Conjecture & Proof #tmwyk

I’m doing a short bit of homeschooling with my 11yo right now and we’ve been doing some counting routines with decimals. She’s been asking big “why” questions about it all, especially fourths.

Things are going better on that front now but, with relational understanding as a goal, I devised an investigation that was ostensibly into the nature of fourths. I had a bunch of different regular and irregular paper polygons prepped and MY plan was that she would fold each shape and then reflect on how/if the fourths were same and/or different.

Of course, things went off course almost immediately, but I’m not complaining. I was actually thrilled that she had conceptualized fourths of a square in a completely novel way (to me, anyhow).

This image shows the result of where she was when we stopped this morning. Her initial folding and cutting had not been precise enough to fully prove her conjecture, so I scaffolded that process a little by reproducing the cuts a little more precisely. The two videos, below, share how we got to this point.

conjecture-and-proof

At about 1:17 I ask (but very quietly) “How can you prove that?” 

I hope she’ll want to revisit/finish up her original conjecture soon.

One thought on “Conjecture & Proof #tmwyk

  1. I love her attitude at the end of the first video. She was okay with taking the time to think about it instead of asking you for the answer. Awesome job!

    Like

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