Exploring some polynomial basics with kids

I asked the boys what they waned to talk about for a project today and got a bit of a surprise when my 6th grader suggested polynomials. It seems that the topic has just come up in his math class at school and he’s interested in learning a bit more.

To start the project I asked him what he knew about polynomials:

Next I asked my younger son to explain adding and subtracting polynomials, and then to try to see how to multiply them since he said that he didn’t know how to multiply in the last video:

Now I wanted to show an unusual property of polynomials that was relatively easy to understand. My hope was to show my older son something that he’d not seen before but also something that was still accessible to my younger son. I chose to show them a short exploration of a difference table for a quadratic

Finally, I showed how you could use the difference table to reconstruct a quadratic function if you knew the values of the function at three consecutive integers:

So, despite the surprise topic request, this was a fun little project. It was nice to be able to find a topic that you could explore if polynomials were “new to you” and still get something out of if polynomials were a familiar topic.