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Irrational

We were playing "guess the number" at breakfast today. It goes like this: "I'm thinking of a number between 1 and 10," "Is it 5?" "Higher." "7?" "Lower." "6?" "That's it!"

Eleanor brought up the idea of using fractions, and her number turned out to be 3.5. Then Michael started in. "I'm thinking of a number between 3 and 4." 3 1/2? lower. 3 1/4? lower. 3 1/8? higher. I figured out as soon as he started that the number was pi, and so we had a discussion about the fact that you could get closer and closer with fractions, but never guess the exact right number. This is hard for much older kids, I'm not sure exactly what Eleanor got...

Then we had to discuss what pi measures. The idea that you want to know the exact distance around a circle makes sense, although Eleanor figures that in the real world, you could just take a measurement and it would be good enough. I started drawing the picture of Archimedes' pi approximation, which she watched for a while. Then Amanda came up and watched for a while, until the polygons got to be too much like circles to draw. I finished up by explaining some more, and then she asked, "And now can I color the pi(e)?" It was beautiful.
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