**MSRI Mathematical Circles Library**

Volume: 10;
2012;
208 pp;
Softcover

MSC: Primary 11; 97;

**Print ISBN: 978-0-8218-8798-1
Product Code: MCL/10**

List Price: $39.00

AMS Member Price: $31.20

MAA Member Price: $35.10

**Electronic ISBN: 978-0-8218-9482-8
Product Code: MCL/10.E**

List Price: $39.00

AMS Member Price: $31.20

MAA Member Price: $35.10

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#### Supplemental Materials

# Integers, Fractions and Arithmetic: A Guide for Teachers

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*Judith D. Sally; Paul J. Sally, Jr.*

A co-publication of the AMS and the Mathematical Sciences Research Institute

This book, which consists of twelve interactive seminars, is a
comprehensive and careful study of the fundamental topics of K–8
arithmetic. The guide aims to help teachers understand the
mathematical foundations of number theory in order to strengthen and
enrich their mathematics classes. Five seminars are dedicated to
fractions and decimals because of their importance in the classroom
curriculum. The standard topics are covered in detail, but are
arranged in an order that is slightly different from the usual one.
Multiplication is treated first, and with that in hand, common
denominators and equivalent fractions are more readily understood and
are available for use when discussing addition.

The book is intended for the professional development of teachers.
It is appropriate for teacher education programs as well as for
enrichment programs such as Mathematical Circles for Teachers. There
are numerous activities in each seminar that teachers can bring into
their classrooms.

In the interest of fostering a greater awareness and appreciation of
mathematics and its connections to other disciplines and everyday life, MSRI
and the AMS are publishing books in the Mathematical Circles Library series as
a service to young people, their parents and teachers, and the mathematics
profession.

Titles in this series are co-published with the Mathematical Sciences Research Institute (MSRI).

#### Readership

Undergraduate students, graduate students, research mathematicians, and teachers interested in K–8 arithmetic.

#### Table of Contents

# Table of Contents

## Integers, Fractions and Arithmetic: A Guide for Teachers

- Cover Cover11
- Title page iii4
- Contents v6
- To the reader ix10
- Introduction xi12
- Number systems 116
- Divisibility and order in the integers 1530
- GCD’s and the division algorithm 3146
- Prime numbers and factorization into primes 5166
- Applications of prime power factorization 6580
- Modular arithmetic and divisibility tests 8196
- More modular arithmetic 99114
- The arithmetic of fractions 115130
- Properties of multiplication of fractions 131146
- Addition of fractions 145160
- The decimal expansion of a fraction 161176
- Order and the number line 179194
- The mysterious long division algorithm 199214
- The pigeonhole principle 205220
- Index 207222
- Back Cover Back Cover1225