# Order! Order! (four-digit numbers)

Stage 2 and 3 – A thinking mathematically context for practise resource focussed on using place value knowledge to create and order numbers

Adapted from Askew, M. (2015), A Practical Guide to Transforming Primary Mathematics: Activities and tasks that really work, Routledge

## 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-RN-01
• MA2-RN-02

• MAO-WM-01
• MA3-RN-01

## Collect resources

You will need:

• markers
• sticky notes (or blank number cards)
• 4 x 0-9 dice (you could also use playing cards, a spinner or numeral cards).

## Watch

Watch the Order! Order! (two-digit numbers) video (6:26).

Create and reorder four 2-digit numbers in the fewest moves.

### Michelle

Hello there mathematicians. And hello to one of my most favourite mathematicians, Barbara!

[Screen shows a red bowl containing 2 zero to 9 dice. One is green, the other black. On the large piece of paper there are also some sticky notes.]

### Barbara

Hello Michelle. How are you?

I am fantastic.

I missed you.

### Barbara

I missed you too. I've been doing a lot of maths by myself, but much more fun to do with a friend.

### Michelle

So have I! All right, well, let's, um, I learnt this game from Mike Askew, so do you want to learn it with me? It's called Order! order!

### Michelle

I really like it. It's like order, order.

### Michelle

Order in the maths court!

So, what we need to do is we've got 2 dice, 0 to 9.

[Michelle picks up the bowl and shakes dice and then picks up the black dice and puts it back down.]

Okay.

### Michelle

And you can play this game in lots of different ways, like with 2 dice, 3 dice, 4 dice, 5 dice.

We're gonna use 2 dice and make 4 numbers today.

Okay.

### Michelle

So do you want to just roll them, and create a number, and tell me what it is.

### Barbara

[Barbara rolls dice. She gets a 3 and a 1.]

Okay, 13.

### Michelle

Okay, you could also have made 31, if you wanted, but you made 13.

[Barbara picks up the dice and places it next to the sticky note. Michelle writes the number 13 on the sticky note and places it on the white piece of paper.]

### Barbara

Yeah, because I think sometimes 13 has a bad reputation about being unlucky, I wanted to give 13 some fun.

### Michelle

That's so generous, in some cultures 13 is a lucky number.

[Michelle rolls the dice. It lands on 9 and zero.]

### Barbara

Yeah, I think so, you make your own luck. Oh, I've got a question.

Mm-hmm.

### Barbara

So, you've got a 9 and a zero.

Yeah.

### Barbara

You could make 90.

Yes.

### Barbara

Could you make 9?

Hmm.

### Michelle

Umm, because we could say that you could write it like this but technically we never put the zero.

[Michelle writes 09 on a sticky note. She points to the number to show her thinking before removing it.]

### Barbara

We don't write like that.

### Michelle

And so, you could make a really good argument to say we won't accept that number because it's not convention to write numbers that way, even though when we have 9 of something we know there's zero tens.

Yeah.

### Michelle

We would never write the number but like that. But you could play that way if you wanted to play the game that way.

Okay.

### Michelle

Um, I mean, I'm gonna make 90 though.

[Michelle removes sticky note with 09 from the screen.]

Yeah.

### Michelle

I like it so, but you need to record it for me actually.

### Barbara

We call that 90.

[Barbara writes 90 on a sticky note and places it under the sticky note with 13 written on it.]

### Michelle

Okay, and your turn to roll, and my turn to write and we're just gonna put them in order that we

[Michelle moves the sticky note with 90 written on it to the right on the first sticky note. She starts to make a horizontal line.]

### Barbara

That we rolled them.

Okay. All right let's see. Ahh, 37.

[Barbara rolls the dice. She rolls a 3 and a 7.]

### Michelle

37.

[Michelle writes 37 on a sticky note. She adds it to the row.]

Three tens and 7 more. Okay, you could have also had 7 tens and 3 more. And if you join 3 and 7 it makes it 10.

Oh wow.

### Michelle

And I am going to make, ooh will I make 56, or will I make 65? I will make 56.

[Michelle rolls the dice. She rolls a 5 and a 6. She arranges the dice to create the number 56.]

### Barbara

So, 5 tens and 6 more.

