546 12.1 Recognizing Geometric Shapes—Level 0 549 12.2 Analyzing Geometric Shapes—Level 1 564 12.3 Relationships Between Geometric Shapes—Level 2 579 12.4 An Introduction to a Formal Approach to Geometry 589 12.5 Regular Polygons, Tessellations, and Circles 605 12.6 Describing Three-Dimensional Shapes 620

13 Measurement 644 13.1 Measurement with Nonstandard and Standard Units 647 13.2 Length and Area 665 13.3 Surface Area 686 13.4 Volume 696

14 Geometry Using Triangle Congruence and Similarity 716 14.1 Congruence of Triangles 719 14.2 Similarity of Triangles 729 14.3 Basic Euclidean Constructions 742 14.4 Additional Euclidean Constructions 755 14.5 Geometric Problem Solving Using Triangle Congruence

and Similarity 765

15 Geometry Using Coordinates 780 15.1 Distance and Slope in the Coordinate Plane 783 15.2 Equations and Coordinates 795 15.3 Geometric Problem Solving Using Coordinates 807

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x

16 Geometry Using Transformations 820 16.1 Transformations 823 16.2 Congruence and Similarity Using Transformations 846 16.3 Geometric Problem Solving Using Transformations 863

Epilogue: An Eclectic Approach to Geometry 877

Topic 1. Elementary Logic 881

Topic 2. Clock Arithmetic: A Mathematical System 891

Answers to Exercise/Problem Sets A and B, Chapter Reviews, Chapter Tests, and Topics Section A1

Index I1

Contents of Book Companion Web Site Resources for Technology Problems

eManipulatives Spreadsheet Activities Geometer’s Sketchpad Activities

Technology Tutorials Spreadsheets Geometer’s Sketchpad Programming in Logo Graphing Calculators

Webmodules Algebraic Reasoning Children’s Literature Introduction to Graph Theory

Additional Resources Guide to Problem Solving Problems for Writing/Discussion Research Articles Web Links

Videos Book Overview Author Walk-Through Videos Children’s Videos

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PREFACE

W elcome to the study of the foundations of ele-mentary school mathematics. We hope you will find your studies enlightening, useful, and fun. We salute you for choosing teaching as a profession and hope that your experiences with this book will help prepare you to be the best possible teacher of mathematics that you can be. We have presented this elementary mathematics material from a variety of perspectives so that you will be better equipped to address that broad range of learning styles that you will encounter in your future students. This book also encourages prospective teachers to gain the ability to do the mathematics of elementary school and to understand the underlying concepts so they will be able to assist their students, in turn, to gain a deep understand- ing of mathematics.

We have also sought to present this material in a man- ner consistent with the recommendations in (1) The Mathematical Education of Teachers prepared by the Conference Board of the Mathematical Sciences, (2) the National Council of Teachers of Mathematics’ Standards Documents, and (3) The Common Core State Standards for Mathematics. In addition, we have received valuable advice from many of our colleagues around the United States through questionnaires, reviews, focus groups, and personal communications. We have taken great care to respect this advice and to ensure that the content of the book has mathematical integrity and is accessible and helpful to the variety of students who will use it. As al- ways, we look forward to hearing from you about your experiences with our text.

GARY L. MUSSER, glmusser@cox.net BLAKE E. PETERSON, peterson@mathed.byu.edu

Unique Content Features Number Systems The order in which we present the number systems in this book is unique and most relevant to elementary school teachers. The topics are covered to parallel their evolution historically and their development in the elementary/middle school curriculum. Fractions and integers are treated separately as an extension of the whole numbers. Then rational numbers can be treated at a brisk pace as extensions of both fractions (by adjoining their opposites) and integers (by adjoining their appro- priate quotients) since students have a mastery of the concepts of reciprocals from fractions (and quotients) and opposites from integers from preceding chapters. Longtime users of this book have commented to us that this whole numbers-fractions-integers-rationals-reals

approach is clearly superior to the seemingly more effi- cient sequence of whole numbers-integers-rationals-reals that is more appropriate to use when teaching high school mathematics.

