When I first started teaching AP Calculus, I really thought that approximations to integrals was something I could just fly through because all of my students would understand it. Well, as it turns out, I was completely wrong. For some reason (even though it seems insanely obvious to me), my students had so much trouble understanding how to draw those rectangles! So I had to think of an activity - and fast! That's when it hit me - spaghetti! So I ended up buying lots of spaghetti and four different colors of spray paint and I stayed late in my classroom one night to paint tons of spaghetti (it was a trailer so I had the doors open to the outside). The next day, my students were given an integral that they had to approximate with LRAM, RRAM, MRAM, and the Trapezoid rule. They had to make a poster and, using the spaghetti, had to show me every single rectangle/trapezoid. I've done it two years now, and for some reason, something just clicks with a lot of them and they don't have as much trouble doing it from then on! See my handout below! |

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