The use of a visual representation in learning about proportional relations was studied, examining students' understandings of the invariance of a multiplicative relation on both sides of a proportion equation and the invariance of the structural relations that exist in different semantic types of proportion problems. Subjects were 49 high-ability sixth-grade mathematics students using the Jasper Adventure Series of problems. The first research question was whether the provided visual representation would influence student understanding of proportion. Students spontaneously transferred an extrapolation strategy to a second problem domain, suggesting that instruction facilitated a recognition of the structural equivalence in the two domains. The second question was whether the visual representation would interact differently with student reasoning on the part/whole and rate problems. Students were more successful using the representation presented during rate instruction on part/whole problems than vice versa. Differences in student reasoning tentatively suggest a sequence of instruction in which visually-mediated instruction with rate problems precedes that of part-whole problems. Three figures present study findings. (Contains 8 references.) (SLD)