[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 which makes another rectangle. He’s able to see how the blocks show that this quadratic factors into .
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 . He did seem to see the geometry here, which made me happy. I was especially happy that he saw how a block was taken away twice.
So, I think this is a really great project from Henri. I’m really excited to try some more with it this weekend.