Parker has told me that he knows what 90 and 90 is (or sometimes what 70 and 70 is). About. A. Million. Times. Here was our latest conversation about this:
P: I know what 90 and 90 is.
M: What?
P: 170
M: How did you get that?
P: ... I mean 180
M: How did you get that?
P: Because it's 160 and two more.
Parker knows that 80 and 80 is 160. I'm not sure why that particular fact got stuck in his brain, but it did and he likes to use it. So basically, he's thinking this problem is like 80 and 80, but with 2 more tens needed, so it's 180.
M: How did you get that?
P: At first I thought it was just one more, but you need two more.
M: Two more what?
P: Two more than 160
M: Two more than 160?! That's 162!
P: [starting to get a little frustrated] No, two more tens.
M: Do you know that one of the most important things mathematicians do is explain their thinking. That's one of their main jobs. They have to explain each step very carefully so they can make sure they are correct and so other people can understand it.
P: Okay, so I made one of them [one of the 90s] 100, and that made the other one 80. So it's just one hundred and eighty.
Here Parker switched gears and used an entirely different strategy. I think he felt like it would be too burdensome to explain his original strategy, so he used a different one that would be easier to explain. He turned 90 + 90 into 100 + 80 by taking 10 away from one 90 and giving it to the other one. I called him out on his pulling a switcheroo and asked if I could try explaining what he did the first time. Then I told him:
M: You just did another really important thing that mathematicians do, which is use a different strategy. Some strategies might be easier for other people to understand. And different strategies might show other different important math ideas.
P: Yeah, and some strategies might help you more on another problem.
Repetition
As I've said, Parker has told me what 90 and 90 is (or 70 and 70) many times and he generally uses the same strategy (along with the initial mistake of only adding 1 ten at first). He doesn't seem to get tired of doing this. At least not when it's his idea. It may seem repetitive and redundant to me as an adult who both knows the fact and knows the strategy, but for Parker it's something he needs to (and thankfully enjoys) working through multiple times.
Derived Facts
Both Parker's strategies involve using derived facts. Parker does not have 90 + 90 (or 9 + 9 for that matter) memorized as a fact. But he does have 80 + 80 memorized and he can use that to figure out other related calculations. Children naturally begin to do this after repeated opportunities to engage in problem solving. As they learn some facts automatically (just through doing problems with the same numbers) they then mentally manipulate them like this to help with other problems.
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