Lesson video

Hello there.

My name is Mr. Tilstone.

I'm a teacher and it's a real pleasure to be here with you today to teach you this lesson, which is all about percentages.

Percentages are everywhere.

For example, have you got a device such as maybe a tablet or a rechargeable DVD player or a laptop, something like that, that shows how much battery life is left in terms of the percentage? Well, that's just one of many examples.

Let's explore percentages even further.

If you're ready, I'm ready.

Let's begin.

The outcome of today's lesson is this.

I can calculate any percentage of a number and solve problems in a range of contexts.

Perhaps you've had some recent experience of finding, for example, 50% of a number that's useful.

10%, that's very useful as well, but maybe other ones as well, like 90%, 75%, 5%.

Today let's find any percentage of a number.

And our keywords, just got one.

My turn, percentage.

Your turn.

Hopefully, by now you've got some idea about what percentages mean, but let's have a look anyway.

A percentage is a proportion of a whole.

Today's lesson is split into two parts, two cycles.

The first will be calculating any percentage of a number and the second solving problems using any percentage of a number.

Let's begin by calculating any percentage of a number.

In this lesson, you will meet Aisha and Lucas.

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

Aisha is using a laptop and you might notice the battery icon there.

Have you got a device that's got a battery icon that looks a little bit like this? What could you say about this battery icon? It's on 100%.

It's fully charged.

When the battery is full, there's enough power to run the laptop for 10 hours.

Lucas says, "Wow, 10 hours is equal to 600 minutes." So that's got 600 minutes of battery life when it's fully charged.

After a couple of days, the laptop's battery is on 29%.

Hmm, how many minutes of power are left in the battery? 29%.

How can we work out 29% of a number? What do you think? Well, let's start by working out 10% of 600.

That's nice and easy to do.

We can just divide that by 10.

And 600 divided by 10, all the digits move one place to the right and that's 60 minutes.

So when it's on 10% charges, it's got 60 minutes left.

It's got more than that though, hasn't it? Now let's work out 30%.

How can we do 30%? I think we can use that 10%, don't you? To find 30% of a number multiplied 10% by three.

Well, let's do that.

60 multiplied by three is equal to 180 and you also might want to do 10%, plus 10%, plus 10%.

But it's efficient to multiply.

So 60 multiplied by three is 180.

So when it's got 30% battery life left, it's got 180 minutes left.

Now we're nearly there.

We're almost at the right number.

We're looking to find 29%, but we've got 30%.

What can we do? Hmm? We need to calculate 1% and I'm sure you've done that before.

How do we calculate 1%? To calculate 10%, wee divide by 10.

To calculate 1% of a number, we divide by 100.

So we move the digits two places to the right.

600 divided by 100 is equal to six.

So when there's 1% left, there's six minutes of charge remaining.

Now we're not quite there yet, but I think we've got enough information now to get to the answer.

I think we've got one more step.

We can calculate 29% of 600, but how? To find 29% of a number, you could subtract 1% from 30% and we know 30% and we know 1%.

So let's use those values.

That's 180, subtract six, which is equal to 174.

So 29% of 600 is equal to 174.

There are 174 minutes remaining.

The battery will last for another 174 minutes.

Aisha recharges the battery.

It's now on 74%.

Hmm, how could we get to 74%? What do you think? How many minutes of power are left in the battery? What could we do here? Well, we could start by working out 50% of 600.

That's one way to do it.

One way to begin, at least.

And to find 50% of a number, as I'm sure you are aware, we divide it by two or halve it.

600 divided by two is equal to 300.

So when there's 50% remaining, there's 300 minutes remaining.

Now it's not 50% we're after it's 74%, but we're on the journey now.

Next we can work out 25% of 600 and how can we do that? We've got 50%.

We could halve that and that would give us 150 minutes.

So 25% of 600 is 150.

What could we do with those values now? We've got 300 minutes and 150 minutes, that's 50% plus 25%.

So we've got enough information to work out 75%, and we can do that by combining them together.

Adding them together, hopefully, nice and straightforward for you.

That's 300 plus 150 is equal to 450.

Now we're really close.

