Kitcher's idea of 'explanatory unification', while originally proposed in the philosophy of science, may also be relevant to mathematics education, as a way of enhancing student thinking and achieving classroom activity that is closer to authentic mathematical practice. There is, however, no mathematics education research treating explanatory unification in detail. In this article, we address this issue by illustrating explanatory unification of statements by proofs with a classroom episode involving an 8th grade class tackling 'star polygon' tasks. Based on analysing this episode, we suggest that another benefit of explanatory unification in mathematics education is in fostering mathematical understanding.