Introduction
Seminar 1. Number systems
Seminar 2. Divisibility and order in the integers
Seminar 3. GCD’s and the division algorithm
Seminar 4. Prime numbers and factorization into primes
Seminar 5. Applications of prime power factorization
Seminar 6. Modular arithmetic and divisibility tests
Seminar 7. More modular arithmetic
Seminar 8. The arithmetic of fractions
Seminar 9. Properties of multiplication of fractions
Seminar 10. Addition of fractions
Seminar 11. The decimal expansion of a fraction
Seminar 12. Order and the number line

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.