I was not intending to write again today, but here we are. It’s just that it was all so exciting our math class today that I couldn’t put off telling this story until the end of the week.
As you’ll recall, we are working toward developing and strengthening the Big Ideas of hierarchical inclusion and part/whole relationships.
I wrote 8+4 = on the board before anyone arrived, and 30 minutes before math was supposed to start, kids were already coming to tell me that they knew the answer. I’m going to start doing that more often! I reminded them that yesterday we had discovered that within a number, say “4”, there are other numbers. There are two 2’s, a 3 and a 1, and even 4 four 1’s. Then I asked for answers to 8 + 4 and most everyone agreed it was 12, except for one person who was sure it is 11. Time for the second problem:
Almost as soon as I had it written up on the board, thumbs were going up. I want to say that we have been using this “thumbs up” routine for a while, and I still (DAILY!) have to remind people of that routine. *sigh*) We agreed it was 12, and then someone said, “I know what you did. You just took one away from that 8 and gave it to the 4, so it’s still just going to be 12.
So, I make a huge deal out of that idea. “What? Do you mean if I take 1 away from the first number, and give it to the second number, I will still have 12??” They said yes. So I said, “Will that always work?” and we tried some other examples. It did work! We even noticed we could use facts we know, like 10 + 10 to help us with other facts, just by moving a number from one side to the other. HOLY COW! Isn’t math amazing?? I probably said that 5 times. I wrote this on the board: “If you take one away from the first number and give it to the second number, the answer will stay the same.” I do have a photo of that, but forgot to edit a kid’s name out. I had written down the name of the child who first said it, and the names of a few who were quick to agree with this.
Soon they were asking for harder numbers. “The problem is that I can’t really give you harder numbers. See, once you know that this works, they’re all going to feel easy.” That’s what I told them. They didn’t believe me, so I gave them a 1000+1000 example and they were stunned. STUNNED! Then I asked the 100+100 = 50 + 110 problem you see in this picture, and we had to add the addendum: It only works if you take add back the same amount you took away.
So it was all great and exciting and I kept thinking, “This is awesome!” But the surprising thing I didn’t expect was how excited kids were too! “Don’t erase it! Leave it up forever!” they kept saying. And “Can you take a picture of that to show my mom?” (We use SeeSaw and they love when photos go home to mom and dad.) While they were doing their Writer’s Workshop writing, several kept saying, “Are you going to add that work to our math board?” So instead of doing some writing conferences, I was doing that. I’m sure you’ll agree it had to be done right then.
One thing I said yesterday is that I wanted to make my own work more organized. I think I was able to do that. But I can’t prove it because I left a kid’s name on the board. I’ll try not to tomorrow! Another thing I am noticing now is that I should have a model up there. I am going to, right now, e-mail my colleagues at school and see who has Cuisinaire rods we can use sometime this week, and I am going to make sure I draw some models tomorrow.
And I feel like I should keep it all real here, and confess that after all that, one child raised a hand to say, “I still think 7+5 is 11.”