Approach to Geometry Geometry is organized from the point of view of the five-level van Hiele model of a child’s development in geometry. After studying shapes and measurement, geometry is approached more formally through Euclidean congruence and similarity, coordinates, and transformations. The Epilogue provides an eclectic approach by solving geometry problems using a variety of techniques.

Additional Topics Topic 1, “Elementary Logic,” may be used anywhere in a course.

Topic 2, “Clock Arithmetic: A Mathematical System,” uses the concepts of opposite and reciprocal and hence may be most instructive after Chapter 6, “Fractions,” and Chapter 8, “Integers,” have been completed. This section also contains an introduction to modular arithmetic.

Underlying Themes Problem Solving An extensive collection of problem- solving strategies is developed throughout the book; these strategies can be applied to a generous supply of problems in the exercise/problem sets. The depth of problem-solving coverage can be varied by the number of strategies selected throughout the book and by the problems assigned.

Deductive Reasoning The use of deduction is pro- moted throughout the book The approach is gradual, with later chapters having more multistep problems. In particular, the last sections of Chapters 14, 15, and 16 and the Epilogue offer a rich source of interesting theo- rems and problems in geometry.

Technology Various forms of technology are an inte- gral part of society and can enrich the mathematical understanding of students when used appropriately. Thus, calculators and their capabilities (long division with remainders, fraction calculations, and more) are introduced throughout the book within the body of the text.

In addition, the book companion Web site has eMa- nipulatives, spreadsheets, and sketches from Geometer’s

xi

FMPreface.indd 11 8/1/2013 12:05:27 PM

mailto:glmusser@cox.net
mailto:peterson@mathed.byu.edu
xii Preface

Sketchpad®. The eManipulatives are electronic versions of the manipulatives commonly used in the elementary classroom, such as the geoboard, base ten blocks, black and red chips, and pattern blocks. The spreadsheets contain dynamic representations of functions, statistics, and probability simulations. The sketches in Geometer’s Sketchpad® are dynamic representations of geomet- ric relationships that allow exploration. Exercises and problems that involve eManipulatives, spreadsheets, and Geometer’s Sketchpad® sketches have been integrated into the problem sets throughout the text.

Course Options We recognize that the structure of the mathematics for elementary teachers course will vary depending upon the college or university. Thus, we have organized this text so that it may be adapted to accommodate these differences.

Basic course: Chapters 1-7 Basic course with logic: Topic 1, Chapters 1–7 Basic course with informal geometry: Chapters 1–7,

12 Basic course with introduction to geometry and mea-

surement: Chapters 1–7, 12, 13

Summary of Changes to the Tenth Edition

Mathematical Tasks have been added to sections throughout the book to allow instructors more flex- ibility in how they choose to organize their classroom instruction. These tasks are designed to be investigated by the students in class. As the solutions to these tasks are discussed by students and the instructor, the big ideas of the section emerge and can be solidified through a classroom discussion.

Chapter 6 contains a new discussion of fractions on a number line to be consistent with the Common Core standards.

Chapter 10 has been revised to include a discus- sion of recommendations by the GAISE document and the NCTM Principles and Standards for School Mathematics. These revisions include a discussion of steps to statistical problem solving. Namely, (1) formulate questions, (2) collect data, (3) organize and display data, (4) analyze and interpret data. These steps are then applied in several of the examples through the chapter.

Chapter 12 has been substantially revised. Sections 12.1, 12.2, and 12.3 have been organized to parallel the first three van Hiele levels. In this way, students will be able to pass through the levels in a more meaningful fashion so that they will get a strong feeling about how

their students will view geometry at various van Hiele levels.

Chapter 13 contains several new examples to give stu- dents the opportunity to see how the various equations for area and volume are applied in different contexts.

Children’s Videos are videos of children solving math- ematical problems linked to QR codes placed in the margin of the book in locations where the content being discussed is related to the content of the prob- lems being solved by the children. These videos will bring the mathematical content being studied to life.

Author Walk-Throughs are videos linked to the QR code on the third page of each chapter. These brief videos are of an author, Blake Peterson, describing and showing points of major emphasis in each chapter so students’ study can be more focused.

