This guide represents the final experimental version of a pilot project which was conducted in the United States between 1973 and 1976. The ideas and the manner of presentation are based on the works of Georges and Frederique Papy. They are recognized for having introduced colored arrow drawings ("papygrams") and models of our numeration system (the Papy "minicomputer") into the teaching of mathematics at the elementary and secondary level in Belgium. This program follows the "spiral approach." This guide includes the following topics: (1) multiplication; (2) multiples and divisors; (3) rational numbers; (4) abacuses and algorithmic thinking; (5) standard algorithms of arithmetic; (6) composition; and (7) hand-calculator puzzles. Old and new concepts are covered within these topics. The situations provided are intended to develop problem-solving skills and an understanding of mathematical ideas and concepts in the world of numbers. (Author/SA)