This paper reports one aspect of a larger study which looked at the strategies used by a selection of grade 6 students to solve six non-routine mathematical problems. The data revealed that the students exhibited many of the behaviours identified in the literature as being associated with novice and expert problem solvers. However, the categories of "novice" and "expert" were not fully adequate to describe the range of behaviours observed and instead three categories that were characteristic of behaviours associated with "naive", "routine" and "sophisticated" approaches to solving problems were identified. Furthermore, examination of individual cases revealed that each student's problem solving performance was consistent across a range of problems, indicating a particular orientation towards naive, routine or sophisticated problem solving behaviours. This paper describes common problem solving behaviours and details three individual cases involving naive, routine and sophisticated problem solvers. (Contains 7 figures and 6 tables.)