Table of Contents:
Chapter 1 An Introduction to Problem Solving
1-1 Mathematics and Problem Solving
1-2 Explorations with Patterns
1-3 Algebraic Thinking
1-4 Logic: An Introduction
Chapter 2 Sets, Whole Numbers, and Functions
2-1 Describing Sets
2-2 Other Set Operations and Their Properties
2-3 Addition and Subtraction of Whole Numbers
2-4 Multiplication and Division of Whole Numbers
2-5 Functions
Chapter 3 Numeration Systems and Whole-Number Computation
3-1 Numeration Systems
3-2 Algorithms for Whole-Number Addition and Subtraction
3-3 Algorithms for Whole-Number Multiplication and Division
3-4 Mental Mathematics and Estimation for Whole-Number Operations
Chapter 4 Integers and Number Theory
4-1 Integers and the Operations of Addition and Subtraction
4-2 Multiplication and Division of Integers
4-3 Divisibility
4-4 Prime and Composite Numbers
4-5 Greatest Common Divisor and Least Common Multiple
4-6 Clock and Modular Arithmetic
Chapter 5 Rational Numbers as Fractions
5-1 The Set of Rational Numbers
5-2 Addition and Subtraction of Rational Numbers
5-3 Multiplication and Division of Rational Numbers
5-4 Proportional Reasoning
Chapter 6 Decimals, Percents, and Real Numbers
6-1 Introduction to Decimals
6-2 Operations on Decimals
6-3 Nonterminating Decimals
6-4 Real Numbers
6-5 Percents
6-6 Computing Interest
Chapter 7 Probability
7-1 How Probabilities Are Determined
7-2 Multistage Experiments with Tree Diagrams and Geometric Probabilities
7-3 Using Simulations in Probability
7-4 Odds, Conditional Probability, and Expected Value
7-5 Using Permutations and Combinations in Probability
Chapter 8 Data Analysis/ Statistics: An Introduction
8-1 Statistical Graphs of Categorical and Numerical Data
8-2 Measures of Central Tendency and Variation
8-3 Abuses of Statistics
Chapter 9 Introductory Geometry
9-1 Basic Notions
9-2 Polygons
9-3 More About Angles
9-4 Geometry in Three Dimensions
9-5 Networks
Chapter 10 Constructions, Congruence, and Similarity
10-1 Congruence Through Constructions
10-2 Other Congruence Properties
10-3 Other Constructions
10-4 Similar Triangles and Similar Figures
10-5 Trigonometry Ratios via Similarity
10-6 Lines in a Cartesian Coordinate System
Chapter 11 Concepts of Measurement
11-1 Linear Measure
11-2 Areas of Polygons and Circles
11-3 The Pythagorean Theorem and the Distance Formula
11-4 Surface Areas
11-5 Volume, Mass & Temperature
Chapter 12 Motion Geometry and Tessellations
12-1 Translations and Rotations
12-2 Reflections and Glide Reflections
12-3 Size Transformations
12-4 Symmetries
12-5 Tesselations of the Plane
Appendix I: Using a Spreadsheet
Appendix II: Graphing Calculators
Appendix III: Using a Geometry Drawing Utility
About the Author :
Rick Billstein is a Professor of Mathematics at the University of Montana. He has worked in mathematics teacher education at this university for 40 years and his current research is in the areas of curriculum development and mathematics teacher education. He teaches courses for future teachers in the Mathematics Department and also is the site director for the Show-Me Project, an NSF-funded project supporting the dissemination and implementation of standards-based middle grades mathematics curricula. He worked on an NSF grant called Tinker Plots to develop new data analysis software and he serves on the Advisory Boards for several other national projects. From 1992-1997, he directed the NSF-funded Six Through Eight Mathematics (STEM) middle school mathematics curriculum project and is now directing the Middle Grades MATHThematics Phase II Project. Dr. Billstein has co-authored 24 books, including eight editions ofA Problem Solving Approach to Mathematics for Elementary Teachers. He typically does about 25 regional and national presentations per year and has traveled to Thailand to work with the international schools there. He has also presented at the International Conferences on Mathematics Education (ICME).
Shlomo Libeskind is a professor in the mathematics department at the University of Oregon in Eugene, Oregon. He is responsible for the "pre-college" teaching major in the department and has continuously been teaching and advising preservice and inservice teachers. Dr. Libeskind has extensive writing experience (books, articles, and workshop materials) as well as experience in directing mathematics education projects. Libeskind is an active member of Oregon Mathematics Council (OMEC) and has been involved in reviewing materials for the state of Oregon's standards for college admission.
Johnny W. Lott began his teaching career in the public schools of DeKalb County, Georgia, outside Atlanta. There he taught mathematics in grades 8-12. He also taught one year at the Westminster Schools, grades 9-12, and one year in the Pelican, Alaska, school, grades 6-12. In addition, he has taught in grade schools in Montana while at The University of Montana. Johnny has been co-author of several books and has written numerous articles and other essays in the "Arithmetic Teacher", "Teaching Children Mathematics", "The Mathematics Teacher", "School Science and Mathematics", "Student Math Notes", and "Mathematics Education Dialogues". He has been the Project Manager for the "Figure This!" publications and website developed by the National Council of Teachers of Mathematics (NCTM) and was project co-director of the State Systemic Initiative for Montana Mathematics and Science (SIMMS) Project. He has served on many NCTM committees, has been a member of its Board of Directors, and was its president from April 2002-April 2004. In the Department of Mathematical Sciences at The University of Montana, Dr. Lott was a full professor and served as department chair. He is currently the Director of the Center for Teaching Excellence at the University. His doctorate is in mathematics education from Georgia State University.
