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[Screen shows a game board draw up with 9 columns and one horizontal row across the top with equations written in each of the top squares, from left to right, 10 plus 1, 10 plus 2, 10 plus 3, 10 plus 4, 10 plus 5, 10 plus 6, 10 plus 7, 10 plus 8 and 10 plus 9. There is also a deck of 9 playing cards (Ace to 10).]

Michelle

Hello mathematicians, I am joined by the mathematician Barbara today.

Barbara

Hello mathematician Michelle, how are you?

Michelle

I am very good. How are you?

Barbara

I'm very well.

Michelle

Um we're going to play a game to today, but we're going to play together this game.

Barbara

So are cooperating and we're thinking together.

Michelle

We're thinking and working together. And this game comes from Cathy Fosnot who works in the US, and it's called Capture 10.

Barbara

Okay, how do you play?

Michelle

So, we need our playing cards, and we only need Ace through to 10 so we took out all the picture cards or except the Jack. I forgot that one. And that one. And I think we're good to go.

[Michelle picks up the playing cards and removes the jacks.]

And then you are an amazing shuffler, so can you please showcase your skills?

Barbara

Sure. Are you ready Mathematicians?

[Barbara picks up the cards and shuffles them before placing them back down.]

Michelle

So, we need to take off 1 card so if you can go first an 8 and I got a 5.

[Barbara turns over a card and gets an 8. Michelle turns over a card and gets a 5.]

So, what we're looking for is can we rethink our numbers and capture a 10?

Barbara

Oh, okay.

Michelle

So, for example, if we have 8 here and I moved 2 of these across I'd then have...

Barbara

Oh, then you'd have 10 and 3 more, so 13.

Michelle

It would go here.

Barbara

Oh, okay.

Michelle

But we write it as the cards that we have. Okay, so show me. So, we would write 5 plus 8 and we've captured a 10.

[Michelle writes in the 10 plus 3 column the equation: 5 plus 8.]

Barbara

One 10 and in fact 3 more. Okay, let's do it again.

Michelle

Can you take a card? Not that one, sorry.

[Barbara turns over another card and gets an ace, which is a one.]

Barbara

So that's 1, right?

Michelle

Uh-hum and a 9.

[Michelle turns over a card and gets a 9.]

Barbara

Oh, that's great!

Michelle

Sort of because we have to capture 10 and 1 more.

[Michelle puts to column one, 10 plus 1.]

Barbara

Ah so we can't capture.

Michelle

That's 10 exactly.

Barbara

Also, we can't exactly, so that doesn't actually belong in our game board.

Michelle

Okay, so we just remove our cards.

Okay. And you take a card. 6 And I will take a card.

[Michelle removes cards, Barbara turns over a card and gets a 6, and Michelle turns over a card and gets an 8.]

Barbara

Okay, so I'm going to do what you said before and I'm going to imagine 2 of these hearts moving across to the 8 so then making 10 and 4.

[Michelle picks up a card and covers the 2 bottom hearts on the 6 card.]

Michelle

Yeah, because if you move those across, I can cover that one like this and go, Oh yeah, there's another 2 here and 10 and 4.

10 and 4 more. And so, 8 and 6 is equivalent to 10 and 4. I captured the 10!

[Michelle writes 8 plus 6 underneath the 10 plus 4 column.]

Barbara

Great!

Michelle

Okay, let's go again.

Oow! What are you thinking this time?

[Barbara turns over an 8 and Michelle turns over a 7.]

Barbara

Well, we can do it a couple of ways because I've already played with 8 before so I can do the same thing and imagine 2 of these 7 moving across, and then I'll have 10 and 5.

[Michelle moves a card over the 2 bottom clubs on the 7 card and circles the top 5 clubs with her finger.]

Michelle

Yeah, because if we cover that you can see the 5 that's left and imagine the 2 here.

Barbara

I could have done it the other way.

Michelle

Talk to me about that way.

Barbara

So, I've got 7 here, so if I actually imagine 3 moving across to make 10.

[A card is placed over 3 of the spades on the 8 card.]

Michelle

So those 3 like that.

Barbara

That's right, and then that becomes 10 and 5 more that way.

Michelle

And when you cover it that. way, you can actually see the 5 looks like a 5 on a dice.

Barbara

It does.

