Lesson video

Hi, everyone, my name is Ms. Chu and I'm really excited to be learning with you today.

We'll be looking at one of my favourites.

We'll be looking at multiplicative relationships.

And it's one of my favourites because it appears so much in real life.

I really hope you enjoy the lesson today.

So let's make a start.

Hi, everyone, and welcome to this lesson on increase by a percentage and it's under the unit understanding multiplicative relationships, percentages and proportionality.

By the end of the lesson, you'll be able to calculate percentage changes and in this lesson, we're going to focus on increase.

Now remember, proportion is a part-to-whole sometimes part-to-part comparison.

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

Today's lesson will be broken into two parts.

We'll be looking at increasing an amount by a percentage and then we'll be looking at using a multiplier.

So let's make a start on increasing an amount by a percentage.

In this lesson, we'll be looking at increasing an amount by a percentage.

However, before starting, it is important to know if it is possible to increase something beyond 100%.

Now, Izzy says to Laura, "You need to try harder, Laura.

Give it 110%." And Laura says, "That doesn't make sense, Izzy." Now why is Izzy's comment incorrect? Well, it's incorrect because the most effort you can give is a 100%.

Meaning, all your effort.

And although it's a common phrase used in sports coaching, 110% is impossible.

What 100% effort looks like can, of course, vary each day.

So what I want you to do is have a quick look at these different statements and I want you to think is 110% possible or not possible in each of these situations.

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

Great work.

So let's see how you got on.

Well, scoring 110% on an exam is not possible, as the maximum score is 100%.

A cost of a house increasing by 110%.

Now yes, it is possible because a house can cost beyond what it was originally bought for.

Now paying 110% of a debt back.

Unfortunately, paying 110% of a debt back is possible and in fact, it's usual to pay more than you borrowed in interest.

Being 110% older than you were when you started school.

Well, being 110% older than you were when you started school is possible.

If you started school age four, then you'll be 110% older if you were 8.

4 years old.

Please note the phrasing here.

If the statement said being 110% of the age you were when you started school, then it would be when you were 4.

4 years old.

Next statement, eating 110% of a cake.

Well, eating 110% of a cake is not possible as 100% would be all of the cake.

So now we know that there are some situations where we can increase beyond 100%.

Let's have a look at this bar model, it shows 600 pounds.

And if someone said, I'm going to give you 10% extra.

<v Narrator>How much would you have in total?</v> <v ->Well, dividing 100% into 10 equal parts</v> means we have 10%.

So knowing each part represents 10%, then we know each part is 60 pounds because we've divided 600 by 10.

Then simply adding 10% means we've added 60 pounds.

So that means, if someone were to give you an extra 10%, they've given you an extra 60 pounds.

So in total, you would have 660 pounds.

Now given that 600 pounds was our original 100%, what percentage of 600 pounds is now shown on the bar model? Now hopefully, you can spot it's 110%.

660 pounds is 110% of our 600.

So drawing a bar model really does help.

So let's draw another bar model together.

Firstly, using square or gridded paper, let's draw a bar model using 10 squares.

One, two, three, four, five, six, seven, eight, nine, and 10.

Now from our 10 squares, let's represent this as 240 pounds.

Now from here, I'm going to indicate it's 100%, so I'd like you to do the same.

Now I'm gonna ask, what percentage do you think each of the 10 squares represent? Hopefully, you can spot each 10 squares represent 10%.

But how much money is 10% of our 240 pounds? Well, it would be 24 pounds.

Now we know this, we can increase 240 pounds by 20%.

What do you think that looks like? Well, we're adding two 10 percents.

We know 10% is 24 pounds, so I'm adding two lots of 24.

Now how much do we have in total? Well, in total, there's our 240 pounds, which was our original 100% and here are our two 24 pounds.

Thus, giving me a total of 288 pounds.

So what percentage of 240 does 288 represent? Well in total, 288 pounds is 120% of our 240 pounds.

Well done if you've drawn this together with me.

So now what I want you to do is have a look at this check question.

