Lesson video

Hi everyone.

My name is Ms Coo and I'm really happy to be learning with you today.

In today's lesson, we'll be looking at percentages and percentages is so important as they appear so much in everyday life.

I really hope you enjoy the lesson, so let's make a start.

Hi, everyone, and welcome to today's lesson on checking and securing understanding of finding a percentage.

Under the unit percentages.

And by the end of the lesson, you'll be able to describe one number as a percentage of another and calculate a given percentage of an amount efficiently.

In today's lesson, we'll be using the keywords equivalent fractions and two fractions are equivalent if they have the same value.

For example, one half is exactly the same as two quarters as they have the same value.

Four fifths is exactly the same as 40 over 50 as they have the same value.

One fifth is not equivalent to three sevenths as they do not have the same value.

Today's lesson will be broken into two parts.

We'll be looking at amounts as a percentage first and then we'll be calculating a percentage of an amount.

So, let's make a start looking at amounts as percentages.

Well, there are lots of different ways we can make sense of how to write one number as a percentage of another number.

For example, the question wants us to write 35 as a percentage of 50.

We could use double number lines, we could use vertical bars, and we could also use our knowledge on fractions.

So, let's have a bit of a recap.

We're going to recap on how to calculate 35 as a percentage of 50 using double number lines.

Firstly, I'm gonna draw my double number line on the top.

I'm gonna identify the line to be percentages and on the bottom I'm going to identify the amount.

From here, I'm going to put 100% as 50.

As you can see from the question, we're asked to work out 35 as a percentage of 50.

So, that means the 50 is 100%.

Now, the question wants us to work out what percentage of 50 is 35.

So, that's why I put a question mark right there.

Now, remember that multiplicative relationship.

We need to work out, what do we multiply 50 by to give 35? Once we know that, then we multiply the percentage by that same amount.

So, let's have a think.

What do you think we multiply 50 by to give 35? Well, it would be 35 over 50, so we need to multiply that 100% also by 35 and 50.

Now, using our knowledge on equivalent fractions, I'm going to multiply 100 by 35 over 50.

Working this out, I finally get a percentage of 70%.

Very well done if you spotted this.

So, we now know 35 is 70% of 50.

We can also show this using vertical bars.

So you can see my big large bar there is 50 and I have my smaller bar is 35 and I need to find out what percentage of 50 is 35.

So to do it, I'm gonna put my 35 in that vertical bar of 50.

Now, we need to find out how can I equally split our vertical bar so I can identify what fraction of 50 is 35.

Well, if I split the vertical bar into 10 equal sections, I've got my 10 equal sections would be 50 and seven equal sections would give me my 35.

Then I can convert my fraction of seven tenths into a percentage.

Converting it into a percentage, I have 70 over 100, which is 70%.

Once again, 35 is 70% of 50.

We can also use equivalent fractions, one of my favourites.

So, let's have a look at calculating what 35 is as a percentage of 50.

While I can do this using fractions, 35 over 50 is what we need to find.

Simplifying this a little further, identifying our highest common factor of five, I can cancel it down to seven tenths.

Therefore, I can convert seven tenths into a percentage using our knowledge on equivalent fractions.

Identifying 35 as a percentage of 50 is 70%.

I also like to use short division because that fraction line means divide.

So we can simplify 35 over 50 and then we can divide.

So 35 over 50 simplified gives me seven tenths.

Then I'm going to use short division now.

Seven divided by 10 is 0.

7, and I could show that using my short division two.

So, we've used quite a few different ways to work out that 70% of 50 is 35.

Which method do you prefer and why? We looked at double number lines, vertical bars, and fractions.

Have a little think.

Well, everybody has a different preference.

For me, I really like the use of fractions because it saves me time drawing vertical bars or double number lines.

Now, what we're going to do is going to do a check.

I'm going to do the first question and I'd like you to do the second question.

Using any method you prefer write 85 as a percentage of 130 to one decimal place.

Well, I'm going to use my knowledge on fractions, so I'm going to write it as 85 over 130.

Now, I'm going to simplify it to give me 17 over 26.

Now, from here, I'm going to use short division because the calculation is the same as 17 divided by 26.

I'm going to work it out.

So how many 26 is going to 17? Well, it's none remaining at one.

How many 26 is going to 17? Well, it's none, so don't forget to put in your decimal place and we put those trailing zeros.

How many 26 is going to 170? Well, it's six remaining 14.

We have another trailing zero.

How many 26 is going to 140, which is five.

We have another trailing zero, giving us how many 26 is going 100, which is three.

Another trailing zero gives us how many 26 is going to 220, which is eight.

I'm going to stop here because given the fact that no 0.

