"The authors have provided a unique, strategy-focused resource supported by a wealth of engaging examples that mathematics teachers can readily use to help students develop a more purposeful, systematic, and successful approach to problem solving." -Howard W. Smith, Superintendent Public Schools of the Tarrytowns, Sleepy Hollow, NY "Helps both new and veteran teachers better understand the nature of problem solving as a critical mathematics process. The authors present in very simple terms the strategies that are the backbone of mathematics instruction. This indispensable material is useful at all levels, from basic stages to advanced student work to the development of top problem solvers." -Daniel Jaye, Principal Bergen County Academies, Hackensack, NJ Help students become skilled and confident problem solvers! Demonstrating there is always more than one approach to solving a problem, well-known authors and educators Alfred S. Posamentier and Stephen Krulik present ten basic strategies that are effective for finding solutions to a wide range of mathematics problems. These tried-and-true methods-including working backwards, finding a pattern, adopting a different point of view, solving a simpler analogous problem, and making a visual representation-make problem solving easier, neater, and more understandable for students as well as teachers. Providing numerous sample problems that illustrate how mathematics teachers and specialists can incorporate these techniques into their mathematics curriculum, this updated edition also includes: A variety of new problems that show how to use the strategies References to current NCTM standards Solutions to the problems in each chapter Extensive discussions of the empowering strategies used to solve sample problems The second edition of Problem-Solving Strategies for Efficient and Elegant Solutions, Grades 6-12 helps teachers develop students' creative problem-solving skills for success in and out of school.

Preface About the Authors 1. Introduction to Problem-Solving Strategies 2. Working Backwards The Working Backwards Strategy in Everyday Life Problem-Solving Situations Applying the Working Backwards Strategy to Solve Mathematics Problems Problems Using the Working Backwards Strategy 3. Finding a Pattern The Finding a Pattern Strategy in Everyday Life Problem-Solving Situations Applying the Finding a Pattern Strategy to Solve Mathematics Problems Problems Using the Finding a Pattern Strategy 4. Adopting a Different Point of View The Adopting a Different Point of View Strategy in Everyday Life Problem-Solving Situations Applying the Adopting a Different Point of View Strategy to Solve Mathematics Problems Problems Using the Adopting a Different Point of View Strategy 5. Solving a Simpler Analogous Problem The Solving a Simpler Analogous Problem Strategy in Everyday Life Problem-Solving Situations Applying the Solving a Simpler Analogous Problem Strategy to Solve Mathematics Problems Problems Using the Solving a Simpler Analogous Problem Strategy 6. Considering Extreme Cases The Considering Extreme Cases Strategy in Everyday Life Problem-Solving Situations Applying the Considering Extreme Cases Strategy to Solve Mathematics Problems Problems Using the Considering Extreme Cases Strategy 7. Making a Drawing (Visual Representation) The Making a Drawing (Visual Representation) Strategy in Everyday Life Problem-Solving Situations Applying the Making a Drawing (Visual Representation) Strategy to Solve Mathematics Problems Problems Using the Making a Drawing (Visual Representation) Strategy 8. Intelligent Guessing and Testing (Including Approximation) The Intelligent Guessing and Testing (Including Approximation) Strategy in Everyday Life Problem-Solving Situations Applying the Intelligent Guessing and Testing (Including Approximation) Strategy to Solve Mathematics Problems Problems Using the Intelligent Guessing and Testing (Including Approximation) Strategy 9. Accounting for All Possibilities The Accounting for All Possibilities Strategy in Everyday Life Problem-Solving Situations Applying the Accounting for All Possibilities Strategy to Solve Mathematics Problems Problems Using the Accounting for All Possibilities Strategy 10. Organizing Data The Organizing Data Strategy in Everyday Life Problem-Solving Situations Applying the Organizing Data Strategy to Solve Mathematics Problems Problems Using the Organizing Data Strategy 11. Logical Reasoning The Logical Reasoning Strategy in Everyday Life Problem-Solving Situations Applying the Logical Reasoning Strategy to Solve Mathematics Problems Problems Using the Logical Reasoning Strategy Afterword by Herbert A. Hauptman Sources for Problems Readings on Problem Solving Index