The goal of this design-based research study was the creation and evaluation of a mini-unit intended to foster perceptually grounded understandings of the concept of slope in middle-school students. Central to this unit was an innovative device designed to create a productive pedagogical space between student intuition for steepness and formal definition of slope. Nine students from a US middle school engaged with the design in one-on-one video-recorded interviews. Analysis of the data indicates that a majority of students appropriated the mathematics of slope to support their intuitive judgments regarding steepness. Comparing the cases of three students suggests conceptual learning milestones. Overall, the findings show that students' successful coordination of steepness and slope demand that their analytical and intuitive constructions be surfaced and integrated multiple times throughout the learning experience. To support students in connecting the mathematics of slope to their perceptions of steepness, educators can plan for students' multiple ways of viewing situations involving slope.