Dicey addition

Welcome back mathematicians, and welcome back Barbara.

Hi Michelle.

How are you?

I am excellent.

How are you?

I am very well. You're looking interested, very interesting.

So this is a game I got from Nrich math and I thought we could play today.

Fantastic. I love it.

And I love competing with you.

I love beating you.

So the way that we play is, you we need a zero to nine spinner or dice.

Ok.

So, so you can go first.

So if you put the pencil in the middle of the paper clip.

And then give the paper clip of flick.

Yes.

You've got nine.

Which is good right?

So you can choose to put your nine anywhere in this three digit number, anywhere in this three digit number and anywhere in this three digit number, but not here.

The goal is to be the person at the end to be the closest to a thousand.

I'm going to think carefully about this, because if I put it in the hundreds in any of these, I'm going to get really close to a thousand, so I can't do that.

So I might just put it in my tens, so I've got nine tens in the tens place.

And then it's my turn to spin.

And I got an eight, so I I think I'm going to follow a similar idea, but I want to start with this number.

Ok.

Just because I like my third number the most so far.

Well with addition, it doesn't matter what order you go in right.

That's exactly right.

Two.

Ok, well I might um make this two hundred because now I have two hundred and ninety something which is not bad if I'm trying to get to one thousand.

I think it's a good idea actually, because it's close to three hundred.

That's what I was thinking.

Three hundred, three hundred, three hundred is nine hundred which is pretty close to a thousand and so I think that's a pretty good spin, or decision.

A three, well, I am going to follow my own advice and put three in the hundreds place of my middle three digit number.

Yeah, that makes sense because now it's, your similar to me.

You've got three hundred and something and I've got nearly three hundred.

Ok.

Two.

Ok.

I might put the two here in the tens place here.

Ok.

'Cause now I'm scared if I put it in the hundreds it would be too low.

I think that's a nine.

I think that was a nine.

Yeah, I think that's a nine.

I'm going to put my nine here so I have nine ones now with eight tens which is eighty nine.

So you're close to one hundred there.

Yeah.

Is that a nine or a zero?

Re-spin that one.

It was right on the line.

Ok.

Zero.

Ok.

So zero.

Oh, that's interesting, Ok.

I can put it in the ones or in the tens.

You know what I'm going to put it here because I want it to be close to three hundred and I'm pretty close to three hundred at that spot.

I got a seven.

So I'm gonna put that, well, I definitely don't want to put it in my hundreds place.

That's how I felt about the nine.

'Cause then already it would be, if that was seven hundred and eighty nine, then another three hundred would be a thousand and eighty nine, it would already be over a thousand.

And even though the game is closest, I feel like that's already too much, so I might put it in the tens place of this number now, so I already know I've got thirty seven tens, so it'll be three hundred and seventy something.

Ok.

Two.

Ok.

I might put this in the hundreds and then when I, if I get a larger number this can, I could, I could then put that in the other hundred, Ok.

Five and a half.

Two.

I'm going to put that here.

Oh look, my number two hundred and eighty nine is only one number away from two hundred and ninety.

Oh, and you've got here these two.

That's nearly three hundred and that's pretty close to four hundred.

Oh yes, I'd better be careful.

Ok, see now I want a big number, something larger than six, I think.

Seven is, is seven perfect?

Ooh it might be a bit too big,'cause I've got about five hundred.

Oh Ok.

Ok, so I'm going to put my seven in my tens in the second number.

And a one.

I'm happy with that.

But now I've got to make a hard choice.

Because, that's about three hundred.

That's about four hundred.

So about seven hundred and if I put that there, here.

Oh yeah.

I could get some big numbers to get about two hundred.

You know if I got like a hundred and ninety something.

Yeah.

But it could be too soon to get a one like, ideally it would be a two but my chances of getting a two is one in ten.

Of course, ok.

So what are you thinking?

I think, usually I risk it.

You can risk it.

I'm happy for you to risk it.

I know you're happy.

If I beat you that works with my plan.

I am not going to be conservative but I will put the one here so that the number isn't too big.

I think.

I should have put it in the hundreds Michelle.

Then I could have definitely beat you.

Well this was my fear.

Oh, a two.

I would like a bigger number.

So, oh, I'm running out of chances though.

Now it does feel like I'm taking a lot of chances here 'cause I want like, I want five.

I want like five hundred I think, so definitely not two.

So I might.

Oh, you're taking risks too.

I am.

A four.

A four is good.

Four is good and it's going here.

'Cause you can go over a thousand.

It's the closest to a thousand.

So I like this 'cause look, four hundred and seven, four hundred.

That's about four hundred.

That's eight hundred, three hundred and we're at eleven hundred which is a thousand, one hundred.

It's pretty good so far.

That's not too bad.

There's only two spins left.

You could get a nine and a nine, and then I win.

