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.

If I have met you before, you might know that I love maths.

What you don't know about me is that I also love a bargain.

I was shopping last night in my local supermarket and I picked up a few bargains, a few reduced items. Let me show you.

I managed to pick up these chicken steaks and they were 30% off! Not bad! 30% off the original price.

But I went one even better than that.

I managed to pick up these green beans, and they were 50% off their original price, so they were half price.

Pretty good, but that wasn't the best one.

My best deal of all was I managed to get these raspberries, and these raspberries were a whopping 75% off of their original price.

Wow! Percentages are everywhere.

Because I know a bit about percentages, I was able to work out how much each item would be after the reduction, and that's going to be the theme of today's lesson.

We're going to work out percentages of amounts, so if you're ready to begin, let's begin.

The outcome of today's lesson is, "I can use common percentages of a number to solve problems." And we've got two keywords.

My turn, efficient.

Your turn.

And my turn, percentage.

Your turn.

What do those words mean? Let's have a reminder.

Efficient means working in an organised way without wasting time or effort, and a percentage is a proportion of a whole.

Our lesson is split into two cycles, two parts.

The first will be finding 25% and 75% of a number.

And you might have had some recent experience of finding 10% of a number, 1% of a number, and 50% of a number.

How, I wonder, could you work out 25% and 75% of a number? And the second part of the lesson will be finding other percentages.

Let's focus first of all on 25% and 75%.

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

They're here today to give us a helping hand with the maths.

Aisha loves the Tour de France.

She loves it! She says, "It's a brilliant cycling race held every year, mostly in France." Have you watched it? And Lucas says, "Let's use the Tour de France to help us understand percentages." Pierre has completed 25% of a 220 km race.

Hmm.

"I'm not sure what 25% looks like," says Aisha.

"I know that 50% is equal to one half." So, what about 25%? Well, here's 50%, here's one half.

"That's great," says Lucas, "And 25% is equal to one quarter." 25 is half of 50, and one quarter is half of half.

"One quarter is half of one half." "Exactly! Which means that 25% is half of 50%." This bar model helps to illustrate that.

Have a look at the bar model.

We've got 100%, and then, when that's split into two equal parts, each one's worth 50%.

And when it's split into four equal parts, each one is worth 25%.

Or you might like to focus on that 50% part of that bar model, and then notice that that has been split into two equal parts, and each is worth 25%.

So, half of 50% is 25%.

Aisha and Lucas calculate 25% of 220 km.

"To find 50% of a number, we need to divide it by 2." 100 divided by 2 is 50, so 220 km divided by 2, or halved, is 110 km, so we can fill that part in on our bar model.

That's 50%, but we're trying to find out 25%.

"To find 25% of a number, we need to divide by 2 again." So, let's do that.

We need to find half this time of 110 km.

"25% is equal to one quarter, which is half of one half." Half of 110 is 55.

"25% of 220 km is equal to 55 km." Sasha has completed 25% of a 320 km race.

"To find 50% of a number, we need to divide it by 2." So, let's do that.

100 divided by 2 is 50.

320 divided by 2 is 160.

So, 50% of 320 km is 160 km.

We're not trying to find 50%, though, are we? We're trying to find out 25%.

"To find 25% of a number, we need to divide it by 2 again." So, that's what we do, we halve and halve again.

"25% is equal to one quarter, which is half of one half." Half of 50% is 25%, and half of 160, well, half of 16 is eight, so half of 160 is 80, so that's 80 km.

So, we can say that 25% of 320 km is 80 km.

Sasha has completed 80 km of the race.

So, to find 25% of a number, we can halve and halve again.

Let's do a little check.

Pedro has completed 25% of a 180 km race.

"Use halving to find out how far Pedro has travelled so far." Pause the video.

Did you use the bar model? I think that bar model is so helpful for this.

"To find 50% of a number, divide by 2." That's the first step.

Half of 100% is 50%, half of 180 km is 90 km.

That's our 50%, and then we use that to find 25%.

We're going to halve again.

"To find 25% of a number, divide by 2 again." So, let's do that.

50% divided by 2 is 25% and 90 km divided by 2 is 45 km.

"25% of 180 km is equal to 45 km.

Pedro has completed 45 km of the race." If you got that, well done.

You're on track.

Now, Pierre has completed 75% of his 220 km race.

