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 contains alternative activities for low-achieving students in grades 4-6. They are presented in six sections: (1) drill and practice (with whole numbers); (2) story problems; (3) tangrams; (4) patterns; (5) geometry; and (6) challenge problems (34 problems in which students select the problem-solving method to use). Many of the Activities are similar to activities found in the regular PSM books except that the mathematics computation and length of time needed for completion are scaled down. No grade level suggestions are offered since field tests indicated the activities are appropriate for all three grades. Each activity includes mathematics teaching objectives, problem-solving skills students might use, materials needed, comments and suggestions, and answers. (JN)