Sorting shapes and solving riddles develop and advance children's geometric thinking and understanding while promoting mathematical communication, cooperative learning, and numerous representations. This article presents a brief summary of how children develop an understanding of the properties of geometric shapes as well as a description of the shape-sort and riddle activities that the preservice teacher found to be beneficial for deepening students' geometric understanding. To successfully complete the various tasks that the shape-sort and riddle activities comprise, students work in cooperative learning groups and use higher-order thinking skills. (Contains 1 figure.) [A recording sheet template and a sample list of "Who am I?" riddles accompany the online version of this article at www.nctm.org/tcm.]