Lesson video

Hello there.

My name is Mr. Tilstone.

I'm a teacher.

If I've met you before, it's nice to see you again.

And if I haven't met you before, it's nice to meet you.

Today's lesson is about something that's a common part of everyday life, and that is percentages.

There's probably not a day goes by when you don't hear the word percentage or see percentages in action.

So let's learn a little bit more about that now.

If you're ready to begin, let's begin.

The outcome of today's lesson is this.

"I can explain what percent means and represent a percentage in different ways." We've got some key words.

If I say them, will you say them back? My turn, percent.

Your turn.

And my turn, percentage.

Your turn.

I guarantee you've heard these words before, many, many times.

Let's have a little look at what they mean and then we'll investigate it further.

Percent means the number of parts in each hundred.

It literally translates as for every 100, and a percentage is a proportion of a whole.

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

The first will be representing percentages, and the second, estimating percentages.

Let's begin by representing percentages.

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

Aisha and Lucas are talking about percentage.

Aisha says, "Where have you seen percentages, Lucas?" And before Lucas answers, maybe you'd like to chat about that too.

Where have you seen percentages? The symbol for percent looks like this.

And Lucas says, "When my dad makes me go shopping, there's sometimes a sale." Hmm.

Yes, have you ever seen something like this before? Was 10 pounds, now, 50% off.

And it's not always 50%.

Was 50 pounds, now, 30% off.

Our school is raising money for some playground toys.

The target is 200 pounds.

"My teacher said we've raised 90% of the money and have 10% left to raise." So it's such a common word.

Percentages are everywhere.

Percent means how many out of every hundred.

Lucas says, "Let's show what that looks like.

What if the UK was really a village of 100 people?" So just imagine that for a second.

Let's start with 100 people to represent the population of the UK.

So let's pretend that's absolutely everybody, exactly 100 people living in the UK.

And 30 of those people that you can see, 10, 20, 30.

30 of those people own a cat.

30 people out of 100 is equal to 30%.

Or as we write it, 30%, using the symbol.

That means that 70% of people do not have a cat.

So you can see seven tens there, 70%.

20 of the people are children.

So I wonder what we could say about the people that are not children.

20 people out of 100 is equal to 20%.

And that's how we write 20%.

That means that 80% are not children, they're adults.

And you can see eight tens there.

80 people, 80%.

80 of the people live in towns or cities.

How could we write that? Like this.

80%, that's the percentage symbol.

80% live in towns or cities and 20% do not live in towns or cities.

So whenever we see that symbol, we read it as percent.

100% is the whole.

So the parts add up to 100% 80% + 20% is equal to 100%.

Aisha represents percentages using a 100 square and perhaps you've got a 100 square in front of you.

What percentage is represented by the 100 square? What can you see? Think about how many tens you can see there.

Can you count in tens? Or perhaps you can see something else.

There are 100 squares altogether and 50 of them are shaded.

Did you maybe see half of them were shaded? 50% of the 100 square is shaded.

That's what we can say.

50% of the 100 square is not shaded.

50% is equal to 1/2 of the whole.

Did you note that? So if something is 50% of, it's half of.

What percentage is represented by the 100 square? What do you think now? It's not 50% anymore, is it? What can you see? Think about how many tens you can see.

There are 100 squares altogether and 30 of them are shaded.

So what percentage is that? That's 30% of the 100 square is shaded.

And again, we're using the percentage symbol.

70% of the 100 square is not shaded.

Aisha represents percentages using a 100 square.

What percentage is represented by the 100 square and what percentage is shaded? What percentage is not shaded? Pause the video and give that a go.

Well, you can see nine tens there.

So 90% of the 100 square is shaded.

So therefore we can say 10% of the 100 square is not shaded.

And well done if you wrote that down using the percentage symbol.

Aisha represents percentages using a number line.

What do you think the arrow is pointing to there? How many equal parts is the number line split into? That might be a clue.

What percentage is represented by the arrow on that number line? Well, each interval marked represents an increase of 10%.

So we can count in steps of 10%.

There are 10 equal parts.

I could count in those steps of 10%.

10%.

Count along, please.

20%, 30%.

So therefore the arrow represents 40%.

What percentage is represented by the arrow on the number line? And remember, we're counting in steps of 10%.

Each interval marked represents an increase of 10%.

"I could count back from 100% in steps of 10%." That's sufficient.

Good idea, Lucas.

So that would be 90%.

That would be 80%.

So the arrow therefore represents 70%.

