Michael Strong guides six-year-old Alana through estimating how many hairs are on someone's head. They brainstorm counting strategies like sampling half the head and scaling up, then practice multiplication by tens to build the math skills estimation requires. The point: making a scientifically informed guess, not an exact count.
How are you?
Good, how are you?
I'm well. So you got caught in the rain?
Yep, rain.
Okay, where were you?
I was at a farmer's market for family shoes.
I see. Do you like farmers markets?
Yes.
Right, so do you remember what we were talking about last time, what we were trying to figure out?
Not quite.
That's okay. I remember— so do you remember trying to figure out how many noodles are in a bowl of noodles?
Oh yep, I do.
Um, the next problem is going to have you solve, and I don't expect you to solve it because this is a really, really hard one, is how many hairs are on Logan's head? Remember that?
Yeah, I remember that. So I was thinking maybe under 100 or over 100.
Either under 100 or over 100?
Yeah.
Well, before, before we actually work on an answer with hard problems, before you even work on an answer, I always like to think how on earth would we figure that out? So do you know what brainstorming is?
Yes.
So let's brainstorm. How could we figure out how many hairs are on Logan's head? Do you have any ideas how we could figure that out?
Maybe we could like when he's asleep maybe we could look through a magnifying glass and then figure out how many hairs are on his head.
So I see you— He's sleeping, you've got the magnifying glass, and are you kind of counting them one by one by one?
Maybe by tens or something if I find 10, 10, 10... 10, 10.
You know what? What's interesting about that, I think that's an interesting idea. What's interesting about that to me is that, um, I think it would be really confusing. There are a lot of hairs on a head, so I think it'd be confusing to figure out. Do you know how to braid hair?
Braid hair?
Yeah.
No, I don't.
I bet your mom or dad knows how to braid hair, don't they?
Yeah, my mom does.
So suppose that and I'm just— this is— we're still brainstorming. But suppose you, every time you counted 10 hairs on his head, you braided those 10 hairs into a little braid, and then that way you know you're not going to recount them. Does that make sense?
Yeah.
Um, of course he would look pretty funny at the end because he'd have all these little, uh, tiny braids all over. Um, but that's one way we could— we could count them by tens And then to avoid recounting them by accident, we just braid every 10 hairs. Is there any other way we could do it?
Maybe we could get a microscope and then look under the microscope?
Okay, and I think with a microscope we'd see like the roots of his hair. We'd even be closer than with a magnifying glass. So in some ways—
then we could be counting by 20s.
Okay, so we count by 20s now. I'm thinking if there are lots and lots of hairs on his head, and he has a lot of hair, doesn't he?
Uh, yeah, pretty much.
I bet it could take a long time to count all the hairs on his head.
Yeah, there it would. I'm looking at his head right now. He has a lot.
He has a lot. So what if— so with noodles, I was trying to get you— help you think about multiplication. Um, do you remember— do you remember talking about multiplication?
Multiplication?
Yeah, that's times in math and arithmetic. That's when you do 2 times 4. Or 3 times 4.
Yeah, I remember that.
Okay, so how about let's, let's just do some practice multiplication before we go back to the hair counting. So suppose we're counting by tens. You know what 1 times 10 is?
1 times 10?
Yeah, 1 times 10.
1 times 10?
Yep. Should I help you?
Sure.
Okay, it's 10. 1 times 10 means we just have one set of 10. But then, do you— can you figure out what 2 times 10 is? 2 times 10 means we have two sets of tens.
20.
Bingo! Brilliant, exactly right. That's exactly right. So you've got a set of 10 toes and you've got a set of 10 fingers. And altogether, if you count fingers and toes together, you've got 20 toes. 2 times 10. So how about 3 times 10?
30.
Bingo. 4 times 10?
40.
5 times 10?
50.
6 times 10?
60.
10 times 10?
100.
Brilliant. You are spot on. So because you got that so fast, now what I'm going to suggest is— I don't know, maybe 10 hairs is too small, but suppose we start braiding the 10 sets of hairs on Logan's head so we know what about them. And suppose— I don't know, well, suppose we did just half of his head. And suppose we had 10 braided sets of 10 on his head. And then we count them, and boy, I bet they're going to be a lot. But maybe if we figured out how many hairs are on half of his head, could we assume that there are more or less the same number on the other half of his head?
Well, do you mean like if there's more or less on the other half?
Yeah, the same on the other half.
I like— how would we like— what would be like brainstorm on like what would we think?
Yeah, I guess I'm trying to think if it's easier if we just could count half by the tins. If we could count half of his head, do you think we could just say on the other half is more or less the same so we don't have to count those all over again?
Maybe we could just like do a check so we could like count the other side and see if it's equal. Okay, then we could add those two numbers together.
Okay, that would give us how many hairs on his head? Um, okay, that, that would work, that would work. Um, I guess I'm trying to figure out— Logan, this could take so long he may have to be sleeping for like 8 hours. Um, and I bet you'd probably wake him up if you're starting to count the hairs on his head. Does he sit still when he's awake at all?
Is he awake?
So does he sit still when he's awake, or is he moving all over the place?
When he's asleep, is he moving all over the place?
Well, if he's— I guess I'm concerned it could take so long to count all the hairs on his head, he would have to sleep a long time before you were done.
Oh, yeah.
So that's why I'm trying to think of faster ways to count it. So I think this is a good math problem, and it's a really good— Do you remember the word estimation?
Uh, no.
That's okay. So when with noodles, we're trying to estimate, which means kind of guess, but guess kind of scientifically, guess accurately. We're trying to kind of figure out about how many noodles were in a bowl of noodles. And with the hairs on Logan's head, you know, we don't have to do this for real, but I thought it'd be good to try to figure out about how many, um, hairs are on his head. And if you want, maybe you could do just an experiment and see how many is, you know, it'd be interesting to know, is, are 10 hairs about this much of his head or 10 hairs kind of little tiny tiny bit of his head? You have any idea?
Like how many hairs?
Yeah, is 10 hairs a tiny bit of his head or is 10 hairs a big part of his head?
I think 10 hairs would be just like a tiny part because hairs would actually be really small for me because like hairs are like from when I see them are really small.
I think you're right, I think you're right, which makes— means that if 10 hairs are small and we're counting by tens, it's going to take a long time. Um, so okay, well let me, let me figure this out. Or let's think about it some more next time. If you want, you can just do an experiment and try to count 10 hairs. Maybe if Logan's head is too small or he moves too much, you could try your mom or dad.
OK.
But let's keep figuring out how to estimate things, OK? OK. All right. I'm going to take off and let you have a wonderful weekend, OK?
OK. Bye-bye. Bye-bye.
