This article presents an origami activity which can lead to rich tasks in several branches of mathematics. This activity is a good first step for preservice teachers to get to know one another, start talking to one another, and start discussing mathematics. It can also show them how mathematics teaching and learning have changed to a more practical, explorative, and collaborative approach. The author will describe how he uses this activity with his students and share some of their questions and contributions. Many of the tasks and activities presented here can readily be adapted to secondary school classrooms. His goal is not to provide activities that teachers can copy and use in their own teaching but rather to develop their skills in thinking mathematically, exploring patterns, and being aware of possibilities for developing activities of their own. (Contains 7 figures.)