We had a long drive this morning which meant that we didn’t do our usual morning math project. Instead I had each of the kids talk through a Mathcounts practice problem in the car. It is always really interesting to me to hear how kids think through math problems – they often go down paths that I find surprising.

Sorry that the videos are of poor quality – the kids were holding my cell phone and recording while they were talking.

First up, my younger son:

The problem is to evaluate the sum:

1 1/2 + 3 1/4 + 5 1/8 + 7 1/16 + . . .+ 19 1/1024

One thing that interested me here is that he evaluated the fraction sum and the integer sum using different approaches.

Next is my older son thinking through a geometry problem. One thing that was interesting here is that he had the idea right away to use the Pythagorean theorem to approach the problem. Something made him switch course for a bit, though, and he searched for similar triangles for a bit before returning to the Pythagorean theorem idea: