Rates and Integrate

We were going over a past FRQ in calculus today that had to do with the rate of unprocessed gravel arriving at a gravel processing plant. (Seriously? I think we can write more interesting problems, College Board. I’ll even freelance for ya.) One of the questions asked the kids to find the derivative of the given rate and then explain their answer in the context of the problem. It was clear they were fuzzy on the explanation. 

“Ok. How about this scenario. Jonas’s doctor just told us that his growth rate is going to start to decrease. Does that mean he’s going to start to shrink?!”

They laughed (laughter is typically a precursor to learning, isn’t it?). “No, it means he’s not going to grow as fast as he’s been growing,” they explained with confidence. 

“Ok, well that’s what we’re talking about when we take the rate of a rate.”

Calculus is literally all around us. One of my goals for my kids once they leave my class is to be able to discuss their world in the language of mathematics, because the more language you have available to you, the more you can connect with others. 

We got a little closer to that goal today thanks to Jonas’s pediatrician. 


After our FRQ, we played Sunken Treasure, at the suggestion of Sarah Carter, to review integration. This is a great game to play, especially if you already have a problem set ready to go. The kids worked on the math I wanted them to work on while hunting for sunken treasure to earn a Twizzler. At the end of each hour, kids would say, “Wait! One more!”

Oh, you’re asking to do more math? I mean, I guess…if you twist my arm…


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