Although physics teachers often seek to help their students make sense of physics concepts, our field has yet to thoroughly explore how and why students engage in sensemaking. In this study we use the epistemic games framework to propose a model for students' sensemaking processes. Our analysis of a series of clinical interviews with introductory physics students discussing electricity and magnetism topics suggests the goal of this sensemaking game is to iteratively construct an explanation in response to a perceived gap or inconsistency in knowledge. We illustrate the model with a case study of two students discussing electric current and use that case to outline the entry conditions, exit conditions, and several moves and constraints within this sensemaking game. We conclude by arguing for the utility of this model in designing learning environments that support sensemaking and in directing future sensemaking-focused research.