This is one of a series of units intended for both preservice and inservice elementary school teachers to satisfy a need for materials on "new mathematics" programs which (1) are readable on a self basis or with minimal instruction, (2) show the pedagogical objectives and uses of such mathematical structural ideas as the field axioms, sets, and logic, and (3) relate mathematics to the "real world," its applications, and other areas of the curriculum. This unit explores with teachers fundamental concepts involving number theory. Chapter 1 answers questions concerning the meaning of theory of numbers and why it should be studied in elementary school mathematics. Chapter 2 deals with various subsets of the whole numbers such as even numbers, odd numbers, prime numbers, composite numbers, and factorization. Chapter 3 presents elementary notions on the greatest common divisor and least common multiple. Chapter 4 introduces to the elementary teacher some enrichment topics from number theory. (RP)