# For each game

A thinking mathematically targeted teaching resource focussed on exploring multiplicative relationships through an investigation based on a classic nursery rhyme

Adapted from Gervasoni, A. Extending Mathematical Understanding: Intervention (2015)

## Syllabus

Syllabus outcomes and content descriptors from Mathematics K–10 Syllabus © NSW Education Standards Authority (NESA) for and on behalf of the Crown in right of the State of New South Wales, 2023

• MAO-WM-01
• MA1-RWN-01
• MA1-RWN-02
• MA1-FG-01

You will need:

## Watch

Watch For each game video (7:10).

Use your mathematical imagination to explore how many figurines.

### Michelle

Hello mathematicians! Hello, Barbara.

Hi, Michelle.

### Michelle

How are you today?

I'm very well.

### Michelle

Hey, we've got a game today inspired by Ann Gervasoni and our LEGO Minifigs.

So, we, you know how we were playing handfuls, and we were showing a different way to play handfuls.

[Screen shows a bowl with mini figurines, a spinner with the numbers 8, 6, 12, 14, 10 and 4, and a bunch of pasta shells and a pen.]

Yeah.

### Michelle

So, we've got a game based on that.

Oh, okay.

### Michelle

Yeah, so what we do is we take turns to spin our spinner that we made.

So, I got 12, and you spin too.

[Michelle spins the spinner and lands on 12.]

### Barbara

Okay. 10.

[Barbara spins the spinner, and she gets 10.]

### Michelle

A 10, and so now we have to visualise and imagine in our minds how many Minifigs would we need to make that many legs?

So how many do you need to make 10 legs? And how many would I need to make 12 legs?

### Barbara

Okay, so I think I've got an answer.

### Michelle

Yeah, what are you thinking?

### Barbara

I think I'm going to need 5.

Okay.

### Barbara

And what I'm thinking is I'm thinking that the legs can sort of make like a ten-frame.

[Barbara gathers 2 mini figurines and places them under the spinner in a row. She moves the legs of the figures so there is one pointing at the top and one pointing at the bottom. She indicates with her fingers that if she had 5 figurines, she would have 10 legs in a ten-frame.]

Oh, yeah!

### Barbara

Where each, oh, we're going to make it stand up. There we go. Does that make sense?

### Michelle

Yeah, cause one at the top, and one directly down below.

Yeah!

Yeah, okay.

### Barbara

Yeah, so then I'd have 5 of these guys.

### Michelle

Five legs at the top and 5 legs at the bottom?

Yeah.

Yeah, okay.

But 5 people.

### Michelle

Yeah, 5 people together, which would make 10, 10 legs.

Yeah.

### Michelle

Okay. Well, I think I would need one more than you, which is 6.

Yeah.

### Michelle

Because if I need 5 to make 10, then 2 more than 10 is 12.

[Michelle and Barbara place 6 figurines in a row under the spinner.]

Yep.

### Michelle

So, I'm going to, we can count them to check. Look, we can count both to check. That's 3, 4, 5.

### Barbara

Ooh, I like this one.

### Michelle

Oh yeah, I like the hair. Okay, so let's count by 2. So, check yours.

### Barbara

Okay.

[Barbara and Michelle count out the legs on each figurine.]

… 2, 4, 6, 8, 10.

So that's 5.

Yep.

So, yep. And,

### Barbara

And you were right about needing only one more.

### Michelle

One more to make 12. So, because I had the biggest number of people that I need, I get a token.

[Michelle moves the sixth figurine slightly to the right.]

Oh, okay.

### Michelle

And it's the first person to 5, and they can go back.

[Michelle places the figurines back in the bowl and takes a pasta shell as a token.]

### Barbara

Is this Harry Potter with fake hair?

[Michelle picks up figurines which resembles Harry Potter only with pink hair, and they have laugh together.]

### Michelle

It looks like Harry Potter on here. My favourite is this one, at the moment.

[Michelle picks up a figurine with a pink pig head and places back into the bowl.]

Oh!

### Barbara

Okay. Might spin the other way, anti-clockwise. Oh, 10.

[Barbara spins and lands on 10.]

### Michelle

Oh, 10! Oh, so you can already imagine that in your mind's eye. All right.

Yeah.

### Michelle

Oh, and that's on the line, so I'll spin again.

[Michelle spins but it lands on the line.]

Okay. 10.

### Michelle

[Michelle re-spins and spins a 10.]

Oh and 10, also. So, so I know we need 5 because you showed us already that we need 5. And I also know 5 twos is 10 because of the structure of the 10 frame.

Yeah.

### Michelle

So, because we both got the same, we both get a token.

[Michelle and Barbara both take a token each.]

Okay.

### Michelle

You can spin again.

### Barbara

Okay, let's see. 4.

[Barbara spins and lands on 4.]

### Michelle

[Michelle spins 8.]

Oh 4, okay. And my go. Oh, does that count?

### Barbara

Yeah, I think that counts.

### Michelle

Okay, 8. So how many people do need to make 4 legs?

### Barbara

I just need 2, 2 people.

### Michelle

Because double 2 is, is 4.

Two is 4.

### Michelle

And I think I need 4, 4 people, because for each person there's 2 legs.

Mm hmm.

### Michelle

So, I can imagine one person, which is 2 legs, another person, that's another 2 legs, another person, that's another 2 legs, and another person, that's another 2 legs. And that would be 2, 4, 6, 8 legs altogether.

