# Double or halve? – Stage 1

A thinking mathematically context for practise resource, focussed on using doubling and halving to reach a target number

## 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-FG-01

You will need:

## Watch

Watch Double or halve? video (7:37).

Reach the target number using doubling or halving.

### Transcript of Double or halve

(Duration: 7 minutes and 37 seconds)

[White text on a navy-blue background reads ‘Double or halve? (Stage 1) From NRICH’. Small white text at the bottom reads ‘NSW Mathematics Strategy Professional Learning team (NSWMS PL team). In the bottom right corner, the NSW Government red ‘waratah’ logo.]

### Female Speaker

Double or halve from NRICH.

[A blue text on white header reads ‘You will need…’ Four bullet points below (as read by speaker). On the right, in a still colour image, a black and white grid sheet has a pink and a green marker and a 6-sided red dice alongside it. Handwriting at the top of the sheet reads ‘Double or halve?’ ]

### Female Speaker

To play, you will need 2 different coloured markers or coloured pencils, something to write on, a blank hundreds chart, and a 6-sided dice or a 1-to-6 spinner.

[White text on a light blue background reads ‘Let’s play!’]

### Female Speaker

Let's play.

[The grid sheet, markers and dice from the earlier still colour image.]

### Female Speaker

Hello there, everybody. I have one of my favourite mathematicians, Holly, with me today. Hi, Holly.

Hi.

### Female Speaker

So we're gonna play a game called Double or Halve, and the aim of the game, Holly, is to try and be the first to reach our target number. So, first of all, what do we want our target number to be? It needs to be between 10 and 99.

### Holly

I want my number to be 27.

[A person’s hand, the teacher, writes ‘27’ with the green marker and circles it in the top left corner of the grid paper.]

### Female Speaker

27, alright. Well, we might write our target number up here so we remember, Holly, 27. OK. Now, Holly, what we have in front of us is a 10-by-10 grid, and this is representing a hundreds chart.

### Holly

Yes, I know this.

### Female Speaker

Oh, you know this, OK.

### Holly

Yes. So, we have one 10, another 10, another 10, another 10, and there's 10 x 10, so that would mean 100.

Yeah, correct.

### Holly

But it will take a really long time if I went 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16...

### Female Speaker

Yes, it would. So, you're right, Holly. So, it is a really efficient way of representing 100 things by putting them in tens, you're right. And, Holly, in this one, we're gonna imagine that this is a hundreds chart, but it's a blank hundreds chart. And normally on a standard hundreds chart, we have one here through to 10.

[The teacher’s hand points to the top left corner of the grid and moves horizontally across the first row before moving on to the subsequent rows.]

### Female Speaker

And then we have again here, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, and then 30 and then 40.

[Holly continues along the rows, pointing with the back of the green marker pen.]

### Holly

40, 50, 60, 70, 80, 90, 100.

### Female Speaker

OK. So, 100. So what we might do, Holly, is represent, first of all, on our blank hundreds chart where our target number would be. So, where would 27 be on our hundreds chart?

### Holly

So, is that one 20 row?

[Holly and the teacher use their fingers to point at various squares on the grid.]

### Female Speaker

Yeah. Yeah. 'Cause you got two 10. Yeah.

### Holly

So, I'll just get through that, 1, 2, 1, 2...

### Female Speaker

So, would that be...?

### Holly

Oh, no, 'cause that would be, what is it called? I forgot its name.

20?

### Holly

And that one will be 10.

### Female Speaker

And this one would be?

30

### Female Speaker

OK. So, where would 27 be? I liked how you revised your thinking there. Oh, that's 20 and this is 30. So, where would 27 be?

### Holly

One, 2, 3. Here.

[Holly uses the green marker pen to write ‘27’ in the third row.]

### Female Speaker

OK. Right. Let's write 27 in that box, so we know. OK. And that makes sense to me, 'cause I can see 27, and then I can imagine 28, 29, 30. OK, alright. So, that's the number that we're going to try and get, Holly. So, what we have here is a 6-sided dice, and we're each going to have a marker. And when we roll the dice, Holly, we can choose to either double or halve the number. And we need to be the first to reach 27. So, I'm going to roll the dice. Oh, 2. Now, if I double 2, that is 4. Or I could halve it, and what would half of 2 be?

One.

OK. Now.

### Holly

Or, can you keep it?

### Female Speaker

No, it's double or half, you can't keep it. So, I'm going to double it. So, I know that double 2 is 4. And look, I can see 2 and another 2 here, so I'm just going to... Here's my 4, OK.

[The teacher use the pink marker to outline 4 of the squares in the first row of the grid paper in the top left corner. She then fills them in with strokes of her pen. On the right of the grid she then writes ‘4’.]

