ABSTRACTCURTIS D. KENDRICK. The case for building on students’ proportional reasoning for slope-related tasks. (Under the direction of DR. DAVID K. PUGALEE)The purpose of this research was to identify the proportional reasoning strategies that seventh-grade students use to solve slope-related problems relating to the origin and nonzero y-intercept. In this qualitative study, students worked in pairs to complete problems and then participated in interviews in which they explained how they had arrived at their answers and why they had used specific approaches. The aim was to contribute to the limited research that has yet been done on connecting proportionality and slope by assessing students’ thought processes based on their prior knowledge and collaboration when they encountered graphic and tabular questions relating to slope. The approach here was informed by the work of Skemp (1976), who encouraged building on students’ prior knowledge in order to improve their ability to adapt to uncertain situations, reduce their need to memorize rules and heuristics, and enhance their intrinsic motivation to learn mathematics.