This report was part of the total scope of The Microcomputers and Middle School Problem Solving project. It employed representational models during problem solving in order to study: (1) observable patterns in self-directed use of representational models; (2) correlations between use of models and problem-solving ability; and (3) the motives of students for choosing to use representational models. Seventh-grade students were given 25 number theory problems in the context of some meaningful situation, as opposed to a mathematically abstract situation. A set of representational models was provided for voluntary use. The project covered the entire year and took place in three stages. A Cold Test, a Pretest, and a Posttest were administered to the students. Attitudes and other information were gathered from questionnaires given before and after the study. Each ability group used models a greater percentage of time on the Posttest than on the Cold Test, and the percentage of problem solving success increased from the Cold Test to the Posttest for each ability group. Above average and average ability males used representational models more on the Pretest and Posttest than above average and average ability females. The more concrete the model, the more it was used. Problems, including Cold Problem solving pretest and problem solving pretest and posttest, questionnaires, and computer menu are appended. (LMO)