The purpose of this study was to document and trace how students' understanding of situations that involve finding a fractional part of a fraction developed during a course of instruction in which students explored and represented various kinds of situations using each of the five representational systems. A class of 5th grade students (n=22) participated in this study which involved 13 days of instruction spread over 4 school weeks. The results of this study suggest that understanding the process of making connections among representations is of crucial importance. Examining student solution methods in various representational systems for problems involving the multiplication of a fractional quantity by a fractional operator and attempting to tease out the connections among those representations suggests that students can develop the double partitioned model as a meaningful physical representation for the product of two fractions. (Contains 22 references, 9 figures, and 2 tables.) (ASK)