Requiring no more than a knowledge of high school mathematics and written in clear and accessible language, this book will give all readers a new insight into some of the most enjoyable and fascinating aspects of geometry. Everyone knows what a triangle is, yet very few people appreciate that the common three-sided figure holds many intriguing "secrets." For example, if a circle is inscribed in any random triangle and then three lines are drawn from the three points of tangency to the opposite vertices of the triangle, these lines will always meet at a common point-no matter what the shape of the triangle. This and many more interesting geometrical properties are revealed in this entertaining and illuminating book about geometry. Flying in the face of the common impression that mathematics is usually dry and intimidating, this book proves that this sometimes-daunting, abstract discipline can be both fun and intellectually stimulating. The authors, two veteran math educators, explore the multitude of surprising relationships connected with triangles and show some clever approaches to constructing triangles using a straightedge and a compass. Readers will learn how they can improve their problem-solving skills by performing these triangle constructions. The lines, points, and circles related to triangles harbor countless surprising relationships that are presented here in a very engaging fashion.
100 ways to get students hooked on math! That one question got you stumped? Or maybe you have the answer, but it’s not all that compelling. Al Posamentier and his coauthors to the rescue with this handy reference containing fun answers to students’100 most frequently asked math questions. Even if you already have the answers, Al’s explanations are certain to keep kids hooked. The big benefits? You’ll discover high-interest ways to Teach to the Common Core’s math content standards Promote inquiry and process in mathematical thinking Build procedural skills and conceptual understanding Encourage flexibility in problem solving Emphasize efficient test-taking strategies
How exactly does What Successful Math Teachers Do work? It couldn't be easier to navigate. The book's eleven chapters organize clusters of strategies around a single aspect of a typical instructional program. For each of the 80 strategies, the authors present: A brief description of that strategy A summary of supporting research The NCTM and Common Core Standards it meets--and how Classroom applications, with examples Precautions and possible pitfalls Primary sources for further reading and research
Games are seen only for recreation. However, this book shows that games can be used to strengthen problem-solving skills and beyond. This book presents strategy games and discusses for each one solutions towards a winning position in the game. In most cases, these strategies are analogous to problem-solving strategies in mathematics. Readers are also exposed to a wide variety of games from several different cultures, which will broaden the perspective of the readers.
This book introduces ten problem-solving strategies by first presenting the strategy and then applying it to problems in elementary mathematics. In doing so, first the common approach is shown, and then a more elegant strategy is provided. Elementary mathematics is used so that the reader can focus on the strategy and not be distracted by some more sophisticated mathematics.
Undiscovered Ideas at the Frontiers of Space and Time
Author: Tom Siegfried
Publisher: Joseph Henry Press
Scientists studying the universe find strange things in two places-out in space and in their heads. This is the story of how the most imaginative physicists of our time perceive strange features of the universe in advance of the actual discoveries. It is almost a given that physics and cosmology present us with some of the grandest mysteries of all. What weightier questions to ponder than, "How does the universe work?" or "What is the universe made of?" There are any number of bizarre phenomena that could provide clues or even answers to these queries. The strangeness ranges from unusual forms of matter and realms of existence to wild ideas about how time and space are related to one another. Many of these proposals may well turn out to be wrong. But how many will be proven to be right? This book speaks for the scientific theorists who are bold enough to imagine and predict the impossible. New ideas are percolating in their heads every day. One physicist may dream of subatomic particles that could resolve a variety of cosmological conundrums while another may study the likes of "funny energy," which may explain how rapidly the universe is expanding. This is the stuff of Strange Matters. In broad terms, this book is about a variety of discoveries that theorists of the past imagined before the observers and experimenters actually saw them. Moreover, it is about the things that today's are now imagining-but haven't yet been discovered or confirmed by the observers. Strange Matters artfully mixes the present with the past and future, reporting from the frontiers of research where history is in the process of being made. Each chapter examines a different step along the twisted path we've walked to gain our rudimentary understanding of the universe, incorporating historical examples of successful "prediscoveries" with current stories that relate brand new ideas. We come to see the universe not only in terms of what has already been discovered, but also in terms of what has yet to be observed. Strange Matters is a guide to the discoveries of the twenty-first century, a series of visions dreamt by the most imaginative scientists of our time merged with the achievements of the past-to point the way towards even greater accomplishments of the future.
This excellent book, written by the established author David Acheson, makes mathematics accessible to everyone. Providing an entertaining and witty overview of the subject, the text includes several fascinating puzzles, and is accompanied by numerous illustrations and sketches by world famous cartoonists. This unusual book is one of the most readable explanations of mathematics available.
a wise and witty introduction to the joy of numbers
Author: David G. Wells
Publisher: John Wiley & Sons Inc
A guide to the potential and pleasures of math explores the patterns and properties associated with numbers, reveals the origins of mathematical theories and principles, and includes more than one hundred mathematical puzzles
The Complete Kit includes 6 copies of each of the 16 Math Readers per grade level (96 books total), Teacher's Resource Guide, Teacher's Resource CD, 16 full-colour problem solving transparencies, and an Interactive Mathematics Activities CD featuring 8 mathematical games.