Today's math project was pattern discovery. Yesterday, we did a worksheet that was intended to help the kids discover the communitive principle of multiplication. He did the work reasonably well, but it seemed clear that he had not noticed the pattern. So today we got out the completed worksheet and the rods, and we went after the pattern.
First, we built rod trains for yesterday's problems. And I made a new train, following the same pattern.
At this point, he thought he had this figured out, and he didn't like my train; he wanted to build his own. I knew he didn't have the pattern figured out yet, but I also knew that he'd learn more being more active, so he built his train. It was wrong. Now I had his attention. We looked closer at the patterns in the other trains, and he was able to figure his out.
Once his train was following the pattern, we grabbed a new sheet of paper and started looking at yesterday's problems as a model for problems he would.
This was tricky at first, but soon he was really understanding what he was looking at, and the hardest part was writing small enough to fit on the page. At that point, I helped with the writing again.
Then, we looked at a new problem, and how we could use this idea of "switchable" numbers in addition & multiplication to solve easier problems.
Altogether, I feel like it was a very successful lesson!