Michelle

So that made it 10 and 5. So it's 7 and 8 is equivalent to 10 and 5. Okay, 2 more cuts.

[Michelle writes in the 7 plus 8 underneath the 10 plus 5 column.]

Barbara

Okay. Sorry, Jack. Hit the road. Okay.

Michelle

Oh, Okay.

Barbara

So, 6 and 9. Do you want me to talk through it?

[Barbara turns over a 6 and a 9.]

Michelle

Yes.

Barbara

I think I'm having all the turns.

So, 9 is really close to 10, just need 1 more, so I'm going to. I'll do what you did as well. I'm going to imagine one of these diamonds moving across.

Michelle

And I've got some counters so...

Barbara

Okay.

Michelle

Yeah, we're going to do it together. Ready? You use the card.

You cover it.

[Barbara covers one of the diamonds on the 6 card with another card, and Michelle puts a blue counter on top]

Barbara

Ok.

Michelle

And I'm going to. So that's the one that you covered.

Barbara

Oh ok.

Michelle

And then we're moving that across to here, so that now becomes 10

[Michelle then moves the blue counter across underneath the 9 of diamonds card and counts the 9 diamonds and one more to equal 10.]

Barbara

I like that. That really helped me. So now 10 and 5.

Michelle

Did that help?

Barbara

Yeah. So, 6 and 9 is 10 and 5.

Michelle

Oops 6 plus 9.

[Michelle writes 6 plus 9 under the 10 plus 5 column.]

Barbara

Oh, you need to put it over here.

Michelle

I do too. Thank you for helping. Because I would never really have thought before that 6 and 9 is equivalent in value to 7 an 8, which is equivalent in value to 10 and 5.

[Michelle put a line through what she wrote in column 6 and writes the equation 6 plus 9 in column 5.]

Barbara

Yeah.

Michelle

Cause they look so different!

Barbara

But they make the same total.

Michelle

Hold on a second. Let's let's have a look at this 'cause now I'm really curious to know.

Wait. Can you make 9?

Barbara

Sure. Anyway, that I like?

Michelle

Yeah, and I might get 6 - 2, 3, 4, 5, 6. Actually I might use all blue.

Barbara

Now I like colour. I need some more too.

Michelle

Would you like green?

Barbara

Sure. That's enough for me.

Michelle

Can you make 9 in green?

Barbara

All green?

Michelle

Yeah 'cause it might help our brains be able to see what we're thinking about a bit more.

Yes. Have you got enough?

Barbara

Yeah.

Okay, so there we go, there's 9.

[Barbara places 9 green counters in a ten-frame formation on the right and Michelle places 6 blue counters on the left in a dice pattern.]

Michelle

Okay, so you've got 9 and I've got. 6 here .So 9, 10 oh look like a 10 frame.

Barbara

Yep.

Michelle

So, 11, 12, 13, 14, 15. So 10 and 5.

[Michelle now moves one of the blue counters into the ten-frame formation to show 10 counters and she moves the remaining 5 blue counters into a column next to the ten frame.]

Barbara

Oh, I really like how that's set out.

Michelle

But look, wait, wait, that's that's 9 and 6.

And then, hoosh. Now 8. And 7.

[Michelle now gathers the 6 blue counters together indicating 6 then she adds one of the green counters and circles with her finger showing there are now 7 counters grouped together. She circles the group of 8 counters to show 8 plus 7.]

Barbara

Oh, which is the other one that we had up there?

Michelle

Hey, so, it's still the same in total, but it's just the collections are arranged differently.

[Michelle moves the counters to their original positions.]

Barbara

Alright, that's really made my brain so that's very cool.

Michelle

Alright mathematicians, over to you to have a game of capture 10. What a fun game.

Barbara

Really fun. Have fun.

Michelle

Enjoy.

Okay, so what's the mathematics we're using in this game?

So, some of it is that this game gives us a really meaningful opportunity to use the ‘make 10’ strategy. Sometimes we call this bridging to 10, sometimes we call it using landmark numbers.

Either way, it's a really important strategy to help us use what we know to solve what we don't know yet.

And this game also reminds us that we can think flexibly about numbers so that when I see 6 and 9, I can rethink of it as 5 and 10. Still 15.

Enjoy playing mathematicians.

[End of transcript]