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Hello there.
My name is Mr. Tilstone.
Nice to see you today, and I hope you're having a great day.
I'm going to set you a little challenge now.
In between this maths lesson and the next maths lesson, I want you to pay attention to how many times you see or hear about percentages in your everyday life, and I think you'll find it's a lot, they're everywhere.
Today's lesson is all about percentages.
If you're ready to begin, let's begin.
The outcome of today's lesson is this.
I can calculate 50%, 10%, and 1% of a number and use this to solve problems. Our keywords, we've just got the one today.
My turn, percentage.
Your turn, what does percentage mean? Hopefully you've got a bit of an idea by now, but let's have a recap.
A percentage is a proportion of a whole.
Our lesson today is split into 2 parts or 2 cycles.
The first will be finding 50%, 10%, and 1% of a number, and the second will be problem solving using 50%, 10% and 1%.
Let's begin.
In this lesson you'll meet Aisha and Lucas.
They're here today to give us a helping hand with the maths.
Aisha loves the Tour de France.
Have you ever watched the Tour de France before on the television perhaps? She says, "It's a brilliant cycling race held every year, mainly in France." And Lucas says, "I like the Tour of France too.
There are 21 days of racing, called stages, and the cyclists travel about 200 kilometres everyday.
Sometimes a bit less, sometimes a bit more." Stage one of the tour is 210 kilometres long.
This is Pierre, he's completed 50% of stage one.
So remember, the stage is 210 kilometres long.
How far could we say he's cycled? To find 50% of a number we need to halve it.
Now, that's one of the three big generalisations that I'd like to explore with you today.
So, we're going to say it again, but this time you're going to say it with me.
Are you ready? To find 50% of a number we need to halve it.
The stage is 210 kilometres long, so we need to find half of 210 kilometres.
Hopefully that's something you can do mentally.
That's mental arithmetic, I can do that in my head.
Half of 210 kilometres is equal to 105 kilometres.
This is Luke, he's completed 10% of stage one.
Hmm, so how far can we say he's gone? Remember, the stage is 210 kilometres long.
To find 10% of a number, we need to divide it by 10.
That's our second big generalisation of today.
So once again, we'll say that together.
Are you ready? To find 10% of a number we need to divide it by 10.
And you can see that again, that bar's been split into 10 equal parts.
It's got 10 intervals, 10 sections, he's completed one.
The stage is 210 kilometres long, so we need to divide 210 kilometres by 10.
What skills have you got for dividing by 10? How would you do that? 210 divided by 10 is equal to 21 kilometres.
We move all the digits one place to the right.
This is Bradley, he's completed 1% of stage one.
He's only just started, tiny little amount, hmm.
What could we say this time? How far has he gone? Well, to find 1% of a number, we need to divide it by 100, and that's our third and final big generalisation of today.
So once again, let's say that together.
Ready? Go.
To find 1% of a number, we need to divide it by 100.
So, the stage is 210 kilometres long, so we need to divide 210 by 100.
What skills have you got for dividing a number by 100? Well, we could move it 2 places to the right.
All the digits 2 places to the right, and that's 2.
1.
So 210 kilometres divided by 100 is equal to 2.
1 kilometres, that's how far he's gone.
And let's see those divisions by 10 and 100 again.
To divide by 10, move the digits one column to the right.
So, 210 divided by 10 is equal to 21.
So, 10% of 210 is 21.
Zero isn't used, because it's no longer needed as a placeholder.
So, that's 21.
And to divide by 100, move the digits 2 columns to the right.
Zero isn't used, because it's no longer needed as a placeholder, so we can get rid of that.
So, 210 divided by 100 is equal to 2.
1.
So, 1% of 210 is 2.
1.
Fractions and percentages are connected.
100% of 210 kilometres is equal to 210 kilometres.
To find 50% of a number, we need to divide it by 2.
We've explored that already.
50% of 210 kilometres is equal to half of 210 kilometres, and half of 210 kilometres is 105 kilometres.
To find 10% of a number, we need to divide it by 10.
We've already explored that.
10% of 210 kilometres is equal to one 10th of 210 kilometres.
And one 10th of 210 kilometres is 21 kilometres, so hopefully you can see that link.
To find 1% of a number, as we've already discovered, we need to divide by 100.
1% of 210 kilometres is equal to 100th of 210 kilometres.
100th of 210 kilometres is 2.
1 kilometres.
Now, stage 2 of the tour, that's a different length, that's 170 kilometres long.
100% of 170 kilometres is equal to 170 kilometres, that's all of it.
50% of 170 kilometres is equal to half of 170 kilometres.
So, what's that? To find 50% of a number we need to divide it by 2, one of our three big generalisations of today.
Half of 170 kilometres is 85 kilometres, and 10% of 170 kilometres is equal to one 10th of 170 kilometres.