Children’s Literature and Reflections from Research margin notes have been revised/refreshed.

Common Core margin notes have been added through- out the text to highlight the correlation between the content of this text and the Common Core standards.

Professional recommendation statements from the Common Core State Standards for Mathematics, the National Council of Teachers of Mathematics’ Principles and Standards for School Mathematics, and the Curriculum Focal Points, have been compiled on the third page of each chapter.

Pedagogy The general organization of the book was motivated by the following mathematics learning cube:

The three dimensions of the cube—cognitive levels, representational levels, and mathematical content—are integrated throughout the textual material as well as in the problem sets and chapter tests. Problem sets are organized into exercises (to support knowledge, skill, and understanding) and problems (to support problem solv- ing and applications).

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Preface xiii

We have developed new pedagogical features to imple- ment and reinforce the goals discussed above and to address the many challenges in the course.

Summary of Pedagogical Changes to the Tenth Edition

Student Page Snapshots have been updated.

Reflection from Research margin notes have been edited and updated.

Mathematical Structure reveals the mathematical ideas of the book. Main Definitions, Theorems, and Properties in each section are highlighted in boxes for quick review.

Children’s Literature references have been edited and updated. Also, there is additional material offered on the Web site on this topic.

Check for Understanding have been updated to reflect the revision of the problem sets.

Mathematical Tasks have been integrated throughout.

Author Walk-Throughs videos have been made avail- able via QR codes on the third page of every chapter.

Children’s videos, produced by Blake Peterson and available via QR codes, have been integrated through- out.

Key Features Problem-Solving Strategies are integrated throughout the book. Six strategies are introduced in Chapter 1. The last strategy in the strategy box at the top of the second page of each chapter after Chapter l contains a new strategy.

Mathematical Tasks are located in various places throughout each section. These tasks can be presented to the whole class or small groups to investigate. As the stu-

dents discuss their solutions with each other and the instructor, the big mathematical ideas of the sec- tion emerge.

FMPreface.indd 13 8/1/2013 12:05:28 PM

xiv Preface

Technology Problems appear in the Exercise/Problem sets throughout the book. These problems rely on and are enriched by the use of technology. The tech- nology used includes activities from the eManipulaties (virtual manipulatives),

spreadsheets, Geometer’s Sketchpad®, and the TI-34 II MultiView. Most of these technological resources can be accessed through the accompany- ing book companion Web site.

Student Page Snapshots have been updated. Each chapter has a page from an elementary school textbook relevant to the material being studied. Exercise/Problem Sets are separated into Part A

(all answers are provided in the back of the book and all solutions are provided in our supplement Hints and Solutions for Part A Problems) and Part B (answers are only provided in the Instructors Resource Manual). In addition, exercises and problems are distinguished so that students can learn how they differ.

Analyzing Student Thinking Problems are found at the end of the Exercise/Problem Sets. These problems are questions that elementary students might ask their teachers, and they focus on common misconceptions that are held by students. These problems give future teachers an opportunity to think about the concepts they have learned in the sec- tion in the context of teaching.

Curriculum Standards The NCTM Standards and Curriculum Focal Points and the Common Core State Standards are introduced on the third page of each chapter. In addition, margin notes involving these standards are contained throughout the book.

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Preface xv

Historical Vignettes open each chapter and introduce ideas and concepts central to each chapter.

Mathematical Morsels end every setion with an interesting historical tidbit. One of our students referred to these as a reward for completing the section.

Children’s Videos are author-led videos of children solving mathematical problems linked to QR codes in the margin of the book. The codes are placed in locations where the content being discussed is related to the content of the problems being solved by the children. These videos provide a window into how children think mathematically.

B la

ke E

. P et

er so

n

See one Live!

Reflection from Research Extensive research has been done in the mathematics education community that

focuses on the teaching and learning of elemen- tary mathematics. Many important quotations from research are given in the margins to sup- port the content nearby.

Children’s Literature These margin inserts provide many examples of books that can be used to connect reading and mathematics. They should be invaluable to you when you begin teachig.

