As adults, we represent and think about number, space, and time in at least two ways: our intuitive--but imprecise--perceptual representations, and the slowly learned--but precise--number words. With development, these representational formats interface, allowing us to use precise number words to estimate imprecise perceptual experiences. We test two accounts of this developmental milestone. Either slowly learned associations are required for the interface to form, predicting that deviations from typical experiences (e.g., presentation of a novel unit or unpracticed dimension) will disrupt children's ability to map number words to their perceptual experiences or children's understanding of the logical similarity between number words and perceptual representations allows them to flexibly extend this interface to novel experiences (e.g., units and dimensions they have not yet learned how to formally measure). 5-11-year-olds completed verbal estimation and perceptual sensitivity tasks across three dimensions: Number, Length, and Area. For verbal estimation, they were given novel units (i.e., a three-dot unit called one "toma" for Number, a 44 px long line called one "blicket" for Length, a 111 px[superscript 2] blob called one "modi" for Area) and asked to estimate how many tomas/blickets/modies they saw when shown a larger set of dots, lines, and blobs. Children could flexibly link number words to novel units across dimensions, demonstrating positive estimation slopes, even for Length and Area, which younger children had limited experience with. This suggests that the logic of structure mapping can be dynamically utilized across perceptual dimensions, even without extensive experience.