To find 10% of a number, we need to divide it by 10 as we've already discovered.
So, one 10th of 170 kilometres is 17 kilometres.
And then 1% of 170 kilometres is equal to 100th of 170 kilometres.
And as we've already discovered, to find 1% of a number, we need to divide it by 100.
So 100th of 170 kilometres is 1.
7 kilometres.
Let's do a little check.
Stage three of the tour is 140 kilometres long.
So, 50% of 140 kilometres is equal to half of 140 kilometres.
So, what is that? 10% of 140 kilometres is equal to one 10th of 140 kilometres.
So, what is that? And 1% of 140 kilometres is equal to 100th of 140 kilometres.
So, what is that? Pause the video.
Let's see.
So, you're finding 50%, 10%, and 1% of 140 kilometres.
Well, half of that is 70, half of 140 is 70.
140 divided by 10, so we move all the digits one place to the right, that's 14.
And then 140 divided by 100, we move the digits 2 places to the right, that's 1.
4.
Well, if you've got those, you are on track if you did.
Stage 4 of the tour is 156 kilometres long, so 100% of it is 156.
As we've already discovered, to find 50% of a number, we need to divide it by 2.
So, divide that by 2, and divide that by 2, and we get 78 kilometres.
To find 10% of a number, as you already know, we need to divide it by 10.
So, 100 divided by 10 is 10, 156 divided by 10, move everything one place to the right, is 15.
6.
And then to find 1% of a number, we need to divide it by 100.
And that's what we've done here, and we do the same here.
This time we're moving all the digits 2 places to the right, and that gives us 1.
56 kilometres.
Stage 5 of the tour is 147 kilometres long.
Let's use the table to help us organise the information.
To find 50% of a number we need to divide it by 2, as you know.
147 can be partitioned into 140, and 7.
So, 140 divided by 2 or halved is equal to 70, and 7 halved is equal to 3.
5.
So let's combine them and we get 73.
5.
So, that is 50% of 147 kilometres.
To find 10% of a number, we divide it by 10.
So, moving all the digits one place to the right.
This time we've got 14.
7 kilometres.
And to find 1% of a number, we need to divide it by 100.
So, we're moving all the digits 2 places to the right, and that's 1.
47 kilometres.
Let's have another check.
Complete the table for stage 6 of the tour.
That's 122 kilometres.
Can you find 50%, 10%, and 1% of 122 kilometres? Pause the video.
Did you do it? Did you manage it? Well, let's use the table to help you organise the information.
To find 50% of a number, you need to divide it by 2, so you're halving, and that's 61 kilometres.
To find 10%, you're dividing it by 10, moving the digits one place to the right, that's 12.
2 kilometres.
And to find 1% of a number divide it by 100, moving the digits 2 places to the right, and that's 1.
22 kilometres.
It's time for some practise, and I'm confident that you're ready for this.
So, number one, complete the sentences.
100% of 152 kilometres is equal to 152 kilometres.
So, 50% of it is, 10% is, and 1% is.
Remember, to find 50% of a number, divide it by 2.
To find 10% of a number, divide it by 10.
And to find 1% of a number, divide it by 100.
And then complete those tables.
So, you're finding 50%, 10%, and 1% of each distance.
The first is 190 kilometres, the second 166 kilometres, and the third 204 kilometres.
I remember to find 50% of a number, divide it by 2, to find 10% of a number, divide it by 10, and to find 1% of a number, divide it by 100.
If you can work with a partner and your teacher's okay with that, I always recommend that.
Then you can share ideas with each other and approaches and check each other's thinking and arithmetic.
Pause the video, and away you go.
Welcome back, how did you get on? Let's give you some answers and you can check.
So, half of 150 is equal to 75, and half of 2 is equal to one.
Combine those together.
You've got 76, so that's 50% of 152 kilometres.
10%, we're going to move the digits one place to the right, that's 15.
2 kilometres.
And 1%, we're going to move the digits 2 places to the right, that's 1.
52 kilometres.
2A, 50% is equal to 95 kilometres.
So 10%, move the digits one place to the right, that's 19 kilometres.
And 1%, move them 2 to the right, that's 1.
9 kilometres.
For B, 100% is 166 kilometres.
Half of that, 50% of that is 83 kilometres.
Move the digits one place to the right and that's 16.
6 kilometres, and move them 2 places to the right is 1.
66 kilometres.
And for C, 100% is 204 kilometres, so 50% is half of that, that's 102 kilometres.
10%, move the digits one place to the right, that's 20.
4 kilometres.
1%, move the digits 2 places to the right, that's 2.
04 kilometres.
So, 100, 190 kilometres is equal to 1.
9 kilometres.
In C, zero needs to be used as a placeholder when 204 is divided by 10 and 100.