75%, hmm.

I wonder how we could work that out.

Is there enough information in what we've done so far? "I'm not sure what 75% looks like," says Aisha, "But I do know that 25% is equal to one quarter." Hmm.

How could we use that 25% to help us work out 75%? "That's great," says Lucas.

"Because 75% is equal to three one-quarters, or 3/4." What could we do? We're trying to calculate 75% of 220 km.

We know 25%.

"75% is equal to 3/4.

There are different ways to find 75% of a number." Let's explore a few of those now.

"We could multiply 25% by 3." Well, we know 25%, don't we? It's 55 km.

So, we can multiply that by 3.

"55 km x 3 = 165 km.

75% of 220 km = 165 km." That's one way of arriving at that answer.

We're going to arrive at that same answer a different way, now.

See if you like this one better.

"Pierre has completed 165 km of the race." Now, let's find it a different way.

"75% is also equal to 50% add 25%." Well, we know 50%.

We've worked that one out.

And we know 25%, we've worked that one out.

What could we do? "50% + 25% = 75%." So, we combine those two values.

On 110 km, that's the 50%, plus 55 km, that's the 25%, is equal to 165 km.

What do you think about that? Personally, I think that's a little bit easier.

"75% of 220 km = 165 km." There is another way as well.

Can you think of another way? "75% is also equal to 100% subtract 25%.

100% - 25% = 75%." Well, we know the 100% and we know the 25%, so we can take the 25% from the 100%.

That's 220, that's 100%, subtract 55, that's 25%, is equal to 165 km.

That's 75%.

"75% of 220 km = 165 km." What do you think of that method? That's three different methods.

Which did you like best? "Choosing the most efficient method depends on the numbers involved." Pedro has completed 75% of his 148 km race.

"50% of 148 is equal to 74.

25% of 148," halving that again, "Is equal to 37." And Lucas says, "I think the most efficient method to work out 75% of 148 km is to subtract 25% from 100%." That's a matter of opinion, but I think he's right in this case.

"It's most efficient because I don't need to cross a tens boundary for this particular calculation.

148 km - 37 km = 111 km.

75% of 148 km is equal to 111 km." "Pedro has completed 111 km of the race." What do you think about that method, then, 100% subtract 25% to give us 75%? Well, let's have a little check.

Helen has completed 75% of her 208 km race.

"How far has Helen travelled so far? Start by working out 50% and 25% of 208 km." "Which method is the most efficient to use?" We've got 25% multiplied by 3, we've got 50% plus 25%, and we've got 100% subtract 25%.

All of those arrive at 75%.

Pause the video.

What do you think? Well, 50% of 208 is equal to 104.

Therefore, 25% of 208 is equal to 52.

This bar model, I think, is really helpful at this point.

"The most efficient method here is probably 52 x 3.

52 x 3 = 156.

75% of 208 km is equal to 156 km." Well done to you if you got the chance to experiment and try all three methods and see which one you thought was the most efficient.

"Helen has completed 156 km of her race." It's time for some practise, so we're focusing on 25% and 75%.

Number 1, calculate 25% of each distance.

Use those bar models to help.

Remember, you're halving, and then you're halving again.

"Use the bar models to help." "Divide each number by 2 and then divide the result by 2 again to find 25%." And the same for c and d.

And number 2, this time, calculate 75% of each distance.

And remember, we explored three different methods.

Aisha says, "Use the bar models from part 1 to help you." And Lucas says, "Think about the most efficient method to use to calculate each answer." Have a look at the numbers before you decide on which of the three methods to use.

If your teacher is okay with it, I always recommend working with a partner, and you can help each other out, bounce ideas off each other, and help each other if something goes a little bit wrong or you don't understand something.

Pause the video, and away you go.

Welcome back.

How did you get on with finding 25% and 75% of a number? Let's give you some answers and you can compare.

Number 1, 25% of 140 km is equal to 35 km.

"First, find one half, and then half again to find one quarter." And the bar model looks like this.

Half of 140 is 70 and half of 70 is 35.

And for b, "To help you halve 96, you could partition it into 90 and 6." Combine them together and you've got 48, so that's half.

Then, half of that again is 24.

And for c, "To help you halve 188, you could partition it into 100 and 88." Half of 100 is 50, half of 88 is 44.

