Socratic educator Michael Strong with five year old Alana

Putting on headphones, so hopefully you can hear me better with the headphones. Is this better?

Yeah.

Okay, my wife is having a conversation in French with some kids your age, actually, in France, so there's French going on in the background. How are you?

Good, how are you?

I'm well, I'm well. It looks like you're at the beach.

I am.

Good. Um, do you mind if we go back to a conversation we had a while ago?

Sure.

So I remember talking about how you can run faster than Logan. Is that correct?

Yes, I remember that too.

Okay, and I was wondering, do you think you can run twice as fast as Logan?

Twice as fast? Well, I think I can run like faster than Logan. Like, I don't know.

How much faster than Logan do you think you can run?

Maybe like 2 quarters away, maybe.

2 quarters away?

Yeah.

And so I'm trying to figure out exactly how much faster than Logan you can probably run. So you think, what's the difference between running twice as fast and 3 times as fast? What is— Twice as fast?

3 times as fast is like faster than like 2 times. So maybe if I run 2 times, I'm just going a little bit further than him.

So how would we measure if you're going twice as fast or 3 times as fast? Is there any way to figure this out?

Well, we could grab a tape measure And then me and my brother could have a race, and then we would spread the tape out, and then we could like spread it across where we stop and take a break and then see who is further.

Okay, so this is great. I'm glad you know about tape measures. Tape measures are marvelous for this sort of thing. So we have a race. So suppose you have a race on the beach and you run a certain far. So probably in the same time. Should we assume that it's in the same time?

Yeah, we could start at the same time and see who runs faster.

And then stop at the same time too, right?

Yes, like stop at the same time.

And then we measure it and we measure how long you ran and how long Logan ran, right?

Yeah.

So what would that measurement tell us?

Well, it could tell us like how far I or Imran and Imran and— and we can see who run the farthest and then whoever run the farthest maybe be the fastest one.

Okay. And could we tell by means of this measurement method you just came up with If you ran twice as fast or 3 times as fast or 4 times as fast?

We could, if you want.

So what would the measurements look like if you ran twice as fast as Logan?

Then we could see who could do do it in the electrons, and then if the same person won, then maybe they would be the brother or the sister.

I see. Well, I'm willing to bet that you would run faster than him. I think that's a pretty safe bet. Do you think so?

Yes. Right there. I've tested it a lot.

You've tested it a lot? But I guess I'm wondering, do you think you maybe could run 10 times as fast as Logan, or is that too fast?

Um, that's, uh, I think I can do it like 9 or 5, I don't know.

You think 5 times as fast?

Yeah, I think.

So suppose, do you know how long, um, say 10 feet are?

Yeah.

So do you know how tall your dad is roughly?

Well, I don't know because I haven't counted much.

Do you know how tall you are?

I'm not really sure because I haven't found out that much.

Okay, just to get a sense, do you think you're about half the height of your dad or one-third of the height of your dad?

I think like one-third.

Okay, so if we knew how tall your dad was and you're 1/3, then we'd know roughly how tall you are, right?

Yeah.

I bet your dad is maybe 6 foot 2. Oh, you want to ask him?

Okay. Hey Dad, how, how much height are you?

I'm 6 feet tall.

Oh. He's 6 feet tall.

Okay, great. So if you are 1/3 of his height, how tall does that make you?

Um, maybe, uh, 6 foot? 6 foot? I don't know.

If he is 6 feet tall and you are 1/3 of that, First, what if you were half of that? How tall would you be if you were half of 6 feet tall?

I would, um, I'm actually not sure.

Okay, do you know what it means to cut something in half or to be half of something?

Yes.

Okay. Um, do you know what half of 2 is?

Half of 2? Um, like 2 halves of 2, or?

Yeah, so suppose we have a piece of cake that's 2 feet long. So we have a really yummy piece of cake that's 2 feet long. And we agree to cut it in half so that you can have half and I can have half. How long is your half going to be?

Mine is going to be 1 foot tall. Okay, that makes sense.

That makes sense to me that if the whole cake is 2 feet long and there are 2 halves and we cut it equally, you know, I'm fair, let's assume I cut it fairly. Then your, your half would be 1 foot long and my half would be 1 foot long, right?

Yes.

So now let's look at, um, how about what is half of— what is half of 4 then? Suppose we have, um, a really big cake and we're— we want to cut it in half so that you and your dad can have half and me and my wife can have half. What's half of a 4-foot-long cake? Going to be? How long?

