Sharing James Tanton’s area models with my younger son

I saw a really neat tweet from James Tanton yesterday:

I've started a new project on quadratics – simple videos of me chatting in my home and matching PDF essays (perhaps better). The first three are up, all about the story of COMPLETING THE SQUARE. What do folk think? https://t.co/NxsCdZnMRR @cheesemonkeysf @mythemathics @k8nowak

— James Tanton (@jamestanton) March 1, 2019

The video in the “setting the scene” link is terrific and I had my younger son watch it this morning. I can’t figure out how to get the video to embed, so here’s a direct link to the page it is on:

James Tanton’s area model lecture

One reason that I was extra excited to see Tanton’s video is that by total coincidence I’d used essentially the same idea with my older son to explain why a negative times a negative is a positive:

But I’d never gone through the same ideas with my younger son – at least not that I can remember. So, for our Family Math project today I had him watch Tanton’s video and then we talked about it.

Here’s what he thought about the video and area models in general – I was really happy to hear that my son liked Tanton’s area models and thought they were a really great way to think about multiplication and quadratics:

Next I had my son walk through the negative / positive area ideas that Tanton used to talk about multiplication. He did a really nice job replicating Tanton’s process. I think this is a great way for kids to think about multiplication: