# Order! Order! (two-digit numbers)

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
• MA1-RWN-01
• MA1-RWN-02

## Collect resources

You will need:

• markers

• sticky notes (or blank number cards)

• 2 x 0-9 dice (you could also use playing cards, a spinner or numeral cards).

## Watch

Watch the Order! Order! (two-digit numbers) video (4:58).

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

### Transcript of Order! Order! (two-digit numbers)

(Duration: 4 minutes and 58 seconds)

Text over a navy-blue background: Order! Order! -2. (From Mike Askew). In the lower left-hand corner is a white waratah logo of the NSW Government. In the top left-hand corner is small font text which reads: NSW Department of Education.

A piece of butcher’s paper is on a table. On the butcher’s paper is a pad of post-it notes and a red bowl with two ten-sided die. Michelle and Barbara are off-screen.]

### Michelle

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

### Barbara

Hello, Michelle. How are you?

I'm fantastic.

I've missed you.

### Michelle

I missed you too.

### Barbara

I've been doing a lot of maths by myself. It's much more fun to do it with a friend.

### Michelle

(LAUGHS) So have I. Alright, 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! Order in the maths...

Court? (LAUGHS)

### Michelle

(LAUGHS) In the maths court. So what we need to do is we've got two dice, zero to nine.

OK.

### Michelle

And you can play this game in lots of different ways, like with two dice, three dice, four dice, five dice. We're going to use two dice and make four numbers. So you want to just roll them and create a number and tell me what it is.

Barbara rolls the dice in to the bowl.]

OK. 13.

### Michelle

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

Barbara takes the dice out of the bowl and places the one before the 3. Michelle writes the number 13 on a post-it note, removes it from the pad and sticks it on the butcher’s paper.]

### Barbara

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

### Michelle

Oh, that's so generous of you. (LAUGHS)

### Barbara

..13 should have some fun sometimes.

Michelle picks up the dice and rolls them. They land on zero and 9.]

### Michelle

In some cultures, 13 is a lucky number.

### Barbara

Yeah, I think so. You make your own luck. Oh, I've got a question. So you've got a nine and a zero, you could make 90?

Yes.

### Barbara Could you make nine?

Michelle writes zero and 9 on the post-it note.]

### Michelle

Well, we could have a really nice debate about this because we could say that you could write it like this, but technically, we never put the zero...

### 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 nine of something, we know there are zero tens. We would never write a number like that...

No.

### Michelle

..but you could play that way if you wanted to play the game that way. I'm going to make 90 though because I like it. So, but you need to record it for me, actually, so 90, please. Nine tens.

Michelle discards the post-it note with zero and 9 and hands the pad to Barbara. Barbara writes 90 on a post-it note and places it beside the 13.]

We call that 90.

### Michelle

OK, and your turn to roll, and my time to write. And we're just going to put them in order that we...

Barbara rolls the dice in the bowl. They land on 3 and 7.]

### Barbara

So we roll them, OK. Alright, let's see...37.

Michelle writes 37 on a post-it note and places it beside the number 90.]

### Michelle

37. Three tens and seven more. You could have also had seven tens and three more. And if you join three and seven, it makes a ten.

### Barbara

Oh, wow! (LAUGHS)

Michelle rolls the dice. They land on 5 and 6.]

### Michelle

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

Michelle rearranges the dice in the bowl, showing that she can make either 65 or 56 with the two digits. She finishes with the dice arranged on 56. Barbara writes 56 on a post-it note and place it beside the 37.]

### Barbara

So five tens and six more.

### 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're good sharers. (LAUGHS) Equal sharing.

Michelle places the bowl of dice to one side. There are four numbers on post-it notes arranged in a horizontal line. On the far-left is 13, then to the right is 90. The next number is 37 and the far-left number is 56.]

### Michelle

(LAUGHS) They're very good at sharing. OK, so we don't need our dice anymore. And now here comes our challenge that we are going to 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 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 far-left number, 56, ad feigns to swap it with the far-right number 13. She puts 56 back in its position.]

### Barbara

Oh, what can you do?

### Michelle

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

### Barbara

So you're just swapping them over?

### Michelle

Swapping them over. We would call them adjacent numbers. That would be the fancy math word for it.

Swapping.

### Barbara

OK. So what are you doing first?

Michelle points to 13, the far-left number.]

### Michelle

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

### Barbara

I'm glad you said that. I noticed that as well. So I was hoping you'd say that.

### Michelle

Yeah, because I know it's the smallest. Well, how do you know it's the smallest?

### Barbara

Well, it's only got one ten.

(DESCRIPTION: In turn, Michelle points to the numbers from second-to-left to far-right, 90, 37 and 56.]

### Michelle

Yeah. And all the other numbers have more than one ten, nine tens, three tens.

### Barbara

And five tens.

Michelle points to the 90, currently second from left, and then the 56, which is the number in the far-right position.]

### Michelle

OK, so we need to get the 90, nine tens up to here.

Michelle points to the 37 and 56, the two numbers on the right.]

### Barbara

And these are in the right order, but we can't make the 90 jump over?

No.

### Barbara

So we're going to have to swap.

### Michelle

Yeah.

Barbara points to the far-right number 56 and the number to its left, 37.]

### Barbara

OK, so I'm thinking, I'm not going to swap these two around because they're in the right order anyway. So I might swap 90 and 37.

### Michelle

Alright. So that makes one move.

Michelle swaps the middle two numbers, 90 and 37, so that 37 is now to the right of 13 and 90 is to the left of 56. Michelle makes a single stroke on a new post-it note]

### Barbara

OK. And now I'm going to swap these two.

Barbara swaps the 90 and the 56 so that the 90 is now on the far-right and that all numbers are ordered from smallest to largest. On the far-left is 13, then 37, 56 and 90. Michelle makes another stroke on her post-it note tally.]

### Michelle

OK, and that's two moves. So it took us two... two 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.

White text on a blue background: What’s (some of) the mathematics? In the bottom right corner is a white waratah logo of the NSW government. Small font text in the top right corner reads: NSW Department of Education.]

New slide: Dark text on a white background: This game provides us an opportunity to share what we know about place value when working with 2-digit numbers. We have to think strategically to try to order the numbers from smallest to largest, and largest to smallest, in the fewest possible moves.

Below the text is a photo of the four post-it note numbers. From right, the numbers are 13, 37, 56 and 90.]

### Michelle

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 two-digit numbers. 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!

The NSW Government logo flashes on screen. Text below reads: Copyright, State of New South Wales (Department of Education), 2021.]

End of transcript]

## How to play

• Roll the dice and create and record a 2-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

Help Michelle and Barbara order these numbers from largest to smallest.

• Record how many moves it takes to order them.

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

## Other ways to play

• Make bigger numbers by using more dice.
• Use only a few playing cards to form numbers (for example, use A, 1 and J (to represent 0) only).
• Does that increase the challenge of working out the order?