01 is equivalent to 1%, we can convert it.

So that means we know 85 as a percentage of 130 to one decimal place is 65.

4.

Now, what I'd like you to do is I'd like you to do this question.

Using any method you prefer, write 26 as a percentage of 150 to one decimal place.

See if you can give it a go.

Press pause for more time.

Great work.

Let's see how you got on.

Firstly, I'm going to use the method of fractions.

So, I'm going to write it as a fraction 26 over 150.

And then I'm gonna simplify to give me 13 over 75.

I'm going to be using short division here to work out my answer.

So, you can see all my wonderful working out here.

Now from here, I know given the fact that 0.

01 is equivalent to 1%, I've successfully converted 26 as a percentage of 150 as 17.

3% to one decimal place.

Well done if you got this one right.

Now, regardless of the method or model you use to work out the amount as a percentage, it is important to know what is represented as 100%.

Sometimes it's not clear in the question and you have to carefully read and extract the information.

For example, without working out the percentage, I want you to explain how you would find out what percentage of each shop sales were mobile phones.

Have a little look at each of these images and see what you think.

Press pause for more time.

Great work.

Let's see how you got on.

Well, for shop A, how will we work out what percentage of sales were mobile phones? Well, the total sales would represent the 100% and the total can be found by summing up all those frequencies.

So, adding up the sales of each of our devices, we know there are 32 sales in total.

Now, given the fact the question wants us to find the percentage of mobile phones, we're basically asked to find out what four is as a percentage of 32.

Well done if you spotted this.

Now, let's have a look at shop B.

How are we going to identify what percentage of each shop sales were mobile phones? Well, the total sales would represent the 100% and the total sales can be found by summing up all the sales.

So, if you sum up all the sales, we have 80.

And from here, we know to find the percentage of mobile phones sales.

We are asked to find out what 45 is as a percentage of 80.

Last thing, let's have a look at shop C.

We only have the angles.

So how are you able to identify what percentage of each shop sales were mobile phones? Well, to do this, the total sales would represent 360 degrees, given that all the results are represented in a pie chart.

So, that means the percentage of mobile phone sales is finding out what 205 is as a percentage of 360.

Well done if you've got any of these and spotting that sometimes you have to identify what 100% is from the context of the question.

Now, let's have a look at a check.

Here's a table of sales from a closed door in a week.

What percentage of the sales were T-shirts? And I want you to give your answer to one decimal place.

See if you can give it a go and press pause if you need more time.

Great work.

Let's see how you got on.

Well, the total sales is found by 23 at 27, at six at 64, which is 120.

So, the question is asking us to find what is 64 as a percentage of 120? Using fractions, I've simplified this to give me eight over 15 and then have you short division to work this answer out.

So, the percentage of T-shirt sales is 53.

3% to one decimal place.

Well done if you've got this one.

Great work everybody.

So, now it's time for your task.

Given any method you prefer, I want you to work out the following given your answer to two decimal places where appropriate.

See if you can give it a go.

Press pause for more time.

Great work.

Let's move on to question two.

Question two shows a bar chart and the bar chart shows how some Oak pupils get to school.

What percentage of pupils travel by scooter? See if you can give it a go.

Press pause for more time.

Great work.

Let's have a look at question three.

Question three states, Aisha and Jun are both competitive and they've both taken two different math tests.

Aisha is a little bit disappointed as she thinks Jun has done better than her.

Show how you are working using one decimal place where necessary to explain why Aisha is incorrect.

See if you can give it a go.

Press pause for more time.

Great work.

Let's move on to question four.

Here's a table of sales from a clothes store in a week and the manager wants to find out the percentage of returns, which of the items has the highest percentage of returns compared to the sales of that item.

See if you can give it a go.

Press pause for more time.

Well done.

So let's move on to question five.

Question five shows a pie chart and the pie chart shows the approximate proportion of vitamins in an orange.

What percentage of an orange is vitamin C? I want you to give your answer to one decimal place.

See if you can give it a go and press pause for more time.

Great work.

Let's move on to question six.

Question six says, "A maths competition has two papers, mental arithmetic and problem solving.

A mental arithmetic has 20 marks.

The problem solving has 40 marks.

Now, to move to the next round, a mean average of 78% or more is needed in both papers.

Lucas gets 16 marks for the mental arithmetic and he gets 30 marks in the problem solving paper.

Does Lucas move on to the next round and I'd like you to show all your working out." See if you can give it a go.

Press pause for more time.

Great work everybody.

So let's go through our answers.

For question 1A, it's 36%, for B, it's 48%, for C, it's 79.

2% to one decimal place, and for D it is 87.

5%.

Well done.

For question two, hopefully you've worked out the total number of pupils is 80, so we needed to work out what fraction of 10 of 80 and that would be 12.

5%.

Very good.

For question three, can you help Aisha? Well, working out 39 out of 45 is a percentage for Aisha is 86.

7% to one decimal place.

And for Jun, well that's 24 outta 28, which is 85.

7%.

So Aisha has done better than Jun.

For question four, we need to work out which of the items has the highest percentage of returns compared to the sales of that item.

So for dresses, you're working out 12 as a percentage of 23, which is 52.

2%.

For trousers, you're working out six as a percentage of 11, which is 54.

5%.

For hats, you are working out three as a percentage of six, which is 50%.

And for T-shirts it's 33 as a percentage of 64, which is 51.

6%.

So, the trousers have the highest percentage of returns.

For question five, what percentage of an orange is a vitamin C? Well, you had to work out 277 as a percentage of 360 and that works out to be 76.

9% of an orange is vitamin C.

That's a lot of vitamin C there.

So it's important to eat your oranges if you can.

Question six, Maths competition for Lucas.

Let's work it out.

Well, if he gets 16 outta 20 in his first paper, that's 80%.

And then, if he gets 30 outta 40 in the problem solving paper, that's 75%.

The mean of these two papers is 80 plus 75, then divide it by two, which gives us 77.

5%.

Now, if you round this in the nearest integer, Lucas qualifies, it gives us the 78%.

But if they use the exact percentage, unfortunately, he won't move on to the next round.

So, hopefully they've rounded to the nearest integer.

Great work everybody.

So, now let's have a look at calculating a percentage of an amount.

We can find a percentage of an amount in lots of different ways.

Here are some examples of finding 42% of 340.

We could use a bar model, we could use a ratio table or we could use a double number line, but my favourite is using multipliers.

Each of these have their advantages and disadvantages.

Which do you prefer and why? In this lesson we'll be looking at bar models, ratio tables, and multipliers.

I won't be looking at double number lines as it does take a bit of a while to draw.

So, let's recap and look at a bar model showing 340.

How would 10% be represented in our bar model? Well, we would split it equally into 10 equal parts, thus each part would be 34.

So, remember to find 10%, we divide by 10 and this is because there are 10 lots of 10% in 100%.

Now, how do you think we can find 5% if we know 10%? Well, we simply divide the 10% by two so we know what 10% is, which is 34.

Dividing by two gives us 5%, which is 17.

Because you can work out 10% of a number by dividing by 10, a common mistake is to find 5% by dividing by five.

Why do you think this doesn't work? Well, because there are more than five lots of 5% in 100%, and to find 5% you would divide by 20.

So now, we know what 10% is and we know what 5% is.

How do you think we can find 1%? Well, we would simply divide that 10% by 10.

Let's zoom in so we could find out what 1% is.

Here you can see our 10% and we know that's 34, so that means 1% has to be 3.

4, 34 divided by 10.

So now we know 100% is 340, 10% is 34, 5% is 17 and 1% is 3.

4.

We can find any percentage.

So let's find out our 42% of 340.

Well, one example to work it out would be 40% is 34 times four because we know 10% is 34.

That gives us 136.

Then I can work out my 2% by simply doubling the 1%, giving me 6.

8.

Adding these together gives me 42% to 340 to be 142.

8.

This is a nice method where you're identifying 10%, 5%, and 1%.

So, let's have a look at a quick check.

Andeep says he can now work out 0.

5% of 340.

How do you think he can do this using our bar model? Have a little look and have a little think.

Well done.

Well, it'd be simply dividing that 1% by two and dividing that 1% by two gives us two lots of 0.

5%.

So, that means 0.

5% is 1.

7.

Well done if you got this.

So, let's work out 6.

5% of 340.

I want you to have a look to see if you can work this one out.

Knowing 100% is 340, 10% is 34, 5% is 17, 1% is 3.

4.

And thanks to Andeep, we know 0.

5% is 1.

7.

See if you can give it a go.

Press pause for more time.

Well done.

Let's see how you got on.

Well, we know that 6% can be found by multiplying that 1% by six, giving me 20.

4.

Then, I know 0.

5% is just one lot of 1.

7.

Summing these together, I have my 6.

5% to be 22.

1.

So, therefore, 6.

5% to 340 is 22.

1.

Great work if you got this one right.

Let's have a look at ratio tables now.

You can see these same values put in a ratio table.

Where do you think you can see that multiplicative relationship? Well, there is always a constant multiplier from the percentage to amount.

In other words, we're multiplying by 3.

4 and you can see it here.

And that's what's so important about ratio tables.

They show that multiplicative relationship.

You can also see that multiplicative relationship in each row.

For example, we found 10% by dividing 100% by 10.

