Lesson video

Hello there.

My name is Mr. Tilston.

It's really great to see you today.

I hope you're ready for what's hopefully going to be a fun and stimulating maths lesson, which is all about percentages, and percentages, as I'm sure you agree, are a big part of everyday life.

So if you're ready, I'm ready.

Let's begin.

The outcome of today's lesson is this.

I can solve problems involving percentages in a range of contexts, and our key words, just the one.

If I say it, will you say it back please? My turn, percentage.

Your turn.

I'm sure that by now you've got a fair idea about what percentages are, but let's have a reminder.

A percentage is a proportion of a whole.

Our lesson today is split into two parts.

The first will be problems with an unknown part and the second, problems with an unknown whole.

So let's start by thinking about problems with an unknown part.

In this lesson, you will meet Aisha and Lucas.

And Aisha says, "We're solving lots of problems using percentages." Aisha and Lucas complete the table.

So we can see, we know the hole here.

That's 100%.

That's 150.

Can we work out 30% and 10%? Hmm, what order would you do that in? Would you do the 30% first or the 10% first? Well, Aisha says, "I can work out 10% of 150 by dividing 100% by 10." Good start Aisha, and then we can use that to work out 30%.

So 100% divided by 10 is equal to 10%.

So 150 divided by 10 is equal to 15.

So that's 10% of 150.

How can we then use that to work out 30%? What would you do next? "I can now work out 30% of the number by multiplying 10% by 3," says Aisha.

Yes, you can.

10% multiplied by 3 is equal to 30%, or 15 multiplied by 3 is equal to 45.

So therefore, 30% at 150 is 45.

If I know the value of the whole, I can calculate the value of a part.

Let's look at a different whole, a different known whole.

This time it's 100%, which is 320.

Can you work out 25%, 15%, 10%, 5%? Where would you start? What would be your first port of call there, I wonder? Well, Aisha says, "I can work out 10% of 320 by dividing 100% by 10." So she's starting at the 10%, and I think that's a great idea.

So 100% divided by 10 is equal to 10%, or in this case, 320 divided by 10 is equal to 32.

We can then use our 10% to help us with a different value.

I can now work out 5%.

What would you do? How would you do that? You could halve it.

You could halve that 32.

So 10% divided by 2 equal to 5%, or 32 divided by 2 is equal to 16.

So knowing 10% helped us to work out 5%.

Hmm, what would you do now? There's a link there, isn't there, between 10%, 5% and 15%? "I can work out 15%," says Aisha, "by adding together the 10% and the 5% values." So that's 32 plus 16, which is equal to 48.

So 15% of 320 is 48.

Lots of little steps are getting us there, aren't they? And then, "I can work at 25%," she says, "by adding together 15% and 10%." That's one way to do it.

That's 48 plus 32 is equal to 80.

"25% of a number can also be calculated by dividing 100% by 4." So in this case, 320 divided by 4 is equal to 80.

You can get there by halving and halving again.

And I would say that on this occasion, that's the more efficient way to do it.

Aisha and Lucas work out the new price of the football.

So it was 14 pounds.

Now it's 75% off.

So what's the new price? Hmm.

Well, the price tag says, "75% off." That means we subtract 75% off the cost.

And we know the cost.

We know the whole.

That's 14 pounds.

So 100% subtract 75% is equal to 25%.

That means that the football is only 25% of the original price.

So we could start by working out 50% of 14 pounds.

We do that by, what would you do? Halving it.

So 50% of 14 pounds is equal to 7 pounds.

And we can use that to help us work out 25%.

We're going to halve that 50% to halve that 7 pounds.

So 25% of 14 pounds is equal to 3.

50 pounds.

What would you do now? This means that the new price of the football is 3.

50 pounds because it's 25% of the original price.

We could work out 75% off, but in this case, it's more efficient to work out 25% of the original price.

So the new price of the football is 3.

50 pounds A pair of trainers are in a sale.

They were 45 pounds.

They are now 36 pounds.

What's different this time? Hmm, what's known, and what's unknown? Well, just like before, the whole is known.

It's 45 pounds.

That's the original price.

This time, we don't know what the percentage change was.

We know the final value, the reduced value.

"I wonder what percentage the price has changed by," says Aisha.

I wonder that too.

I wonder how much of a good deal this is.

"I know the price has changed by 9 pounds because 45 pounds subtract 36 pounds is equal to 9 pounds.

So we know the difference between those two prices.

What does that equate to as a percentage, though, I wonder? Well, Lucas says, "Let's start by working out 10% of 45 pounds." Well, we can do that hopefully fairly easily by dividing by 10.

Let's do that.

That gives us 4.

50 pounds.

That's 10% of that price.

10% of 45 pounds is equal to 4.

50 pounds.

Now that wasn't the discount was it? It was 9 pounds, remember.

But I think we're getting there.

4.

50 pounds doubled is equal to 9 pounds, the difference between the prices.

I can double 10% to find 20%.

So 4.

50 pounds doubled is equal to 9 pounds.

That means that 20% is the amount that the price has changed by because remember, the difference between those prices was 9 pounds, and that's also 20% of 45 pounds.

There is 20% off the price of the trainers.

Not a bad discount.

Let's have a little check.

A cuddly toy is in a sale.

This is Pedro the Panda.

He was 15 pounds.

He's now 10.

50 pounds.

Is that a 20% discount, a 30% discount, or a 40% discount? So Aisha wants to know, "What percentage has the price of the toy changed by?" Pause the video and see if you can work that out.

Did you manage to do it? Let's have a look.

Well, Lucas says, "Start by working out the difference between the two prices, and then work out 10% of 15 pounds." So the difference between those prices is 4.

50 pounds, and then 10% of 15 pounds is equal to 1.

50 pounds.

So it's not a 10% discount.

It's more than that.

But 30% of 15 pounds is equal to 4.

50 pounds.

So the price of the toy has been changed by 30%.

That's fairly tricky to work out, so very well done if you got that.

You're definitely on track for the next part of the learning.

And the next part of the learning is practise.

So number one, complete these tables.

So for a, we know that the whole is 170.

That's 100%.

For B, the whole is 1,300, and for C, the whole is 205.

Can you work out the other percentages? Remember, you don't have to go in the order that the table is presented at.

You might like to start with a different particular value.

Think about how to work out each percentage.

And number two, work out the new prices of these items. So we've got this elephant.

The original price, the whole, was 28 pounds, but this 75% offer's a great deal.

What's the new price? And for B, this toy robot was 24 pounds.

Now got 60% off.

What is the new price? Think about how you could do that.

It might take a few little steps.

Use the tables to help you organise your work.

Where would you start? And number three, work out the percentage change.

There is percent off the price of the cuddly snake.

So it was 35 pounds.

It's now 14 pounds.

As a percentage, what's the difference? Lucas says, "I think more than half has been taken off the original price." Let's see if you agree with him.

See if you can find out the exact percentage.

Okay, if you can work with somebody else, I always recommend that because then you can share ideas with each other.

If your teacher is okay with that, go for it.

Righteo, pause the video and away you go.

Welcome back.

How are you getting on? Let's give you some answers.

So number one, if 100% is 170, we can then work out 10%, which is 17.

We can double that to find 20%.

That's 34.

We can double that to find 40%.

That's 68.

And we can double that to find 80%.

That's 136.

So for a, you can use doubling.

Let's have a look at b.

Well, 100% is 1,300, so 10% is therefore 130.

We're dividing by 10.

We can halve that to find 5%, so that's 65.

We can multiply the 10% by 3 to give us 390 for 30%.

And then we can add together the 30% and the 5% to give us 35%, so that's 455.

So lots of little steps got us there.

So "For b," says Lucas, "you can work out 35% by adding together 30% and 5%." And for c, we know that 100% is 205.

10%, that divided by 10 is going to give us 20.

5.

So a decimal answer this time.

That's 10%.

We can use that to work out 20%.

We can simply double that, and that's 41.

And then we can add those two, the 20% and the 10%, to get the 30%.

20.

5 plus 41 is equal to at 61.

5.

And number two, work out the new prices of these items. So the elephant, it was 28 pounds, 75% off.

Well, you may have done something like this.

You may have done it differently too.

You may have thought about 50% first.

That's 14 pounds.

And then halve that to get 25%.

That's 7 pounds.

And then combine them together to get 21 pounds.

That's 75%.