### Female Speaker

And I'm imagining there that I have 1, 2, 3, 4. I can see the number 4 there, so I know we're up to 4. Ooh, OK.

[Holly rolls a ‘4’ on the red dice.]

### Holly

I want to do double 4.

### Female Speaker

OK. And what's double 4?

### Holly

8. So, first, I'm just gonna do this one, and then this.

[Holly uses her green marker to outline the remaining 6 squares on the row and 2 more on the second row.]

### Female Speaker

OK, so you partitioned your 8 into 6 and 2. What's our running total? Where are we up to? So, we had 4 and then 8 more.

### Holly

So, right now we're up to 12.

OK.

10, 11, 12.

### Female Speaker

OK, so, can you write 12 there?

[On the right of the grid, Holly writes ‘12’ below the ‘4’. The teacher rolls the dice again.]

### Female Speaker

OK. Alright. Let's try this one again. Ooh, 6. OK, now I'm going to...

(WHISPERS)

### Female Speaker

If I double that, that would mean I'd be getting pretty close.

### Holly

12 plus 6 would be 18.

[The teacher outlines the squares on the grid with her pink marker pen and then writes ‘24’ in the column on the right.]

### Female Speaker

Alright, so, I'm going to double that, so that's 12. And I can see 8 here. And then plus 4 more. So, 12 and 12 is 24. So, Holly, we need to get 3 more to reach our target. Alright. So, we need 3. So, how are we going to get a 3, I wonder? Let's see.

[Holly rolls the dice again.]

Ooh, 1, so you can double it or you can halve it.

Double.

### Female Speaker

OK.

[Holly outlines the squares on the grid with her green marker.]

### Holly

We only need one more. If you get a 1.

[The teacher points to the right-hand column.]

### Female Speaker

So, before we had 24, 26. Now we have 26.

Yeah. OK, so you write 26.

[Holly writes ‘29’ below the previous numbers.]

### Holly

It's kind of obvious, 'cause...

(GASPS)

### Holly

(GASPS) (LAUGHS) Thanks. I always get mixed up.

### Female Speaker

Yeah, 'cause they do look very similar, don't they?

### Holly

I know.

[Holly circles the ‘9’ in ‘29’ and then writes ‘6’ next to it.]

### Female Speaker

OK, so, 26. Oh, is that what you do when you make a correction? I like that, because you revised your thinking. That's what we do when we're mathematicians. Alright, so, Holly, I need to roll. I need to get one, right? So, the only way that I can get one is...

Is by rolling.

### Female Speaker

It's not by rolling a 1, but by actually rolling a 2 and then halving it.

### Holly

Yeah.

[They take it in turns to roll the red dice.]

### Female Speaker

5. OK. Now, that would bust us, so that doesn't work. ‘Cause in this game, you actually have to roll the exact target number. So, keep going. (GASPS) 5. (LAUGHTER)

(CHEERS)

2!

### Holly

Yes. I'm gonna half.

[Holly fills in the ‘27’ square and then writes ‘27’ in the right-hand column with ‘sunshine’ lines around it.]

### Female Speaker

Halve it. So, half of 2 is 1. You were...

Da-da-da!

### Female Speaker

..the person who reached our target number. (LAUGHS) Have fun playing Double or Halve.

[White text on a blue background reads ‘What’s (some of) the mathematics?’]

### Female Speaker

So, what's some of the mathematics?

[A blue text header on a white background reads ‘What’s (some of) the mathematics?’ Two bullet points below (as read by speaker).]

### Female Speaker

We can use what we know about halving and doubling numbers to make strategic decisions to reach our target number. Knowing the difference between the running total and the target number helps us strategize and increase our chances of winning.

[The NSW Government waratah logo turns briefly in the middle of various circles coloured blue, red, white and black. A copyright symbol and small blue text below it reads ‘State of New South Wales (Department of Education), 2021.’]

[End of transcript]

## Instructions

• Choose a target number between 10 and 99.
• Write your target number on your blank hundreds chart.
• Our target number was 27 so we wrote 27 where it would be found on a top-down hundreds chart that starts at one.
• The first player rolls the dice and chooses whether to double or halve the number.
• Record the roll on the game board, by shading the amount of squares.
• Players record the running total to the side of their hundreds chart game board.
• Players take turns to roll the dice.
• If a player can't go, they miss a turn.
• The winner is the player who reaches the target number exactly.

## Discuss and reflect

• If you played the game again are there any moves you would change?
• Would you choose to halve a number that you doubled? Why or why not?
• Play a game where you can double, halve or keep your roll. Do you think this might make it easier to reach the target number?
• What if you could only halve the number each time?