Let’s investigate 2 

Alright mathematicians, let's investigate. You might have been with us recently when we looked  at this number talk of different ways that we could solve 5 nines and we know many of you know this number fact, but we really wanted to explore with different ways of thinking and develop these ideas of different strategies so that you can apply them in much harder contexts later on. 

And we looked at three different possible strategies, but we just wrote them down and so what we thought we might do today is look at different ways that we could imagine what's happening inside of someones head and with numbers when they are using these strategies.

So let's look at the first one. Here's 5 nines.  And here's the strategy. So the first thing they said they know is at 5 is half of 10. So if we double 5 nines we'd end up with 10 nines and then they used the commutative of property to say, well actually, 10 nines can be renamed 9 tens. And I know that is 90 because of place value I can rename it.

And then they said, well, now we still have to halve that array, so have half of 90 is 45 and we remove that 45. And now we have... our answer. 5 nines is 45. 

That's one strategy. Let's have a look at another one. So these guys were also thinking about what they know and they said, well, we know that we don't have to use 5 nines. We could work with 5 tens.  So they made 5 tens.  And they did this because they know something about place value. That 5 tens is renamed as... 50 and then they just needed to remove the extra 5 ones they used. And they did 50 - 5 ones which left them with... 45.

Yes, so that was a second strategy and let's have a look at a third strategy. Here's 5 nines again. And this team also said we can rethink the numbers.  So what we know about 5 nines is that it's made up of 5 eights and 5 ones. And then they said we could do some doubling and halving of 5 eights. So if you double 10, double 5 you get 10 and if you have eights you get fours to get 10 fours. Mmm. But now I have to shrink this so that you can see it on the screen. So let's shrink this down and then they did the same thing just for fun.

They said 'cause they could have from here said then 10 fours is 40 and five more is 45 but they said they wanted to play so they doubled and halved again. So they doubled 10 to get 20 and halved fours to get twos. And that's what that looks like.

Yes, and and I should I just shrink it down so I can fit on my screen and they doubled and halved again, look. 20 twos became... 40 ones. Uh-huh. And then they joined it together to find 45. And here's what that would look like as an area model. 

So mathematicians that's three different strategies that we just investigated to think about 5 nines. So I'm going to get you to refocus back on a problem we posed yesterday about 6 nines. And don't worry if you know the number fact, what we're really interested in is how could you apply some of those these strategies into that context of 6 nines?

And see how you could use diagrams, drawings, materials to represent your ideas. Ok, back to you mathematicians.