mishna and Pythagorean theorem

altar with the ramp and aravos towering over

Today 9 yo had his mishna lesson. He is in 4th chapter of mishna Succah. His teacher asked him at the end what kind of review he wanted and he said that he wanted to build a mizbeach (altar) surrounded by aravot (willow branches). His teacher agreed, but it ended up being up to me to enforce it. When the time came, he built a slapdash quick version out of construction paper. I said that it is unacceptable and it needs to be scaled properly. He was annoyed, as by that point whatever idea he had from the morning left his head. Then he said that he does not know how to build to scale. I used example of Legos and said that one ama ( hand span) could be one Lego block. He complained that he did not know the dimensions. I pulled out my handy-dandy Mishkan book and showed him a  picture, with all dimensions and descriptions. He took it downstairs and started building.

His final product was all yellow, to reflect the color of copper, I guess. It was ten amos high and five amos on each side. Then the discussion turned to the ramp. He found a Lego block which can pivot and attached flat boards to it. He excitedly said that he knows the ramp to be 30 amos.

While I was making dinner, and he was finishing building, an idea crossed my mind. When he brought the final model up, I asked him, which dimension of the ramp was 30 amos? Of course it was the base, but, as I expected, he built the actual ramp to be 30 Lego blocks long. I was able to detach it and show him how it makes a difference whether the base is 30 amos, or the ramp part (hypotenuse). Then I told him that there is a simple way to calculate how long the ramp should be, once you know the length of the base and the side. I was also hoping that I will do it correctly, as any calculations while holding a kvetchy baby tend to be off. I counted out loud: "The mizbeach is 10 amos, that's 100 once you square it, and the base is 30 amos, that's 900 squared, add them together and you get 1000. Now the square root of 1000 is..." and I realized that I cannot do it in my head. I discovered that my phone calculator does not have a square root function. 9 yo knew that the one on the computer does. He tried guessing the answer while I was finding an appropriate device for our math. He was surprised by the answer. He tried a few estimates, and played around for a bit, squaring numbers with more and more decimals, approaching closer and closer to 1000.

I told him that there was a Greek by the name of Pythagoras, and made up how he had to build up ramps, too, especially when people got tired of running out of wood. He did not exactly buy my story, and he was not so keen on adding 1.6 amos to his ramp, but we had a great fun with this mizbeach.

A few days ago he expressed fear and upset over falling behind his peers in school. Specifically he mentioned math and fractions and division. I said that I do not think he is behind, but if he's worried, we can do some math. He did not want to do math, he said that he just used it as an example. After we finished our calculations today, I whispered to him that I am pretty sure they are not learning about Pythagoras in fourth grade.