Remainders game

Hi Barbara.

Hi Michelle.

How are you today?

I'm very well. How are you?

Great. We are going to play a game called the Remainder's game.

Ok.

Ok. so, we each have twenty four counters and we're using dried pasta, nonedible.

Well, if you cook it, it is.

And we have six squares of paper that we can use to help us do some calculating if we need it, and I have six 'cause we're using a one, six sided dice ok, so, we could change, like if we use a spinner to five, we would just have five for example. So you can change it as we like. So you roll and I'll tell you how to play.

I've rolled a three.

So what we need to think about is dividing your twenty four counters into three equal groups. So you can put these out if you like.

They're my groups.

They're your groups, to help you move the pasta into, if you want to do that or to help you visualise. You can also just use what you know if you have some number facts as well.

So. So I know that three fives are fifteen. Ok, so I can make those straight away without having to count them out. Three fives.

Ok.

Get that right? Ok.

That's five and that's five and now, I've got nine left.

So.

Oh yeah, another three in each group. Yeah, is that what your thinking?

Exactly.

So I was going to do twenty four divided by three. The answer is eight. Eight in each group and for you there's no remainder.

No remainder.

So you don't get to keep any of the pasta just yet.

Ok. So put it back into your pile.

So in this game you want remainders right?

You want remainders.

Ok, so I'm going to put this here while I roll.

And I got a four and I actually already know that twenty four divided by four will have no remainders.

How do you know that?

Because half of twenty four is twelve and half of twelve is six and that's the same as dividing by four. Ok, no reminders for me either. But you need to record my move.

So, twenty four, shared into four equal groups, this is why mathematicians invented symbols, is equivalent in value to six in each group.

Ok.

Yeah. So no reminders, no remainders for me either. Your go.

Five, oh yeah. Fives makes me happy because if I have five groups, I want, I'll put these out, but I don't think I need to move the pasta this time.

Um.

Like a dice, nice. Ok, so what I'm imagining is four in each one, and that's going to give me twenty.

Yes.

And I'm going to have four leftover. Oh yes, do you agree? Do you want me to make it.

No, I agree with you. So you're saying twenty four shared equally into five equal groups. Means you'd have four or four fives is twenty and then there'd be four left over, this many left over.

That's right, Yep.

That would mean that you can't put an equal number in each group, so they're are the left overs, so we call them remainders. So four in each group and then four remainder. So what that means now is that you get to keep those four counters.

Ok, great.

And they are still are in play.

Ah, so, I've got less counters now.

So next time you start you're starting with twenty.

Oh, ok.

Well that was clever writing it down so we don't forget.

Yeah. Alright my turn. Ah hey, same. This is nice. So I can actually just use your reasoning, which is if I had my fives out like this. If I had four on each one, that would be twenty and because this is twenty four. Twenty minus. Twenty four, the difference between twenty four and twenty is four and I can't equally share four into five groups without fractioning them. So that gives me a reminder of four.

Fantastic. So twenty four, shared equally into five equal groups, means there is four in each group with four left over. And we call that a remainder.

Ok, and now the next one. Starting at twenty. Ok, so we're exactly the same at the moment.

We are.

I'll even put this one back.

I know what our move will be. Ok, your turn. Oh, now five's is not a good roll. No, it's not. It was so good before.

It was.

Ok, so well we already covered that isn't. If we have five groups there'll will be four in each group and I have nothing, there'll be no remainders.

No remainders. It partitions equally.

Now I don't want to five. Now I'd like a six or a three. Oh, and I don't want a four either because four fives is equivalent to twenty, so, no remainders, no leftovers.

So twenty. Yep, shared into four equal groups is five in each group. Ok, your turn.

Ok, so I don't want a four. I don't want a five. I'd like a six.

A six would be good or a three.

So twenty shared into five equal groups is equivalent to four in each group. Ok, your turn.

That's a good known fact for us now.

Oh, and a three. Ok. I like this. So, I might put my three groups out just so I can get you to visualise with me. So, So what I'm going to think about is, I know that um I know I have twenty left and I know that can't be divisible by three.

Ok, how do you know that?

Because it would be twenty one 'cause seven threes is twenty one, so it can't be divisible. Twenty can't be divisible by three, 'cause there's only a difference of one between twenty one. So I will have leftovers. So from twenty one, knowing twenty one, if I take one more group away, that would be eighteen.

Ok, that makes sense.

So that would mean that from eighteen shared into three groups I could count up if I wanted so I could say three, six, nine, twelve, fifteen, eighteen. Six in each group. So I'm going to make it now.

[Video speeds up here - no sound]

Alright, so Barbara, we've come to realise something in the game that it's the person who gets to two is the winner.

Oh, ok, yeah, because after that you can't go anymore, right.

You can't go 'cause even if I rolled a two then it would be equally divisible. There's no possible remainders I can get. And a one as well. And a one is also, so its the first person to get down to two.

Oh, ok.

And look how many goes it took us and look all of a sudden all your fives over here, they just disappeared and weren't helping you any more.

I really wanted the five over here. I have to go waste all my fives.

So this is a really good game. And over to you mathematicians to adapt.