2, 4, 8

How many of you out there have seen the Veritasium video where he goes around talking to random people on a beach, asking them to guess his rule with… heck, just check it out:

[youtube https://www.youtube.com/watch?v=vKA4w2O61Xo]

Did you watch it? No? Seriously, watch it!

Okay, good. Ever since I saw this video, I wanted to try it in my class. I wanted to have my kids guess the rule. I wanted to be the one saying “yes” and “no” to their three numbers. And today, finally, I did.

In geometry, we’re starting a short excursion into proof and reasoning. Yes, we’ve done a few proofs. And my kids are learning to justify their ideas. But we’re about to embark on a few days where they think about proof, the importance of proofs, assumptions, and other such things. And in our next class, we’re going to start talking about induction and deduction. So today, this was a perfect warm up.

I gave each group a whiteboard. They threw up three numbers. I said yes or no. After they got 3 yes/nos, they were allowed to guess the rule. Then they did it again. Some groups were looking to get the rule in the least amount of guesses. Others were guessing willy nilly. It definitely took longer than I thought. No group got it, but they were making interesting choices with their three numbers in order to figure out the rule.

After about 7-8 minutes of this, I stopped them. I started playing the Veritasium video. It was awesome. Why? Because the random beach people that Veritasium interviewed gave almost identical answers as my kids gave! They saw that the way they were approaching the problem was the same. They heard a few more sets of three numbers that worked/didn’t work, and then I paused the video. Why? Because I heard kids whispering and murmuring that they think they had it. I gave those kids an opportunity to share what they thought the rule was (I did not confirm or deny their guesses). And then I finished the video.

I loved doing this because the kids were totally engaged. And when we start talking about induction and deduction, counterexamples, and keeping an open mind when problem solving, we can use this exercise as an activity we can refer back to.

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10 comments

  1. Love, love, love this. Thanks for sharing it. Have you seen Anthony’s Butterfly. A bit elementary, HOWEVER, it was really cool to see who it inspired and who thought it was applicable in a math class. I had my students write one big idea, one take away, and one thing they might change about their own practices.

      1. Just catching up on my blog reader & noticed this post. In case you haven’t figured it out, it’s Austin’s Butterfly. http://engagedlearning.co.uk/?p=1644
        I showed it last week in a session on formative assessment that was for beginning teachers. It is a beautiful story. It had not occurred to me to show it to my students, though. So thanks, Amy, for that idea!

      2. OMG I just watched that video. I’m dying with how much I love it. I just put it on the listserv for my school, for everyone to see. Thanks!

  2. I’m sure you know this one already, but it seems just so fitting for a unit about reasoning and proof that I want to mention it anyways: the Moser’s chord problem. Put n points on the circumference of a circle, then connect them with chords so that no three intersect in the same point. How many regions is the circle divided in? Start with n = 2 and build up, and you get 2, 4, 8, 16… case closed, right? Except of course it’s not.

  3. So did you talk to the students about confirmation bias? This video does a brilliant job introducing that concept. What is so striking is how once the people on the beach heard the interviewer give the 2,4,8 example they jumped to a conclusion. None of the participants thought to come up with a contradictory example to prove the rule. This is such an important part of mathematical and scientific discovery, but very hard to teach. I love that you used this in your class.

    1. Greg! Look at you coming upon my blog! I didn’t talk about confirmation bias too much. It was more about using data to build up patterns to rules that you think are true (induction), in opposition to deduction. (We’re about to do a bunch of stuff on geometric proofs… so I wanted them to understand the type of logic we are allowed to use versus the “oh I have a thousand examples that show it, so it must be true.”

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