Pairing Up with Gauss — Follow-up II
Today I got to meet with my middle school group again. We reviewed the Pairing Up with Gauss worksheet from 2 weeks ago. They remembered a lot and moved quickly through a few review examples. I made sure that the kids who had seemed a little overwhelmed the first time were feeling more confident. I still stumped several kids with figuring out the number of items in a sequence that didn’t start from 1. I think we finally cleared that up. I first wrote the series:
10 + 11 + 12 + … + 19 + 20
When someone correctly identified that there were 11 terms in the series, several kids admitted that they had thought there were 10. So then I used the space in front of the series on the board to fill it in, in a different color.
1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12 + … + 19 + 20
Everyone could of course correctly identify that there were 20 items in this series. Then I asked how many were in orange. Everyone knew that too (9). So then I said, so how many are in the black part? Of course that is 20-9=11.
I told them that this is how I think about things like this to make sure I am figuring these out correctly myself. I told them that I could give them a formula to memorize (last – first + 1) but then they’d be lost if they forgot it. If they remembered how to think about it, they’d always get the right answer. I’d like to think that’s going to stick this time, but we’ll see.
Then we moved onto the “Finding the Rules” part of the exercise. We worked through those 3 examples together, and there were lots of “aha!” moments from the kids. The last one, I think, was a bit much for some of them, but probably a third of them were quite excited by it.
Overall, I think it was a good activity.
After that we did a little mental math, and then moved on to an exercise on triangle numbers and other figurate numbers. I’ll post more about that soon.