Lesson video

Hello, everyone, my name is Miss Coo and I'm really happy to be learning with you today.

Today, we're going to be looking at percentages.

Such an important topic as we use it so much in real life.

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

Hi, everyone, and welcome to the lesson on checking and securing understanding of percentage increase, under the unit percentages.

By the end of the lesson, you'll be able to increase an amount by a given percentage.

We'll be looking at the word proportion, and proportion is a part to whole, sometimes part to part comparison.

And if two things are proportional, then the ratio of the part to whole is maintained and the multiplicative relationship between parts is also maintained.

Today's lesson will be broken into three parts.

We'll be looking at increasing by a percentage first, non-calculator methods, then increasing by a percentage using a calculator, and then finally, finding the original amount after an increase.

So let's make a start by looking at increasing by a percentage, non-calculator methods.

Here's a bar model showing 600 pounds.

And if you had 600 pounds and a friend said they'd give you an extra 10%, how much money would you have in total? Have a little think.

Well, we know to work out 10%, we have to divide 100% into 10 equal parts.

Thus, we know each part is 10%.

Then if knowing each part is 10%, we've worked out each part to be 60.

From here, we can simply add that 10% that our friend is giving us.

So that means, we would have 660 pounds.

Now given that 600 was the original 100%, what percentage of 600 is now shown in our bar model? Have a little think.

Well, it would be 110%.

660 pounds is 110% of 600 pounds.

In mathematics, there are many different ways to write a question, but they all mean the same thing.

For example, increase 600 pounds by 10% is the same as find 110% of 600 pounds.

What I want you to do is I want you to have a look at this check question.

I've drawn some bar models and I want you to fill in the blanks using the bar models.

52 is what of 40? And something is 160% 50.

See, we can fill in these bar models.

Press pause one more time.

Well done.

Let's see how you got on.

Well, let's work out that 10% first.

10% has to be four, so that means 30% are three lots of four.

Now you can see, 52.

So 52 is 130% of our 40.

Let's have a look at our 50.

Now remember, 100% is represented as 50, so that means 10% must be five.

So we have six lots of our 10%, which is 60.

Therefore, we know 80 is 160% of 50.

Well done if you got this one right.

And this approach can be applied with any percentage.

For example, here's a bar model showing 240 pounds.

How would you find 1% of 240 pounds but just in one calculation? See if you have a little think.

Well done.

Well it could be found by simply dividing 240 by 100 and this will give you 1%.

So 240 divided by 100 is two pounds 40.

This is our 1%.

So if the question asked what would increasing 240 by 3% look like? What do you think we'd have to do to our bar model? Well, we'd have to add our 3%, which is here.

And then adding our 3%, do you think you know what the answer is when we increase 240 by 3%? Well, it'd simply be 1% is two pound 40.

So that means 3% has to be two pound 40 multiply by three.

Thus, giving me my 3% to be seven pounds 20.

So therefore, increasing 240 pounds by 3% gives you my 240 pounds and that 3%, which is our seven pound 20, giving me a total of 247 pounds and 20 pence.

Now let's transfer the same information from the bar model into a ratio table.

From our bar model, it's clear to see that we know 100% is 240.

So let's see if we can work out 1% by simply dividing by 100 and you can see it represented in our bar model and more simply in our ratio table.

Now from here, we can work out our 3%.

Remember that multiplicative relationship using our ratio table.

Multiplying our 1% by three gives me 3% to be seven pounds 20.

Now sum make up 100% and 3% gives us our 103%, which is 247 pound 20.

So bar models or ratio tables can help us increase an amount by a percentage.

So now let's have a look at a check question.

Two pupils are given this bar model and are asked to increase 900 pounds by 1.

5%.

I want you to have a look at the two workings out from Alex and Sam.

Who's correct and what error has the other pupil made? See if you can give it a go.

Press pause one more time.

Great work.

Well, hopefully you spotted Sam is correct.

