Although learning mathematics certainly depends upon accurate understanding of the facts of multiplication, it requires much more. This study examines the relationship between a meaningful understanding of arithmetic operations and the mastery of basic facts. The study began with a joke about a mistaken mathematical fact. The children appreciated the joke, and they also were able to use that error as a basis for learning mathematics. The study demonstrates that children can learn the facts of multiplication, while also learning to explain the meaning of their answers. Children can construct their understanding by literally creating their own models. (Contains 6 figures and 3 online resources.)