Circles and stars

Hello Barbara.

Hello Michelle. How are you?

I am great. How are you ?

I'm very well. We are going to play a game today from Marilyn Burns, called How many stars? Okay, so we need to organize our game board to start with. So with our game board, we need to make eights. Okay. So, one way that I make eights is, I halve my paper. You can halve it a different way if you want. You don't have to do the same. And then from my half, if I halve it again and then halve it again I'm now quartering each half and that will make me have eighths.

Ohh, maybe I could go this way?

Oh well, a bit too skinny.

Too skinny. I think I'll go this way then. You know what's interesting about that, is that we folded them in a different order. Yes but we still got the same.

And you know what else it looks like? An array.

It does.

Look, it looks like four twos or two fours. Yeah. Our game's called circles and stars so we're gonna write circles and stars.

Okay. Okay.

Okay, so we are using playing cards two, fives and tens today and that's gonna tell us how many is in each of our groups.

Okay.

And we roll the dice to say, how many groups do we need? So here, you go first.

Okay.

Roll the dice.

So two groups. Two groups. So draw your two groups. In this? Oh one of those?

Yeah, we don't use that one.

Oh we don't use is one?

Nah.

Okay.

Okay and then pick a card and that tells you how many.

Awesome.

Now if you know it, you don't have to draw it. You can just explain how many two tens would be.

Okay so two tens would be 20. Mmm, cause of place value.

So just rename it?

Yes, so just put 20 here cuz you know this.

Okay.

And then if we don't know it, we can use it to help us.

Okay, so one group. One ten. Okay. So, so I actually know that one ten is ten, so, and that's ten. So I don't need to draw them. Should I label mine as ten and ten?

Yes, that's a good idea.

Okay.

Okay, your go.

One. Oh rats!

So I'm guessing by that, that's not a good thing, right? We want to have lots?

Well it could be if you get a 10 because 10 is a good move. But imagine now you get one two.

Okay, so I want as many?

You want as many stars as possible at the end.

Oh so these are stars? So I should put in 20 stars.

Oh that's a good idea! I should put stars too.

10 stars, 10 stars is 20 stars.

Okay, so now I've got one two. Okay so that's just two stars. Yes, it's a known fact so you don't have to draw it.

Okay, my go. Ohh three. Fives. Okay, so if I didn't know three fives I could draw my three and then I could draw my five stars. Two, three, four, five and what I might do is now imagine in my mind's eye that there's 5 here, 5 here and five here.

Okay.

And what I do know is it that five and five combines to make 10.

Yep.

And one 10 and 5 more is 15.

Okay, yep.

So I don't have to draw everything. Just enough. But I can if I need to. I just draw enough to help me, you know, work out how many stars it would be in total. So that would be 15. Okay. 15 stars.

Where do we put that? At the bottom after you've used it?

Yes.

Okay, so two. Tens.

Oh, two tens is nice. Also nice because you can just use renaming with place value.

Exactly, if you know place value, then you instantly two tens can be renamed as 20.

Okay, my go! Ohh 5 is good.

Imagine if you get a 10.

That would be good, imagine if I got a two. Ok let's see. Oh yes! Yes! So I can draw one, two, three, four, five, like a dice.

Yeah.

And each one is worth ten, but I actually just know that that's renamed as 50, because of place value knowledge.

Okay now I want six tens. Reroll or?

You can reroll because I saw what it was.

All right, two fives. Well I know that I know two fives is 10. Mmmm. It's just...

How do you know it? Is this a fact you know?

It's a fact I know, but it's also my two hands.

Yes because two fives together.

Yeah, and also the two rows of a 10 frame. Because five here and five there. 10.

Yeah. Okay.

Okay so, 10 stars. Oh I should do 5.

Okay, ohhh six is nice! Imagine if I got 10.

Imagine if you get one.

No, there's no one in there, there's only two, five or ten.

Come on two.

Oh, rats! So, um, here's six and there's two in each one. And actually I know that's 12 because if this was a 10 frame, say that moved to there and that moved to there. You know, my 10 frame is going in this orientation. What I know is that for each dot there, there's actually two.

Yeah.

And then I'd have one more left over and I know that it's 12.

Okay. I like how you explained that. It made sense. Okay, six. Fives. Not bad, not bad.

Oh, I know how you could work that out.

Yeah?

Cuz, you could say if you halved six, that would be three.

Yeah.