We've got 75%, but we need to work out 74%.

What could we do? What else do we need? Well, working out 1% would be helpful at this point and I'm sure you've done that before.

We divide it by 100.

That's 600 divided by 100 is equal to six.

So six minutes is 1%.

Okay, so we've got 75% and we've got 1%.

What could we do with those two numbers? We can work out 74% of 600 by subtracting the 1% from the 75%.

Or, in other words, 450 that's the 75%; subtract six, that's 1%; and that gives us 444.

So 74% of 600 is equal to 444.

The battery will last for 444 minutes.

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

Let's do a little check.

The following day, the laptop's battery was on 41%.

Hmm? And the question is, how many minutes of power are left in that battery? Have a good think.

If you want to work with somebody else, please do.

Pause the video and away you go.

So how can we arrive at 41%? We need a few steps, I think.

What did you do? Did you start by finding 10%? I think that's a really good starting point.

So 10% dividing that by 10, that's 60 and then we can multiply that by four.

That would give us 40%, so that's 240 minutes.

We're really close now.

We just need one more percent.

How can we get that? Well, we can find 1% of 600 and that's six.

That's dividing that by 100, that gives us six.

And then we just add the 240 minutes to the six minutes or the 40% to the 1% and that gives us 246.

The battery will last for 246 minutes.

Very well done.

If you got that, you're on track and you are ready for the next part of the lesson.

And the next part of the lesson is practise.

So how many minutes of power are left in the battery? A, 39% of 600 minutes is equal to how many minutes? How could you get to 39%? There's some clues there.

Look carefully at the total number of minutes available on full charge and complete the table to help you work out The number of minutes of charge remaining.

And B, 81% of 600 minutes is equal to how many minutes? So fill in those different percentages to help.

C, 43% of 600 minutes is how many minutes? And this time we haven't given you the percentages.

You're going to have to think for yourself.

What will be some helpful percentages for you to consider and work out? Pause the video and away you go.

Welcome back.

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

So for A, you could start by working out 10% of 600 and that's 60.

You can then work out 40% of 600 by multiplying that 10% by four, that's 60 by four and that's 240.

And then you could work out 1% of 600 by dividing by 100 and then subtract it.

So 40%, subtract 1% is equal to 39%.

Or in other words, 240 minutes, subtract six minutes is equal to 234 minutes.

Well done if you got that.

And then for B, you could start here by working out 50% of 600, that's 300.

Nice easy one.

And then work out 10% and 30% of 600.

So 30% will be 180 minutes, work out 1% of 600 and then add them all together, that gives you 81%.

Or 300, plus 180, plus six, all of those minutes added together give you 486 minutes.

And for C, you could start by working out 10% and 40% of 600, then work out 1% of 600 and then add them all together.

That would give you 43%.

Or instead, you could add together 40% and 5% of 600 and then subtract 2%, that would give you 43%.

In other words, 270 minutes subtract 12 minutes is equal to 258 minutes.

So lots of different ways that you could arrive at the answer.

You're ready, I think, for the next part of the lesson, which is solving problems using any percentage of a number, just like you've been doing.

Now we've been thinking about percentages.

Let's think about them in terms of pie charts.

This pie chart shows how children travel to school.

We asked all of the children in our school how they travel to school and we created a pie chart showing our results.

How do you travel to school? The pie chart represents all of the children.

So the total of that pie chart is 100%.

First little task for you, estimate each percentage.

Start by estimating the percentage of children using each method and, remember, the total should add up to 100%.

You're not likely to be dead on with these, but give it a good go.

Pause the video.

Welcome back.

What did you say? What were your estimates and, importantly, did they add up to 100%? Well, let's look at the answers.

64% of children walk to school.

So you can see that's more than 50%.

It's more than half.

It's less than 75%, less than three-quarters.

64% would be a good estimate.

And 14% of children came by car.

19% of children travelled by bicycle.

And then that small percentage, just 3%, travel by bus.

Well done, if your estimates were close to the actual percentages.

But importantly, they should've added up to 100%.

Aisha works out how many children walk to school.

There are 300 children at our school altogether.