[Barbara writes 56 on a sticky note and places it in the row of sticky notes.]

### Michelle

I really like even numbers.

### Barbara

Why do you like even numbers?

### Michelle

I don't know, I just feel comforted by them.

### Barbara

Yeah, they are good sharers.

Equal sharers.

### Michelle

They are very good at sharing.

Okay so we don't need our dice anymore.

[Michelle moves the dice to the top of the screen.]

And now here comes our challenge, that we're gonna work together on.

Is, we need to think about how we can relocate these numbers, and move them, so that they are in order, from the smallest to the largest, or the largest to the smallest, or both.

Okay.

### Michelle

In the fewest number of moves, but you can't just pick this up and go, I'm putting it here.

[Michelle picks up the sticky note with the number 56 on it. She hovers it over the first sticky note to show that the sticky notes cannot just be picked up and placed into random spots.]

### Barbara

Oh, what can you do?

### Michelle

You can only move numbers that are next to each other, one at a time.

[Michelle gestures to the sticky notes placed next to each other, she moves to show that they can be swapped over.]

### Barbara

So, you are just swapping them over.

Swapping them.

Oh, okay.

### Michelle

We would call them adjacent numbers, that would be the fancy maths word for it.

Swapping.

### Barbara

Okay so are we, what are you doing first?

### Michelle

Let's go smallest to largest, because 13 is here and I already know it's the smallest.

[Michelle points to the first sticky note which has 13 written on it and moves her finger across the remaining 3 sticky notes to the right, which line up across the paper.]

### Barbara

Okay. I noticed that as well, so I was hoping you'd say that.

### Michelle

Yeah, because I know it's the smallest.

[Michelle points to the sticky note with 13 and circles her finger around the number.]

### Barbara

Well, how do you know it's the smallest?

### Michelle

Well, there's, it's only got 1 ten.

### Michelle

Yeah, and all the other numbers have more than 1 ten. 9 tens, 3 tens and 5 tens.

[Michelle points to each number moving across left to right, pointing to the number in the tens place value for each one.]

Okay, so, so we need to get the 90, 9 tens up to here.

[Michelle points to the 90 and circles it with her finger and then she points to the last sticky note which is 56.]

### Barbara

And it's, well these, these are in the right order, but we can't make the 90, jump over.

[Barbara points to the sticky notes with 37 and 56 on it, signalling that they are in the right order. She shows how the number 90 cannot jump 2 spaces.]

No.

### Barbara

So, we're gonna have to swap.

Yeah.

### Barbara

Okay, so I'm thinking I'm not gonna swap these 2 around because they're in the right.

Okay.

### Barbara

Because they're in the right order anyway. So, I might swap 90 and 37.

[Barbara swaps the 90 and 37. Michelle writes a tally mark on the sticky note.]

### Michelle

All right, so that makes it one move.

### Barbara

Okay, and now I'm gonna swap these 2.

[Barbara now swaps 56 and 90 around. Michelle creates another tally mark and underlines them.]

### Michelle

Okay, and that's 2 moves.

So, it took us to 2 moves to order them from smallest to largest, what if we had ordered it from largest to smallest?

Over to you mathematicians to help us problem solve that, and to have a play!

Have fun!

So, what's some of the mathematics?

This game provides us with an opportunity to share what we know about place value when working with 2-digit numbers.

[Screen shows 4 sticky notes horizontally across the screen with number written on them. The first one has 13, the next has 37 the next has 56 and the last one has 90.]

We also have to think strategically to try to order the numbers from smallest to largest and largest to smallest in the fewest moves possible. Have fun mathematicians.

[End of transcript]

## How to play

• Roll the dice and create and record a 4-digit number.

• Repeat until you have 4 numbers.

• Order them from smallest to largest, and largest to smallest in the fewest moves possible, moving adjacent cards only.

## Instructions

• Can you help Michelle and Barbara? Is it possible to order these numbers from smallest to largest in less than 5 moves?
• Record how many moves it takes to order them.

• Remember you are aiming to use the fewest moves possible!

## Another way to play

• You can make bigger or much smaller numbers (like decimals and fractions).
• Use only a few playing cards to form numbers (for example, use Ace-4 only).
• Does that increase the challenge of working out the order?