Let's talk 3

Hello there mathematicians, we hope you're having a really lovely day today. Yes, that's great that you are. So I wanted to show you two things. This one to start with, it's a ten frame. Can you show me what that's representing? Can you show me using your fingers?

Ah, I can see some of you are holding your fingers like this. With five and one more, and I can see some of you are holding your fingers like this. With four and two more. Uh-huh. Which is the same as five and one more. Look, if I add one more here and get rid of one they're still the same isn't it? Mm-hmm.

And some of you are doing, oh I can see three and three. Uh-huh because it is six, yes, and you could represent it like five and one, or four and two, or three and three. Mm-hmm. Okay, how many dots can you see on this card? What's it representing? Can you show me using your fingers again? Oh, I see some five and threes, to represent eight. Uh-huh, what else have you, ah, some four and fours to represent eight. Uh-huh. Oh I see and someone is doing this, they're saying, look it's ten and take away two, to show that, I know, my finger I can't stop it moving! I know our hands do weird things sometimes. Yes, so, it's eight.

So my question for you today is mathematicians, is how could we work out how many dots we have all together? You know there's eight here and there's six here, how could we work out how many there are all together? Ah, yeah, so we're gonna do this a bit like a number talk. You might do this in your classroom, where we're thinking, we share our fist to say I'm thinking, and then when we have one strategy, one way of solving, we might go I have one way I could think about it. Mm-hmm. Yeah, when we've thought about one possible strategy, yeah, we're gonna look for a second one and maybe even a third one. Oh. I can see you're thinking hard!

Okay, I think everybody's got one strategy now, uh-huh. Okay, well let's think about how some other people solved this problem. So we asked some students to, and they're going to be represented today by our pirate, ahharrr. Yes, I know, we really like pirates and a pony. Yes, because we love ponies too. I mean and what could you have, think of better friends, then for mathematics, than a pirate and a pony? Oh, I know Yoda. Aha, so Yoda also thought about how he would solve this problem. So let's look at their three strategies and we might represent Yodas thinking in green, to match his body. Mm-hmm.

So Yoda was thinking, or the team represented by Yoda, was thinking. First of all, he's lucky he's got a coat on because it's cold and wintry, and you know how lovely to have a snake as a, as a scarf, you know. Lucky it's not a real one! So, so Yoda was thinking that he could count the dots. Uh-huh and he said, but hold on a second, I already know this is eight and I already know this is six, so I don't need to count all of them again, I just need to count some of them. Mm-hmm. So he said this is eight over here and so then I can say 8, 9, 10, 11, 12, 13, 14. 14 dots. So Yoda was thinking about, I know there's eight and then he counted on six more. So he said, 8, 9, 10, 11, 12, 13, 14. Is that six number words? One, two, three, four, five, six. Yes, so he said eight and six is equivalent to, equivalent to 14. Or 14 is eight and six.That's even more efficient way to write it. Mmm-hmm.

So that was Yoda's way of thinking, but we're also joined by the pony and the pirate. Who would you like to know next? Aha, the pony, okay, well the pony, who we can represent in pink, the pony was thinking about the dots. Mm-hmm, and she said I want you to imagine something in your mind's eye, because if I moved two of these dots over here, I'd have one full 10 frame. Yes, and one not full 10 frame and that would help me, because if I move two dots over, how many dots would be here? Aha, four. And how many dots would be here? 10! And one 10 and 4, we can just rename as 14. So in her mind what she did, was let's represent these two dots here, and she said I'm gonna move these over, so imagine them disappearing they're no longer fall over to here, and now I can see one 10 and 4 more and I know that's 14. Uh-huh. So the pony said, well I know that 8 and 6 is equivalent to 10 and 4. Uh-huh and 14 is ten and four. Uh-huh, do you like that strategy by the pony? Yeah, she was a bit proud of herself.

Gee, so then the pirate came along, ahhh harrr, my hearties, and the pirate, I think we should represent him in red, hopefully you can discern the difference. Oh yeah. I know, Yoda had all the writing space and the ponies got a little bit less, and now the pirate got hardly any. But the pirate thought of a similar strategy to the pony, in the idea of moving dots, and he said what he could see is that inside of eight there's actually seven, because look, if you remove one dot, you now have seven. Aha. And he said and if I put a dot over here, I now have two sevens. And he said I just actually know in my brain that two sevens is 14. Yes, and so he said, well eight and, oh that's pink, sorry pirate, eight and six is the same as saying seven and seven. And that 14 is 7 and 7, and that was the pirate's strategy.

So isn't that really cool, little mathematicians, to think about the idea that you can visualize the dots moving. So even though you see 8, you could change the 8 into 14 if you wanted by visualizing these two dots here moving over here. Aha, or if you know double 7, then you could imagine this dot, moving over here to make double 7.

So what's some of the mathematics here? Yeah, we saw that you can solve the same problem in different ways. So here are three different ways that we could think about combining 6 with 8. We also saw that you can use numbers flexibly and today we saw this when the pony and the pirate visualized dots moving from one 10 frame to another, so they could use what they know to solve the problem. The pony thought about 8 and 6 as 10 and 4, and she imagined 2 dots moving from the 6, so she could make one 10. She then what knew, used what she knew about one ten and four and she renamed that as 14. Have a great day mathematicians!