**Playing Nice with the Mean Value Theorem**

Early opportunities for student discussion of the average rate of change in a calculus class cements understanding and develops deeper meaning of the Mean Value Theorem later in the year. Attendees will explore the concept of average rate of change with a focus on conceptual understanding using dynamic graphical explorations. While these explorations are tied to the concept of motion, discussion will be applied to many other areas. This conceptual understanding will serve as a foundation for discovering the conclusion of the mean value theorem in the context of the race between the tortoise and the hare. With the conclusion in mind, attendees will explore the necessary conditions required for the conclusion to be met.