I've been working on building up the limit definition of the derivative conceptually with my non-AP Calc class for the last week (see my recent post on what I've been doing so far ) and today we started putting it all together!
To into this activity, I used an awesome warm up from Math Teacher Mambo (Thanks, Shireen, for sharing on the AP Calc Facebook group). As soon as she shares it publicly, I'll link it here. It's so, so good!
Future Home of Warm Up Activity Link
After completing the warm up, here's how the carousel worked:
1) Put students in to groups and have them start at a blank poster or piece of VNPS
2) Each group completes one step at their poster, then rotates. They will then check the next group's work, correct it, and then add the next step to the poster. Here were the directions:
- Draw a blank axis- I told them just first quadrant- and a function of their choice
- Sketch a secant line
- Label x, x+h, and h
- Label f(x) and f(x+h)
- Write an expression for slope of the secant line
- Transform expression into slope of the tangent line
Here were some of our results:
Awesome conversations ensued, including whether it would make sense for f(x) to equal f(x+h) and what that would mean for the secant line (Helllllloooooo, Rolle's Theorem!). Kids were explaining to each other, critiquing each other's work, and doing a lot of sense making among themselves!
We'll see how this translates to retention beyond today on their next quiz, but I loved seeing the progress that they're making. I think many could explain it better than a few of my AP kids right now- a good "challenge accepted" moment for me to amp this conceptual understanding up more in AP, too.