Mathematics for Elementary Teachers

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 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 Professor William F. Burger joined the OSU Department of Mathematics in a similar capacity, the two of them began to write the first edition 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 Peterson 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 Education 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 mathematics 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 University, 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 responsibilities, playing basketball, mountain biking, water skiing, and working in the yard.

• Preface xi1 Introduction to Problem Solving 21.1 The Problem-Solving Process and Strategies 51.2 Three Additional Strategies 212 Sets, Whole Numbers, and Numeration 422.1 Sets as a Basis for Whole Numbers 452.2 Whole Numbers and Numeration 572.3 The Hindu–Arabic System 673 Whole Numbers: Operations and Properties 843.1 Addition and Subtraction 873.2 Multiplication and Division 1013.3 Ordering and Exponents 1164 Whole Number Computation—Mental, Electronic, and Written 1284.1 Mental Math, Estimation, and Calculators 1314.2 Written Algorithms for Whole-Number Operations 1454.3 Algorithms in Other Bases 1625 Number Theory 1745.1 Primes, Composites, and Tests for Divisibility 1775.2 Counting Factors, Greatest Common Factor, and Least Common Multiple 1906 Fractions 2066.1 The Set of Fractions 2096.2 Fractions: Addition and Subtraction 2236.3 Fractions: Multiplication and Division 2337 Decimals, Ratio, Proportion, and Percent 2507.1 Decimals 2537.2 Operations with Decimals 2627.3 Ratio and Proportion 2747.4 Percent 2838 Integers 3028.1 Addition and Subtraction 3058.2 Multiplication, Division, and Order 3189 Rational Numbers, Real Numbers, and Algebra 3389.1 The Rational Numbers 3419.2 The Real Numbers 3589.3 Relations and Functions 3759.4 Functions and Their Graphs 39110 Statistics 41210.1 Statistical Problem Solving 41510.2 Analyze and Interpret Data 44010.3 Misleading Graphs and Statistics 46011 Probability 48411.1 Probability and Simple Experiments 48711.2 Probability and Complex Experiments 50211.3 Additional Counting Techniques 51811.4 Simulation, Expected Value, Odds, and Conditional Probability 52812 Geometric Shapes 54612.1 Recognizing Geometric Shapes—Level 0 54912.2 Analyzing Geometric Shapes—Level 1 56412.3 Relationships between Geometric Shapes—Level 2 57912.4 An Introduction to a Formal Approach to Geometry 58912.5 Regular Polygons, Tessellations, and Circles 60512.6 Describing Three-Dimensional Shapes 62013 Measurement 64413.1 Measurement with Nonstandard and Standard Units 64713.2 Length and Area 66513.3 Surface Area 68613.4 Volume 69614 Geometry Using Triangle Congruence and Similarity 71614.1 Congruence of Triangles 71914.2 Similarity of Triangles 72914.3 Basic Euclidean Constructions 74214.4 Additional Euclidean Constructions 75514.5 Geometric Problem Solving Using Triangle Congruence and Similarity 76515 Geometry Using Coordinates 78015.1 Distance and Slope in the Coordinate Plane 78315.2 Equations and Coordinates 79515.3 Geometric Problem Solving Using Coordinates 80716 Geometry Using Transformations 82016.1 Transformations 82316.2 Congruence and Similarity Using Transformations 84616.3 Geometric Problem Solving Using Transformations 863Epilogue: An Eclectic Approach to Geometry 877Topic 1. Elementary Logic 881Topic 2. Clock Arithmetic: A Mathematical System 891Answers to Exercise/Problem Sets A and B, Chapter Reviews, Chapter Tests, and Topics Section A1Index i1Contents of Book Companion Web SiteResources for Technology ProblemseManipulativesSpreadsheet ActivitiesGeometer’s Sketchpad ActivitiesTechnology TutorialsSpreadsheetsGeometer’s SketchpadProgramming in LogoGraphing CalculatorsWebmodulesAlgebraic ReasoningChildren’s LiteratureIntroduction to Graph TheoryAdditional ResourcesGuide to Problem SolvingProblems for Writing/DiscussionResearch ArticlesWeb LinksVideosBook OverviewAuthor Walk-Through VideosChildren’s Videos