The purpose of this study was to relate children's cognitive processing capabilities and their grade level to their performance and to the strategies they used when working addition and subtraction problems. From two sets of data which assessed memory capacity and cognitive processing capacities, six groups of children with different cognitive characteristics were identified. For a sample of 44, children in five classes at Grades 1, 2, and 3 were selected and interviewed as they worked a set of addition and subtraction problems. Each child was interviewed on three occasions. Each interview consisted of six tasks given under four of six conditions. Codes for three or four categories were assigned to each child's response: model used, correctness, strategy, error, and if incorrect. These data were then summarized in terms of percent correct and general strategy. For both percent correct and strategy used, there were important variations due to problem set (size of number), to specific task, to instruction over time, and to grade. However, what is clear is that children who differ in cognitive processing capacity consistently performed differently regardless of the other important factors. (Author/MP)