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xvi Preface

People in Mathematics, a feature near the end of each chapter, high- lights many of the giants in mathemat- ics throughout history.

A Chapter Review is located at the end of each chapter.

A Chapter Test is found at the end of each chapter.

An Epilogue, following Chapter 16, provides a rich eclectic approach to geometry.

Logic and Clock Arithmetic are developed in topic sections near the end of the book.

Supplements for Students Student Activities Manual with Discussion Questions for the Classroom This activity manual is designed to enhance student learning as well as to model effective classroom practices. Since many instructors are working with students to create a personalized journal, this edition of the manual is shrink-wrapped and three-hole punched for easy customization. This supplement is an extensive revi- sion of the Student Resoure Handbook that was authored by Karen Swenson and Marcia Swanson for the first six editions of this book.

ISBN 978-1-118-67904-3

Features Include:

Hands-On Activities: Activities that help develop initial understandings at the concrete level. Discussion Questions for the Classroom: Tasks designed to engage students with mathematical ideas by stimulating communication. Mental Math: Short activities to help develop mental math skills. Exercises: Additional practice for building skills in concepts. Directions in Education: Specially written articles that provide insights into major issues of the day, including the Standards of the National Council of Teachers of Mathematics. Solutions: Solutions to all items in the handbook to enhance self-study. Two-Dimensional Manipulatives: Cutouts are provided on cardstock.

—Prepared by Lyn Riverstone of Oregon State University

The ETA Cuisenalre® Physical Manipulative Kit A generous assortment of manipulatives (including blocks, tiles, geoboards, and so forth) has been created to accompany the text as well as the Student Activity Manual. lt is available to be packaged with the text. Please contact your local Wiley representative for ordering information.

ISBN 978-1-118-67923-4

Student Hints and Solutions Manual for Part A Problems This manual contains hints and solutions to all of the Part A problems. It can be used to help students develop problem-solving profi- ciency in a self-study mode. The features include:

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Preface xvii

Hints: Give students a start on all Part A problems in the text.

Additional Hints: A second hint is provided for more challenging problems.

Complete Solutions to Part A Problems: Carefully written-out solutions are provided to model one correct solution.

—Developed by Lynn Trimpe, Vikki Maurer, and Roger Maurer of Linn-Benton Community College.

ISBN 978-1-118-67925-8

Companion Web site http://www.wiley.com/college/musser The companion Web site provides a wealth of resources for students.

Resources for Technology Problems These problems are integrated into the problem sets throughout the book and are denoted by a mouse icon.

eManipulatives mirror physical manipulatives as well as provide dynamic representations of other mathematical situations. The goal of using the eManipulatives is to engage learners in a way that will lead to a more in-depth understanding of the concepts and to give them experience thinking about the mathematics that underlies the manipulatives.

—Prepared by Lawrence O. Cannon, E. Robert Heal, and Joel Duffin of Utah State University, Richard Wellman of Westminster College, and Ethalinda K. S. Cannon of A415software.com.

This project is supported by the National Science Foundation.

The Geometer’s Sketchpad® activities allow students to use the dynamic capabilities of this software to investigate geometric properties and relationships. They are accessible through a Web browser so having the software is not necessary.

The Spreadsheet activities utilize the iterative properties of spreadsheets and the user friendly interface to investigate problems ranging from graphs of functions to standard deviation to simulations of rolling dice.

Technology Tutorials The Geometer’s Sketchpad® tutorial is written for those students who have access to the software and who are interested in investigating problems of their own choosing. The tutorial gives basic instruction on how to use the software and includes some sample problems that will help the students gain a better understanding of the software and the geometry that could be learned by using it.

—Prepared by Armando Martinez-Cruz, California State University, Fullerton.

The Spreadsheet Tutorial is written for students who are interested in learning how to use spreadsheets to investi- gate mathematical problems. The tutorial describes some of the functions of the software and provides exercises for students to investigate mathematics using the software.

—Prepared by Keith Leatham, Brigham Young University.