Did you get that? Let's do another little check.

Aisha represents percentages using a number line.

And the question is, what percentage is represented by the arrow on the number line? Pause the video.

While the intervals are each worth 10%.

So we're going up and down that number line in steps of 10%.

50% is halfway.

We could use that so we don't have to start at the start or the end.

So the arrow therefore represents 10% more and that's 60%.

Well done if you said 60%.

You're on track.

And it's time for some practise.

Number one, represent each percentage in different ways.

So we've got 20%.

How can you show that on our 100 square? And by the way, there is more than one way to do that.

How could you show that on a number line? Shade the 100 square and draw an arrow on the number line to show 20%.

And what about 70%? How could you represent that on the 100 square and the number line? And what about this one? This time, we don't know the percentage.

We can see it on the 100 square.

It's been represented.

So what is our percentage and can you then represent it on the number line? What percentage is shown on the 100 square? I don't think that will take you too long.

So I'll see you very soon for some feedback.

Pause the video.

Welcome back.

How are you getting on? Do you think you get into grips with percentages? Here's 20%.

That's one way that you could have shaded a 100 square to show 20%.

And that's the way to show 20% on a number line that goes from zero to 100%.

And as Aisha says, "You could have shaded any 20 squares on the 100 square." Can you think of a different way to do it? Those are vertical tens.

Perhaps you could shade horizontal tens, but really, any 20 of those squares would do the same job.

And what about this? This is 70%.

That's one of many ways to shade 70% of that 100 square.

And that's the way to represent it on a number line, going from 0% to 100%.

And this was 40%.

So well done if you recognise 40%.

And that's how we showed that on the number line.

40 out of the 100 squares are shaded, which represents 40%.

And what about this one? So this is 60%.

That's 60% on the 100 square and that's 60% on the number line.

You're doing really well.

So far, so good.

Let's see if we can continue in that fashion.

Next, we're going to look at estimating percentages.

Percentages can be used to represent everyday life.

So Aisha's watching television on her tablet.

"My favourite TV show is 'Rocket Girl,'" she says.

That's what she's streaming at the moment.

"I pause the latest episode on my tablet." And Lucas says, "I can estimate the percentage of the show that Aisha has watched." So that bar that you can see, that's got a red and a yellow part is showing percentages.

But what does it not have? It doesn't have numbers.

I bet you've seen lots of examples of that.

On my phone, the battery doesn't show numbers.

It just shows a bar.

So this is the length of the episode, and that's the part that Aisha has watched.

"Aisha has watched less than half." Yes, that's fair to say, isn't it? "I estimate that she's watched 30% of the episode." I think that's a good estimate, isn't it? It's less than half.

"Brilliant," she says.

"I still got about 70% of the episode left to watch." That's good news.

Aisha checks the battery power left on her tablet.

Here we go.

Look at that battery.

And again, you might have seen lots of things like this before.

Maybe your tablet does the same thing.

Maybe it shows a little battery icon like this and how full it is.

So this is full power, and that's the remaining power.

So Aisha says, "There's more than half the remaining power left." Yeah, that's over 50%.

That's over halfway.

Lucas says, "I estimate that there's 60% of the battery power left." What do you think? Is that a good estimate? Yes, I think so.

It's very difficult to say exactly how much it is, but I think something like 55% or 60% sounds about right, looks about right, just over half.

She says, "I hope that's enough to watch the episode." Me too.

Let's have a little check.

What's the battery power on Aisha's tablet now? And I'm sure you'll agree, it's not looking quite so healthy, is it? Well, this is full power and this is a remaining power.

And the question is, estimate the percentage of power that's left.

So what's the remaining power as a percentage? What's your estimate? And it might be slightly different to other people's.

Pause the video.

What do you think? Well, I think it's much less than 50%.

It's much less than half.

It's much closer, in fact, to zero.

She's hardly got any left.

So I think something like 10%, maybe a little more, maybe a little less.

What do you think? Lucas agrees.

He says, "There's approximately 10% of the battery power left." I could visualise that bar, that empty bar being split into 10 equal parts and that being one of them.

So yes, approximately 10%.

"I'd better recharge the batteries," says Aisha.

Yes, you had if you want to watch the end of that show.

Some children take part in a race.

Here they are.

So we've got Alex, Sofia, Izzy, and Jacob.

They're taking part in a race.

We can see the start, we can see the finish.

We're using percentages to estimate how much of the whole race each child has run.

Hmm, what do you think? The halfway mark is equal to 50%.

