Lesson video

Hello there, my name is Mr. Tilstone.

It's great to see you today.

Let me ask you a question.

Have you ever been shopping, maybe clothes shopping or food shopping or game shopping, something like that, and seen a percentage sign on the label? So it might be, for example, 25% off.

What does that mean? What does that tell you? Well, that's what we're going to investigate today, percentages.

If you're ready, I'm ready, let's begin.

The outcome of today's lesson is this, I can solve percentage problems where the whole is changed.

And we've just got one keyword.

So if I say it, will you say it back? My turn percentage, your turn.

Now I'm sure that by now, you've got lots of experience with percentages.

I'm sure you've got a fair idea of what that means, but let's have a little reminder anyway.

A percentage is a proportion of a whole.

Our lesson today is split into two parts or two cycles.

The first will be calculating a percentage change to the whole and the second, finding the whole after a percentage change.

Let's start by calculating a percentage change to the whole.

In this lesson, you're going to meet Aisha and Lucas.

Have you met them before? They're here today to give us a helping hand with the maths.

Aisha wants a pair of sunglasses for her holiday.

Hmm, some fine choices there.

I'm sure you'll agree.

Let's have a look.

They've got some labels on.

What do the labels say? The first one says, "Was 20 pounds, but now 30% off." Hmm, do we know the new price? Not yet.

The second one says, "Was 14 pounds, now 25% off." So again, we know the old price, but that's not the price you'll pay.

The third one, "Was 15 pounds, now 40% off," and the final one, "Was 12 pounds, now 20% off." So we need to work out the new prices.

Aisha says, "I wonder which sunglasses are the least expensive?" And Lucas says, "We can work out the new prices using our knowledge of percentages." They work out the new price of the first pair.

So this pair was 20 pounds and it's now 30% off.

What can we say about 30%? It's a multiple of 10 for starters.

Can we use that? The price tag says 30% off.

This means we subtract 30% off the cost.

And we know the original cost.

How do we work out the 30% then? Lucas says, "Let's start by working out 10% of 20 pounds." And well done, if that was your first thought.

He says, "We can divide 20 pounds by 10." And hopefully that's a nice easy skill for you.

Do that very quickly.

That's two pounds.

And then, "Let's use a bar model to represent this," says Aisha.

Absolutely, bar models are fantastic for representing percentages.

When I'm calculating percentage change, I can picture a bar model in my head.

So here we can see the 20 pounds.

That's the original price divided into 10% parts.

And each of those parts is worth two pounds.

"We can now use that," says Aisha, "To work out 30% of 20 pounds." So what's your next step? We know 10%, how do we work out 30%? The bar model hopefully makes it nice and clear.

Well, 30% of 20 pounds is equal to six pounds 'cause it's three lots of 10%.

20 pounds subtract six pounds is equal to 14 pounds.

The new price for the sunglasses is 14 pounds.

Not bad.

100% subtract 30% is equal to 70%.

So Lucas has got a different way of thinking of this.

We could work out instead 70% of 20 pounds.

So we could work out 30% off the original price or we could work out 70% of the original price.

Seven multiplied by two pounds is equal to 14 pounds.

So they both arrived at the same answer.

Which way did you like best? Aisha and Lucas work out the new price for the next pair.

Very snazzy sunglasses was 14 pounds.

Now 25% off.

Is that a multiple of 10? No, but there's something quite special about 25%.

What could you say about 25%? The price tag says 25% off.

This means we subtract 25% off the cost.

Let's start by working out 25% of 14 pounds.

How would you do that? What would you do? We can do this by dividing 14 by four.

Well done if you said that, maybe you halved and halved again, that's what Lucas is going to do.

So 14 pounds divided by two is equal to seven pounds.

That's 50% and then seven pounds divided by two is equal to three pounds 50.

That's 25%.

Now that's the saving, that's discount.

That's not the new price.

That's what you're taking off the old price.

So there's still one more step.

What would you do next? Let's use a bar model to represent this good idea.

Here we go.

So that's a 14 pounds split into four equal parts.

Each of them worth 25% and E 25% is equal to three pounds 50.

Remember we're taking that off.

We can now subtract 25% from the price.

25% of 14 pounds is equal to three pounds 50.

14 pounds subtract three pounds 50 is equal to 10 pounds 50.

And hopefully that was a mental skill for you.

