By varying task conditions and constraints on subjects, this study attempted to extend and refine a developmental theory of partitioning as a foundational process undergirding children's construction of a rational number. Subjects were 31 preponderantly higher-grade pupils enrolled at an elementary school in Nova Scotia, Canada. Two tasks were used in the experiment. The first, taken directly from an earlier study and used to introduce and familiarize the child with the clinical setting, involved the partitioning of circular and rectangular "birthday cakes." The second, designed specifically for the present study, involved the partitioning of "giant cookies" in regular triangular and regular pentagonal shapes. This latter procedure allowed subjects to choose the number of pieces into which they could partition the shapes before they actually did so. Results indicated that children think it is easier to partition into two or four parts than into three or five parts, even when the shapes of the objects to be partitioned are as much or more suited to partitioning into three or five parts. In addition, children experienced much more success when partitioning into two and four parts than they did when partitioning into three or five. (RH)