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Schwartz, Richard Evan. You Can Count on Monsters: The First 100 Numbers and Their Characters. (Illus.) J K Peters, 2010. 244pp. $24.95. 2009038661. ISBN 9781568815787. C.I.P.

Level: EA, GA
Rating: + +

In this book, the old saying “A picture is worth a thousand words” has been twisted around. Here, each counting number has multiple pictures, except for the prime numbers. The author says that he wrote the book for his daughters so that they would understand prime numbers and factoring. The only thing a reader needs to know is how to multiply two numbers (as long as their product is no greater than 100). There are no chapters and no (identified) sections, but a reader may realize that there are three parts. An introductory part shows how to represent numbers with pictures and tree diagrams. For example, the number six might appear as a 2 x 3 patterns of dots; two as 1 x 3 patterns; or as a tree diagram showing the factors in decreasing magnitude. Color is used extensively, with bright colors imposed on a black background. The “Monsters” are the primes, and they appear as somewhat abstract, Picasso-like figures. Thus, the composite numbers can appear as compilations of these basic figures.

Following the introductory part is a pair of pages for each of the numbers from 1 to 100 (including the primes). A dot pattern, a tree diagram, and a figure (or a compilation of figures) appear for each of the numbers. For the composite numbers, the fun will be in deciphering how the figure was constructed from the individual prime-number figures. After the part for the 100 numbers is a short part at the end showing the sieve of Eratosthenes, albeit in graphical form. This part finishes with an explanation of Euclid’s proof that there is no largest prime.

There is very little reading in the book; the ideas will become clear from the pictures and drawings. Except perhaps for the very last part, the volume should be accessible for elementary school students, and even for some of them, the last part should not be too difficult. The review of the basic multiplication table does not require knowing how to do more complicated multiplication, and the use of the figures might suggest ideas for art projects. There is no mention of supplementary materials such as posters or a PowerPoint presentation, but students might be able to create their own posters. Because of the color and the emphasis on pictures, the book may even have some appeal to more advanced students and to adults who are “afraid” of mathematics, because it doesn’t repeat what they may have already experienced, but instead brings out new ideas with little demand on prior knowledge. --Donald E. Myers, University of Arizona, Tucson, AZ