So that's our total.

That's our 100%.

And then we could work out some other useful percentages.

For example, 50%, 10%, 5% and 1% and those are all skills that I know you've got.

She says, "I'll start by working out some percentages." Let's go.

So 50%, we can just halve it.

Divide it by two, that's 150 children.

10%, that's dividing it by 10, that's 30 children.

5%, that's half of that, that's 15 children.

And 1%, that's the 300 divided by 100, that's three children.

So we've got some useful information.

Now we can use a combination of operations to arrive at those exact percentages.

I need to work out 64% of 300.

What would you do? With the information we've got, those useful percentages, what could we do? What could you combine? What could you subtract? What could you multiply? That kind of thing.

Well, Aisha says, "I'll start by working out 60% of 300." Lots of ways to do this.

I can think of a few.

I wonder what the most efficient is? This is what I would do too, Aisha.

That's 50% plus 10%.

So 150 children, plus 30 children And that equals 180 children, that's 60%.

But that's not what we're trying to find out, but it's helpful.

So that's 180.

Then if we do 5%, which we know; subtract 1%, which we know; that gives us 4%.

In other words, 15 children, subtract three children is equal to 12 children.

That gives us a 4%.

So 4% of 300 is equal to 12.

And now we can combine them.

We know 60%.

We know 4%.

We can add them together.

180, plus 12 is equal to 192.

192 children walk to school.

So that was lots of little easy steps.

Lucas works out how many children cycle to school.

So we've got 19%.

We need to work out 19% of 300.

What would you do? What would your next step be? I wonder what the most efficient way is? The one that takes the fewest steps.

The one that's the quickest.

I'll start by working out 20%.

Okay, that's good, Lucas.

There's no 20% there, though.

So what could you do? You can multiply 10% by two because we do know 10%.

That's 20%.

Or in other words, 30 multiplied by two.

So double 30 is equal to 60.

So 20% of 300 is equal to 60.

We're very close.

We need to find out 19%.

What would you do now? And you can subtract 1% from the 20%.

In other words, that's 60, subtract three, which is equal to 57.

57 children cycle to school.

Aisha works out how many children caught the bus.

This time, it's just 3%.

How would you work out 3%? What would your next move be? I need to work out 3% of 300.

So we could do 1%, which we know, multiplied by three, and that will give us 3%.

In other words, three children multiplied by three is equal to nine children.

3% of 300 is equal to nine.

Nine children caught the bus.

Over to you now.

Can you work out how many children travelled by car? So we're looking for 14% of 300 children.

Pause the video.

Did you manage to get the answer? Let's have a look.

So you had to work out 14% of 300.

You probably started with 15%.

We don't have 15%, but we can combine the 10% and the 5% to find it.

And that means 30, plus 15 is equal to 45, that's 15%.

And then we can subtract the 1%, which we already know and that will give us 14%.

In other words, 45 children, subtract three children is equal to 42 children.

42 children travelled by car.

Very well done if you got that, you're on track and you are ready for the next part of the lesson.

Aisha and Lucas check their answers.

If we add the number of children together, it should be equal to 300.

We need to add together 192, 57, 9 and 42 and we'll give them a little time to do that.

But the answer is 192 plus nine is equal to 201.

57 plus 42 is equal to 99 and 201 plus 99 is equal to 300.

It does, it adds up to 300 which means our answers are probably correct.

It's worth having that check.

Aisha and Lucas find the missing percentages.

So this time nine is equal to hmm percent of 60.

Hmm? This is tricky.

Yes, Aisha, definitely it is.

I'll work out some percentages to help me find the answer.

So 10% of 60 is equal to six, 5% of 60 is equal to three, but we're looking for nine.

But six plus three is equal to nine, so nine is equal to 15% of 60.

Nine is equal to 15% of 60.

Now, Lucas is trying to find out, 18 is equal hmm percent of 90.

Hmm? What could he do here? What would you do? Well, he started by finding 10% of 90 and that's nine.

Okay, but he needs to find 18, but there's a link isn't there? There's a relationship between nine and 18.

You can double nine to get to 18.

