Handfuls

Hello there, mathematicians! We hope you're having a really nice day today! We are black, black! Well I am in a

black shirt, but we're also back! Back in black.

Back in black!

Like Batman! Anyway we could keep going but we, we mustn't! Um we are back to talk about playing handfuls, which you might have seen us play before, using things like pasta, where we grab a handful of pasta or counters and we have to try to visualize about how many we have.

Yep! I really like that game.

Looking and thinking and then I might estimate, I don't know, I reckon I might have about 15 pieces of pasta? Uh huh.

And then I could, I'm going to think of how I could arrange it, so that Barbara, you can work out how many there are by looking and thinking.

Sounds good!

So I could make it into fives, because I think you would know fives on dice patterns.

I do.

And so if I make these into the shapes on the same structure as a dice pattern or, and I said they were 15, but I'd now

revise my estimate to be a bit more.

So I think, um, I can see that there are two fives here. Okay. Like two hands, so I know that that's ten.

Yeah.

Ten and then another five is fifteen and two more is seventeen.

Aha! So you could use it by looking and thinking. If I put it like this, can you see how many there are by looking and thinking?

No, not really.

What about if I like made fives, but push them like, really close together?

Well, no, because then I can't really tell that it's five.

Oh so it's a bit like with the words, where you need space between them as you're writing?

Yeah because otherwise, you know, with these I'd still have to count them to know that's five.

Ok, I could have also made it, maybe like this, because I think you might know this, um, structure?

Oh yep, there's a ten frame!

Uh-huh and hold on, don't say it yet! Ah well, I like that actually! Maybe I'll put it like this closer together so you can see the chunks.

Yeah that's better. So now I can see a ten frame and then I can see some dice patterns, so I can see a five and a two.

Uh huh.

So ten, so, and five, five and two is seven, and then another ten so seventeen.

You know what else I could have done? Is made it like a seven on a domino.

Oh yeah.

Like that.

I like dominoes. Because then it's ten and seven. And you can tell that it's seven, because it looks like a six but with just one more in it.

Yeah that's true, so if you know number after then you know seven. Okay so we're gonna play handfuls, but this time, thinking about not just how many ones things that we have, but how many legs!

Oh okay! So not arms though, just legs?

No, legs. So we're gonna have to think multiplicatively now. Okay so if I take a handful of my mini figs, oh, it's a shame I didn't pick up that one because we could break out into karyoke! Look! This guy's got a spider for a hat, and he looks like he's having a very bad day!

He does!

Anyway, um, so now I've got to think about about how many mini figs I think I'm holding um, and they're bigger than the pasta shells, so if I had 17 pasta shells, I definitely don't think I have 17 mini figs so I think I might have about maybe 9 mini figs, and so that would.

Your hand looks quite full, as well.

Yeah, and I think that would mean that I have, um, 18 legs because nine two's is eighteen. Double nine is eighteen. So, um, I'm going to challenge myself to try to arrange them in a way that you could work out how many there are by looking and thinking.

Yep.

So I'm going to try a few different things because if it was 9, I might make it like, like, I see the symbol on TV. Like a three by three. But it's not nine.

But that's still useful.

Yeah but what I think I might do is, I could do it like this and if you know domino's, you might know what that is. Do you know what that is when you see it straight away?

I do, but I also knew it before because it looks like nine with one missing.

Ah, so you can see that's eight.

Yeah, because it was one less than nine, so even though this doesn't, this is not a pattern, that I, that I see often. Yeah. I could see that, you know, that you were trying to make um, a nine. Yes. And then I just thought well one's gone. And that one was missing, and that's actually why they make eight looking like this.

And it's easy to see which one's missing. The one is missing, there in the middle. So, so you can see that's eight and then, eight twos would mean that there's sixteen.

Sixteen legs. I'm gonna try to make it another way. What about like this? What can you see now?

Well now I can see two fours.

Uh huh. Um. So how many legs?

Uh, well, eight and eight. Uh huh. Which is also 16. Yep, okay, what about what about now? Try another way by looking and thinking.

Oh I like that one. So that's like a, like a ten frame and I love working with ten frames. Um and I can see that two are missing.