[Michelle places her palm flat and taps 2 fingers down on her palm counting out 2, 4, 6, 8 legs.]

### Barbara

You could also imagine that you know how we already worked out 5, 5 people is 10 legs.

Oh, yeah.

### Barbara

Taking one person away.

### Michelle

Yeah, that's right. If I imagine it as a ten-frame, like this, and then I know there's like 2, 4, 6, 8, 10, and one less.

[Michelle places 5 figurines in a row, she then points to each figurine legs and count 2, 4, 6, 8 and 10. She then removes one figurine, and counts one less. She now places all the figurines back into the bowl.]

Yeah.

### Michelle

Oh, that's a good strategy.

### Barbara

So, you get the counter.

### Michelle

I get the counter. Your go.

[Michelle gives herself one token.]

### Barbara

Okay. 12.

[Barbara spins and spins 12.]

### Michelle

Oh, 12. That's actually a good spin, I think. And 4.

[Michelle spins and lands on 4.]

Four.

### Michelle

Okay, so I know in my mind's eye, for each person, there's 2 legs. So, one person would give me 2 legs, and 2 people would give me 4 legs altogether.

[Michelle displays 2 fingers then a closed hand and then displays 4 fingers indicating 2 people gives her 4 legs.]

### Barbara

And I'm, I know that 5 people give me 10 legs.

Uh huh.

### Barbara

And so, I need another 2 legs, so I need another person.

Mm hmm.

### Barbara

So that means 6 people.

[Barbara takes a token.]

### Michelle

Six people. So, you get the token, cause you need 6 people and I only need 2, okay.

[Michelle spins and lands on 8.]

Oh, 8 legs I need.

### Barbara

Okay. 6 legs.

[Barbara spins and lands on 6.]

### Michelle

Okay, so how many people do you need for 6 legs?

### Barbara

Okay, so I'm imagining 2, 4, 6. So that means 3 people.

### Michelle

Oh yeah, cause you said 3 counting words. 2, 4, 6.

[Michelle displays 3 fingers one at a time, saying you said 3 counting words 2, 4, 6.

### Barbara

So, every time I said a word, I was imagining a person. So, I was imagining like 2, then I was adding another person, and I was saying 4.

[Barbara places 3 figurines down, counting their legs. She then circles the first 2 figurines with her finger, then she circles all 3 figures.]

Yeah.

### Barbara

Then I was imagining another person, and that's when I said 6.

### Michelle

Oh yeah, cause for each person there's 2 legs.

Yeah.

### Michelle

[Michelle points to each of the 3 figurines then adds one more and points to the figures indicating 2 legs on each figurine equals 8, she then places the figurines back in the bowl and gives herself a token.]

So, each person was a count of 2. Two, 4, 6. And I would need one more person to have 8 legs.

### Barbara

So, you need more people?

### Michelle

Cause 6 and 2 more, is 8. So, I need more people, so I get the token. Oh, it's close, your go.

### Barbara

Line, or 6.

[Barbara spins and lands on a 6.]

### Michelle

Oh. I think that's a 6.

I think so.

### Michelle

[Michelle spins and lands on 10.]

Okay. And I got a 10. So how many people do you need to make 6?

3.

### Michelle

Yes, cause you just did that.

### Barbara

I just did it, I just did it.

### Michelle

[Michelle points to 10 on the spinner.]

### Barbara

Now it's like something that I can, I don't know if it's, it's a fact that I'll know forever, but it's something I can remember now.

### Michelle

For now, yeah. And I actually remember 10 now, because I just think about the 2 rows of 5.

[Michelle points to 10 on the spinner and gives herself a token.]

Yeah.

### Michelle

On a ten-frame. And so, I need 5 people to make 10 legs, and you need 3 people to make 6 legs.

So, I get the token. Oh.

[Michelle points to 6 on the spinner.]

Okay.

### Michelle

And that's the end of the game. Cause once you get to 5 tokens, that's the winner.

### Barbara

Oh, congratulations.

### Michelle

Oh, thank you very much. And you know, we could play this with these guys by looking at the number of legs.

[Michelle picks up the bowl of figurines and shakes the bowl, then she places to the side.]

Yeah.

### Michelle

Or we could play with, like, bear miniatures, and so the number of paws?

[Michelle picks up a bowl of counting bears and indicates that you could play by counting their paws.]

Oh...

### Michelle

So, we would have to think in fours, then.

Oh, okay. Yeah.

### Michelle

And we could then just change our game board. Or you could change it to anything else that you'd like. You could play it with 'one is a snail, 10 is a crab' characters.

Yeah.

### Michelle

And just change a spinner.

### Barbara

Octopuses. Octopi!

### Michelle

Octopi! Over to you, mathematicians.

So, what's some of the mathematics here?

This task helps us build our mathematical imagination. Being able to imagine quantities helps us work with numbers with greater flexibility and confidence.

Using different equipment like the figurines and bears, we can enhance our understanding of working with multiplicative situations.

And we can think about, ‘for each’ ideas, by using knowledge such as skip counting, counting by ones, known facts, and imagining structures like ten-frames.

Have fun playing, mathematicians.

[End of transcript]

## Instructions

• Make a spinner with 4, 6, 8, 10, 12, 14.
• Spin the spinner to determine how many legs you need in total.
• Imagine and then collect the number of figurines you need to make that many legs.
• The player with the most figurines each round wins a token.
• The first person to win 5 tokens wins the game.