A two-year study was conducted with fourth-grade children in the context of extensive teaching experiments concerned with the learning of rational number concepts. Representational difficulties in using the number line model were investigated. While instruction in the second year attempted to resolve observed learning difficulties, the results of both years showed that children have considerable difficulty with number line representations which show an unreduced form of a given fraction. Explorations of the data suggest difficulty with partitioning and "unpartitioning" number line representations, with translations between various representational modes, and with coordinating symbolic and pictorial information on a number line (Author)