The new price of the sunglasses is 10 pounds 50.

Now Lucas is gonna think of it a different way like he did before.

So what's he going to say? He's saying 100% subtract 25% is equal to 75%.

We could instead work out 75% of 14 pounds.

So we can work out 25% off 14 pounds or we can work out 75% of 14 pounds.

Either way we're going to get the same answer.

So three multiplied by three pounds 50 is equal to 10 pounds 50.

Aisha and Lucas work out the new price of the third pair.

Was 15 pounds now 40% off.

Is that a multiple of 10? Yes it is.

I noticed something about it too.

Let's see if you do too.

The price tag says 40% off.

This means we subtract 40% off the cost.

So that's the discount.

The 40% is a discount.

Let's start by working out 10% of 15 pounds.

That's a good idea.

It's a multiple of 10.

We can do this by dividing 15 pounds by 10.

Hopefully that's pretty straightforward for you.

This time we're using a table to organise our thinking.

Here we go.

It's not a bar model, but it's a table.

100% is 15 pounds.

10% of that is one pounds 50.

We can now work out 40% of the price.

So 40%, that's one pounds 50 multiplied by four and that's equal to six pounds.

Maybe you did that by doubling and doubling gain.

So that's six pounds.

15 pounds subtract six pounds is equal to nine pounds.

The new price of the sunglasses is nine pounds.

Now you might have had a slightly different way to do that.

For example, maybe you found 50% and then subtracted 10% from that.

Let's see what Lucas did though.

He's got that different approach, hasn't he? What would he say? He's thinking of it like this 100% subtract 40% is equal to 60%.

So he's thinking of 60% of the price, not 40% off the price.

So we could work out 60% of 15 pounds.

Well we know one pound 50 is 10%.

So what can we do with that? We can multiply it by six.

So six multiplied by one pounds 50 is equal to nine pounds.

So once again, that's either 40% off or 60% of both will give you the same answer.

Let's do a little check.

Let's look at these sunglasses was 12 pounds now 20% off.

The price tag says 20% off.

This means you need to subtract 20% off the cost.

So give that a go.

That's the Aisha way.

Maybe when you've done that, you can do it the Lucas way.

Pause a video and off you go.

Did you get it? Well, Lucas says, "Let's start by working out 10% of 12 pounds." Yes, that's useful.

Well 10% is one pound 20, but it's 20% off, not 10%.

So we can see 10% is one pound 20.

So 20% must therefore be two pounds 40.

But that's not the answer is it yet? That's the discount.

So well done if you didn't stop there, well done if you did one final step, we now need to subtract that from the original price.

That's 12 pounds.

Subtract two pounds 40, which is equal to nine pounds 60.

The new price of the sunglasses is nine pounds 60.

I wonder if you then checked and did it the second way, the Lucas way and found 10% and multiplied it by eight.

You could do that.

That would give you 80% of, I wouldn't say that's as efficient in this case though.

Which sunglasses will Aisha choose, I wonder.

Well we know the prices now that was the original prices.

She says, "I think I'll choose this pair because they are the least expensive." That doesn't always make them the best or the best value, but in this case they are the least expensive and she does like them.

So let's go for this pair.

Oh, they look fantastic.

Looking good Aisha.

And Lucas says, "They're my favourite pair too." Well I'm afraid Lucas, in this case, hard luck.

Pick a different pair.

Let's do some practise.

Lucas wants to buy a new hat.

Some very snazzy choices of hat here.

Let's have a look at this first one.

That was 13 pounds.

Now 30% off.

What's the new price? Remember 30% will be the discount, but then you've got to work out what the actual price is.

And then this other hat, this sort of wizard hat.

That was 19 pounds.

Now 50% off.

Hmm, something special about 50% isn't there? "These are my four favourites, which is the least expensive," he says.

Work out the new prices of the hats.

Use bar models or a table to help you entirely your choice.

Let's have a look at some more hats.

This is called a fez.

You don't see many of those.

That was 23 pounds and now 60% off.

Probably not very popular.

They're gonna have to get rid of that one.

So a big discount on that 60% off.

What's the new price? And then finally this baseball cap that was 16 pounds.

Now 40% off.

Remember there are two ways you can do this.

You can do this the way that Aisha likes to do it, which is to work out what the discount is and then subtract.

Or you could do it the way Lucas does it, which is to find out the percentage off the original price.

