Kids Can Press: Tonawanda, NY, 2011.
Mathemagic! features a mix of mathematical tricks. All of them have explanations; some of them even have a history. They are meant to be performed for others, exhibiting your genius. Two of them have to do with properties of the digits 6 and 9 which make them easier to calculate multiplication. Some of the tricks are puzzles in which the audience participates. Mathematical operations are performed to confuse the audience. Quicker participants may figure out what the magician is doing.
The most interesting part of the book to me is the four entries which are different ways of calulating. The Egyptians had a doubling technique making it easier to multiply larger numbers quickly. Binary cards are used for guessing a participants number choice within a given range, and a discussion of binary is included. Napier's Bones, used by merchants in the 1600s, are also discussed for multiplication. They are charts of multiplication facts carved on bone which simplify the process when used together. This is a process that is done in multiplication anyway; Napier set it out visually. The fourth is division dowels, a set of rulers for division similar to Napier's multiplication. In the 1800s, Henri Genaille and Edouard Lucas worked out all of the possible quotients and remainders for a table to be used for simplifying long division. It looks complicated, but it is a simple way of accurately figuring.
The book is designed to encourage thinking about number theory. Math can be like puzzles, something to figure out for enjoyment. And there is always the fun of knowing something that stumps someone else. The author presents these tricks as ways to calculate problems quickly and mentally. Some of them can be used to figure quickly for any reason. When a student can develop this proficiency in mathematics, he/she can start to really enjoy the theory (reasons for doing math).
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