Adding integers
I don’t know why I did it. Every year the kiddies in algebra roll their eyes when I get ready to teach addition of integers. But this year I decided to test if they really did “already know it.” Gave them an on the spot quiz, 5 mixed questions. All but 2 kids got all 5 right. 1 kid is sloppy. And the last might need some work.
Anyway, instead of teaching from scratch, I presented 2 ‘models’ of addition: a number line model, and a “connected” model:
let + be points for us, let – be points for sophomores. -3 + 5 is 3 for them, 5 for us, we are ahead by 2 (and so on).
Then I let them explain how they got correct answers: their explanations of the “rules” were shockingly bad. Shocking to them as well. They can add, but it is hard for them to explain. So I threatened to make them learn ‘my’ models if their explanations didn’t improve, they grumbled their acceptance of what seemed hard but fair, they also agreed to learn some more perfect squares (up to 20 eventually, just to 13 for now) and we started the McNuggets Puzzle.
More McNuggets tomorrow. (Actually, I was going to kick off with “Handshakes,” but when I said “problem solving” one girl said, “like the handshakes?” and on the spot I decided on McNuggets.
They have been working on four fours, and were at first disappointed that we were not going to continue. This class likes doing math. It will be fun working with them.
JD2718 
Jhonathan.
Can you tell us what their “rules” were?
For negative + negative “SInce they are both negative, ignore the signs, and the answer will be negative,” or “negative plus negative is always negative.” Those answers were ok.
For negative + positive “when they signs are different you have to subtract” “you can just tell if it will be negative or positive” “since the negative is bigger than the positive the answer will be negative” and that sort of thing.
But mostly they came close to those words, but made mistakes. The kids’ faces were easy to read; they could tell their classmates were not getting the words right. But most on their own turn ran into the same difficulty all the same.
“Doing” and “explaining how” are quite different skills. These guys were fine with doing the addition. And just as good today with subtraction (I was a bit surprised. I expected a handful of problems with subtaction)
hi