In this paper we illustrate how a task has the potential to provide students rich explorations in algebraic reasoning by thoughtfully connecting number concepts to corresponding conceptual underpinnings.

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### George J. Roy, Jessica S. Allen, and Kelly Thacker

### Tim Erickson

We modify a traditional bouncing ball activity for introducing exponential functions by modeling the time between bounces instead of the bounce heights. As a consequence, we can also model the total time of bouncing using an infinite geometric series.