Problem Solving in Mathematics (PSM), a program of problem-solving lessons for grades 4-9, is designed to be integrated into the regular mathematics curriculum. Although the content objectives of the lessons are similar to those of most textbooks, PSM emphasizes problem-solving skills and a variety of instructional strategies which foster the development of such skills. These strategies include direct instruction, guided discovery, laboratory work, small-group discussions, nondirective instruction, and individual work. This PSM book for grade 9 algebra consists of 10 parts. The first nine parts contain activities arranged under these headings: getting started (focusing on five problem-solving skills); algebraic concepts and patterns; algebraic explanations; equation solving; word problems; binomials; graphs and equations; graph investigations; and systems of linear equations. The last section contains 25 challenge problems in which students select the problem-solving method to use. Each of these parts has an overview teacher commentary which includes information on PSM philosophy and suggestions as to how the activities within the part should be used. In addition, each activity includes mathematics teaching objectives, problem-solving skills students might use, materials needed, comments and suggestions, and answers. General information on the PSM program and PSM strategies are provided in an introduction. (JN)