We found 5% by dividing 10% by two.

We found 1% by, for example, dividing 5% by one, and we divided 1% by two to give me 0.

5%.

So, do you think using that ratio table you can find 6.

5% to 340? See if you can give it a go and press pause for more time.

Although lots of different ways you could do this, for me I'm going to look at summing 5%, 1%, 0.

5%, and you can see it right here.

And in summing those values, I have my 22.

1.

Now, let's have a look at multipliers and we're gonna be looking at 42% of 340.

We know that finding percentages of a given amount is like finding a fraction of an amount.

For example, 42% of 340 is the same as 42 over 100 of 340.

So, to find the fractions of an amount, remember we use multiplication in place of the word of, so that means it's the same as 42 over 100 times 340.

Now, remember this is equivalent to 0.

42 times 340 because 0.

42 is the decimal equivalent to 42 over 100.

So, that means we can use a multiplier to work out 42% of 340, 0.

42 times 340.

And we can do this using the associative law and an area model.

For example, the associative law states 0.

42 times 340 is the same as 42 times 340 times 0.

01.

I can work out the multiplication of 42 by 340 using an area model and I get the lovely big number, 14,280.

And I'm gonna multiply that by 0.

01, thus giving me a final answer to be 142.

8.

So, that means I know 42% of 340 is 142.

8.

So using multipliers now, I want you to work out 6.

5% of 340.

Don't forget that associative law and using an area model if you choose.

See if you can give it a go.

Press pause for more time.

Great work.

Let's see how you got on.

Well, first things first, using the associative law, we know 0.

065 multiplied by 340 is the same as 65 multiplied by 340 times 0.

01.

Working this out, I have 22,100 is multiplied by 0.

01, which gives me a final answer of 22.

1, exactly the same as what we worked out before, but using a different model.

So, that means 6.

5% is 340.

Out of curiosity, which method do you prefer for more complicated percentages, for example, 6.

5% to 340, and why do you prefer this method? We've looked at bar models, we've looked at ratio tables, and we've looked at multipliers.

Which do you prefer? Each have their own advantages and disadvantages, but which method would you use if you had a calculator? Well, using a calculator will speed up all three methods, but without a doubt using multipliers will be the most efficient.

So, in our next check, I want you to fill in the ratio table without using a calculator and work out 7.

2% of 840.

See if you can give it a go.

Press pause for more time.

Great work.

So let's see how you got on.

Well, filling in our ratio table.

I've worked out the following percentages to be these.

Now, from here, how am I going to get 7.

2%? I'm going to choose 5% to be 42.

I'm gonna double 1% to gimme 16.

8.

And then I've done a double my 0.

1%, give me 1.

68.

Summing them all together gives me my 7.

2%, which is 60.

48.

So that means we've worked out 7.

2% of 840 is 60.

48.

Well done.

Now, it's time for your task.

Without a calculator, I want you to work out the following use the method you find most efficient.

See if you can give it a go.

Press pause for more time.

Great work.

Let's move on to question two.

And Oak teacher owns shares in three businesses, which have increased in value over the past month by a given percentage.

Which company has earned the Oak teacher the most amount of money? I want you to work this question out without a calculator.

See if you can give it a go.

Press pause for more time.

Well done.

For question three, what efficient non-calculator strategy would you use to quickly work out 5.

55% of a number? And for B, does this strategy work when trying to work out 2.

22% of a number? See if you can give it a go.

Press pause for more time.

Well done.

So let's go through these answers.

For A, you should have 524.

8, for B, 29.

9, and for C, 14.

84.

For question two, working out the amount gained, we have these, so therefore we know Coffee World has earned the Oak teacher the most amount of money.

For question three, one efficient strategy to work out 50% by dividing the original amount by two.

Then to find 5%, you divide the 50% by 10, that will give you 5%.

Then to find 0.

5%, you divide by 10 again.

And finally to find the 0.

05, divide the 0.

5% by 10, summing the 5%, the 0.

5%, and the 0.

05%, give you 5.

55%.

Does this strategy work when finding 2.

22%? Yes it does.

All you need to do is find 20%, divide this by 10 to give you 2%.

Divide this by 10 to give you 0.

2% and then divide this by 10 to give you 0.

02%.

Summing up 2%, 0.

2%, and 0.

02% gives you 2.

22%.

Well done.

Great work everybody.

So in summary, we've looked at finding an amount as a percentage and in a percentage of an amount using double number lines, vertical bars, bar models, ratio tables, and a wonderful decimal multiplier.

These different methods each have their own advantages and disadvantages.

Having a good understanding of each will allow you to work with percentages more efficiently.

Well done everybody.

It was great learning with you.