Here's an interesting exercise I thought up as a Day 1 activity for Calculus in the new semester. Having covered the ideas of position, velocity, and acceleration and their more general relationship in f, f prime, and f double prime, I decided to hand out some scenarios with a simple request: would an integral or derivative be helpful?
No actual answers to determine, just tell me the method. Prompted a lot of good discussion. The most common confusion was the phrase "area under the curve" which is a little weird because I had been keying in on the relationship between "area" and "integral" for a while, but it worked out. Having them catch on to a correct method by spotting units is also a handy skill.
It didn't take a lot of class time (12 minutes + discussion) and it was a nice restart activity. I think a second round of these questions is in order.