We introduce an embodied-interaction instructional design, the Mathematical Imagery Trainer (MIT), for helping young students develop grounded understanding of proportional equivalence (e.g., 2/3 = 4/6). Taking advantage of the low-cost availability of hand-motion tracking provided by the Nintendo Wii remote, the MIT applies cognitive-science findings that mathematical concepts are grounded in mental simulation of dynamic imagery, which is acquired through perceiving, planning, and performing actions with the body. We describe our rationale for and implementation of the MIT through a design-based research approach and report on clinical interviews with twenty-two 4th-6th grade students who engaged in problem-solving tasks with the MIT.