We can estimate where halfway is.

So what do you think? I bet you're really good at finding about half of something.

What would you say is a halfway point and who's really close to it? Yeah, Sofia.

She's pretty much on the halfway mark, isn't she? Sofia has run about 50% of the race.

That's our estimate.

So Alex then has run about 40% of the race.

So just a little bit less than half, 40%.

I could imagine that line being split into 10 equal parts, and Alex being on the fourth one, 40%.

What about Izzy? Izzy has run about 60% of the race.

He's just over half.

What about Jacob? Well, he's not halfway, and I wouldn't say he's just under half or just over half.

What do you think? Would you say he's closer to half or closer to the finish? That should help with our estimates.

Jacob has run about 80% of the race.

I think that seems about fair.

About 80%, might be a bit more, might be a bit less.

Maybe about 75%, maybe as much as 82%, 83%, something like that.

But I think saying 80%, we're definitely in the right neck of the woods.

So time for a little check.

Estimate how much of the race each child has completed this time.

Pause the video.

What do we think? Well, I can see that some of those children are over halfway and one of those hasn't reached the halfway point yet.

Sofia has run about 60% of the race.

She's just over halfway, not much past halfway.

60% is a good estimate.

Jacob's run about 30% of the race.

He's not gone to halfway, but it's probably a little bit closer to halfway than to the start, I would say.

So 30% seems a good estimate.

Alex then has run about 70% of the race.

It's a bit more than Sofia, gone a bit further along.

70% seems a reasonable estimate.

And then Izzy, she's almost finished the race.

She's run about 90% of the race.

90% is a very good estimate.

Alex and Izzy run a certain distance.

Alex and Izzy have both run the same distance, but Izzy has much further still to go.

Can you see? Alex, we can say, has run about 50% of his distance.

Yeah, he looks like he's halfway.

So, 50%.

Izzy has only run about 20% of her distance.

So even though they've run the same amount, Izzy's distance is going to be longer in the end.

So she's run about 20% of her total distance.

In this example, 50% of a shorter distance can be equal in length to 20% of a longer distance.

Question, which battery is more fully charged? Is it battery A or battery B? And think about what we just said about the races.

Pause the video.

Battery A is about 80% charged.

That's a good estimate for that, about 80% is.

It's almost fully charged, just a bit less than that 80%.

Battery B is larger, but it's only about 60% charged.

So battery A is, in fact, more fully charged.

It's got a higher percentage.

It is time for some more practise.

Five children journey to school.

Use the diagram to answer each question.

So we've got Jacob, Izzy, Sofia, Jun, and Alex.

They all live different distances and different directions away from school.

So question A, which child has travelled the furthest distance? Question B, which two children have completed the same percentage of their journey? And question C, which child has completed the greatest percentage of their journey? Question D, which child has completed the smallest percentage of their journey? Question E, which two children have travelled the same distance so far? Question F, complete the table.

Estimate each answer.

So we've got the children's names and then the percentage of the journey completed, and multiples of 10% are just fine for that.

If your teacher is okay with you doing so, I always recommend working with a partner.

Then you can share ideas and compare answers.

Pause the video and I will see you soon for some feedback.

Welcome back.

How did you get on? Let's give you some answers and you can see.

So which child has travelled the furthest? That's Jacob.

Which two children have completed the same percentage of the journey? Well, Alex and Jun have both completed the same percentage of their journey.

Which child has completed the greatest percentage of their journey? That's Izzy.

Which child has completed the smallest percentage of their journey? That's Sofia.

Which two children have travelled the same distance so far? That's Alex and Izzy.

And then an estimate for each one.

You might be slightly different to this, but for Alex, well, it is 50% for Alex.

For Izzy, we're looking at something like 90%.

For Jacob, approximately 80%.

For Jun, approximately 50%.

And for Sofia, approximately 30%.

We've come to the end of the lesson.

You've done really well today.

Today, we've been explaining what percent means and representing a percentage in different ways.

I wonder if you can think of any other ways to represent percentages.

I wonder if you can find any more examples of percentages in real life.

Percent means a number of parts in each hundred.

It literally means for every hundred.

Percentages are parts of the whole.

Percentages can be represented using 100 squares or number lines among other things.

And we'll explore other representations in future lessons.

You've done really well today.

I hope you're proud of yourself.

I think you deserve a little pat on the back.

So go for it.

You've earned it.

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

But until then, enjoy the rest of your day.

Whatever you've got in store, be the best version of you that you can possibly be.

Take care and goodbye.