Order! Order!

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

Hello Michelle. How are you?

I am fantastic.

I missed you.

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

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!

Yes, please.

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

Order in the maths court!

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

Okay.

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.

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

Okay, 13.

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

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

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

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

Mm-hmm.

So you've got a nine and a zero.

Yeah.

You could make 90.

Yes.

Could you make nine?

Well we could have a really nice debate about this.

Hmm.

Umm, because we could say that you could write it like this [09] but technically we never put the zero. We don't write like that. 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.

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.

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

Yeah.

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

Sorry, 90 please, 9 tens.

We call that 90.

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

That we rolled them.

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

37.

3 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.

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

So 5 tens and 6 more.

I really like even numbers.

Why do you like even numbers?

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

Yeah they are good sharers.

Equal sharers.

Okay so we don't need our dice anymore. 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.

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

Oh what can you do?

You can only move numbers that are next to each other, one at a time. So you are just swapping them over.

Swapping them. Oh, okay.

We would call them adjacent numbers, that would be the fancy maths word for it. So you're only moving adjacent numbers, swapping adjacent. Swapping.

Okay so are we, what are you doing first?

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

I'm glad you said that.

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

Yeah, because I know it's the smallest.

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

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

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

Okay, so, so we need to get the 90, 9 tens up to here. And it's, well these, these are in the right order, but we can't make the 19, jump over.

No.

So we're gonna have to swap.

Yeah.

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

Okay.

Because they're in the right order anyway. So I might swap 19 and 37.

All right, so that makes it one move.

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

Okay, and that's two moves.

So, it took us to 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!

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.