Yesterday, we figured out that the derivative of e^x is itself, so today we had a quick discussion to try to figure out why. I showed a clip of Pay It Forward, when the little boy is explaining his scheme, to spur the discussion. I think that this gave them something more concrete to talk about. The derivative is how fast people are being helped, and it's easy to see that this rate is very much related to how many people are part of the project. So, the more people there are, the faster the helping spreads.
I call this portion of the course “Proportional Rates” to try to drive this big idea home.