 Author: Elliot Benjamin

### Numberama: Recreational Number Theory In The School System

eBook: US \$19 Special Offer (PDF + Printed Copy): US \$95
Printed Copy: US \$86
ISBN: 978-1-68108-513-5 (Print)
ISBN: 978-1-68108-512-8 (Online)
Year of Publication: 2017
DOI: 10.2174/97816810851281170101

#### Introduction

Numberama: Recreational Number Theory in the School System presents number patterns and mathematical formulas that can be taught to children in schools. The number theories and problems are reinforced by enjoyable games that children can play to enhance their learning in a fun-loving way. Key features of the book include:

• - information about a number of well-known number theory problems such as Fibonaccci numbers, triangular numbers, perfect numbers, sums of squares, and Diophantine equations
• - organized presentation based on skill level for easy understanding
• - all basic mathematical operations for elementary school children
• - a range of algebraic formulae for middle school students
• - descriptions of positive feedback and testimonials where recreational number theory has been effective in schools and education programs

This book is a useful handbook for elementary and middle-school teachers, students, and parents who will be able to experience the inherent joys brought by teaching number theory to children in a recreational way.

# Foreword

With all the push toward applications of mathematics where some are at best artificial, it is refreshing to find a text that does not have the pretense of giving any real applications, but rather a book on number theory just for fun. The conception of the book, Numberama, could have been conceived by the first real number theorist, P. Fermat, through a bunch of problems (without any thought of applications).

This book is a text about problems in number theory intended to aid teachers from early elementary school to early high school in giving an appreciation of number theory to their students. The text is divided into four parts and an Appendix: Chapter I is devoted to several basic problems in number theory which can be appreciated using only elementary arithmetic: addition, subtraction, multiplication, and division. Chapters 2, 3, and 4 are devoted to board games based on the problems in Chapter 1, where each chapter requires successively higher level arithmetic skills to play the games in the chapter. For each of the problems given in Chapter I, there is a code indicating the level of skills needed to work on at least parts of the problems. Teachers are given plenty of advice as to how to present the material to the students. The Appendix includes excerpts from various student and teacher participants in Dr. Benjamin's Numberama program, which describes both the benefits and the joy they received from participating in this program.

A couple of the problems included are the following, (some going back to antiquity): Finding perfect numbers. Here the students get to use their skills at multiplication and division, as well as being exposed to prime numbers. This problem leads, of course, to open questions such as the existence of infinitely many even perfect numbers and also the existence of at least one odd perfect number. There is also the problem of representing integers as the sum of two squares, a problem which Fermat himself worked on. Again the teachers are given hints as to how to proceed.

Chapters 2, 3, and 4 are devoted to 19 different board games concerning the problems in Chapter I, which seek to hone the skills of the students, involving many of the properties of numbers given in the first chapter. The text is written well and seems to be accurate. I would certainly recommend it to teachers interested in enriching the mathematics content and honing basic arithmetic skills of the students.

Chip Snyder
Professor of Mathematics,
University of Maine,
Orono,
Maine