True/false number sentences.
I started by asking the children to make up a problem they could solve in their head. I was hoping they would choose numbers that they could mentally manipulate; but as I found out, it requires a degree of metacognitive awareness about what’s easy and what’s hard relative to their own understanding.
My example for them was 10 plus 10 plus 10. I wasn’t subtle at all here: I wanted the children to use tens in their problems. But, as usual, they had other things in mind.
Sunny wanted a story to go with her number problem. So she made up her own: Sunny and Daniella go to the store and buy 90 candies. They eat 8 of them. How many are left? I suspected the problem was too hard for her to solve in her head – and it was. She got 80. Based on her explanation of how she got 8o, it seemed she was trying to do something in her head with the standard algorithm. She mentioned crossing out. But when I suggested she solve it another way using the cubes, she easily modeled everything using tens, and counted what was left to get 82.
We moved on. I had my index cards ready. I wanted to start with a number relationship I knew that they knew: 10 + 10 = 5. I asked the children to write the sentence down then put “t,� “f,� or “?� after it. This one was easy. They all knew it was false.
Then we did: 5 + 5 = 10 + 10. I expected there wouldn’t be consensus on this since many children interpret the “=â€? as “and the answer is…â€? Under this interpretation, the number sentence is true. Sure enough, two of the children said, yes it’s true and one put a question mark. I introduced the language of “is the same amount asâ€? for the equal sign and we talked a little about whether 10 was the same amount as 20. No problem there. But I didn’t necessarily expect the children to have fully assimilated the meaning of “=”.
Next we did: 10 + 10 + 10 + 3 = 33. This one was really designed to see how they figured the sum. Jack counted the 10s then the 3 and said it was true. Daniella used 10 plus 10 is 20, but then counted up by ones. Sunny modeled it with tens to get 33. True.
Next: 22 + 10 = 30. I was so pleased with Sunny’s response on this one! She used relational thinking and I think her prior work with the unifix cubes may have helped. She said that 20 plus 10 is 30, but since the 2 is with the 20 it should “be taken out of� the 10 and 22 plus 8 is 30. It was a flash of insight.
Next: 10 + 10 + 10 + 10 + 10 = 100. Jack counted up by tens. It was easy for him to figure out it was false. Sunny wrote that it was true, but I didn’t find out her reason. Daniella got out 5 tens, said it was 50, but then to prove it, she counted on by ones from 20. It’s just not clear to me how much she understands. She’s right on the cusp.
Then, a controversial one. (Sunny wanted to know what “controversial� meant.) 12 + 10 = 10 + 12. At first, they all said it was false, although Jack wavered a little and wanted to put a question mark. So I told them I was going to make up a story problem to help them think about it. It went something like this: Sunny had 12 cents. Then she got 10 cents for her birthday. Daniella had 10 cents. Then she got 12 cents for her birthday. Do they have he same amount of money or not? The answers were interesting! Daniella added both sides up (counted on by ones from the first numbers for each), got 22 for each. Jack said you could add the numbers in either order, it didn’t matter. As we talked, I wrote this for them:
But the next number sentence brought a nice surprise from Daniella: 10 + 2 = 5 + 5 + 2. Sunny and Jack though it was false but Daniella argued it was true and her reason was just beautiful. She grabbed the card from me and wrote on it:
For next time: what does Daniella understand about grouping tens? Sunny? Can Jack use invented strategies for adding double digit numbers? We’ve got one more session together.
Posted in Case Study: Four Second Graders, Daniella, Jack, Sunny, Uncategorized | Comments (0)
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