[sorry for the tired write up – I’m a little sick today]
Saw this neat tweet from Henri Picciotto last night:
At the end of the blog post is this activity:
Geometry and Graphing Connection by Henri Picciotto
and the last page of this activity really caught my attention. I’d been doing a bit of work on factoring and completing the square with my older son anyway, so I thought I’d give it a try with him tonight.
One warning is that I’m pretty sick and out of gas today. I wanted to see how he’d react to using factoring ideas with geometry, but I didn’t have the energy to pursue all of the ideas. That said, I’m actually very happy with how he reacted to the ideas – especially with little help from me since I was fully in the useless zone tonight. We’ll definitely be revisiting this activity.
I started off with a quick introduction to how the blocks could be used to represent the various pieces of a quadratic polynomial. He seemed to catch on fairly quickly using the example 
At the end of the last video he’d picked a 2nd example quadratic with negative coefficients. I wanted to do an example with negative coefficients, but I wanted to wait to do that example later in the project.
Here he pics the example 
The next two examples showed what this method would look like for a perfect square, and how it could be used for completing the square.
Now we returned to a polynomial with negative coefficients. The geometric ideas here were a little harder for him to see. I need to find a better way to communicate the ideas for this part so that he sees the -2 as -3 + 1:
My only idea for helping him see the geometry in the case with negative coefficients was to use an example that was a little easier. That example was 
So, I think this is a really great project from Henri. I’m really excited to try some more with it this weekend.
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