Hmm, um, it would be 4 or 2 feet.

Okay, when you say 4 or 2 feet, can you explain what you're thinking?

I'm thinking that if they cut up like a half of me and cut up my piece of cake for my Dad and me and you cut up a piece of cake for you and your wife, maybe it would be like now 4 pieces.

Okay, 4 pieces. And if the whole thing is 4 foot long, how, how much is the half? How long is the half for you and your dad?

Both, um, 1 foot maybe.

And if you have 2 1-foot pieces, one for you and one for your dad, How long is 1 foot plus 1 foot?

2 foot.

2 feet. Okay. So does it make sense that if we had a 4-foot-long piece of cake, we'd be cutting half of it would be 2 feet for my wife and I and 2 feet for you and your dad?

Yeah.

Okay. So how about suppose your dad is 6 feet tall. Can you figure out how, how big you would be if you were half as tall as he is?

Maybe like a quarter of half of the size he is, because I'm only maybe the size of his leg.

Okay, so you, you're pretty sure you're not half of his height. So if you, if you're a quarter of his size and he's 6 feet tall, can you figure out how tall you would be?

Uh, you would be like I don't know, like 6 or— so if I'm the half of him, how tall would I be, or him be?

Let's start with if you're the half of him, how tall would you be?

I would be, uh, 6 or 5 feet.

If he's 6 feet And you're half of him, you would be 5 feet or 6 feet?

Um, well, if I was like a quarter of him, maybe I would be like 10 or 7 feet tall.

Is 10 feet bigger— is 10 feet bigger than 6 feet or smaller than 6 feet?

60—

is 10 feet bigger than 6 feet or smaller than 6 feet?

Smaller.

10 feet is smaller than 6 feet?

Wait, are you talking about 6 or 16?

6. So your dad is 6 feet tall, right? 6. And we're asking if you're half as high as he is, how tall would you be?

Actually, I would be, uh, 7, I guess.

You'd be 7 feet. Is 7 feet bigger than 6 or smaller than 6?

Bigger.

So are you taller than your dad?

No.

But if you were 7 feet—

Maybe I would just be 5.

So you're just— 5 is just a little bit smaller than 6, right?

Yeah.

So are you just a little bit smaller than your dad?

Actually, wait, um, maybe I'm just 3 feet, I guess.

And how do you figure 3?

Because when I say 6, it's, um, I'm the same height as my dad. If I'm 7, I'm way more taller than my dad. And if I'm 3 feet, I'm way smaller than my dad.

Do you think that 3 is half of 6? Or not?

I think so.

How could you tell?

Because I like— I don't know, but I'm just guessing.

Okay.

If—

so if something is twice as much— so remember with the cake, so we— you and I had a cake that was 2 feet long and we split it and I got a foot-long piece, you got a foot-long piece. So half of 2 is 1, right?

Yeah.

And so if we— and then we were going to do a 4-foot piece, and of 4 feet, you and your dad would get a 2-foot piece, and my wife and I would get a 2-foot piece, right?

Yeah.

So 2 is half of 4, 1 is half of 2. Going the other direction, Does it make sense to say 2 is twice as big as 1 and 4 is twice as big as 2?

Or bigger? Is—

do you think it— does it make sense to say that 2 is twice as big as 1?

Yes, I think I would say that.

How about does it make sense to say that 4 is twice as big as 2?

Maybe a little bigger, but I think I would say that.

Okay. Have you learned any of these numbers in— at school at all?

No.

Okay. Do you realize that you are figuring out on your own how math works?

Yes, I think I— but my mom and dad taught me a little.

Do you like to figure it out on your own as well?

Yes, I do.

Okay, well, we've got a lot more figuring out to do, but bit by bit I want you to be— in addition to the math you learn at school and the math you learn at home, I like the idea of you thinking through math in your own head. Does that seem possible?

Yes.

Okay, I think you did a great job on the cakes, you know. You were figuring out the cakes. So one of these days hopefully we'll all get to split a cake together. And for now it looks like you are in a wetsuit. Are you going swimming or surfing or body surfing?

I went surfing, so now after this I'm gonna have a snack, then I'm gonna practice standing up on the shore.

In getting ready to like really surf?

Yeah, I'm trying to get ready.

That's so cool. Well, I will let you and your dad have a wonderful day, and I look forward to thinking about things again on another Sunday. Okay?

Okay.

Bye, Alana.

Bye.