Michael Strong uses Socratic questioning with six-year-old Alana on addition and subtraction, starting with warm-ups like 4 + 4 and 40 + 40 to reveal patterns, then moving to problems like 10 + 11 and 11 + 12. He pushes her to notice that 10 + 12 and 11 + 11 both equal 22, and to explain why changing a number changes the sum.
How are you?
Good, how are you?
I'm well, I'm well. You remember what we talked about last week?
Yes, I do.
What did we talk about? Math. And that's exactly right. Do you remember what we talked about in math?
No, not really.
That's okay, that's okay. So math, and you told me about addition and subtraction. You know you're learning both. And then I asked some problems. You knew, probably you figured out ways to solve bigger problems. Does that sound right?
Yes.
Okay, should we keep going in math? Sure. Okay, so let's just kind of do a warm-up. Excuse me, what is 20?
20 plus 10?
20 minus 10. Minus 10.
Okay, that's 10.
That's right. Let's see, how about 200 minus 100?
Um, 100.
You remember the pattern, I think. Um, how about 2,000 minus 1,000?
1,000.
Ah, you totally have a pattern. Just in different ways then. Um, how about what plus 4?
What plus 4?
4 plus 4.
8.
How about 40 plus 40?
40 plus 40, 80.
400 plus 400?
400 plus 400 is 800.
You're getting the patterns. How about 4 million plus 4 million?
8 million.
There you go. Alana knows her math patterns. So let's— let me see if I can do a trickier one. What is 12 plus 12?
Maybe not that one.
Okay, that one's hard. How about, how about 10? You know what, what's 10 plus 10?
20.
How about 10 plus 11?
21.
How about 10 plus 12?
22.
How about 11 plus 12?
11 plus 12? Maybe not that one.
Well, you just figured out what 10 plus 12 was, right? What was it?
What?
What was 10 plus 12?
10 plus 12 was 12 or 13.
You know, 10 plus 12.
Oh, 10 plus 12, 22.
Okay, now you want to try 10, I mean 11 plus 12 again?
Sure.
What do you think it is?
14.
14. So 10 plus 12— oh, 11 plus 12. You think 11 plus 12 would be 14?
Yeah, I think so.
So let's see, how far apart are 12 and 14?
About, about one number away or two.
Okay, I would say they're 2. 12 plus 1 is 13, plus 2 is 14. I would say 12 and 14 are 2 apart. Does that make sense?
Yes.
So if 12 and 14 are 2 apart, then do you think that if we added 11 to 12, it could still be 14?
Maybe. Yeah, I think so.
Is 11 bigger than 2?
Yes, it is.
So if 12 plus 2 is 14, how could 12 plus 11 also be 14? I guess it seems to me like if 11 is bigger than 2, then 12 plus 11 is probably going to be bigger than 12 plus 2. That make sense?
Yes.
So let's, let's see if we can figure out what 12 11 is. Um, maybe let's go a different direction. How about we have— what's 10 10 again?
10 10?
Yep.
20.
Okay, how about 10 11?
21.
And how about 11 11?
11 11?
Mm-hmm.
Um, maybe 22 or 21?
So if 10 11 was 21, then 11 11 is probably going to be bigger than 10 11, don't you think?
Yes.
So if 10 plus 11 is 21 and 11 plus 11 is bigger than 21, and you thought it might be 22, do you think it still might be 22?
Um, I think it could be.
Okay, that's right, that's 22. So earlier we had, um, Do you remember what you said 10 plus 12 was?
Excuse me?
Do you remember what you said 10 plus 12 was?
10 plus 1?
10 plus 12.
10 plus 12?
Mm-hmm.
10 plus 12 is, I think, 22.
Yep. So now I want you to notice something. You've got 10 plus 12 is 22. And we also have 11 11 is 22. Does that make sense?
Yes.
And the way I think about it is if you think of 11, 11 is right between 10 and 12, correct?
Yes.
So if you have 11 and 11 and you have 10 12, in some ways they're similar because the 10 is one less than 11 and the 12 is one more than 11. So on one side you have 10 plus 12 is 22, and on the other side you have 11 plus 11 is 22. And you could go from 11 plus 11 to 10 plus 12 just by taking one off the 11, one of the 11s, and adding one more to one of the other 11s. Does that make sense?
Yes.
So we have 10 plus 12 equals 22, and 11 plus 11 equals 22. How about what if we added 1 more either to, to any of those numbers? What would we get?
Like 22 plus 1?
Yeah, let's start there. What is 22 plus 1?
23.
Okay, so what if we had 10 plus 13? How much is that?
23.
Okay, how about if we add 11 plus 12? How much is that?
22.
But you said 11 plus 11 is 22, right?
Yes.
So if we added 1 to it to make it 11 plus 12, how could it still be 22?
Maybe they're the— maybe they're different numbers but they could equal the same?
So you think it might be the case that 11 plus 11 is 22 and and that 11 plus 12 is 23.
Daddy! Bye, Mommy! Or maybe they're just different, but maybe they're just equaling the same.
Okay, let's play with smaller numbers. Do you think, um, what's 2 plus 1?
2 plus 1?
Yeah.
3.
And what is, um, 1 1?
2.
So do you think we may be able to do 1 2 and get 2, or do you think we have to get 3?
I think it could be— it's 1 1 is 2 instead of 3.
Okay, 1 1 is 2 instead of 3. I guess I'm thinking, can Can you have— when— how do we know if numbers change? So usually I think if you add 1, then a number gets bigger, right?
Yes.
So we had 11 11 is 22, right?
Yes.
And suppose we add 1 to one of the 11s and make it into 12. Then what do you think the result needs to be?
Maybe, maybe it could be in the 20s or 10s.
Probably going to be in the 20s, probably bigger than 22 is what I'm thinking, because if 11 plus 11 is 22 and we add 1 to one of the 11s, probably it's going to be bigger than 22. Does that make sense?
Yes.
So what is 1 bigger than 22?
What is 1 bigger than 22?
Yep.
23.
There you go. So I think— do you ever write down problems when you try to solve them?
Excuse me?
Do you ever write down problems when you try to solve them?
Um, sometimes I do, yes.
I think we'll get into hard problems. Someday we should do hard problems and write them down because I think it's much, much easier when you write them down.
Okay.
When you write them down, then you don't have to hold numbers in your head, you know what I mean?
Yeah.
Sometimes it's hard to write down whole numbers in your head. What are you guys doing today?
We're waiting for my friends here at Balboa Park.
Ah, that sounds like fun. And you're gonna play in Balboa Park?
Yes, we're gonna ride bikes and stuff.
That sounds like a real whole bunch of fun. And have you had any Tournaments recently?
I have two more coming up. It's NAGA and Grappling X.
Okay, you look forward to them, or are you a little bit nervous?
Pretty nervous.
But you are courageous, yes?
Yeah, but I also am very excited.
Okay, nervous and excited, that works. Okay, I'm gonna let you have a real wonderful day in Balboa Park, and we'll hopefully talk next week, okay? Okay, bye-bye.
Bye, see you next week, hopefully.
Yep.
