These materials are intended to explain the approach adopted by the writers of the SMSG textbook, First Course in Algebra. This book is not a ninth-grade textbook or teacher's commentary. Many of the ideas presented are too difficult for most beginning students, but they are ideas which the author believes teachers should master. It is assumed that the teacher already masters these skills. Chapters included are: (1) Historical Background; (2) Language; (3) Structure of the Real Number System; (4) Sub-Systems of the Real Numbers; (5) Completeness of the Real Number System; and (6) Functions. The appendices include materials on infinite decimals, complex numbers, algebraic numbers, and answers to exercises. (RH)