The Roots of the Equation

I was looking for a derivative-based game to play in Calculus as we were just closing out our first unit on derivatives and the semester was ending. That’s when I found Derivative Clicker:

https://gzgreg.github.io/DerivativeClicker/

It hit the spot with my students. I explained the game and had them all start playing simultaneously, and then saw who had earned the most money in 20-25 minutes. Yes, it’s a little addictive and “brain rot” (as one student said, but, like, it was a positive review) but they had a lot of fun.

The thing about math games, though, is that the real power is not in the game itself but in the debrief. Just the lesson before this was my students’ first exposure to the idea of higher order derivatives. They asked “But what does a second derivative actually tell us about the function” and I explained, but it still felt ungrounded to them. So I thought this would help them feel the power of derivatives viscerally.

Then we filled out some tables: what if I just had a single 1st derivative (or, in other words, f'(t) = 1), how much money would I have after time? What if instead f”(t) = 1? f”'(t) = 1? This helped build up the idea of increasing rate and how the rates grew polynomially.

They also had debate question about strategy – in the game, with $500, you can buy 1 second derivative or 65 1st derivatives. Which is better? (There’s no a clear answer here – if you were to buy the second derivative and then walk away, it’ll probably be better for you by the time you get back. But if you buy the 65 1st derivatives, you’ll have enough money to buy a second derivative way before buying a second derivative will get you 65 1sts.)

Below is the debrief sheet we did today.