Unfortunately, Alex has made mistake, but can you spot where the mistake is? Well, Alex has incorrectly worked out 1%.

1% of 900 pounds is nine pounds.

It's 900 divided by 100.

Now let's have a look at another check question.

"Two pupils used a ratio table now to increase 380 pounds by 6%.

Whose method is correct?" Have a little look and press pause for more time.

Well done.

Let's see how you got on.

Well, they are both correct.

It's really nice to see that both methods are correct.

They might have been slightly different in their workings out, but they're absolutely fine.

Out of curiosity, which do you prefer? So what do you think the advantages and disadvantages are when using the bar models or ratio tables? Well, bar models are really good visual representations.

You can see what's going on.

You can see that 100 and you can see the 103%.

However, they do take a long time to draw, especially if you're going to divide a bar model into 100 pieces to show 1%.

Ratio tables are far more efficient, but the visual representation of an increase is not seen as easily.

For efficiency, we will use ratio tables in this lesson, but do feel free to draw a bar model if it helps you visualise the question and answer more clearly.

Let's have a look at a check.

I'm going to do the first one and then I'd like you to try the second.

Use a ratio table to increase 640 pounds by 3.

6% and we're not allowed to use a calculator.

Well for me, I'm going to use my ratio table and show 640 as 100%.

I like to work out 1% by dividing by 100, so I have six pound 40 as 1%.

Then multiplying by three and I have 3%, which is 19 pound 20.

Then I'm gonna multiply by two to give me 6%, which is 38 pounds 40.

Now from here, I'm going to divide my 6% by 10 because this will give me 0.

6%, which is three pounds 84.

Now if I sum the 3% and the 0.

6%, I have my 3.

6%, which is 23 pounds four pence.

So therefore, increasing 640 pounds by 3.

6% is simply adding our 640 to the 23 pounds four P, which gives me 663 pounds and four pence.

Now what I'd like you to do, I want you to use a ratio table or you can use another method if you prefer, but you are not allowed to use a calculator and I want you to increase 280 by 2.

8%.

See if you can give it a go.

Press pause for more time.

Great work.

Let's see how you got on.

Well, knowing that 100% is 280 pounds, we can work out 1% to be two pound 80, 2% is five pounds 60, that means 8% is 22 pound 40 and then I can work out 0.

8% to be two pounds 24.

Summing my 2% and 0.

8% gives me seven pounds 84.

So that means increasing 280 by 2.

8% is 287 pounds and 84 pence.

Well done if you got this one right.

Great work, everybody.

So now it's time for your task.

Using a ratio table or any other method, I want you to work out the following, but don't use a calculator.

See if you can give it a go.

Press pause one more time.

Great work.

Let's move on to question two.

"Lucas has worked out an increase of 410 pounds by 3.

4% to be 409 pounds and 56 pence.

Without calculating the answer, how do you know Lucas is incorrect?" See if you can give it a go.

Press pause one more time.

For question three, "Andeep says increasing 1,200 pounds by 4.

5% and then increasing it by another 4.

5% is the same as increasing 1,200 pounds by 9%." I want you to explain why Andeep is incorrect and work out the correct answer.

See if you can give it a go.

Press pause one more time.

Well done.

Let's go to our last question.

"A mathematician has his salary of 2000 pounds per month increased by 6%.

Now 60% of her new salary does pay for the bills, which is rent, et cetera, et cetera.

And a quarter of her salary is spent on food.

She does kindly donate 2% of her salary to a charity.

How much does she have left per month for savings?" See if you can give it a go.

Press pause one more time.

Great work.

Let's go through these answers.

Well, for question one, you should have got these answers.

A huge well done if you've got these answers.

For question two, how did you know that the answer is incorrect? Well, Lucas is increasing by a positive percentage, 3.

4%.

So the amount of money should be greater than the original value, so it should be greater than 410 pounds, not less.

For question three, well, Andeep is incorrect because after the first increase, there is now a new 100%, which is then increased by the 4.

