This study looks at how students embody their ideas about geometry conjectures and how those ideas travel within and between student groups. In one classroom of a Title 1 high school, students participated in a three-part program in which they: (1) played "The Hidden Village," a motion-capture video game where they assess the veracity of geometric conjectures (i.e., if it is always true or ever false) while their intuitions, insights, and rationales (including their gestures) are video recorded, (2) designed their own directed actions (i.e., a sequence of movements that represents a body-based interpretation of the structure and transformation of a spatial configuration), and (3) re-played the game with a mixture of previous conjectures combined with the conjectures designed by their peers. Multiple cases revealed ways that simulated enactment and collaborative construction can convey mathematical ideas. [This paper was published in: "CSCL 2021 Proceedings," International Society of the Learning Sciences, 2021, pp. 177-180.]