Kelsey Houston-Edwards’s ‘Proof’ video is incredible

Kelsey Houston-Edwards’s latest video is amazing:

It absolutely blew me away. The kids have a late karate class today so I had to wait a few extra hours to use the new video for a project – WORST WAIT EVER!!!

To start the project I had the boys look at three of the problems in the video to see what approach each kid would take to prove the mathematical statement. My younger son is in 5th grade and my older son is in 7th grade, so I’m not expecting perfect proofs (by any stretch of the imagination) but rather just looking for their ideas.

Here’s the first problem – can you cover an 8×8 checker board with 2×1 dominoes if you remove two opposite corners:

The next problem was to show that the sum:

1 + 3 + 5 + \ldots + (2n - 1) = n^2

Here’s what they had to say – both ideas here were really interesting and used arithmetic. I was excited to see their reaction to the geometric proof in the video:

The next problem was to show that ” n choose 2″ was equal to 1 + 2 + 3 + \ldots + (n-1).

My younger son had a nice idea to start small and work his way up. He got stuck so I helped him a little. As in the last video, my older son did the proof by calculating.

After working through these three problems we watched the new video together. The problem about the L-shaped tile covering the 2^n x 2^n grid caught my youngers son’s eye. That led to a short discussion of induction.

The problem about breaking the stick into 3 parts and forming a triangle caught my older son’s eye. He reconstructed the cool proof from the video. I’d like to show him some alternate proofs from geometric probability, too, since they are all so fun!

I’m really enjoying the math videos that Houston-Edwards is making. This one is especially amazing. How great would it be for every math class in the country to watch her video tomorrow! I think it would change the way that kids see math.


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