# 10 or bust (additive strategies)

This is a thinking mathematically context for practise focussed on developing additive thinking and reasoning strategies.

## 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

## Outcomes

- MAO-WM-01
- MAE-CSQ-01
- MAE-CSQ-02
- MAE-RWN-01
- MAE-RWN-02

## Collect resources

You will need:

- a game board (for example use a number track, a ten-frame, a drawing of 10 fingers, a drawing of a known number combination to 10)
- counters or dried beans or pasta
- a dice, spinner or numeral cards from 1–6
- pencils or markers.

## Watch

Watch 10 or bust video (6:23).

### Michelle

Alright, welcome back mathematicians!

Hi Ayesha.

### Ayesha

Hi Michelle.

[Screen shows a white piece of paper with 10 coloured blocks in a row on the paper. The name Michelle is written on a sticky note which is on the white paper. The name Ayesha is on another sticky note to the right of the white paper. Above the white paper is one pile of yellow counters and another pile of green counters.]

### Michelle

How are you today?

### Ayesha

I'm good and you?

### Michelle

Very well thank you. So today Ayesh and I are playing our game together but remotely so I'm gonna keep a track of your game as well as my game at the same time so I could see what was happening as if we were together so well, because we're going to play ten frame or bust or sorry, 10 or bust.

What structure did you want to use today for, for your, to keep track of 10? You could use like a number line. Or you could use a drawing of your hands.

Or you could use your favourite dice patterns or something?

### Ayesha

I'm thinking because it's around the number 10. I would like to use a ten frame.

### Michelle

Oh, so I think I have one from something I was doing before, so I've got your ten frame here and Ayesha, I thought I might like to use a number line today.

So, I, so I just made it out of blocks. I have 10, I'll just check. I've got 2, 4, 6, 8, 9 and I need one more, so that I've got 10 and I can use that to measure my number line on and I'll draw my number line and then I can draw the numbers on there.

And then I can label them 1, 2, 3, 4, 5, 6, 7, 8, 9 and 10. OK. Have you got dice over there, Ayesha?

[Michelle places a blank ten frame next to the paper with the coloured blocks. The ten frame is 5 rows of 2 squares. She puts the sticky note with the name Ayesha above the ten frame. Michelle then counts the row of coloured blocks two at a time, 2, 4, 6, 8, 9, and adds one more coloured block to make 10. Michelle draws a number line beneath the coloured blocks and labels the number line with the numbers 1, 2, 3, 4, 5, 6, 7, 8, 9 and 10.]

### Ayesha

I do.

### Michelle

And I've got some counters. I've decided that you're going to be green and I'm going to be yellow.

[Michelle moves the yellow counters onto the piece of paper with the number line and the name Michelle displayed and the green counters onto the ten frame with the name Ayesha displayed.]

### Ayesha

All right.

### Michelle

And then do you want to roll the dice first, or will I?

### Ayesha

Here, I'll have to go.

### Michelle

OK.

Right, I got 4.

OK, so are you putting that on your ten frame?

[Michelle points to the ten frame.]

### Ayesha

I've decided to add that to my ten frame.

### Michelle

And did you make it 4 so it looks like a square, Ayesha? Or did you make it four so it's in one line and you see one less than 5?

[Michelle points to the first two rows of the ten frame, which is four squares. She then points to the top 4 squares in the first column of 5 squares.]

### Ayesha

I did it so I see one less than 5.

### Michelle

Ok, so 1, 2, 3, 4.

[Michelle puts one green counter on each of the 4 squares in the first column of the ten frame, beginning from the top of the column.

OK, now remember when we play, we only get 3 rolls of the dice and you can only choose not to use one, but it has to be in your first move or your second move.

### Ayesha

OK, so I've got a decision to make for the next go.

### Michelle

Yeah, I'm rolling my dice and I got a three.

[Michelle rolls the dice and she rolls 3.]

So, I'm going to put down 3 on my number line 1. 2. 3. OK, Ayesha, your turn again.

[Michelle adds 3 yellow counters to the number line, on the numbers 1, 2, and 3.]

### Ayesha

Alright... This time, I got a 6.

### Michelle

Oh, what are you gonna do?

### Ayesha

Well. I know that next turn I have to use it so whatever I roll is going to take me over 10, so

I think I'll skip this one and sit this one out. So, I'm not going to add 6 to my ten frame.

### Michelle

Yeah, because I'm just going to show everybody what that would look like if you had six more. It would mean your ten frame is full and no matter what number you rolled; you would be busted.

[Michelle adds 6 yellow counters to the 10 frame, and outlines the full 10 frame with her finger. She picks up the dice and displays the different numbers on the dice.]

### Ayesha

That's right.

### Michelle

OK, that's, that's a good strategy. I feel disappointed you chose it, 'cause you know I like to win, but I think it's good thinking Ayesha.

[Michelle removes the 6 yellow counters and puts them back into the pile.]

OK, and now we're only one number apart too, you're on 4 and I'm on 3.

[Michelle points to the 3 counters on the number line and the 4 counters on the ten frame.]

OK, guess what, Ayesha? I rolled a 6 too. And I'm so tempted to play it because that would get me to 9.

[Michelle points from the number 4 to the number 9 on the number line.]

I'm going to try it and see what happens.

So, I've got three and I need to add 6 more so I'll just get six counters first. And 3, 4, 5, 6, 7, 8, 9. I hope I get a one.

[Michelle picks up 6 yellow counters. She points to the number 3 and then adds the counters to the numbers 4, 5, 6, 7, 8 and 9 on the number line.]

### Ayesha

Yes, so I see here. I really need to get a 9 or more for us to even tie or for me to win so that means to get a 9 that means I need to at least roll a 5 and to get 10 I'll have to roll a 6.

### Michelle

Yeah, but I also have one more roll that I can't cancel out, so I could bust. Your go Ayesha, roll your dice!

### Ayesha

Hey. I got a 4.

### Michelle

OK. So, Ayesha, where do you want me to put your 4?

[Michelle picks up 4 green counters from the pile.]

Do you want to continue down the line?

### Ayesha

Right underneath on the bottom row. So, that I have 4 on the top row and 4 on the bottom row.

[Michelle rotates the ten frame so it is now 2 rows of 5 squares. She moves the 4 green counters on the ten frame to the first 4 squares on the top row.]

### Michelle

Oh yeah, I had my ten frame turned the other way so I just turned it so that I could do what you were saying.

[Michelle adds another 4 green counters to the first 4 squares on the bottom row, so they are beneath the 4 counters on the top row.]

So, so now it looks like each one on the top row has a partner down the bottom?

### Ayesha

That's correct.

### Michelle

And there's 2 empty boxes. So that means you're on 8.

[Michelle rotates ten frame back to original position of 5 rows of 2 squares. The top row is empty. Each of the other 8 squares has a green counter.]

OK, I hope I get lucky and get a one. Let's see what happens.

[Michelle rolls the dice and she rolls 4.]

Oh, oh Ayesh. I got a 4 so I am definitely busted 'cause I get 10 and then I actually would need three more.

[Michelle adds one yellow counter to the number 10 on the number line and shows the extra counters she still needs to place.]

So, congratulations, Ayesha, you won that round.

### Ayesha

Yay!

### Michelle

Do you want to play again?

### Ayesha

Of course! Let's have another go.

### Michelle

Alright. Have fun out there you mathematicians.

[End of transcript]

## Reflection

- How could we change the game to make it more/less challenging?
- Did you work out a way to play this game so that you didn’t lose?
- What was your strategy?
- Did it work?