What learning math looks like somethings – geometry and geometric series edition

Yesterday we found a neat problem in the 1991 AJHME (now the AMC 8). It was problem 25:

Problem #25 from the 1991 AJHME

I thought that talking through the problem would make a great evening math conversation last night, so we dove in. It turned out to be a great conversation about several topics:

(i) fractions,
(ii) arithmetic (including intuition about even and odd numbers),
(iii) geometry,
(iv) geometric series, and
(v) factoring

I think that talking about this problem is a fantastic exercise for kids – so many great ideas are lurking just below the surface! Here’s our 15 minute conversation:

Part 1:

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Part 2:

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Part 3:

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As I said above – a fun conversation and a great problem!