Oh yeah, like this. Oh I like your two left behind strategy, or two missing strategy. So it would be ten, if there were men here. But because they're on there... But there's no figs there, so it must be eight. And that's an interesting way to think about it because if you had a full 10 frame of figs you would have 20.

Legs.

20 legs, right. So then you can go well actually, I need to take four legs away.

Oh nice, yeah I like that and that helps you see like, you know, how we talk about numbers that combine to make ten like six and four?

Yeah. It helps you see numbers that combine to make twenty, like one, ten and six which is sixteen and four more is twenty. Yeah!

Okay, so that's another way to play handfuls, and we could play with mini-figs where we say how many legs or how many hands for example or how many eyes?

Oh I like this guy! He's dirty.

Yeah, he looks like he's escaped from something.

But she looks very happy about his escape, so maybe she helped him escape out of prison,

I don't know. Anyway and Batman's coming to chase them.

But we could also play with, um, bears and we could say, how many paws.

Oh, okay.

But now we're talking about four. Yeah, so for each bear there's four paws, whereas here for each mini fig there's

two legs or two arms or two eyes. So that's another way that we can play. Do you wanna have a go? Grab a handful.

Oh, okay.

Okay and about how many do you estimate?

I think, I've got about, oh, they're quite chubby these little bears. I think about eight.

Okay, so arrange them so that I can see how many by looking and thinking.

Okay.

Now I've put them down and I think that I've underestimated already.

Have you revised your thinking?

I'd revise my thinking, yeah. What would you think now that you see it like that? Uh well I think probably ten. Okay. Maybe a little bit more. I think I have to stand them up. What do you think?

Oh yeah, I can see, um, the structure of a ten frame here and one more, so I would say there's 11, um, bears and if I have to work out the number of paws. I know that each bear represents four, so that's four tens and I know that that's called 40. And then four more is 44.

44.

So I can see like the big rectangle around the outside, here, I can imagine it there. I can imagine the four internal lines and I can imagine the one line down the middle.

And I think that's what, what you said, space is really important because when I first did the ten frame and it was a bit bunched up, it was when they were lying down, it wasn't as easy.

Yeah. Can you arrange it in another way so I can see how many by looking and thinking?

Yeah, let's do it. I'm gonna put this one over here and this one over there. What do you think now?

Oh okay, I can see, um, five on a dice. So one five and two fives and one more, so, so five fours, I actually know that's 20 because I just, I just, it's something I know so that would be 20 and another 20, and, um, and I know that if I rename I can go two tens and two tens, which is four tens, we call that forty, and then four more would be 44.

44. You want one more way?

Yeah, do it one more way.

Okay. Oh, I don't know if this is going to be useful or not. I'm not sure if it will help with thinking.

Oh okay, so I can see a chunk of six because it's like a dice pattern, turned sideways and I can see a chunk of five because it's almost a six. Yeah, so I thought...

With one missing.

I could have put it this way, so you'd know it was five straight away, but then I thought maybe, because it looks the same, you could see..

That's right, that's how I thought about it. So, actually this is a near double now.

Yeah, it is.

Because it's double six, double six minus one or double five plus one. And so I could think about it like that.

Yeah.

So because double five is ten and.

Then the one.

And then one more group of legs so, double five, double five is ten, double five fours is ten fours because each of those is worth four paws, and that's 40 and then one more set of four paws is 44.

So 44. Three different ways of thinking about that, I really like it.

All right, let's look at how we could record some of those ideas so with the bears we just realized that for each bear there are four paws. So, 44 is ten fours and one four. We also saw that 44 is five fours and five fours and one four. And we also saw that 44 is double five fours and one four more.

All right over to you, mathematicians to play handfuls, thinking about groups of fours like our teddy bears or groups of two like our mini figs. You choose! Over to you!

So what's some of the mathematics here? This task help, this task helps us build our mathematical imagination. Being able to imagine quantities helps us learn to imagine moving and changing quantities so we can work with flexibility and confidence. By structuring quantities in different ways, we can see quantities within quantities. And we notice that some arrangements are more easily identifiable than others, and using different equipment like figurines and bears we can enhance our understanding of working with multiplicative situations.

Have fun mathematicians!