I've drawn some bar models and we're missing some information.

See if you can fill in anything that you need in order to help you answer the question.

Take your time, press pause if you need.

Great work, everybody.

So let's see how you got on.

Well identifying 30%, let's identify 10% first.

Well, 10% has to be eight.

So given the fact that we've identified 30%, that means I've got three lots of eight, so 104 is 130% of our 80.

Now let's have a look at part B.

Remember, let's identify that 10%, 10% is seven.

So this would be six months of our 10%, which is 60%.

Adding this all together, that means we know 112 is 160% of our 70.

Great work if you've got this one right.

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

For example, how many different ways can you write work out 60% of 900? Have a little think and write some things down.

Well, I've got some examples here.

There are lots of different ways.

You could say, 0.

6 times 900.

We could say, 3/5 of 900.

We could say, 3/5 x 900 or we could even say decrease, 900 by 40%.

There are lots of different ways that we can represent the same question.

And it's the same with percentage increase.

I want you to look at the bar model and I want you to create some different questions where the answer is 48 pounds.

See if you can give it a go.

Press pause for a bit of time.

There are lots of different ways.

Here are just a few.

Increase 40 pounds by 20%.

That gives us an answer of 48 pounds.

You could be asked to work out 120% of 40 pounds.

That gives us an answer of 48 pounds.

Or you could be asked something is 120% of 40 pounds.

Same again, that gives us the answer of 48 pounds.

It's so important to know how these ask the same question.

So what I want you to do now is do a quick check question.

I want you to pair up the equivalent questions, see if you can give it a go, and press pause for more time.

Great work.

So let's see how you got on.

Increasing 500 by 45% is the same as working out 145% of 500.

Work out 120% of 45 is the same as increasing 45 by 20%.

Increased 20 by 45% is the same as workout 145% of 20, and workout 145% of 200 is the same as increase 200 by 45%.

Really well done if you got that one right.

What I'm gonna do now is I'm going to do a question and then from here, I'd like you to do the next question.

The question wants me to increase 20 by 30% and I can use a bar model to illustrate.

Well, first things first, I know my 20 represents 100%.

From here, I can identify 10% by simply dividing it into 10 equal parts.

So knowing 10% is represented by two, then increasing by 30%.

I have two and two and two, which is my 30%.

So thus the 30% represents a total of six.

Therefore, increasing 20 by 30% gives me an overall answer of 26, my 100% and my 30%.

Now what I'd like you to do and I want you to draw a bar model if it helps to work out 140% of 50, Well done.

Let's see how you got on.

Well, 50 represents 100%, so I identified 10% just because it's easier, so 10% is five.

Because we're trying to find 140%, I have 100% on the screen, but I need to find out what that 40% is or 40% is four lots of those 10%.

So that means adding them all together gives 140% of 50 is 70.

Massive well done if you got this one right.

Now let's have a look at a conversation between Jacob and Sofia.

Jacob says, "How would I increase 240 by 35%? My bar model only shows 10% parts." And Sofia says, "Easy.

Just find 5% by having 10%." And she's right.

So if you know 10% is 24, what do you think 5% would be? Well, 5% would simply be half of our 10%.

So that means 5% would be 12.

So now Jacob can find 35%.

And Sofia says, "How do you intend to do that?" Well, three lots of 10% make 30% and then add on that 5%.

From here, you can see the increase of 35%.

Sofia asks, "What's the answer when you increase 240 by 35%?" Well, it's 240 add our 24 times 3, add our 12.

Well done, Jacob.

So you can work out any percentage of an amount using a bar model and by finding 10%, 5%, and 1% is generally helpful.

So now what I'd like you to do is your check.

I want you to draw a bar model to help to work out 155% of 120.

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

Well done.

Let's see how you got on.

Well, this is my bar model showing 100% is 120.

I've shown 50% is five lots of our 10%, so five lots of our 12, and then I've worked out 5%.

Remember, 10% represents 12, so 5% is six.

