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Hello, and welcome to this online lesson on growth and decay and our third lesson in this series on finding a hundred percent.

What I'd like you to do is to make sure you got some pen and paper, you can write things down on and to make sure you've got a calculator just in case you struggle with some of those trickier calculations.

Make sure as well that you're in a quiet space and that you're going to be distraction free.

So you can really concentrate on that powerful maths that we're about to do.

So without further ado, let's take it away with Mr. Thomas' lesson.

So for our Try This, what I'd like us to consider is that the number 60 is in either the green, purple, or pink box.

Find the possible values of the other empty boxes given that information.

So I'm going to pause the video there.

I'm going to give you 10 minutes to think about that.

Off you go.

Awesome.

Let's come back to it then.

So if it's in the purple box then, what we could say is 60 would be there.

So this would be 60 here, that'd be 60.

That'd be 60, and that would be 60.

We could then say 60 would be over here potentially.

Right? We're not sure about that though, are we? 'Cause it should be there.

Right? So if it was going to be zero over here and 60, we could then say, well that's half way.

So that would be a 120.

We could then say 60 over here, could it be 10? 10, 20, 30, 40, 50, 60, good, so we could do it there, couldn't we? 10, 20, 30, 40, 50, 60, 70, 80, 90, a hundred, a 110, and a 120.

So, when we get to it then, could we have 60 here? Well, that is halfway between there and zero.

So that would be, 30.

We could then say this is going to be 90, a 120, and then a 150.

Well, using the assumption that these are sort of evenly spread, we could say maybe that is going to be 40.

And we can see that that's lined up with the 40 there.

So that's 40.

That one is 80.

And that one is a 120.

Now if 60's here.

That can't mean that that's going to be 60, but what would that could mean is that we need to spread out evenly, we could say that is, how many spaces we've got to travel? We've got one, two, three, four, five, six, seven, eight, nine, 10.

So we may go up at sixes.

So, six, 12, 18, 24, 30, 36, 42, 48, and 54.

And then 60 finally there.

We could then say that that of course would be 30 there.

We could say that would be 90.

And that would be a 120 as a result.

So where else could we have it? Well, we could have it, so we've got 60 there.

That would then be, we could say that one would be 40.

That one would be 20.

And then of course this one here could be 80.

And this one here is a hundred, and then a 120, just there.

So we know that the only option it could be, it can't be that one because all the other ones are a 120, can't be this one, 'cause it's got to be a 120.

So this one here is the one that it is going to be.

Yes, very good if you match to get that.

Well done.

So for our Connect today, what I'd like us to consider is the following.

If I buy a car at a 25% off sale and it costs £10,000, how much did that car originally cost? Now we know the original price for something we can say is a hundred percent.

So we know it's a 25% off sale.

So a hundred percent subtract 25%, gives us 75%.

We can even represent that pictorially, if we wanted to, with a bar model and just slice off 25% of it.

Right? So we're left with 75%, assuming that we've got the whole amount there, which is a hundred percent, and then we're getting rid of 25%.

So therefore we can say that 75% is equal to £10,000, and then we can scale it appropriately from there.

So if we were to do that then, what we could do is divide it by three, divide it by three, and then times it by four.

So we are left with 25%, is equal to would 25% be equal to would be £3,333.

33, et cetera.

And then times it by four.

So if you times that by four, what do you get? Well you could put that into your calculator, if you really need to.

What would it give you? It would give you a hundred percent.

Oh, that's a thousand percent, a hundred percent is equal to, what would it be equal to? Any ideas? Be, £13,300.

32 to the nearest pen, to the nearest pence.

So we're just scaling numbers now, right? We're trying to digest the information we've got there and scale it appropriately.

Now, if I produce cereal, and the cost of my packaging is increased by that to that amount there, £1.

50 per box, how much the cereal costs me to produce originally? Well, this one's slightly different.

This is a hundred percent you start with.

And then you're adding on 54.

3%.

So you've got in total, 154.

3% of the cost there.

So what you could do, is you could say 154.

3% is equal to £1.

50.

We could then divide it by 1.

543.

That would take us to a hundred percent.

So therefore a hundred percent would be equal to, what would it be equal to? £1.

50 divided by 1.

543, that would be equal to 97 pence to the nearest pence.

So you see, we can scale things, if we divide by whatever this number is, the decimal equivalent of it, we can get to a hundred percent.

And when we get to a hundred percent, it gets us parts of that original numbers, it's really helpful.

So what I'd like you to do is to have a go at these examples here.

So pause the video now and have a go at this exercise for the next 12 minutes, please.

Off you go, Great.

Let's get back to it then.

So if I buy a car at 20% off sale and it costs that, how much did the car cost originally? Well, we can say that 80% of the amount is equal to £20,000, and then scale it accordingly.

So we get to £25,000.

And then if we say that it grew by 6.

5%, we can say that 106.

5% is equal to that.

And we'd divide, as result by 1.

065.

And we get this figure just here.

If I decrease the amount I paid for my car insurance by that, what I'd say is of course 80% is equal to £250.

Scale it accordingly.

It's going to have to go up because I've got that decrease, and I've registered that decrease there.

If the amount of patients infected with a virus decreased by 1% to that, well you'd say that 99% is equal to 5940.

So therefore you'd scale it.

You could divide by 99 or you could, and then times by a hundred, that would work, right.

We eventually get to this number here.

So if you've got that very good, well done.

Give yourself a tick.

So for our explore task today, what I'd like you to consider is to just fill these boxes in and play around with it, and see if you can think of any different ways you can fill those boxes, so that the sofa has the same original price.

So I'm going to give you 12 minutes now to have a go at doing that.

So pause the video now, unless you need some support or want to go through the answer in the next slide.

Excellent.

Let's go through it again.

So let's have a play around, just first of all, can we get anywhere? So after a, let's go with 50% increase, the cost of the sofa we could say, or what should we say the cost of the sofa is? Should we go with, should we say £180? Right? So if I wanted to get back from there, I'd say that a 150% is equal to a £180.

I could then scale it by doing a 180 divided by 1.

5.

Right? And if I do that, what I get is a hundred percent is equal to £120.

So the original price of the sofa was a £120.

So I've used one of those ones there and I've got one of those back as well, which is nice, but we don't need to do that, but it's very good.

So can we think of any others that would give us £120? Gosh, can we think of any? 'Cause to get from 60 you'd have to increase it.

You could then do, oh, we could do a £180, after a, we could say, a 33.

3% decrease.

The cost of the sofa would be, what could we say? We could say the cost of the sofa was, oh, could we do maybe £96? What would the original price there be? Well, we've got 66.

6 recurring.

So if I did, if I divide that by two, I could get back to 33.

3, recurring.

So 96 divided by two and then times it by three.

So I get a 144.

So unfortunately that doesn't actually give me the answer just there, but what I'm hoping you can do is you can play around, 'cause I haven't got all the time in the world just yet, but play around with that and see what you can get in terms of the values, 'cause it's really, really, really good, if you could get those values, you see those differences between them.

With that, we've got the end of the lesson.

I just want to say a big congratulations, if you've managed keep up with that.

There's some quite complex stuff there, requires a lot of thought power and comprehension, to be able to do those sorts of questions.

So, very good.

Remember to have a go and smash that exit quiz, and to really make sure you're doing well with your learning.

For now, take care and I hope to see you soon.

Bye bye.