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 attempts to generalize a concept of number from the physical world. Then by considering certain finite physical situations involving relations between sets, a way is found to abstract from these situations a new concept about numbers. This leads ultimately to a definition of the rationals. Operations on the rationals are defined from generalizations from finite physical world situations. The six parts of this unit are (1) one-to-one correspondence and ratios, (2) subset and measurement ratios, (3) new ratios from old, (4) from ratios to rational numbers, (5) some special rational numbers, and (6) applications. (RP)