# Mathematics K–12

Stage 2 – A thinking mathematically context for practise, focussed on deepening understanding of factors and multiples of five

## 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
• MA2-MR-01
• MA2-MR-02

You will need:

## Watch

Capture 3 numbers in a row using multiples.

### Michelle

Ok, welcome back mathematicians and welcome back Barbara.

[Screen shows a 0-9 spinner and paperclip, 10 counters 5 red and 5 green, a gameboard which is a square 5 vertical lines and 5 horizontal lines, creating 25 smaller squares.

In the top row across there is a number written in each square, 45, 5, 10, 15 and 40.

The second row is, 25, 5, 40, 35 and 15.

The third row is 20, 25, 0, 20 and 25.

The fourth row is, 10, 30, 35, 45 and 5.

And the fifth row is, 0, 20, 15, 30 and 10.

And underneath players record card. With 2 player details each. Top row has Player 1 and Player 2, and the next line has columns which have headings, rolled, number sentence and covered under player one and the other side has the same for player 2.]

### Barbara

Hi Michelle, it's nice to see you.

### Michelle

It's battle number seven million, five hundred and twenty two about to commence.

And this time I'm hoping to beat you.

Ok.

### Michelle

So, this is how we play.

I'll allow you to start.

### Barbara

That’s very kind, thank you.

### Michelle

You're welcome, we only get 5 counters each, so this time you can be representative for red and I'll be representative for green for go.

### Barbara

And red for, I'm going to stop you.

### Michelle

Red for stop.

And so, spin the spinner.

### Barbara

Oops, there we go.

[Barbara uses a pencil to put in the end of the paperclip which she then puts in the middle of the 0-9 spinner. She then flicks the paperclip to make it spin, and she spins the number one.]

Ok, one.

### Michelle

So, you get one, fives, or 5 ones as your go.

Ok.

### Michelle

So, what is 5 times 1 or 1 times 5?

Ah, 5.

### Michelle

Ok.

So, I record it for you.

So, you got one and that's 1 times 5 which is 5 and then you have to cover 5 on the game board using one of your counters.

[Michelle writes on the record card for player 1, 1 for rolled and 1 times 5 for the number sentence and 5 for covered.

Barbara puts a red counter on the number 5 in the fourth row, far right.]

Ok.

### Michelle

Uhm, and you'll notice that fives in different places, so you could use any of those.

Ok, how do I win? What do I do?

Three in a row.

Oh ok.

### Michelle

The first person to get 3 in a row.

### Barbara

So, I need to be clever about where I put it.

### Michelle

Yes, ok.

Ok, it's my turn.

There you go.

### Michelle

Would you mind passing me the spinner?

### Barbara

Sure, there you go.

[Barbara passes the 0-9 spinner to Michelle]

### Michelle

Thank you.

[Michelle uses a pencil to put in the end of the paperclip which she then puts in the middle of the 0-9 spinner. She then flicks the paperclip to make it spin, and she spins the number 6.]

I got a 6.

So, 6, fives is 30.

It's a number fact I know, but I could check by going 5, 10, 15, 20, 25, 30.

So, you would write that I rolled a 6, and then 6 X 5 or 6, fives.

### Barbara

Yep, what would you like me to write?

### Michelle

Six, fives, I like that better. I feel like it means more.

### Barbara

Yeah, 'cause it's like they're in groups of 5 and there are 6 of them.

### Michelle

You have 6, fives and I covered thirty in total.

And I'm going to choose this thirty because I think it's the only one there.

Oh no, there's one there as well.

[Barbra writes on the record card for player 2, 6 for rolled and 6 fives for the number sentence and 30 for covered.

Michelle puts a green counter on the number 30 in the fourth row in the second square.]

### Barbara

So now I have to be clever.

If I get a 45 I would, oh no, I could still go for this one.

Yeah.

Yeah.

### Barbara

I'll spin this way.

One, again.

[Michelle writes on the record card for player 1, 1 for rolled and 1 five for the number sentence and 5 for covered.

Which is?

### Barbara

Which is 5. Ok.

But I don't have any that are lined up with this one, so I guess I'll just put it here.

[Barbara puts a red counter on the number 5 in the second row in the second square.]

### Michelle

Ok, my turn.

Thank you.

And 3 and so 3, fives is 15. That's a number fact, I know, but if I didn't know, I could use that skip counting again.

So, 5, 10, 15.

[Barbara writes on the record card for player 2, 3 for rolled and 3 fives for the number sentence and 15 for covered.]

And I am going to go here.

[Michelle puts a green counter on the number 15 bottom row third across.]

Because that's too far away, I think.

[Michelle points to the number 15 in row 1]

Oh OK.

### Michelle

If I get a 4 it could be game over already.

Alright.

### Michelle

It could be the fastest victory in history.

That would.

### Michelle

Unless you get a 4 and you block me.

### Barbara

Yeah, ok, so I want a 4 or I actually just want something that goes next to my like fives.

Ok, let’s see.

Zero.

### Michelle

So, you rolled a zero and you have zero fives which means…

[Michelle writes on the record card for player 1, zero for rolled and zero fives for the number sentence and zero for covered.

### Barbara

I have got nothing, so zero. But that’s ok.

### Michelle

Cause there is a spot for zero.

### Barbara

There is a spot for zero, but it doesn't actually really fit in very well.

Oh, no, this one does. Ok

[Barbara puts a red counter on the zero in the third row in the third square across.]

Ok. My turn.

### Barbara

They often, you know in a lot of games when you roll a really low number or you spin a really low number, you can't go or it doesn't, whereas this game it doesn't really matter.

### Michelle

That's true.

I didn't get a 4 but I got a 3.

