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. The present unit has emphasis in the area where the field properties for rational numbers are used in developing arithmetic as it is currently taught in elementary school. Focus is on the arithmetic of positive and negative rational numbers, and on the field properties in teaching arithmetic. (RP)