Let's talk 4

Let's investigate this idea a little further. Recently we said that you can use numbers flexibly. And we saw this when the pony and the pirate visualized the dots moving from 1 ten frame to another, so they could use what they know to solve problems. And the pony thought about 6 as 2 and 2 and 2. And she imagined 2 dots moving to form 8 into 1 ten then another 2 dots moving to make 8 into another 10. And then she just had 2 tens and 2, which she renamed as 22.

So let's have a look at how these strategies work by exploring them on an equal arm balance. Hello there mathematicians! We thought we'd have a further look at these strategies, to think about how we could prove, mm-hmm, that you can think about 8 and 8 and 6 as 10 and 10 and 2 for example. So that was the pony's strategy, remember here's our little pony. Good morning, or good afternoon, depending on what time you're watching!

So let's have a look at this idea over here. So let's make our original problem which was 8 and 8 and 6. And we can tell it's now not equivalent, that's right, because the balance scale isn't equal, isn't even. Mmm-hmm and what the pony was saying was, inside of 6 I know that I can break it up into 2 and 2 and 2. Let's have a look at that, to start with.

Look here's 6. And what they're saying is 6 is equivalent to 6, which we know that balances. But she's also thinking that inside of 6 is 2 and 2 and 2. So 6 is equivalent to 3 twos or 3 twos is 6. And so what the pony did was use this knowledge. Because when she says 6 and 8 and 8, she said what I know is that 8 and 2 makes 10 so I can take 2 from the 6 and add it to the 8 and make a 10 and I can do that again and then I'll have 2 left. Aha, and it balances. And so what we can see here is that 8 and 6 and 8 is equivalent to 10 and 10 and 2. Yeah, and then she just renamed that. 2 tens is 20 and 2 more is 22.

Let's have a look at the pirates thinking. I'm going to leave those pegs over there, and here's our pirate, ahh haarr. And what the pirate was thinking about first, was that he knew double 8 was 16, so he he kept the double 8. Mm-hmm and then he said I know 6 is composed of 4 and 2. So let's have a look at that together. There's our 6 and we know this is equivalent to 3 twos, cuz we checked that. Look, mm-hmm, that works. The pirate said 6 is also 4 and 2. So let's see what happens.

Aha and so here you use this knowledge. So he said over here there's double 8 and double 8 is 16, I know this. And I know inside of 6 is 4 and 2 and 16 and 4 more is 20 and then I still have the 2 and that will make 22.

And so that's how we can prove here, this idea, that 8 and 6 and 8 is equivalent to double 8 plus 4 plus 2. Nice work mathematicians. So what's some of the mathematics? We can use an equal arm balance to investigate equivalence. This helps us see that we can think flexibly about numbers when solving problems. Allowing us to use what we know to work out what we don't know yet. So young mathematicians, what other quantities can you find that are equivalent in value to 8 plus 8 plus 6?

Over to you mathematicians.