5%.

You could show this using a ratio table perhaps.

Increasing by 4.

5% gives us 1,254 pounds.

Then increasing that by 4.

5% gives us a brand new 100%.

Remember in our ratio table.

So that means increasing it by another 4.

5% gives me 1,310 pounds 43 pence.

Now if you were to increase 1,200 by 9%, that's 1,308 pounds.

So you can see, increasing 1,200 by 4.

5% and then increasing by another 4.

5% is not the same as increasing 1,200 by 9%.

Question four.

Let's work out how much she has in her savings.

Well, there's salary increased by 6%, giving her 2,120 pounds.

Now from here, we need to work out 60% of this new salary.

So 60% of our 2,120 pounds is 1,272 pounds gone to bills, rent, et cetera, et cetera.

Then we know a quarter is spent on food.

So that means she spends 530 on food.

And we also know she kindly donates 2% to charity, so 42 pound 40 goes to charity.

That means, let's subtract all of these outgoings from her new salary and see how much savings she has.

2,120 is her new salary.

Subtract of 1,272, subtract of 530, subtract 42 pound 40, gives her 275 pounds and 60 pence savings per month.

Well done if you've got this one right.

Great work, everybody.

So let's have a look at increasing by a percentage using a calculator.

Now using a calculator to increase by a percentage is really straightforward.

For example, we're asked to increase 430 by 68%.

This is the same question as, "Find 168% of 430." So to do this, remember how to find percentages of a given amount is like finding a fraction of an amount.

So 168% to 430 is the same as 168 over 100 of 430.

Then we replace that word of with a multiply.

So we end up with 168 over 100 times 430.

Then we can use our knowledge on equivalent fractions and decimals.

We know 168 over 100 is the same as 1.

68 as a decimal.

So that means to work out 168% to 430, it's 1.

68 times our 430.

Don't forget when you put it into your calculator, it'll probably return it as a fraction.

Press format, select decimal, and it'll convert it into a decimal for you.

So that means we now know increasing 430 pounds by 68% gives us 722 pounds 40.

So we can use our knowledge of the fractional equivalent of a percentage to use a multiplier to find any increase.

Great work, everybody.

So let's have a look at our check question.

What I want you to do is work out the decimal equivalent to each of these percentages.

See if you can give it a go.

Press pause one more time.

Well done.

Let's see how you got on.

Well 126% is 1.

26.

189% is 1.

89.

154% is 1.

54.

103% is 1.

03.

102.

5% is 1.

025 and 105.

8% is 1.

058.

Massive well done if you got that.

Just remember to convert the percentage into the decimal equivalent, you simply divide by 100.

So very well done if you got this.

Now what I want you to do is match each question to the correct decimal multiplication.

See if you can give it a go.

Press pause one more time.

Well done.

Let's see how you got on.

Well, increasing 560 by 5.

6% is 560 multiplied by our 1.

056.

Find 113% to 560, 1.

13 times 560.

Increase 104.

4 by 8% is 104.

4 multiplied by our 1.

08, and find 104.

4% of eight, well, that would be 1.

044 times eight.

Really well done if you got these.

Now let's have a look at our last check.

I want you to use your calculator to work out the following.

I also like you to show you're working out.

Now to show you're working out using a calculator, you basically write down the calculation that you want to input into the calculator.

See if you can give it a go.

Press pause one more time.

Great work.

Let's see how you got on.

Well, increasing $3,845 by 23% is simply 3,845 multiplied by 1.

23.

This gives us $4,729.

35.

We're asked to increase 896 by 12.

5% so that would be 896 multiply by 1.

125, giving us 1,008 pounds.

We're asked to increase 560 by 1.

3%, 560 multiply by 1.

013.

Very good if you got this, which is 567.

28.

Lastly, work out 167.

2% of 847.

This would be 847 multiplied by 1.

672, which is 1,416.

184.

Notice how the wording was slightly different from the last one, but it's exactly the same question as increase 847 by 67.