Webmodules The Algebraic Reasoning Webmodule helps students understand the critical transition from arithmetic to algebra. It also highlights situations when algebra is, or can be, used. Marginal notes are placed in the text at the appropriate locations to direct students to the webmodule.

—Prepared by Keith Leatham, Brigham Young University.

The Children’s Literature Webmodule provides references to many mathematically related examples of children’s books for each chapter. These references are noted in the margins near the mathematics that corresponds to the content of the book. The webmodule also contains ideas about using children’s literature in the classroom.

—Prepared by Joan Cohen Jones, Eastern Michigan University.

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xviii Preface

The Introduction to Graph Theory Webmodule has been moved from the Topics to the companion Web site to save space in the book and yet allow professors the flexibility to download it from the Web if they choose to use it.

The companion Web site also includes:

Links to NCTM Standards

Links to Common Core Standards

A Logo and TI-83 graphing calculator tutorial

Four cumulative tests covering material up to the end of Chapters 4, 9, 12, and 16

Research Article References: A complete list of references for the research articles that are mentioned in the Reflection from Research margin notes throughout the book

Guide to Problem Solving This valuable resource, available as a webmodule on the companion Web site, contains more than 200 creative problems keyed to the problem solving strategies in the textbook and includes:

Opening Problem: an introductory problem to motivate the need for a strategy.

Solution/Discussion/Clues: A worked-out solution of the opening problem together with a discussion of the strategy and some clues on when to select this strategy.

Practice Problems: A second problem that uses the same strategy together with a worked out solution and two practice problems.

Mixed Strategy Practice: Four practice problems that can be solved using one or more of the strategies introduced to that point.

Additional Practice Problems and Additional Mixed Strategy Problems: Sections that provide more practice for par- ticular strategies as well as many problems for which students need to identify appropriate strategies.

—Prepared by Don Miller, who retired as a professor of mathematics at St. Cloud State University.

Problems for Writing and Discussion are problems that require an analysis of ideas and are good opportunities to write about the concepts in the book. Most of the Problems for Writing/Discussion that preceded the Chapter Tests in the Eighth Edition now appear on our Web site.

The Geometer’s Sketchpad© Developed by Key Curriculum Press, this dynamic geometry construction and exploration tool allows users to create and manipulate precise figures while preserving geometric relationships. This software is only available when packaged with the text. Please contact your local Wiley representative for further details.

WileyPLUS WileyPLUS is a powerful online tool that will help you study more effectively, get immediate feedback when you practice on your own, complete assignments and get help with problem solving, and keep track of how you’re doing—all at one easy-to-use Web site.

Resources for the Instructor Companion Web Site The companion Web site is available to text adopters and provides a wealth of resources including:

PowerPoint Slides of more than 190 images that include figures from the text and several generic masters for dot paper, grids, and other formats.

Instructors also have access to all student Web site features. See above for more details.

Instructor Resource Manual This manual contains chapter-by-chapter discussions of the text material, student “expectations” (objectives) for each chapter, answers for all Part B exercises and problems, and answers for all of the even-numbered problems in the Guide to Problem-Solving.

—Prepared by Lyn Riverstone, Oregon State University ISBN 978-1-118-67924-1

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Computerized/Print Test Bank The Computerized/Printed Test Bank includes a collection of over 1,100 open response, multiple-choice, true/false, and free-response questions, nearly 80% of which are algorithmic.

—Prepared by Mark McKibben, Goucher College

WileyPLUS WileyPLUS is a powerful online tool that provides instructors with an integrated suite of resources, including an online version of the text, in one easy-to-use Web site. Organized around the essential activities you perform in class, WileyPLUS allows you to create class presentations, assign homework and quizzes for automatic grading, and track student progress. Please visit http://edugen.wiley.com or contact your local Wiley representative for a demonstration and further details.

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http://edugen.wiley.com
ACKNOWLEDGMENTS

During the development of Mathematics for Elementary Teach- ers, Eighth, Ninth, and Tenth Editions, we benefited from comments, suggestions, and evaluations from many of our col- leagues. We would like to acknowledge the contributions made by the following people:

Reviewers for the Tenth Edition