Taking a Problem Apart

Yesterday my AP Calc BC kiddos had a quiz. One version of the quiz gave three coordinates for a triangle and I asked them to use Calculus to find the area of said triangle. We started clas today talking about how to tackle this problem and we ended up talking for twenty minutes doing the problem four ways. One student showed us what he called ‘the shoelace method’ which involved matrices but he did not write it that way. We talked about the formal Calculus approach. We boxed in the triangle inside a rectangle and identified three right triangles bordering our triangle in question. One student commented that this was a ‘subtractive approach’ remembering a conversation earlier in the year that we had. This made me smile. Finally, a student mentioned Pick’s Theorem and we looked at GeoGebra and a Wikipedia explanation. What a fun day, we really dug in a explored this problem at length. I appreciate the patience and creativity of these students.

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