Maybe if you have the chance and the time, you could even use both methods.

Use one as a check.

Okay, pause the video and away you go.

Welcome back.

How are you getting on? Let's have a look.

Let's give you some answers.

So A, the new price is nine pounds 10.

This is how we got there.

So it was 13 pounds.

Now 30% off or 10% start by finding 10%.

That's one pounds 30, multiply it by three and then subtract.

So 30% of 13 pounds is equal to three pounds 90 and then 13 pounds subtract three pounds 90 is equal to nine 10.

And then let's have a look at B.

This wizard hat, the new price is nine pounds 50.

So it was 19 pounds and well done if you just halved that.

50% is the same as one half.

You could get there by finding 10% and multiplying by five.

It's not as efficient though.

That involves one more step.

Half of 19 pounds is equal to nine pounds 50.

Well then if you got that and then C, the fez was 23 pounds now 60% off.

Well 10% of 23 pounds is equal to two pounds 30.

I think that's the easy part.

And then you can multiply that by six to get 13 pounds 80.

You might have done it a slightly different way.

You might have thought I'm gonna work out 50% and then 10%.

Whatever way you did it 23 pounds.

Subtract 13 pounds 80 is equal to at nine pounds 20.

Lucas says you may have instead worked out 40% of 23 pounds rather than 60% off it.

Four multiplied by two pounds 30 is equal to nine pounds 20.

So either way the answer is nine pounds 20, that's a new price.

And then D, this baseball cap, it was 16 pounds.

Now 40% off.

Well the new price is nine pounds 60.

Let's see how we got there.

Well it is a good idea to start with 10%.

That's one pound 60.

You could then multiply it by four.

That would give you six pounds 40.

You might have thought of 50% and then subtracted 10% as well.

That's a different way to do it.

But 16 pounds subtract six pounds 40 is equal to nine pounds 60.

And again, Lucas like this method.

You might have done it this way.

Well done if you did.

He said, "You may have instead worked out 60% of 16 pounds." That's six multiplied by one pound 60 and that's equal to nine 60 once again.

So here are the answers.

And Lucas says, "Wow, all the hats are now very similar prices." Indeed they are.

So go for the one you like best I think Lucas, what do you think? Which one would you choose? Aisha says, "But hat A is the least expensive." That's definitely the best hat as well.

She thinks.

You know what I think she's right.

Looking good Lucas looking snazzy.

Let's move on.

Now we're going to find the whole after a percentage change.

So sometimes when you see items in the sale, they look just like they've done in the examples that you've looked at already.

But sometimes it looks like this.

Sometimes it tells you what the discount has been and what the new price is.

So let's have a look at this example.

This very funky T-shirt.

It's got 40% off and it's now 18 pounds.

So it's not telling you what it was, it's telling you what it is now.

But it's helpful to work out if that's a good deal or not and what the original price would've been.

So Aisha says, "What was the original price of my T-shirt?" Lucas says, "I can work this out using the percentage change and the new price." So what would you do? What might you do? Well, we're working out 100%, subtract 40%.

So that's equal to 60%.

60% of the original price is equal to 18 pounds.

So we know that.

What do you do with that information though? Hmm? 60% I've noticed is a multiple of 10.

Did you notice that too? Is that helpful? So it's 60% and 40%.

The extra 40% when added on will give you the original price.

Lucas says, "I need to work out 10% of the price first." Great idea.

I can do this by dividing that 18 pounds by six into six equal parts.

So here we go.

That will give us the 10%.

So 10% is three pounds and we can show that 10 times 18 pounds divided by six is equal to three pounds.

Giving us a 10% and multiplying 10% by 10 gives us 100%.

So three pounds multiplied by 10 is equal to 30 pounds.

The original cost of the T-shirt was 30 pounds.

That's helpful to know.

Lucas buys a T-shirt, nice T-shirt he's got good tastes.

30% off now 17 pounds 50.

So we don't know what the price was.

We know what it is now and we know what the discount's been, what the percentage change has been.

Is it a multiple of 10? Yes it is.

Could we use that? So what was the original price of my T-shirt? Well Aisha says, "I can work this out using the percentage change and the new price." Let's do that.

So this is 100% subtract 30% is equal to nice and easy.

70%.

So 70% of the price is equal to 17 pounds 50.

Okay, what could we do with that 70% then? I need to work out the 10% of the price first.