How you're doing ever so well, let's see if we can put that into practise a little more by problem solving using 50%, 10%, and 1%.
So you know what to do hopefully by now with those percentages, let's do some problem solving.
Aisha wonders, "What happens if the whole is unknown?" Hmm, that's a bit different.
So, what happens if you know what the 50% is, or the 10% is, or the 1% is of an amount, but you don't know the 100% of the same amount? You don't know the whole.
You could use multiplication to work out the missing whole, so going the other way.
So, let's take this example.
50% of a number, we don't know what the number is, is 32, what's the number? So, if 50% is 32, we could double that 32 to find the missing whole.
So, double 32, multiply by 2, that's 64.
So, 100% is 64 and 50% is 32.
So, we're using our inverse operations.
Mark has completed 50% of stage 7, so far Mark has travelled 83.
5 kilometres.
How long is stage 7? So, we know the 50%, we don't know the 100%.
How could we get there? Well, let's represent that in a table, that's a 50%.
What could we do to get that 100%? How can we go from 50% to 100%? Again, we can double it, we can multiply it by 2.
And when we do that, we get 167.
So, that's the whole of that stage length.
Stage 7 is 167 kilometres long.
Asia and Lucas complete this table, so 50% is known.
50% of this so far mystery number is 68.
This time we don't know the 10%, the 10%, or the 1% of the number, but I think we could work it out.
What would you do first? What would be your first port of call? We know 50% of the numbers, so just like before we can double it to work out 100%.
It's a good idea.
So, double 68, or 68 multiplied by 2 is equal to 136.
So, that's 100%.
Now, we should be able to work out the 10% and the 1% by moving the digits.
So, if we move the digits one place to the right, that would give us 10%, that's 13.
6, and 2 places to the right gives us 1.
36, so that's the 1%.
This time we know the 1%, that's 1.
45 kilometres, but we don't know 100%, or 50%, or 10%, but we do know 1%.
So, how could we find out that 100%? Hmm, well, we could multiply it by 100 this time, using our inverse operations.
So, 1.
45 multiplied by 100, so we're moving the digits 2 places to the left, is equal to 145.
That should help us to work out the 50% and the 10%.
Well, the 50% is half of that, and that's 72.
5.
And the 10%, move the digits one place to the right, and that's 14.
5.
Aisha and Lucas find the missing numbers, so 10% of 122 is equal to something, and 1% of 153 is equal to something.
Can you do that? To find 10% of a number we need to divide it by 10.
I'm sure you'd know that really well by now.
So, that 100% is 122.
10%, move the digits one place to the right, and that's 12.
2.
And then 1% of 153, to find 1% of a number, as you know, we need to divide it by 100.
So, we're going to move those digits 2 places to the right, and that gives us 1.
53.
So, 1% of 153 is equal to 1.
53.
What about this? Something percent of 225 is equal to 2.
25? That's tricky, isn't it? And then something percent of 178 is equal to 89.
Now remember, today we're working with 50%, 10%, and 1%, so it's going to be one of those three.
What do you think? Well, 225 has been divided by 100.
So, therefore, to find 1% of a number, we need to divide it by 100.
225 divided by 100 is equal to 2.
25, so that must be 1%.
1% of 225 is equal to 2.
25.
And what about this one? 178 has been divided by 2.
So, to find 50% of a number, we need to divide it by 2, as you know.
178 divided by 2 is equal to 89, so therefore the missing number is 50%.
50% of 178 is equal to 89.
So, that's using our inverse operations.
Let's do a little check, find the missing number.
Hmm percent of 150 is equal to 15.
What do you think? Pause the video.
So, we know the 100%, 100% is 150.
150 has been divided by 10.
150 divided by 10 is equal to 15, so therefore it's 10%.
To find 10% of a number, as you know, we need to divide it by 10.
10% of 150 is equal to 15.
Well, that if you've got that, you're ready for the next stage of the learning.
Aisha and Lucas find the missing number.
10% of 230 is equal to 50% of hmm.
That's a bit trickier, isn't it? How would you approach this? Have a little think about that.
Well, Aisha says, "Let's start by working out 10% of 230." That's a good idea, we know how to do that.
We divide that by 10.
Move everything one place to the right, that's 23.
We need to divide 230 by 10, so it's 23.
So, we know that 10% of 230 is equal to 23, which is equal to 50% of what? Let's move on to the other part of the equation.
We know 50% of the number is equal to 23.
You need to multiply 23 by 2 to calculate 100% of the number.
That would help us to find the 100%, so double 23 is equal to 46, so that's the answer, 46.
50% of 46 is equal to 23, and now we can complete that equation.
10% of 230 is equal to 50% of 46.
1% of 1,200 is equal to 10% of what? Hmm? What do you think this time? So, start as we did before, find out 1% of 1,200.