So, 3, fives is 15 and I know that.

So, my only other option for fifteen is up here for now.

[Michelle puts a green counter on the number 15 in the top row in the fourth square.]

### Barbara

Would you like me to write it 3, fives or another way?

### Michelle

Do 3 times 5 this time using symbols.

But it's the same.

### Barbara

Ok, my turn, alright.

So now what do I want?

I want 45.

So, I want.

### Michelle

Oh, yeah you do too.

And you've got 2 choices.

Look 45 and 45.

[Michelle points to the number 45 in the fourth row, fourth square across and the first row in the first square across].

### Barbara

I know I could double win.

### Michelle

Oh, and if you got 35, you'd be so close.

Oh, Ok.

### Barbara

Right.

Eight, Ok so.

I've got eight, fives.

Yes.

### Barbara

So, I know 4, fives is 20.

Yes.

### Barbara

So then double that, is 40.

### Michelle

Yep, I agree with you.

### Barbara

I'll put that there.

[Barbara puts a red counter on the number 40 in the second row in the third square across.]

### Barbara

So that's actually a pretty good spot.

[Michelle writes on the record card for player 1, 8 for rolled and 8 fives for the number sentence and 40 for covered.]

### Michelle

So, 8, 8, fives is 40.

Ok, that's very close.

May I please have the, thank you.

Spinning pencil.

### Michelle

The spinning pencil of doom?

Five, oh, I like this, 5 fives are 25.

I just actually really like that 'cause it sounds nice 5, fives are 25.

### Barbara

I like how it looks when you imagine it.

### Michelle

Oh yeah ‘cause it’s a square.

I love square numbers like 16.

Um, and now I need to decide whether I go here, or here.

[Michelle points to the first square in the second row and the second square in the third row.]

But here's more useful for me so I'm gonna go there.

[Michelle puts a green counter on the number 25 in the third row in the second square.]

### Barbara

Ok. It is more useful for you but in that one you kind of blocked me a little bit, so.

[Barbara writes on the record card for player 2, 5 for rolled and 5 fives for the number sentence and 55 for covered.]

I know.

### Barbara

It depends whether you're playing offense or defence.

### Michelle

Well, I'm probably not playing either.

### Barbara

Oh, hold on it was 5, wasn't it?

Five, fives yep.

Five, fives.

Nice revising.

### Barbara

You're paying attention.

Oh, we're going to run out of counters, so then we are going to have to make some choices, right?

### Michelle

Yep, then you have to move one.

### Barbara

Yes.

Yes.

Ok, now 9, fives.

### Michelle

Don't put that tone on because you’ve won.

### Barbara

Oh well, I need to explain my thinking.

So, I know that 5, tens is 50.

Yes.

### Barbara

Um, so that 5, tens is also 50.

So then if I take one of those fives away, I'll have 45.

[Michelle writes on the record card for player 1, 9 for rolled and 9 fives for the number sentence and 45 for covered.]

### Michelle

Yes.

And you have actually got multiple choices for victory.

You could have victory in the top left corner.

[Michelle points to number 45 in the first square in the first row being the top left corner, then points to the number 45 in the fourth row in the fourth square across.

Barbara puts a red counter on the number 45 in the first row first square and then moves another counter from the number 5 in the fourth row, fifth square to the fourth row, fourth square to cover over the number 45.]

### Barbara

Can I even move that one over there and get double?

Oh look.

I got a connect 4.

Ok, I'll settle for just 3 in a row.

Congratulations.

### Barbara

That’s a great game.

### Michelle

It's a very heartfelt congratulations.

Yeah, it is a great game, and we actually have a version of this that you can play using

twos.

[Screen shows a gameboard which is a 5 x 5 square, creating 25 smaller squares.

In the top row across there is a number written in each, 2, 0, 12, 4 and 14.

The second row is, 10, 12, 6, 16 and 4.

The third row is 16, 6, 18, 0 and 10.

The fourth row is, 4, 10, 8, 18, and 16.

And the fifth row is, 14, 18, 12, 8 and 6.

Underneath the gameboard is a players recording sheet. Heading row has Student 1 and Student 2, and the sub-heading row has columns which have the headings, ‘Rolled’, ‘Number sentence’ and ‘Covered’.]

So, you can work on understanding multiples of 2 and also tens.

[Screen shows a gameboard which is a 5 x 5 square, creating 25 smaller squares.

In the top row across there is a number written in each, 0, 10, 40, 80 and 60.

The second row is, 30, 70, 20, 50, 30.

The third row is 50, 20, 0, 40 and 60.

The fourth row is, 90,10, 70, 80 and 50.

And the fifth row is, 40, 60, 30, 90 and 20.

Underneath the gameboard is a players recording sheet. Heading row has Student 1 and Student 2, and the sub-heading row has columns which have the headings, ‘Rolled’, ‘Number sentence’ and ‘Covered’.]

So, there are some other number facts that you can use this game to get more confident

with.

So over to you mathematicians.

You might even come up with your own version of the game.

[End of transcript]

## Instructions

• Players take turns to roll the dice or spin the spinner and multiply the number selected (for example 6) by the number rolled and work out the product, explaining their thinking to their partner.
• Their partner records their thinking and if they agree, the first player is able to place one of their counters on the number on the game board, claiming that place.
• If the number is taken, players miss a turn.
• A player wins by getting three counters in a row (in any orientation).
• Since players only have 3 counters, they will need to choose which counter to move once all 3 have been placed on the game board.

## Resources

For different variations of the game:

## Other ways to play

• Play with 4 counters to win.
• Play with a multiplication grid to check your partners answer, giving players an opportunity to have a second attempt if they answer incorrectly initially.