2%.

So we're using the Casio fx-570/991 ClassWiz to increase by a percentage.

And remember scientific calculators are fantastic tools but only give the correct answer if the input is correct.

So it is important to carefully input the calculation in order to have the correct output answer.

What I want you to do is have a look at these calculations.

Which calculation correctly shows 457 increasing by 4.

5%? See if you can give it a go.

Press pause one more time.

Let's see how you got on.

Well, remember 104.

5% is the same as 1.

045 as a decimal because we're dividing the percentage by 100.

Therefore, C is the correct answer.

Well done if you got this.

Let's look at another check.

"Aisha correctly inputs this into her calculator.

Write a question that Aisha could be answering." See if you can give it a go.

Press pause more time.

Well done.

Well, some examples could be increase 895 by 3.

6%.

Another example could be work out 103.

6% of 895.

Now Jacob's spots a percentage function on the Casio ClassWiz.

And he says, "To work out an increase of 2.

8% of 780, the equivalent calculation is 102.

8% of 780." And he's correct.

So this is the same as 102.

8% times 780, and he can insert this into the calculator.

If you press 102.

8 and then go to catalogue and then Probability, you'll actually see a percentage symbol and then you select the percentage sign and then complete the rest of the calculation to show 102.

8% of 780, and that will give you the right answer.

But some calculators don't have this function but it's not a thing to worry about because the calculator has just simply done one thing, so that 102.

8% to make the right answer.

What do you think the calculator has done with that percentage sign? The calculator has simply converted it into a fraction, but we already know these equivalents and we know how to convert between a fraction, decimal, and a percentage.

So why would using decimal multipliers be more efficient? We'd have a little think.

Well, the decimal multipliers require less input into the calculator.

So using a multiplier is a little bit more efficient than using a fraction button or even the percentage sign in the calculator.

Now it's time for a quick check.

Explain why increasing 800 by 256% is the same as 800 multiply by 3.

56.

See if you can give it a go.

Let's see how you got on.

Well, it's quite hard to see but I'm gonna demonstrate in a bar model.

We know 100% is 800.

Now from here, if we're asked to increase it by 100%, this means we have another 100% which have illustrated here in yellow.

Now, if we're asked to increase this by another 100%, I can see here, I've got two lots of 100% which is indicated in yellow, and then I have to add my 56%.

And what you can see is this is an increase of 256%, but what percentage of 800 does all of this represent? Well, it represents 356%.

So that's why when we're asked to increase 800 by 256% we're actually multiplying 800 by 3.

56.

Bar models are such a powerful way to illustrate this.

Great work, everybody.

So now it's time for your check.

I want you to use a calculator to work out the following and make sure you show you're working out.

See if you can give it a go.

Press pause one more time.

Great work.

Let's move on to question two.

Here are two calculations from Jun's calculator screen.

Write a question that Jun could be answering for each calculation.

See if you can give it a go.

Press pause one more time.

Great work.

Let's have a look at question three.

"Aisha correctly inputs this into our calculator.

Write a question that Aisha could be answering." See if you can give it a go.

Press pause one more time.

Well, done.

Let's go to question four.

Using a calculator, I want you to work out the following, showing you're working out.

See if you can give it a go.

Press pause one more time.

Well done.

Let's go through these answers.

Mark these answers and press pause if you need more time to check.

Well done.

Question two.

Here are different examples.

We could say, increase 654 by 25.

8% or perhaps find 125.

8% of 654.

Some other examples for part B, increase 658 by 5.

8% or find 105.

8% of 658.

Well done.

For question three, here are some example questions.

Press pause if you need more time to mark them.

For question four, here are all our answers.

Massive well done if you've got these right.

Press pause if you need more time to mark.

Great work, everybody.

So let's have a look at the final part of our lesson, finding the original amount after an increase.

I think of a number and I increase it by 15%, and my new number is 55.

2.

