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The Golden Ratio: The Story of PHI, the World's Most Astonishing Number
Throughout history, thinkers from mathematicians to theologians have pondered the mysterious relationship between numbers and the nature of reality. In this fascinating book, Mario Livio tells the tale of a number at the heart of that mystery: phi, or 1.6180339887...This curious mathematical relationship, widely known as "The Golden Ratio," was discovered by Euclid more than two thousand years ago because of its crucial role in the construction of the pentagram, to which magical properties had been attributed. Since then it has shown a propensity to appear in the most astonishing variety of places, from mollusk shells, sunflower florets, and rose petals to the shape of the galaxy. Psychological studies have investigated whether the Golden Ratio is the most aesthetically pleasing proportion extant, and it has been asserted that the creators of the Pyramids and the Parthenon employed it. It is believed to feature in works of art from Leonardo da Vinci's Mona Lisa to Salvador Dali's The Sacrament of the Last Supper, and poets and composers have used it in their works. It has even been found to be connected to the behavior of the stock market! The Golden Ratio is a captivating journey through art and architecture, botany and biology, physics and mathematics. It tells the human story of numerous phi-fixated individuals, including the followers of Pythagoras who believed that this proportion revealed the hand of God; astronomer Johannes Kepler, who saw phi as the greatest treasure of geometry; such Renaissance thinkers as mathematician Leonardo Fibonacci of Pisa; and such masters of the modern world as Goethe, Cezanne, Bartok, and physicist Roger Penrose. Wherever his quest for the meaning of phi takes him, Mario Livio reveals the world as a place where order, beauty, and eternal mystery will always coexist. From the Hardcover edition..
Price: $6.24
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If You Hopped Like A Frog (If You.)
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If Dogs Were Dinosaurs
If your dog were the size of a dinosaur, his dinner would fill your bedroom! If the moon were the size of a marble, earth would fit in your hands! If your submarine sandwich was as big as its name, the pickle would be as big as a life raft! Mighty math-man David Schwartz's amazing examples of relative size, and James Warhola's hilarious, literal depictions make these mind-bending math concepts crystal clear and tons of fun. Concise, easy-to-follow back matter provides equations that show just how readers can solve these fascinating, outrageous proportional problems! .
Price: $6.80
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Let's Fly a Kite (MathStart 2)
Let's Fly a Kite When Bob and Hannah split something, the two pieces had better be symmetrical--exactly the same. BUt to fly their kite, they'll have to learn something new--cooperation! .
Price: $2.57
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Dosage Calculations: A Ratio-Proportion Approach
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Teaching Fractions And Ratios For Understanding: Essential Content Knowledge And Instructional...
This popular text, Teaching Fractions and Ratios for Understanding, addresses the urgent need for curriculum materials that cross traditional boundaries to include many of the elements that are integrated in the teaching/learning enterprise: mathematics content, teacher understanding, student thinking, teaching methods, instructional activities, and assessment. The book pushes readers beyond the limits of their current understanding of rational numbers, challenging them to refine and explain their thinking—without falling back on rules and procedures they have relied on throughout their lives. Written in a conversational and easy to understand style, this is not a textbook as much as it is a resource book. An underlying assumption is that facilitating teacher understanding using the same questions and activities that may be used with children is one way to help teachers build the comfort and confidence they need to begin talking to children about complex ideas. Unlike a textbook that is used to study formal theory and then discarded when it comes to putting ideas into practice, the many problems and activities included to facilitate teacher learning are valuable resources for use in elementary and middle school classrooms. Changes in the second edition include: • even more student work incorporated in every chapter; • discussion of the connectivity between the topics addressed in the book and the elementary and middle school mathematics curricula; • an increased emphasize on measurement; • expansion of some topics, including number sense, percent, scale factors, similarity, and linear graphs; • clarification of the characteristics of ratio and proportions and how to use these to generate discussion with children; and • content-related interview questions for exploring children's thinking. This book is a valuable resource for researchers and curriculum developers in mathematics education, pre-service and in-service teachers of mathematics, those involved in the mathematical and pedagogical preparation of mathematics teachers, and graduate students in mathematics education. The methods and activities it includes have been tested with students in grades 3-8 and with pre-service and in-service teachers and other adults. This text is accompanied by MORE—a supplement that is not merely an answer key but a resource that includes in-depth discussions of all the problems in the text; develops and extends discussion of the issues, teaching problems, and other considerations raised in the chapters; and contains additional problems—with and without solutions—that instructors may find helpful for assessment purposes..
Price: $35.95
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Making Sense of Fractions, Ratios, and Proportions: 2002 Yearbook (Yearbook (National Council of Teachers of Mathematics).) (Yearbook (National Council of Teachers of Mathematics).)
NCTM's 2002 Yearbook emphasizes that although fractions, ratios, and proportions are pivotal concepts in the middle school, their development and understandings begin in the elementary school. The companion booklet presents activities that illustrate some of the ideas in the yearbook and that go beyond the content of the yearbook itself. Teachers' notes and handouts are designed to bring the yearbook to life in the classroom. 261 pp., companion booklet 58 pp..
Price: $37.95
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More: In-depth Discussion Of The Reasoning Activities In "teaching Fractions And Ratios For Understanding"
This book is a supplement to the text Teaching Fractions and Ratios for Understanding It is not merely an answer key, but a resource that includes in-depth discussions of the problems in the text; develops and extends discussion of the issues, teaching problems, and other considerations raised in the chapters; and contains additional problems—with and without solutions—that instructors may find helpful for assessment purposes. In the second edition, MORE has been reorganized so that supplementary activities immediately follow the discussions of the activities from the text. Solutions to these supplemental activities have been removed to facilitate the use of MORE in courses. Nevertheless, because the number of activities in each chapter of the text has increased and complete discussions of all of them are provided in MORE, there is ample opportunity to learn reasoning methods..
Price: $22.50
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