16. Self-Aware


Creating a new Play With Your Math problem is a long, multi-step process. Here’s a quick recap of how 16. Self-Aware came to be.

Find and try the problem. I think I first saw this problem a few years ago in some puzzle book, but I haven’t been able to figure out what book that was. I dropped everything to solve it right then and there.

Play with the problem. We played with this problem at a meeting of the Boston Math Teacher’s Circle. As usual, I was impressed with how naturally those people asked their own questions and extensions. We explored: what if the number didn’t have 10 digits?

Invite our students to play with the problem. I thought this problem would be a fun Friday warm up, where maybe a couple students would figure it out and a few would try and lose interest. That “warm up” lasted 30 minutes, and it kinda ruined my lesson plan, but it was worth it. When the first few students figured it out, they stayed engaged, trying really hard to give their classmates hints without ruining the problem.

Design the poster. We spent entirely too long trying to find an appropriate name that captured the self-referential nature of the problem. We debated whether we should use boxes or lines as placeholders for the numbers. We tried to invite the exploration we experienced at the Math Teacher’s Circle. We used examples and non-examples to try to make the problem easier to make sense of and get started.

And now for the final step: We invite you and your students to play!


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