This is volume one of a two-volume manual for teachers using SMSG text materials for students in grades 7 and 8 whose mathematical talents are underdeveloped. The overall purpose for each of the chapters is described and the mathematical development detailed. Background information for key concepts, answers for all exercises in each chapter, and suggested test items are provided. Chapter topics include: number symbols, whole numbers, non-metric geometry, factoring and primes, rational numbers and fractions, rational numbers and the number line, decimals, and ratio and percent. (MN)