And combined, then, we've got 94.

That's half, that's 50%, and half again, that's 47.

So, 25% of 188 km is 47 km.

And for d, "To help you halve 252, you could partition it into 200 and 52.

1/2 of 200 is equal to 100 and 1/2 of 52 is equal to 26." Combine them together and we've got 126, and then we can add that to our bar model that shows 50%, and then we halve that again to get 25%, which is 63 km.

And for number 2, "It might be the most efficient in this case to add 50% and 25% together." You might not have done that.

You might have multiplied, it doesn't really matter.

And, "Here, it might be the most efficient to subtract 24 from 96." Again, you might have chosen a different method, but still got the right answer.

For a, it's 105 km, and for b, it's 72 km.

And for c, 75% of 188 km is equal to 141 km.

And you may have subtracted that 47, that 25%, from the 188, the 100%.

You might not have done.

You might have done it a different way.

But the answer is 141 km.

And for d, it may have been most efficient to multiply 63 by 3, but again, you might not have done it that way, and that gives us 189 km.

You're doing really, really well, and I think you're ready for the next part of the lesson, which is finding other percentages.

Pierre completes a 220 km race.

"We can easily work out 50% of this distance and use that to calculate 25% and 75%," just as we've done before.

"We can also work out 10% by dividing 220 by 10." And I'm sure you've had lots of recent experience of doing that.

"We can use 50% and 10% to work out lots of other percentages." Well, let's do that.

Aisha and Lucas calculate 60% of 220 km.

Right, have a look.

Look at what we've got so far.

We know 50% and we know 10%.

How could we find 60%? Hmm.

Well, 60% is 10% more than 50%, so we could combine those two values together.

We can add, in this case, the 110 km and the 22 km to calculate 60%.

110 plus 22, hopefully, you can do that in your head, that's 132.

"60% of 220 km is equal to 132 km." This time, Aisha and Lucas calculate 40% of 220 km.

How could they do that? Have you got any good ideas based on the information we've got? Well, 40% is 10% less than 50%, so instead of adding them this time, what could we do? "We could subtract that 22 from the 110." In other words, subtract the 10% from the 50% to calculate 40%.

In this case, 110 subtract 22 is equal to 88, so we can say 40% of 220 km is equal to 88 km.

"We could also multiply 10% by 4." Did you notice that one? 22 km multiplied by 4 is equal to 88 km.

That's a different method.

And with percentages, there's often more than one way to arrive at the answer.

Aisha and Lucas calculate 90% of 220 km.

Okay, well, have we got enough information, there? What could we do with the information we've got to work out 90%? Well, 90% is 10% less than 100%.

We know 10% don't we? We know the 100%.

Let's have a look at that on the bar model.

You can see, yes, it's 10% less than 100%.

That gives us 90%.

So, we can use subtraction.

We can subtract 22 from 220 to calculate 90%.

"220 subtract 22 is equal to 198," so we can say 90% of 220 km is equal to 198 km.

Is there another way to do it? Now, I can think of a different way.

We could maybe multiply the 10% by 9, so the 22 km by 9, but I don't think that would be quite as efficient.

I think we've got a good method by subtracting 10% from 100%.

Aisha and Lucas calculate 5% of 220 km.

What can we do with the information we've got to work out 5%? Hmm, little hint.

Think about 10%.

Well, 5% is half of 10%.

Let's look at that on the bar model.

Yeah, so we're looking to find half of that 10% value.

We can divide 22, that's the 10%, by 2 to calculate 5%, so we're simply halving 22.

22 divided by 2 is equal to 11, so 5% of 220 km is equal to 11 km.

We can find 5% by halving 10%.

We could also multiply 1% by 5, but that method isn't efficient, here, so do take some time before you work each one out.

What would be the most efficient way? Aisha and Lucas calculate 15% of 220 km.

Hmm, what could we use? How could we arrive at 15%? There's no 15% in that chart, but I think with a little bit of arithmetic, we can get to 15%.

What do you think? Well, we can add together 10%, which we know, and 5%, which we've worked out, to calculate 15%.

That's what 15 is, 10 plus 5.

Well, here we go.

That's 10% plus 5% to give us 15%.

That's 22 plus 11, which equals 33.

So, 15% of 220 km is equal to 33 km.

Let's do a little check.