And doubled five you get 10.

Awww.

And then you just rename it.

3 tens.

Because you can use your fives to work out tens.

Yeah, and I like how you actually, cuz I do that sometimes, but I don't always half and double. Sometimes I just I get the

result and then I halve it. I like the way you did that. So how would I draw it then? Would I draw as six fives or would I draw it as three tens?

Good question.

Because that's how we worked it out?

Maybe, can I draw on your paper?

Yes please.

Maybe you could draw like this, and that. So I had five but I thought of them together.

Okay, oh I like that.

And then, there's, yeah, you had them like this and this, and then you know I'm actually thinking about fives as tens, and I only need three of them.

Okay, I really like that.

Okay I don't have to draw them all cause I know it now. So this, so then we said that was 30 stars. So each one here it was 10 stars, 10 stars and 10 stars. Okay, you've got one go, I've got two goes left. We lose, we use the last box to help us calculate. Ah, 2 twos. Well, that's four because I know this. But it would look like this, two twos, which is four stars all together. Your go.

Okay. Oh you're writing the word stars, I'm just drawing a star! Six! Yes! Twos.

Ohh, you go from this hightened state of yes six, oh twos.

Oh and well we've done this one before.

Still better than 6 ones.

Exactly, well twice as good. Okay, so, I know this number fact.

Yes.

But otherwise, I could just think of it, you know, the idea of double five is ten and then two more. So, ummm, with two in each one is 12 stars.

Okay alright, last go for me. I need a good roll.

You've got that 50. So I think you're ok.

That's true. Three fives. So, you know how last time I drew it and I said I could work that out as 5 and then visualize?

Yes.

This time what I could think of is double 5, which is 10 and 1 more 5.

Yeah.

Because when you do your threes you can work out double plus, plus one more. So how would I draw that? I could do the same idea here? Oh, I know. I could go 1, 2, 3, 4, 5, 1, 2, 3, 4, 5, and then one more group of five.

Oh good.

And then there's the threes, look.

Yeah, that's good recording.

Hmm, so that's 15 all together.

So now Barbara, what we need to do is work out how many stars we had and the person with the most number of stars is declared the winner!

Okay, great.

So, so now the fun part comes, right because we can use some really cool strategies. But we can work together to help each other. So what are you thinking when you look at your numbers? Because I might, what I might do is write down all of mine. So I've got ten joined with four, with 12, with 15, with 15 and with 50. And that helps me start to look for things. Oh I found something.

Oh yeah, I can see some stuff too. Okay. I ran out of space but I'll put it down here. Okay, so when I wasn't, when I was writing them out I realized that twenty and twenty and ten actually makes fifty. Yeah. So all of that together, that's fifty there.

Yeah, so you could rewrite that now as two, plus 50, plus 30, plus twelve, because our equivalent. If that helps?

No, that helps me, because then it's a much, it's a shorter number sentence as well. Okay, so.

Oh, now I can see something else.

Well, what I'm thinking, do you want to tell me what you're thinking? Or should?

Yeah, because I was thinking like five tens and three tens is eight tens.

Yeah.

So then it's two plus eight tens, which is 80, plus twelve. Yeah and that's even nicer to work with. Yeah, or even, even get that 10 from here.

Oh yeah.

So five tens and three tens is 8 ten and then nine times.

Yeah!

So I've got nine tens. Plus two, plus two! Plus two.

Oh that is nice!

Yeah. Okay and then that's 9 tens and four, which we would rename as 94.

I think you've won!

So, but let's have a look. But it is close. Very close. So, so what I know actually, is that double 15 is 30. Yeah. I just happened to, I don't know why I know that but I do. So I'm gonna go.

I think you've won you know.

Well let's see. 10, plus 4, plus 12 plus 30, oh now I feel more confident, plus 50.

Yeah.

Yeah, because now what I can see is that there's another hidden 50.

Yeah.

In there. So if I take the 10 and the 10.

Oh yeah.

So one 10 and one 10. Is 2 tens. Plus 3 tens is 50. So that would be 50, plus 4, plus 2, plus 50.

You won.

And then 5 tens and 5 tens is 10 tens, which you call 100. Plus 4, plus 2 and that's a hundred and six.

Awww but it was close.

It was pretty close! Only 12 away.

This one was really good.

That was a good lucky go!

Over to you mathematicians to enjoy Marilyn Burns' circles and stars!