Abstract
ABSTRACT In this paper, I will discuss two related activities that I have developed for use in a college geometry course directed at pre-service secondary and elementary school teachers. These activities ask students to develop geometry on pool tables and on cones. The two activities are closely related, and both ask students to relate computer models with physical models. The pool table activity was developed as a lead in for the cone project, which is by far the most successful project that I have used for getting pre-service teachers actively engaged with the full cycle of exploring a new space, making conjectures about it, and then coming up with explanations for and proofs of the conjectures.
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