The first day, I showed him how to do the activity, using a 3x3 square and the word ONE. Then, we worked together to do a 4x4 square with the word MORE. By the end of that, he had the idea, and I was just watching while he figured things out. Next, he did a 5x5 with his name. That one was more difficult, because he hadn't yet realized that working systematically will make his life much easier. I think this might be the first problem he's run into where working systematically mattered - the activity would have been a success just for that discovery, I think. (There's pictures showing our work in the first post.) For each square, we figured out an equation suggested by the book:
That was as far as we got the first day. I was intrigued, so I played with a 6x6 square that evening, which we talked about the next day. My own weakness with numbers had lead me to misidentify this as an activity working with square numbers, so I started out trying to show him square numbers on our Cuisenaire Rods... which didn't match up. I love the way that I get to (re)learn along with the kids. I never understood how math was related to patterns until I started doing math things with Hero, and it's pretty exciting to me to see how these things fit together. He got to watch me be confused and then work it out -- which is not a bad thing. And looking at the Rods was cool.
I don't know that I'd ever really seen an exponential relationship laid out and made touchable like that. We started out building long skinny towers, and later Hero added the blocked versions as we were starting to run out of space on the table.
Because it meant we were able to use our hundreds flats, the blocked versions allowed us to go even larger (we added another after the photo was taken) without running out of pieces. I was pleasantly surprised at how far our Rods went. That was as far as we got the second day, building the answers to the equations we'd built. I'm not sure if Hero feels like messing around with this anymore, but I am planning to play with at least one more set. We've done a 7 letter word set, which makes 32 solutions. I want to play with an 8-letter word, giving 64 solutions, and see if I can predict what the equation will be. And there's some cool patterns in how the letters fall on the graph that I'm intrigued by. I don't know if Hero's interest is strong enough to keep him engaged at a third sitting for our "9 minute" activity (that would bring us to around 1.5 hours), but if he is, there's plenty to play with still.
Math is pretty amazing.
How come nobody ever told me about playing with numbers?!