Table of Contents

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

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

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

About the Author

Gary L. Musser is Professor Emeritus from Oregon StateUniversity. He earned both his B.S. in Mathematics Education in1961 and his M.S. in Mathematics in 1963 at the University ofMichigan and his Ph.D. in Mathematics (Radical Theory) in 1970 atthe University of Miami in Florida. He taught at the junior andsenior high, junior college and university levels for more than 30years. He spent his final 24 years teaching prospective teachers inthe Department of Mathematics at Oregon State University. While atOSU, Dr. Musser developed the mathematics component of theelementary teacher program. Soon after Professor William F. Burgerjoined the OSU Department of Mathematics in a similar capacity, thetwo of them began to write the first edition of this book.Professor Burger passed away during the preparation of the secondedition, and Professor Blake E. Peterson was hired at OSU as hisreplacement. Professor Peterson joined Professor Musser as acoauthor beginning with the fifth edition. Professor Musser has published 40 papers in many journals,including the Pacific Journal of Mathematics, Canadian Journalof Mathematics, The Mathematics Association of America Monthly,the NCTM s The Mathematics Teacher, the NCTM sThe Arithmetic Teacher, School Science and Mathematics, TheOregon Mathematics Teacher, and The Computing Teacher.In addition, he is a coauthor of two other college mathematicsbooks: College Geometry A Problem-Solving Approachwith Applications (2008) and A Mathematical View of OurWorld (2007). He also coauthored the K-8 series Mathematicsin Action. He has given more than 65 invited lectures/workshops at a variety of conferences, including NCTM and MAAconferences, and was awarded 15 federal, state, and local grants toimprove the teaching of mathematics. While Professor Musser was at OSU, he was awarded theuniversity s prestigious College of Science Carter Award forTeaching. He is currently living in sunny Las Vegas, were hecontinues to write, ponder the mysteries of the stock market, enjoyliving with his wife and his faithful yellow lab, Zoey. Blake E. Peterson is currently a Professor in theDepartment of Mathematics Education at Brigham Young University. Hewas born and raised in Logan, Utah, where he graduated from LoganHigh School. Before completing his BA in secondary mathematicseducation at Utah State University, he spent two years in Japan asa missionary for The Church of Jesus Christ of Latter Day Saints.After graduation, he took his new wife, Shauna, to southernCalifornia, where he taught and coached at Chino High School fortwo years. In 1988, he began graduate school at Washington StateUniversity, where he later completed a M.S. and Ph.D. in puremathematics. After completing his Ph.D., Dr. Peterson was hired as a mathematicseducator in the Department of Mathematics at Oregon StateUniversity in Corvallis, Oregon, where he taught for three years.It was at OSU where he met Gary Musser. He has since moved his wifeand four children to Provo, Utah, to assume his position at BrighamYoung University where he is currently a full professor. Dr. Peterson has published papers in Rocky Mountain MathematicsJournal, The American Mathematical Monthly, The MathematicalGazette, Mathematics Magazine, The New England Mathematics Journal,School Science and Mathematics, The Journal of Mathematics TeacherEducation, and The Journal for Research in Mathematicsas well as chapters in several books. He has also published inNCTM s Mathematics Teacher, and MathematicsTeaching in the Middle School. His research interests areteacher education in Japan and productive use of studentmathematical thinking during instruction, which is the basis of anNSF grant that he and 3 of his colleagues were recently awarded. Inaddition to teaching, research, and writing, Dr. Peterson has doneconsulting for the College Board, founded the Utah Association ofMathematics Teacher Educators, and has been the chair of theeditorial panel for the Mathematics Teacher. Aside from his academic interests, Dr. Peterson enjoys spendingtime with his family, fulfilling his church responsibilities,playing basketball, mountain biking, water skiing, and working inthe yard.