So 10% is nine, so 20% is 18.

18 is equal to 20% of 90.

Over to you for a little check.

Can you find the missing percentage? 12 is equal to hmm percent of 40.

Hmm? What will you do here? Pause the video.

So what's a good starting point? Well, I think finding 10% is a good starting point and so does Aisha.

So 10% of 40 is equal to four and there's a link between four and 12.

What's the link? 12 is four multiplied by three.

So 30% is 12.

12 is equal to 30% of 40.

Well then if you said that, if you've got 30% there, fantastic, you're on track.

You're ready for the final part of today's learning and that's this.

Number one, the pie chart shows favourite sandwich fillings.

What's your favourite sandwich filling? So we've got tuna, cheese, egg, sausage and (inhales) Marmite.

It wouldn't be my favourite.

We're having a school picnic.

We've asked all 300 children in our school for their favourite sandwich filling.

Use the pie chart to work out how many children chose each type of sandwich filling.

So remember, we've got 300 children and there are the percentages.

So fill in those gaps.

And number two, find the missing percentages and do a little thinking about this.

But you might want to start by, for example, finding 10% of a number and seeing the link between that number and the target number.

Use the tables to work out the useful percentages that'll help you find the missing numbers.

Okay, good luck with that.

If you can work with somebody else, please do.

Pause the video and away you go.

Welcome back.

How did you get on with those last questions? Well, let's have a look.

So number one, here's the answers.

It would be really helpful to complete a table with useful percentages on it just like this.

And then we can combine them together.

We can multiply some of them or subtract one from another or add one to another, that kind of thing.

So 28% chose cheese sandwiches, 30% of 300 is 90 and we can get that by multiplying 10% by three.

30% subtract 2% is equal to 30% and we can get the 2% by doubling the 1% or doubling three children.

So that means 90, subtract six is equal to 84.

84 children chose cheese sandwiches.

What about tuna? 23% chose tuna sandwiches.

How can we get to 23? We could find 20% by doubling 10%, that's 60.

We could add 3%.

That's three lots of 1%.

Three lots of three.

That's 60 plus nine, that equals 69.

69 children chose tuna sandwiches.

And for C, egg sandwiches, we need to get to 22%.

Well, we could do that by getting to 20% and adding 2%.

That's 60 plus six.

That equals 66.

66 children chose egg sandwiches.

And 18% chose sausage sandwiches.

Good choice.

20% of 300 is equal to 60 and that's close to 18, but we need to do one little adjustment.

We need to subtract 2%.

That would be 60, subtract six is equal to 54.

54 children chose sausage sandwiches and then 9% chose Marmite sandwiches.

How can we get to 9%? Well, we could use 10% and then subtract 1% and we know both of those values already.

That would be 30, subtract three and that is equal to 27.

So 27 children chose Marmite sandwiches.

I guess somebody must like Marmite.

Did you add together the totals to check that they're equal to 300? Well done if you did.

69, plus 84, plus 66, plus 54, plus 27 is equal to 300.

So yes, it does.

And number two, A, 48 is equal to 12% of 400 and 220 is equal to 55% of 400.

For B, you needed to add together 50% and 5%.

C, 38 is equal to 40% of 95 and D, 85.

5 is equal to 90% of 95.

And for D, you needed to subtract 10% from 100%.

So it's all about doing a little bit of thinking and using the information that you've got.

95, subtract 9.

5 is equal to 85.

5.

For E, 175 is equal to 25% of 700, and for F, 497 is equal to 71% of 700.

Those are really tricky, those final questions.

So if you've got those, fantastic.

Good work.

We've come to the end of the lesson.

Today, we've been using knowledge of calculating any percentage of a number to solve problems in a range of contexts.

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

It's all about doing that little bit of thinking and making connections.

So for example, if I know 10% of a number, I can halve it to find 5%.

If I know 10% and 5% of a number, I can add them to find 15%.

And you can do all sorts of combinations of percentages to create new ones.

Well done on your accomplishments and your achievements today.

You've been fantastic.

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

But until then, have a fantastic day and be the best version of you that you can possibly be.

Take care and goodbye.