Good starting point, let's do that.
Can you move the digits 2 places to the right? It is 12, so 1% is 12.
So, 12 is equal to 10% of what? Hmm, let's move on to that part.
10% of the number is equal to 12.
So, now we can work out hopefully what 100% is by multiplying by 10.
And that's 120, and that's our missing number.
120, 1% of 1,200 is equal to 10% of 120.
Let's have a check, fit in the missing number.
50% of 50 is equal to 1% of hmm.
Pause the video.
Did you start by working out 50% of 50? That's a great starting point.
That's half of 50, and that's 25.
So, 25 is equal to 1% of something.
1% of the number is equal to 25.
Writing that down in a table really helps, I think, little grid like this.
So, 1% is 25.
So, if we multiply one by 100, we get 100%.
And do the same to 25.
25 multiplied by 100 is equal to 2,500.
And that's the answer, that's the equation.
50% of 50 is equal to 1% of 2,500.
And very well done if you've got that, you're on track.
It's time for some final practise.
Number one, work out how far the cyclists have travelled.
So, A, Helen completes a 229 kilometres cycle race.
How far has she travelled when she's completed 50% of the race? So, you hopefully know by now how to work out 50% of a number.
B, Catherine completes a 178 kilometre cycle.
How far has she travelled when she's completed 1% of the race? And C, Pedro has completed 10% of a cycle race.
He's travelled 20.
5 kilometres so far, so that's slightly different, isn't it? How long is the race? Number 2, complete the tables.
Use the percentage you've been given to help you find the missing numbers.
Think about whether you need to multiply or divide by 2, 10, or 100.
Number three, find the missing numbers.
"And some of these equations," says Aisha, "have a percentage missing." And Lucas say, "Start A, by dividing 1,440 by 10." That will give you the first part of the equation.
That will help you to work out the second part of the equation.
Righteo, pause the video, and away you go.
Welcome back.
How did you get on? How are you finding this? Are you feeling confident and happy about this? Let's have a look.
Number one, here are the answers.
So, Helen completes a 229 kilometre cycle race.
How far has she travelled when she's completed 50% or half of the race? Well, we're dividing that number by 2.
That's not too easy to divide by 2 that number, but when you do, we get 114.
5 kilometres.
Catherine completes a 178 kilometre cycle race.
What's about when she's completed 1% of the race? Move those digits 2 places to the right and we've got 1.
78 kilometres.
And C, Pedro has completed 10% of a cycle race.
He's travelled 20.
5 kilometres so far, so that's the 10% part.
And the question is, how long is the race? What's the 100% part? So, if we multiply that 20.
5 by 10, that would give us the 100%, so move it one place to the left, and we've got 205 kilometres.
And then for A, 100% is 530, so 50% is 265, 10% is 53, and 1% is 5.
3.
In A, 53 multiplied by 10 is equal to 530.
530 divided by 2 is equal to 265.
For B, we know that 50%, that's 164, and we can use that to double it.
Perhaps you went that way to find the 100%, that's 328.
And then we can use that to find the 10% and the 1%, which are 32.
8 and 3.
28 respectively.
In B, 164 multiplied by 2 is equal to 328.
And then, 328 divided by 10 is equal to 32.
8.
And for C, this time we know the 1%, that's 1.
25.
We can multiply that by 100 to get the 100%, that's 125.
And then we could halve that to get the 50%, that's 62.
5, and then we could move that one place to the right, all the digits there.
That would make 12.
5 for the 10%.
Well, there you've got those.
And number three, well, let's look at A.
Start A by dividing 1,440 by 10.
Move them one place to the right, all the digits.
That's 144.
So, the second part of the equation needs to equal 144, and 144 is equal to 50% of 288.
And for B, 1% of 950 is equal to 9.
5, so that's the first part of the equation.
So we've got to make the second part equal to that too.
And 9.
5 is equal to 50% of 19.
And for C, 10% of 2,450 is equal to 245, which is 50% of 490.
And for D, 50% to 160 is equal to 80, which is 1% of 8,000.
Wonder if you got those? I've really enjoyed today's lesson, and I feel like you've made some great progress, so well doing for that.
Today, we've been using knowledge of calculating 50%, 10%, and 1% of a number to solve problems in a range of contexts, right? Can you read this next part with me? Are you ready? Let's go.
To find 50% of a number, halve it.
To find 10% of a number, divide it by 10.
To find 1% of a number, divide it by 100.
And you'll be saying that in your sleep tonight.
Well done on your accomplishments and your achievements today.
You've been fantastic.
It's been a real pleasure working with you, and I hope to work with you again at some point in the near future.
But until then, have a fantastic day, whatever you've got in store.
Remember, be the best version of you that you can possibly be.
Nobody can ask for more than that.
Take care, and goodbye.
