Clock Buddies is our favorite first-day-of-class activity. It starts as a nonthreatening icebreaker activity that helps students learn one another's names, but it soon asks students to find their own strategies for solving a real-world scheduling problem. Even highly math phobic students work with others and succeed. Students gain insight from creating different visual representations of the problem and then comparing and contrasting them. The activity can be adapted to last from one class period to much longer time and for different courses and levels. In this article, the authors discuss the mathematics and the pedagogy of Clock Buddies.