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 4 has nine parts. The first part consists of activities related to five problem-solving skills. The next seven parts consist of activities related to: place value drill and practice; whole number drill and practice; multiplication and division concepts; fraction concepts; two-digit multiplication; geometry; and rectangles and division. The final part presents 21 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. Additional information on PSM philosophy and strategies is provided in an introduction. (JN)