So for a, you can work out 25% of 28 pounds, or you can subtract 75% from 28 pounds.

But either way, the new price is 7 pounds.

And for b, the new price is 9.

60 pounds.

Let's see how we got there.

Well, you could do 100% subtract 60%, which is equal to 40%, and 40% of 24 pounds is equal to 9.

60 pounds.

Number three, work out the percentage change.

So maybe you worked out the difference between those two prices to start with, but what's that as a percentage change? Well, 10% of the original price is 3.

50 pounds, but it's much more than that, isn't it? 50% of the original price is 17.

50 pounds, and now we're getting closer.

So 60% is therefore 21 pounds.

So 60% of 35 pounds is equal to 21 pounds.

Very well done if you got that.

Very tricky, that one, I think.

Let's move on to the next cycle.

That's problems with an unknown whole.

Aisha and Lucas complete this table.

So what do we know, and what don't we know? We don't know the whole this time.

We don't know the 100%, but we know a part of it.

We know that 40% is 28.

Hmm, what could we do to work out that 100%? Well, Aisha says, "I need to work out 10% of the number first, and I can do that by dividing the 40% by 4." So 28 divided by 4, and that gives us 7.

So 10% is 7.

Now we know that 10% of the number is 7.

What would you do to find 100%? We can multiply it by 10, and hopefully, that's pretty easy for you.

10% multiplied by 10 is equal to 100% or 7 multiplied by 10 is equal to 70.

So the 100% in this case is 70.

If I know the value of a part, I can calculate the whole.

So Aisha and Lucas complete this table.

So once again, you might notice we don't know the whole.

We do know a part.

We know that 15% of it is 60.

How could we work out 100%? Got a little clue there.

"I can work out 5% of the number by dividing 15% by 3." That would give us 5%.

So 15% divided by 3 is equal to 5% or 60 divided by 3, in this case, is equal to 20.

So that's 5%.

What could we then do? Well, we could double that to give us 10%.

So double 5% is equal to 10%.

Double 20 is equal to 40.

That's given us 10%.

Now we're not quite there yet, one final step.

We need to work out 100%.

How could we use the information that we've got to work at 100%? We know 10%.

So we can multiply that by 10, and hopefully, that's nice and easy for you to do.

40 multiplied by 10 is equal to 400.

So that took a few little steps, but we got there.

Aisha thinks of a number.

She says, "7% of my number is 49.

What is my number?" What could we do here? How could we work this one out? Well, Lucas says, "I'm going to use a table to help me organise my thinking." Good idea.

He says, "I can divide 7% by 7 to find 1%," and that gives us seven.

So we know 1%.

We're nearly there.

What could we do to find 100%? We can multiply it by 100.

So in this case, we're multiplying 7 by 100, and that gives us 700.

So if 7% is 49, 100%, the whole, is 700.

Well, let's do a little check.

Lucas thinks of a number.

He says, "3% of my number is 120.

What is my number?" Hmm, what is going to be your strategy here, I wonder? Pause the video.

How did you get on with that? Let's see.

Aisha says, "You might have used a table to help you organise your thinking." Tables are great.

So 100%, we don't know, but we do know 3%.

That's 120.

So we could divide that by 3 to give us 1%.

Well, 120 divided by 3 is equal to 40, and then we know 1%.

We can use that to work out 100% by multiplying by 100, and that gives us 4,000.

So if 3% is equal to 120, 100% is equal to 4,200.

Well done if you've got that.

You're ready for the next part of the learning.

Some runners are taking part in a race.

90% of the runners have already crossed the finish line.

Hmm, so nearly all of them, but there are still 12 runners who are still going.

"How many runners took part altogether in the race?" So what do we know, and what don't we know? Well, we don't know the whole.

We don't know the total number of runners, but we know a part, the part that haven't completed the race.

So let's use a table to help us organise our work.

It's working well for us so far, isn't it, using a table? We know that 90% of the runners have finished.

So 100% subtract 90% is equal to 10%.

That means 10% haven't finished the race.

So 10% is 12 people.

Now we know 10%.

So we can work out what the 100% is.

So 12 multiplied by 10 is equal to 120.

So 120 runners took part in the race altogether.

So that's another example of not knowing the whole, but using a known part to work out the whole.