Yeah, it looks like I think I was showing off a little bit too much.

This sometimes happens when we play.

I show off a lot and then I lose.

Oh yes, I'm so happy.

Ok, well the eight has to go here.

And then I just have to really hope for.

Yeah.

For certain numbers.

You've got like three hundred and two hundred right?

So, five hundred.

So I'd be happy with five hundred.

I would go over but I'd be happy.

I'd be happy with four hundred.

I'd be really happy with four I think.

Six and above I win.

Look at my spin, so many twos.

I need to change my spin strategy.

A three, well, I mean this isn't going to make much difference for me, right?

'Cause they're both going to be three in the ones place.

Alright.

So it doesn't make any difference to my total.

I've got one spin left.

Come on nine.

Ok mathematicians wish me luck.

Come on nine.

Michelle says she, I always beat her, but I don't, ok, cheer for me.

I'm the underdog.

Yes.

Oh no!

Oh so far away even, look at that number, that's already nearly a thousand.

Wow.

Look, I don't even need to spin 'cause I've already won but I will do it anyway.

Eight.

Ok, so, so now the challenge is we need to work out exactly what our numbers are but, but we can do that, or in fact what we can do is get the mathematicians out there to help us.

Ok, great.

Work that out too and Barbara, the great thing about this game is you could make your own game boards too, right?

So here's a piece of paper for you.

You make a game board and I'll make one.

Ok.

And then the mathematicians at home can play it.

Ok, I've got an idea.

Oh, I like your idea.

I liked one thousand as the target number, but I thought we could use subtraction.

Really nice idea, and then four digit numbers.

Ok, well I wanted to show that you could have any number as a target number.

Ok, great, oh yeah.

But you could also do multiplication.

Wow, that's really,

So what could you multiply a two digit by one digit to get as close as possible to four hundred and twenty.

And I like your, your game's a quick game.

Yeah, only three digits.

Only three rolls.

So you really need to, where we had a lot of chances before, we got to think about.

So that makes it really, whereas mine has got a eight rolls, So that's a different way of playing isn't it?

Maybe makes it too tricky.

You could do something like you get five spins and you have to choose three of them.

Oh, that's a good idea.

Yeah, Alright.

Over to you mathematicians to have, have a play.

You can use the version that Barbara and I used to start with and then start modifying and making your own game boards.

Good luck.

I hope you can beat Michelle.

Happy mathsing.

Alright mathematicians, we thought we come together to talk about some strategies we might use to join these three collections because it might be something that you would use a written strategy for, but there's some nice things happening with yours, Barbara, that you could use just mental strategies.

So what is it that you noticed?

I noticed that um these numbers here, so this is two hundred and twenty two and this is nine hundred and seventy eight.

But if I was able to move this twenty two across to this nine hundred and seventy eight and that becomes a thousand.

And this becomes two hundred, and they're both really easy.

Two more would make that eighty, nine hundred and eighty and then the other twenty more would make that a thousand.

So why don't you rewrite your number sentence down below 'cause you can do that as a mathematician.

You can adjust the numbers to work for you.

So I've still got two ninety, two hundred and ninety.

But this, now I'm adding one thousand.

Now, I have to remember that now that's not two hundred and twenty two, now that's two hundred.

Yeah,'cause you just took the twenty two from here and put it onto this, right?

Yeah, and so now that looks so much friendlier to work with.

So how would you work with it from here?

Ok, so I've got um one thousand and I've got two hundred, so I could say that I got one thousand two hundred and one thousand four hundred and then one thousand four hundred and ninety.

How would you solve it?

I would do it a little bit differently.

I would take, I'd probably take a chunk out of the two hundred.

Ok, so just for my, Would you still keep that number sentence, that first part the same or would you change it?

No, I would change it actually.

So I would write this, rewrite it as three hundred plus a thousand plus one hundred and ninety.

Because what I know then is it that's four hundred and ninety and then with one thousand it's just one thousand four hundred and ninety.

So the same sort of idea just, just re thinking.

I would just do another step of rethinking, Ok.

And so what looks like a really scary thing to start with if you just use that idea of adjusting numbers, and you know, thinking about landmarks, you can add three, three digit numbers in your head and you don't need a written strategy.

Well done us.

Well done mathematics.

Over to you mathematicians.

Alright, so what's some of the mathematics in this game?

So one of the things we really saw today was that adjusting numbers by using your knowledge of landmark numbers and bridging to tens and other number facts that you know can really help you work more confidently with problems.

So when we rethought 290 + 978 + 222 in a different way, it made it look much more friendly for us to work with.

We also realise that this game um provides a really fun context to use and enhance your knowledge of place value and the operations.

As well as, like with most of the games that we play in mathematics, are really nice space to develop some serious mathematical reasoning that always needs a little bit of luck.

Have fun playing mathematicians.