Rough idea of how I want to use Penny Circle

Been trying to figure out how to use Penny Circle, by Dan Meyer and Desmos.  I think the activity is terrific, but like L Hodge (in the comments on Dan’s blog), I think the activity does some of the intellectual work for students, so they won’t be challenged to think as hard as I’d like.  (However, it’s a great first experience of the IDEA of modeling, so I’m not criticizing it…I just want to take it further).

I only have a second right now (will flesh this out later), but I think I’m going to have students do the activity as intended, and then ask them to create an equation for diameter of the penny circle after Dan has been putting down pennies for t seconds.  The Desmos activity generates the function n(d), where n is the number of pennies and d is the diameter of the circle. My students will have to find the function d(n), and then use some video of Dan putting pennies down to find n(t).  Then they can use composition of functions to get d(t).  I think there is some video of Dan putting pennies down in the 3-Act.  Anyways, back to work, but if anyone has comments or especially criticisms/warnings, I’d love to hear them.