Let's have a little check for understanding.

Sofia has read 150 pages, which is 60% of her book.

How long is her book in total? So we don't know the whole.

That's the number of pages in the book.

We do know a part.

That's the part that Sofia has read.

So Aisha says, "Start by working out 10% of the length of Sofia's book." And we can use a table to help us do that.

Divide 60% by 6 to find 10%.

Use your knowledge of the six times tables to help you find the answer.

Now it's over to you.

How many pages are there in Sofia's book? Pause the video.

Let's see how you got on.

So 60 divided by 6 is equal to 10.

So 120 divided by 6 is equal to 20, and 30 divided by 6 is equal to 5.

So 150 divided by 6 is equal to 25, so 10% is 25.

10% of the book's length is equal to 25 pages.

We're almost there, aren't we? One more step.

We can multiply that by 10, that number of pages by 10, and that gives us 250.

There are 250 pages in Sofia's book altogether.

Well done if you got that.

It's time for some final practise.

Number one, complete the tables.

So in these cases, we do not know the whole.

We don't know the 100%, but we do know a part.

In the first case, we know that 15% is 75.

In the second one, we know that 75% is 126.

And in the third one, we know that 6% is equal to 36.

So Aisha says, "Think about how to work out 100% of each amount." And Lucas says, "Complete the other percentages to help you work out 100%." And number two, which numbers are Aisha and Lucas thinking of? So in the first case, Aisha's thinking of a number.

40% of that number is 108.

What's the number? And Lucas is thinking of a number.

30% of his number is 336.

What is his number? And number three, work out the length of each whole race.

a, Bradley has completed 180 kilometres, which is 75% of his cycle race.

How long is his race? b, Laura has completed 154 kilometres, which is 70% of her cycle race.

How long is her race? And c, Victoria has completed 49 kilometres, which is 35% of her cycle race.

How long is Victoria's race? Pause the video and away you go.

Welcome back.

How did you get on? How are you feeling? Are you feeling confident? Are you feeling good? Let's give you some answers.

1a, we know that 15% is equal to 75.

So if we divide that by 3, that will give us 5%, so that's 25, and then we could double that to work out that 10% is equal to 50.

And then multiply that by 10 to give us 100%, which is 500.

And for b we know that 75% is equal to 126, so if we divide that by 3, that gives us 25%.

And 25% is a factor of 100%, so we can use that.

So 126 divided by 3 is equal to 42, and then if we multiply that by 4, that gives us 168.

That's 100%.

And for c, 6% is equal to 36, so if we divide that by 6, that will give us 1%, which is 6, and then multiply that by 100 gives us 600.

And 2a, Aisha number is 270, so 40% is 108.

We could divide that by 4 to give us 27 and multiply it by 10.

And for b, 30% is 336, so therefore 10% is equal to 112, multiply that by 10, and we've got 1,120.

So it's all about taking a few little steps to get there.

And number 3, Bradley's completed 180 kilometres, which is 75% of his cycle race.

So Bradley's race is 240 kilometre, and we can get that by dividing that 180 kilometres by 3.

That gives us 25%, which is 60 kilometres, and multiply that by 4 gives us 240 kilometres.

And for b, Laura's completed 154 kilometres, which is 70% of her cycle race.

So if we divide that by 7, that gives us 10%, that's 22 kilometres, and multiply it by 10, it gives us 220 kilometres.

And for c, Victoria has completed 49 kilometres, which is 35% of her cycle race.

Victoria's race is 140 kilometres long.

So if we divide 35% by 7, that would give us 5%.

So 49 divided by 7 is equal to 7.

That's 5%.

Double that, that gives us 10%.

That's 14 kilometres.

And then multiply that by 10.

That gives us the 100%.

We've come to the end of the lesson.

Today, we've been solving problems involving percentages in a range of contexts.

If I know the value of the whole, I can calculate the value of a part.

If I know the value of a part, I can calculate the whole.

Addition, subtraction, multiplication, and division can be used to calculate a new percentage from known percentages.

It's all about taking lots of little steps, and it's all about doing a little bit of thinking.

You've been absolutely fantastic in today's lesson, so give yourself a pat on the back.

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

But until then, be the best version of you that you can be.

Whatever you've got in store today, take care and goodbye.