This volume was prepared by the School Mathematics Study Group (SMSG) to help elementary teachers develop a sufficient subject matter competence in the mathematics of the elementary school program. Background material for related SMSG materials for grades four through eight are included. Chapters in the book are: (1) What is Mathematics; (2) Numeration; (3) Whole Numbers; (4) Rational Number System; (5) Coordinates and Equations; and (6) Real Numbers. The appendices include additional materials related to the topics and answers to questions and problems in the text. (RH)