Sharing a nice problem from Fermat’s library with the boys

Saw this tweet from Fermat’s Library earlier today:

In 1895, Nikolay Bogdanov-Belsky painted the famous: "Mental Arithmetic. In the Public School of S. Rachinsky." The problem on the blackboard is (10²+11²+12²+13²+14²)/365, can you find a way to solve it with mental arithmetic? pic.twitter.com/PjhdQf4MAU

— Fermat's Library (@fermatslibrary) July 28, 2018

I was interested to see how the boys would approach this problem – and that was fun to hear. Unfortunately this project got way off the rails at the end when I tried to explain my solution to them. One of those unfortunate moments where something was clear to me but I was not communicating it well at all. I say it a lot in these blog posts – but they don’t all go well.

Here’s my older son’s solution:

Here’s my younger son’s version:

Next we move to me explaining my solution. This part did not go well at all:

Here’s the second part of the explanation of my solution. Neither kid likes my approach. Given the presentation, I’m not surprised at all