Lets talk 2

Hello there mathematicians, I hope you're having a really lovely day today.

To get our brains thinking mathematically we have this question here for you today. And that is how many strategies could you use to solve 5 nines?

Yes, so it's a different question to what is 5 x 9? What we're thinking about is what are the different strategies you could use to solve it. Mhm.

So if you've done number talks in your class, it's like doing a number talk, so we're going to use this symbol to say I'm still thinking [holds out fist], and this would mean [thumbs up hand signal], yeah, I have one strategy and this could mean I have two strategies [two fingers out] for example and you could keep thinking.

OK, you've got one. Great.

So we asked some students this question too and they can't be here so we're going to use these minifigs to help us represent their thinking. So the first one goes over here. They look like construction workers I think.

So the construction workers teams were thinking about this idea of 5 and what they know about 5 is that it's half way to 10. So they said that they know that 5 is half of 10.

So if I have, oh that's a bit wonky, but if I had 10 of something, then this portion is 5 and they said that they could use them that to help them solve this idea 'cause they said they know that 10 nines is the same as saying 9 tens because of the commutative property and so they know that they could just use place value then to rename 9 tens as 90.

And then what they have to do is halve 90 'cause they doubled 5 to get 10. So that now they have to halve 90. So 90 divided by 2 which is the same as halving and they said they knew that as 45 and that's one strategy that you could use to solve 5 nines.

So they used their knowledge of tens to solve fives. Yeah, that's an interesting idea. Was that like yours? No, you had a different way.

Well, that's good cause this guy also had a different way. I think he looks like a foreman on a building project. So let's call him the foreman. And the foreman was thinking about 5 nines and what these guys were thinking about is that 9 is pretty close to 10. So we could think about 5 nines as being 5 tens, minus 5 ones.

Yeah, and they said they wanted to use this because they know something about 5 tens. They said 5 x 10 or 5 tens. They know that is 50 because of place value. You're right because 5 tens we renamed as 50, uhm. And then they said they know 5 ones, 5 ones is 5. And so they just needed to now subtract 5 from 50. So 50 subtract 5 is equivalent to 45.

Yeah, I'll write this in symbols for you. OK, so this would be 5 x 9 is equivalent in value to 5 x 10 minus 5 x 1. Yeah, that's how we would symbolically represent their idea.

And over here the blue team. They look like scientists I think. The scientist teams they were thinking about this number of 9 as well, but they were thinking about this. That 9 is composed of 8 and 1 more. So they were thinking that 5 nines is equivalent to 5 eights plus 5 ones.

Yes, and then what they know about multiplying by 8 is that you can double, repeatedly double and you could also use the doubling and halving strategy. So what they did here was say, well 5 eights is equivalent to 10 x 4. And if they keep going, that's 20 x 2, which is 40, uhm and then 5 ones is 5 and then they just need to join these quantities to have 40 and 5 more equivalent to 45.

Aha so there you go mathematicians, there are three different strategies that we use and because you know, we like to embrace our inner George Polya as we work as mathematicians. And he said that's really good to solve one problem in five different ways.

So here's three strategies, our challenge to you is can you think of another two? And how could you use any of these strategies to think about 6 nines (6 x 9).

Over to you mathematicians.

So as you know, we always love to ask what was the mathematics? So a couple of things here. Two important ones. One was that as a mathematician, you can think flexibly about numbers and situations. So when you see 5 nines you can think about it as 5 tens minus 5 ones, or 5 eights and 5 ones more.

We also found three different strategies we could use to solve the problem and you were asked to find two and this is really important because as Cathy Fosnot says, this is what it means to be a mathematician when we can look to the context of the problem and make decisions about what strategies we used to solve them?

So back to you.