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<p>In this lesson, students explored models to represent successive bounce heights of different kinds of balls. The data they used were rather messy. Invite students to reflect on the process of modeling with such data.</p>
<ul>
<li>“Were the data completely accurate? Why or why not?” (Depending on the tools used, it can be very hard to get exact measurements of rebound heights, and it gets harder the lower the bounces are. Measurement errors are likely.) </li>
<li>“We saw different rebound factors for different pairs of successive data points. How do we decide if an exponential model is still appropriate?” (We might want to see if the differences are small enough to treat them as measurement error. In the lesson, they are all within about 0.05 of 0.5, and most of them are close to about 0.54.) </li>
<li>“Given the inconsistency, how do we find an appropriate factor to use for our model?” (We might disregard the factor(s) that are very different from the rest, or we might consider finding an average of the factors.) </li>
</ul>
<p>If time permits, discuss possible limitations of the models. Ask questions such as:</p>
<ul>
<li>“Do the models we produce work well after 45 bounces? After 78 bounces? What about when the rebound height is less than 1 cm?”</li>
<li>“Can we rely on the models to be appropriate if we bounce the ball on a different hard surface?”</li>
<li>“What level of accuracy should we consider? For example, is 0.5 or 0.54 more appropriate for the rebound factor?”</li>
</ul>