What was my original number? Well, the new number indicates that the original number was 100% and then there was the increase by 15%.

So what I'm gonna do is just illustrate this as a total percentage, 115%.

So simplifying this, the questions actually asking me 115% of something is 55.

2.

Now remember, this word of can be exchanged for multiplication.

So that's the same as 150% multiplied by this number, gives me 55.

2.

Then knowing our equivalence, we know 115% is 1.

15, multiply by this number gives me 55.

2.

So that means to work out this number that I first thought of, I simply divide 55.

2 by 1.

15.

Thus, my original number was 48.

Finding the original amount after an increase can be easily found by using the inverse of multiplication.

In other words, division.

And knowing the multiplier for a percentage increase means you can undo the multiplication using division.

So what I want you to do is I want you to have a look at these questions and working out an answers, and I want you to match each one from each column.

See if you can give it a go.

Press pause one more time.

Well done.

Let's see how you got on.

Well, the amount has increased by 20% and is now 48 pounds is shown as this multiplier.

Something multiplied by 1.

2 because that's a 20% increase, equals 48.

Next, an amount has been increased by 50% and is now 48 pounds.

What was the original amount? Well, that has to be something multiplied by 1.

5 because that's the increase of 50% is 48.

Next one, the amount is increased by 60% and it's now 48 pound.

What was the original amount? Well, it has to be this calculation.

Well, rearranging it to find a.

Let's start with the top one, a times 1.

6 equals 48.

So that means a is equal to 48 divided by 1.

6, which is 30.

Next, a multiply by 1.

5 is 48.

So that means a is equal to 48 divided by 1.

5, which is 32.

Lastly, a times 1.

2 is equal to 48.

So therefore, a is equal to 48 divided by 1.

2, just 40.

Well done if you got this.

Now let's have a look at another check.

Using the calculator to help, I want you to work out the following.

"A shop increases its sales of chocolate bars by 25% and then now two pounds 25 pence per bar.

How much were they originally?" Next, "A hotel increases its prices per room by 11.

5% and a room now costs 223 pounds.

How much was it before the increase?" See if you can give it a go.

Press pause one more time.

Well done.

Let's see how you got on.

Well for A, we should have had the calculation being an amount multiplied by 1.

25 showing the increase of 25% is two pounds 25.

So to work out A, we simply divide, giving us one pound 80.

For B, well, we know the calculation would be the amount multiplied by 1.

115.

So therefore, to find A is 223 divided by our 1.

115, which is 200 pounds.

Great work, everybody.

So now it's time for your task.

I want you to work out the missing information from the table.

The first one has been done for you.

See if you can give it a go.

Press pause for more time.

Great work.

Let's move on to question two.

Here, we have two questions.

Read them carefully and give them a go.

Press pause for more time.

Well done.

Let's move on to question three.

We have some more questions here.

Read them carefully.

Press pause if you need more time.

Great work, everybody.

So let's go through our answers.

For our answers, here they are in the table.

Mark them and press pause if you need more time to see those answers and the working out.

For question two, here's our working out and here's our answers.

Great work.

Press pause if you need more time to mark your answers.

For question three, here's our working out.

Press pause if you need more time.

3B, here's our working out as well.

Great question.

Press pause if you need more time.

Fantastic work, everybody.

So in summary, we've looked at increasing an amount with and without a calculator using bar models, ratio tables, and multipliers.

Bar models are excellent visual aids, but do take a little while to draw.

Ratio tables are more efficient but they don't always show the increases clearly.

We know multipliers are excellent methods and are even more efficient when we're using a calculator.

For example, increase 460 by 12% gives us 460 multiply 1.

12.

We also know using multipliers allows us an easy approach to find the original amount given a percentage increase.

For example, a share increases by 23% and is now 307 pound 50.

How do we find out that original amount? Well, we simply divide that 307 pound 50 by 1.

23, which gives us 250 pounds.

Great work, everybody.

It was wonderful learning with you.

Well done.