In demonstration, speakers use real-world activity both for its practical effects and to help make their points. The demonstrations of origami mathematics, for example, reconfigure pieces of paper by folding, while simultaneously allowing their author to signal geometric inferences. Demonstration challenges us to explain how practical actions can get such precise significance and how this meaning compares with that of other representations. In this paper, we propose an explanation inspired by David Lewis’s characterizations of coordination and scorekeeping in conversation. In particular, we argue that words, gestures, diagrams and demonstrations can function together as integrated ensembles that contribute to conversation, because interlocutors use them in parallel ways to coordinate updates to the conversational record.