Michael Pershan’s Geoemtry problem

Yesterday Michael Pershan posted this geometry question:

The question interested me for two reasons. First it is always neat to hear how kids think out loud. The challenge if this problem is to solve it in your head. Second, by coincidence, we’d just talked about Pick’s theorem last week, and this would be a good chance to review the idea (even though the number of grid points is pretty large).

Here’s my older son’s initial reaction – he sees two different ways to approach the problem:

Next I asked him to approach the problem using the ideas in Pick’s theorem. The interesting thing to me here was how he counting the various grid points, and the little bit of difficulty that he had counting these points made me happy that we looked at the problem this way.

Next up, my younger son. We had to run to an even program that he’s in on Monday’s so I only looked at the problem one way with him. Interestingly, though, his first idea was to approach the problem via Pick’s theorem, though we ended up talking about a more traditional geometric approach.

So, a fun question from Michael Pershan. It is always nice to hear the ideas that are happening in their head rather than just crunching out the numbers on paper.

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