Today we worked on interpreting derivatives and integrals within the context of a situation. One thing I adore about the AP Calculus curriculum is how application-based it is. More than just “Can you find a derivative or integral?” they ask “Now interpret your findings.”

This is a lesson I always looked forward to teaching but around, oh, second hour, I would typically start to lose steam. Since every kid needed to know the calculator commands for the AP Exam but not every kid had a calculator at home, I would always end up teaching all the calculator commands on *both *the 84 and Desmos. All math teachers know how grueling it can be teaching calculator commands. So teaching it (or really, reviewing it) on two platforms on the same day was both hysterical and exhausting. But, truly, I didn’t have another choice without being inequitable to the students who didn’t have their own calculators.

This year everything changed.

This year, my district purchased enough graphing calculators for every kid in Algebra II and above to loan one out.

Every single one of my calculus students now has their own calculator. What a game changer.

So today, yes, we reviewed the commands (which they already knew way better than previous years’ cohorts, no surprise). But we got to really focus on the applications.

We answered questions like: **If you’re pranking your friend by throwing potatoes in his trunk at a rate of ***p(t)* potatoes per minute, how many potatoes are in the trunk after five minutes? What’s *p’(5)*? And what does that tell you about said potatoes?

Yes. My kids know better than to ask when they’ll use this in real life. Because then I make silly problems about potatoes.

When I interviewed for state teacher of the year a couple weeks ago, I was asked if I could briefly explain why calculus is important.

I lit up.

And gave a minute lesson on how most of us use calculus every day without knowing it.

Calculus is important, yes. But calculus is fun. It can be so silly and so deep all at once. It harnesses the power of infinity to answer questions algebra cannot. In this case, if our rate of throwing potatoes isn’t constant, how do we actually arrive at answer?

Calculus.

*****

If you teach calculus and want access to this problem and the others we worked today, you can find it here.

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