Let's talk 4

Hello there mathematicians. We hope you are having a really lovely day today no matter where you might be as you're watching this. So I have some cards here and I'd like you to tell me how many dots you can see? Or the quantities that's represented by them.

So what can you see here? Mmm-hmm, can you show me using your fingers? Uh-huh. Oh yes, I can see some people are showing me 5 fingers and 3 more, and that's 8. Uh-huh, yeah and some of you actually showed me 4 and 4 which is also 8. Mm-hmm and, oh, I was gonna say 6 and 2 but that's a bit. Oh maybe, look, I could do 6 like this and 2 more. Maybe that's 6 and 2.

Uh-huh, all right, so this is 8 and we could also see there's 2 less than 10. How could you show that on your fingers? 2 less than 10? Oh yeah, that's a good idea! Look, you could, if you had cubes you could say well that's 10 and those 2 don't count.

Uh-huh, okay so we know this is 8. I'll just move it over to here. How, what about on this card? What can you see? How many dots are there? Can you show me using your fingers? Oh okay, some of you have got this, 5 and 1, and some have 3 and 3. Uh-huh and some of you have, oh yeah, 4 and 2 and they're all six. Uh-huh, and that's right, it's 4 less than 10.

Mm-hmm, and what about this quantity? How many dots can you see here? Show me on your fingers. Uh-huh, it is 5 and 3. It's 8. Yeah, like this one isn't it, just arranged differently, and I know they're the same quantity, because there's 2 dots missing and 2 dots missing. Mm-hmm, or 4 and 4. Aha, and what's another way to show 2 dots missing? Oh yeah, you could do something like this, where you're like trying to show, look, it's 10 and 2 missing. 10 and 2 missing. And I know that finger just moves! It has a mind of its own.

Okay, so now our, my question for you, mathematicians, is if I wanted to join all of these quantities together, how many dots would there be in total? And what are some different strategies that we could think of to solve this problem? Uh-huh, so it's exactly like a number talk if you've done one of those before. [Shows fist] So this means we're thinking hard about what could be one possible strategy. Uh-huh, and when we thought of a strategy we could use, [Shows thumbs up] we can show our thumb to say, I've got one way of thinking about this. Yeah and our second finger would show, actually I've got a second strategy I could use, and you might even have a third strategy.

Okay, because remember we're thinking about what are the strategies you could use, that's what we really want to focus on. Ah okay, shall we talk together? Great! Okay, so to help us with our thinking today, I can't, I don't have any students here with me today, but we did ask them and they're gonna be represented today by the pirate, aharrr harrr. You should be doing your pirate sound too. You should give me your best ahaarrr me hearties. Oh yeah, that was pretty good from some of you, some of you need some practice. We also have a pony, you know cuz, this is what you need in mathematics. Pirates and ponies. Uh-huh, and you know to offer us some great wisdom, we also have Yoda.

Yes, so let's actually start off with Yoda's strategy. So Yoda was working with some students and they said well we know we could do some stuff with counting, actually, because we, we know stuff about numbers and we could count them. And they said they know this is 8, and they know this is 6, and they know this is 8 so they don't actually have to count all of them again. But they might count some of them. Mmm so Yoda was thinking well if we know this is 8, we could then count the rest. So, let's have 8 and then let's count together. Ready? 8, Yoda is gonna try to help, he's got little arms, but they're not very good at pointing. 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22.

Uh-huh, so we're going to represent Yoda's thinking in green, and I guess a number line might be a really good way to show their thinking. They started with 8, and then they counted on. So how many did they count on here? 6? Okay, so I need to do six little jumps. 9, 10, 11, 12, 13, 14 and that's my 6, and then, mm-hmm, another 8. So 14, 15, 16, 17, 18, 19, 20, 21, 22. 22. And that's a jump of 6 ones, and that's a jump of 8 ones, to work out that 8 combined with 8 combined with 6 is equivalent in value to 22.

Okay so that was Yodas way of thinking but what about, who would you like to hear from next? The pirate or the pony? Ohhh, the pirate. Nice choice. So we're going to represent the pirates thinking in red. That's a good idea isn't it? Yes, so the pirate actually thought quite differently. He said, well I know stuff about counting but I also know stuff about numbers. Mm-hmm, and he said well actually what I might think about first is double 8, because I know that double 8 is 16. That's a number fact I have in my head and that, then what I'm going to think about the 16 is that 16 and 4 more would make 20. So inside my 6 I can see 4 and 2 more. So the 16 and the 4 combines to make 20 and then 2 more is 22.

Yeah, so let's think about how we could record that. So what he said was I'm gonna rethink 8 plus 6 plus 8 as 8 plus 8 plus 6. Now I'm gonna use the commutative property, he said, good little pirate, knows his mathematical vocabulary, mm-hmm and then he said double 8 is 16. Mm-hm and then he said I know 6 is 4 and 2 so then 16 + 4 combines to make 20. And 20 and 2 combines to make 22. Uh-huh, yeah,and I could draw that as a tree diagram for you. So 8 plus 6 plus 8. So he said double 8 is 16 and the 4, I, the 6 I can partition into 4 and 2 more. 16 and 4 is 20 . And 20 and 2 more is 22.

Uh-huh, that just fits on the page I think. Oops, not quite, I'll do it sideways. 16 and 4 is 20 and then 2 more makes 22. Uh-huh, so that was another way from the pirate and he was thinking about using what he knew and so then along came the little pony. And we'll represent the pony in pink. It's a good idea and we'll move these blocks and we'll put our question back. We'll re-commute it.

And the pony was thinking, well, hold on a second, I can imagine something happening to the numbers. And she said, imagine here on my 6 if I moved some of these around. So actually here in my 6 I can see 4 and 2 more, or 2 and 2 and 2. And if these dots here moved across over here, like this, that would now be blank. Mm-hmm, so now I have a 10, a 4 and an 8. Aha, can you imagine what's happening next? Yes! Then she said, well I can move these 2 over to here. I really need some other white counters, I'll use blocks, and said well now I've got a full ten frame and a full ten frame and 2 more. And actually I'm going to join those together first, a bit like the pirate did, and say well 1 ten and 2 tens, we just call that 20. And 2 more is called 22. Aha, so she actually thought about the problem of 8 plus 6 combined with 8 is equivalent in value to 10 plus 10 plus 2. Uh-huh, and then she said I know 2 tens is renamed as 20. And 20 and 2 more is just called 22.

Ahhh so she used her mathematical imagination to visualize the quantities moving. Yeah, would you like to see that one more time? To see what she did? Mm-hmm so she said, well I know something about these numbers. I can be flexible with them, so I can use them. I don't have to use them exactly as they are and, and, what I can do is move these 2 dots here, to come here. So let's move those 2 dots from 6, because 6 is made up of 4 and 2, and move them across which now means I have a 10, a 4 and an 8. And then she said well I could do this again, look, I could do this again. Inside my 4 is 2 and 2 so, I can slide those across to here, and now I have 2 full ten frames and 2 more. Look, it's 2 full ten frames. 20, 2.

What's some of the mathematics here? Yeah, you can solve the same problem in different ways. And today we saw 3 different ways that we could think of combining 8 and 6 and 8. Yes, and you can use numbers flexibly and today we saw this when the pony and the pirate visualized dots moving from 1 ten frame to another so they could use what they know to solve the problem. The pony thought about 6 as 2 and 2 and 2, so she imagined 2 dots moving to form 8 into 1 ten. She imagined another 2 dots moving to form the other 8 into another 10 and then she knew that 2 tens and 2 more can be renamed as 22. Have a great day mathematicians.