Alfred S Posamentier

If you've been waiting for a book that will evoke the delight and intrigue that mathematics has to offer, this is the book for you. What are the odds of finding two people who share the same birth date in a room of thirty-five? Most people would guess they're pretty low. In actuality, the probability is better than 80 percent. This is just one of many entertaining examples of mathematical curiosities presented. Two veteran math educators have created the perfect introduction to the wonders of mathematics for the general reader, requiring only a high school background in the subject. Among the entertaining and useful tricks they teach are shortcuts in arithmetic, such as ways to determine at a glance the exact divisors of any given number. They also demonstrate how the properties of certain numbers can lead to infinite loops. What is particularly exciting is how many correct answers turn out to be counterintuitive. Exploring all these features will instill insights into the nature of numbers, improve your ability to manipulate them, and give you an appreciation for the inherent elegance of mathematics. As you marvel at the many unusual relationships and novelties revealed in this ingenious and delightful presentation, you'll be learning more math than you ever thought possible - and will be relishing every moment of it!

State curriculum standards are mandating more coverage of geometry, as are the curricula for pre-service mathematics education and in-service teaching. Yet many secondary teachers know just enough geometry to stay one chapter ahead of their students! What’s more, most college-level geometry texts don’t address their specific needs. Advanced Euclidean Geometry fills this void by providing a thorough review of the essentials of the high school geometry course and then expanding those concepts to advanced Euclidean geometry, to give teachers more confidence in guiding student explorations and questions. The text contains hundreds of illustrations created in The Geometer’s Sketchpad Dynamic Geometry® software, and it is packaged with a CD-ROM (for Windows®/Macintosh® formats) containing over 100 interactive sketches using Sketchpad™ (assumes that the user has access to the program).

"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, NJHelp 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 strategiesReferences to current NCTM standards Solutions to the problems in each chapterExtensive discussions of the empowering strategies used to solve sample problemsThe 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.

"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, NJHelp 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 strategiesReferences to current NCTM standards Solutions to the problems in each chapterExtensive discussions of the empowering strategies used to solve sample problemsThe 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.

Explores the complexity and wide-ranging applications of the Fibonacci sequence, which appears in nature, art, economics, and the "golden ratio," which is derived from this simple pattern of numbers.

Multiply math mastery and interest with these inspired teaching tactics! Invigorate instruction and engage students with this treasure trove of "Great Ideas" compiled by two of the greatest minds in mathematics. From commonly taught topics in algebra, geometry, trigonometry and statistics, to more advanced explorations into indirect proofs, binomial theorem, irrationality, relativity and more, this guide outlines actual equations and techniques that will inspire veteran and new educators alike. This updated second edition offers more proven practices for bringing math concepts to life in the classroom, including114 innovative strategies organized by subject area User-friendly content identifying "objective," "materials," and "procedure" for each technique A range of teaching models, including hands-on and computer-based methods Specific and straightforward examples with step-by-step lessonsWritten by two distinguished leaders in the field-mathematician, author, professor, university dean and popular commentator Alfred S. Posamentier, along with mathematical pioneer and Nobel Prize recipient Herbert A. Hauptman-this guide brings a refreshing perspective to secondary math instruction to spark renewed interest and success among students and teachers.

Through dozens of examples from arithmetic, algebra, geometry, and probability, Alfred S. Posamentier reveals the amazing symmetries, patterns, processes, paradoxes, and surprises that await students and teachers who look beyond the rote to discover wonders that have fascinated generations of great thinkers.

Professional mathematicians often speak of the beauty of mathematics and the elegance of its solutions. Yet the esthetic appeal of math is rarely conveyed to students at the elementary, secondary, or even college level. Instead, most of us develop phobias in school about math's elusive logic and then pass these negative impressions on to our children. We should all be having fun with math and helping our kids to do better in life by encouraging them to appreciate not only its usefulness but especially its charm. That's just what veteran math educator Alfred Posamentier sets out to do in this delightful exploration of math's many intriguing, interesting, and fun qualities. Beginning with the beauty of the number system, thr author doesn't just talk mathematics; he entices readers to do math and discover for themselves just how stimulating the process can be! Brief and entertaining introductions to each chapter invite readers to try their hands at arithmetic marvels, surprising solutions, algebraic entertainments, geometric wonders, and fun mathematical paradoxes, among other topics. Presented in a reader-friendly, conversational tone, the text is very accessible and the examples are geared to a beginner's level, so that even the most math-phobic individual will discover the hidden joy and inherent appeal of doing math. This is the ideal book for adults looking for a way to turn their kids on to an important subject or discover for themselves what they might have missed in their own math education.

Stimulating collection of over 300 unusual problems involving equations and inequalities, Diophantine equations, number theory, quadratic equations, logarithms and more. Problems range from easy to difficult. Detailed solutions, as well as brief answers, for all problems are provided.