I can do this in this case by dividing it by seven.

Not really very easy to do is it, that, it's quite tricky unless you notice something.

You might notice that you could partition it into 14 pounds, which is a multiple of seven and three pounds 50, which is a multiple of seven.

So 14 pounds divided by seven is equal to two pounds and three pounds 50 divided by seven is equal to 50P.

Therefore 17 pounds 50 divided by seven is equal to two pounds 50.

That's 10%.

Now we can use that 10% to work out 100%.

We just need to multiply it by 10 and hopefully that's pretty straightforward for you.

Two pounds 50 multiplied by 10 is equal to 25 pounds.

So the T-shirt was originally 25 pounds.

Helpful to know.

Let's have a little check.

Aisha buys another T-shirt.

It's got 20% off, it's now eight pounds 80.

What was the original price of that T-shirt.

Pause the video and away you go.

Well 80% is a multiple of 10, so perhaps that's useful.

We know what the 80% is.

Let's work it out.

So eight pounds 80 divided by eight is equal to one pounds ten.

One pound 10 is 10% of the price.

And then multiply that by 10, that gives us 11 pounds.

So the original price of the T-shirt was 11 pounds.

Well done if you got that.

If you did, you are definitely ready for some practise.

Work out the original price of each T-shirt.

Let's have a look at these very, very funky T-shirts.

They're all good.

Let's see what the prices are though.

Use bar models and tables to help you find the original prices.

So the first one's got 25% off and it's now 12 pounds.

What was it? The second one's got 60% off.

It's now four pounds 80.

What was the original price? The third one's got 20% off.

It's now seven pounds 20.

What was the original price? And the final one? It's got 40% off.

It's now eight pounds 40.

What was the original price? You may notice that three of those are multiples of 10, but what about the other one? What could you do there? Hmm? I'll leave you to think about that.

If you can work with a partner and your teacher's okay with that, I always recommend that.

Then you can bounce ideas off each other.

Pause the video and away you go.

Welcome back.

How did you get on with these percentage changes? Let's have a look.

Well, for A, the original price was 16 pounds.

If it's 25% off and it's now 12 pounds, the original price was 16 pounds.

Let's see how we got that.

75% of the original price is equal to 12 pounds.

So therefore 25% of the original price is equal to four pounds.

Four pounds multiplied by four is equal to 16 pounds.

The original price was 16 pounds.

And the next one, 40% of the original price equal to four pounds 80.

We know that already.

So we can use that to work out 10% by dividing by four.

That's one pounds 20.

And then we can multiply that by 10.

That's 12 pounds.

The original price was 12 pounds.

And for C, the original price was nine pounds.

Let's see how we got there.

Well, 80% of the original price is equal to seven pounds 20.

We know that.

We could divide that by eight to give us 10%.

So 10% of the original price is equal to 90P.

And then we can multiply that by 10 to give us 100%.

And that's nine pounds.

The original price was nine pounds.

And D, let's have a low at the original price.

14 pounds, 60% of the original price is equal to eight pounds 40.

We know that.

So therefore 10%, because that's a multiple of 10 is equal to one pound 40.

And we can get that by dividing eight pounds 40 by six.

That gives us 10%.

And then we can multiply that by 10, which is hopefully quite a straightforward for you.

That's 14 pounds.

The original price was 14 pounds.

We've come to the end of the lesson.

I've had so much fun today, I hope you have too.

Today we've been solving problems with a known percentage part and size represents a change to the whole, identify the part and how it relates to the whole.

If the percentage part is a factor of 100, and we've seen lots of different examples of that today, two of them being 10% and 25%, you can multiply the part to calculate the whole.

EG 25% multiplied by four is equal to 100%.

If the percentage part is not a factor of 100 EG 30%, you can use division and multiplication to calculate the whole.

For example, 30% divided by three is equal to 10% and then 10% multiplied by 10 is equal to 100%.

So look out for those percentages that are multiples of 10%.

Be careful though, 'cause in some examples like 50% it's easier just to half.

Well you've been fantastic today.

Very well done.

Give yourself a very well deserved pat on the back and say, "Well done me." I hope you have a fantastic day whatever you've got in store and that you are the best version of you that you could possibly be 'cause you can't ask for more than that.

I hope we get the chance to spend another math lesson with you at some point in the near future.

But until then, take care and goodbye.