How could you calculate 70% of 220 km? And we've got some information, there.

There is more than one way to do this, so if you arrive on a way, maybe explore a different way and see what you think is the most efficient.

Pause the video.

Which way did you use? Well, "We need to find an efficient way of working out the answer." "You could start with 50%, add 10%, add another 10%." Is that the method you used? That would be 110.

That's 50% plus 22, that's 10%, plus 22, that's 10%, which equals 154.

So, 70% of 220 km is equal to 154 km.

Instead, you could double 10% first and then add this to 50%.

See if you think this is more efficient.

That's double 22, that's 44.

And then, add it to the 110, that's 154.

I can think of some more ways.

We could multiply the 10% by 7 or we could multiply the 10% by 3 and subtract it from the 100%.

Lots of different ways, but I think we've probably found the most efficient one, there.

Aisha and Lucas calculate percentages of 170 km.

"Let's start by calculating 50%." That's always a nice, easy one, isn't it? That's halving.

Half of 170 is 85.

What would you do next? What's another pretty easy one that you've got lots of practise doing? What about this, calculate 10%.

That's 17 km.

We've moved all the digits one place to the right.

170 divided by 10 is equal to 17.

Okay, where would you go now, then? What's your next choice? Well, you can calculate 90% by subtracting 10% from 100%.

We know 10%, so that will be 170 subtract 17, which is equal to 153 km.

Okay, we're getting there.

What could we do now? We're looking to find 40% and 5%.

Hmm.

"We can calculate 5% of 170 km by halving the 10%." Half of 17 is 8.

5.

Now, over to you for the final one.

Can you calculate 40% of 170 km? How would you do it? I can think of at least two ways.

Pause the video.

Which way did you choose? I think you could find 50%, which we have already, and subtract 10%.

Let's have a look at that.

That's 85 subtract 17, which is equal to 68.

You can also calculate 40% by multiplying 10% by 4, so in this case, 17 multiplied by 4.

Maybe you found that more efficient.

That also gives us 68.

Either way, 40% of 170 km is equal to 68 km.

It's time for some final practise.

Number 1, Catherine completes a 190 km race.

How far has she travelled when she's completed a certain percentage of the race? Can you fill in the blanks? "Start by working out 50% and 10%, and then go from there." It's up to you how you proceed from there.

Number 2, Pedro completes a 225 km race.

How far has he travelled when he's completed a certain percentage of the race? And once again, start with 50% and 10% and build on it from there.

Okay, as always, if you can work with a partner, do.

Pause the video, and away you go.

How did you get on? Let's have a look.

Number 1, here are the answers.

50%, that's 95 km, that's half of 190 km.

10%, that's 19 km.

We're just dividing into 190 by 10, and then we can build on that from there.

"To calculate 5% of 190 km, halve 10%." And that gives us 9.

5.

"To calculate 15% of 190 km, you can add 10% and 5% together, and that will give us 28.

5%." How did you find the 60%? Personally, I would add the 50%, that's 95 km, to the 10%, that's 19 km.

And what's about the 90%? I would subtract 10%.

In this case, I would subtract 19 from 190, and that gives 171 km.

Lots and lots of ways to do this, then.

And number 2.

We've got 50%, that's 112.

5 km, that's half of it.

And 10%, that's 22.

5 km.

We've divided that by 10.

You can find 20% by doubling the 10%.

To calculate 90% of 225 km, you could subtract 10% from 100%, and I do think that's a very efficient way to do it.

That gives us 202.

5 km.

And then, what about that 60%? Lots of ways to do this.

I think the most efficient way is to add 50%, which you know, and 10%, which you know, together.

112.

5 plus 22.

5 is equal to 135.

We've come to the end of the lesson.

You've been fantastic.

You've impressed me so much.

Today, we've used knowledge of calculating common percentages 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.

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%.

So, top tip.

If you find 50% and 10% of a number, you can build on that from there and find all sorts of different connections and different ways to make the other percentages.

It just needs a little bit of thinking.

Well, congratulations.

That's one more step on your mathematical journey.

Give yourself a pat on the back and say, "Well done, me!" I'd really like to spend another math lesson with you at some point the near future.

But until then, have a fantastic day, whatever you've got in store, and look out for those percentages,.

Be the best version of you that you can possibly be.

Take care and goodbye.