Summing them all together, I've worked out 155% of 120 to be 186.

Really well done if you've got this one right.

Great work, everybody.

Now it's time for your task.

I want you to write questions and answers for the representations of these bar models.

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

Well done.

Let's move on to question two.

Question two says, "Drawing bar models show how you would work out an increase of 30% to 640, 125% of 900, and increasing 700 by 95%.

See if you can give these a go, press pause for more time.

Well done.

So let's have a look at these answers.

Well, for question one, what questions and answers did you work out? Some possible questions would be increase 40 by 50%.

Another question could be work out 150% or 40.

Another question could be what percentage of 40 is 60? And the answers would be 60, 60, and obviously 150%.

Really well done if you got this.

For B, your possible questions could be increased 200 by 57% or work out 157% of 200 or even what percentage of 200 is 314? And our answers would be 314, 314, and obviously 157%.

Great work.

For C, some questions could be increase 80 by 25%, work out 125% of 80, or what percentage of 80 is 100? Our answers would be 100, 100, and 125%.

Really well done.

For question two A, a bar model should look something like this, giving you an answer of 832.

For B, a bar model should look something like this, giving you an answer of 1,125.

And for C, your bar model should look something a little like this, giving you a final answer of 1,365.

Really good work if you've got this one.

Another really efficient method for C is to add 100% and subtract 5%.

If you've got that method, super well done, as this is a really efficient approach.

Great work, everybody.

So let's move on to the second part of our lesson where we'll be using a multiplier.

Now here, we have a double number line showing a 100% is 80 and we can extend the double number line to find percentages beyond 100%.

So let's look at working out 120% of 80.

Well, 120% would be around about here.

So how do you think we can find the value of 120% of 80? Well, if we know 10% is eight and 20% is 16, that means we can simply add 20% onto our 100%, thus making 120%.

Given the fact that we know 20% is 16, we simply add 16 to our 80, thus giving us 96.

Now there is another approach using that multiplicative relationship.

Can you spot it? What do you think we multiply 100 by to give 120? Well the multiplier would be 120 over 100, which is 1.

2.

So we multiply 100 by 1.

2, it gives 120% and if we multiply our 80 by 1.

2, it gives us our 96.

Using a multiplier is such an efficient way as we're only using one calculation to work out our answer.

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

Here, I've drawn you some double number lines and I want you to label the correct multiplier on these number lines.

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

Well done.

Well, let's have a look at the first one.

What do you think the multiplier is to change a 100 into 130%? That same multiplier must be applied to 120 to give 156.

Well, it has to be 1.

3.

Let's have a look at part B.

What do you multiply a 100% by to give 115%? And that same multiplier must be applied to 340 to give 391.

Well, you multiply by 1.

15.

Really well done if you've got these.

So removing the double number lines, can you work out the multiplier to increase any amount by 35%? Well, we simply multiply by 1.

35.

But can you explain how to quickly find this multiplier? Well given 35% as a decimal is now 0.

35 and 100% as decimal is one, summing them gives 1.

35.

That's a nice little way to identify the multiplier quite quickly.

Alternatively, you could have done 135 over 100, which gives you 1.

35.

Now, I want you to do as a quick check is identify the multipliers of the following.

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

Great work.

Well, if you increase anything by 40%, you multiply by 1.

4 or 1.

40.

Increase something by 34%, you multiply by 1.

34.

To increase something by 78%, you multiply by 1.

78.

Increasing by 16%, you multiply by 1.

16.

To increase by 4%, you multiply by 1.

04.

To increase by 200%, you multiply by three.

That was a good one well done if you got that.

And to increase by 2.

3%, you multiply by 1.

023.

Well done if you got this.

So using a multiplier and the associative law makes finding the percentage of an amount so much easier without a calculator.

For example, increase 48 by 32%.

Well first of all, we're going to multiply 48 by 1.

32, and then from here, we're going to use our associative law.

This is the same as 48 multiply by 132 times 0.

01.

I'm going to use the area method to work out 48 multiply by 132, which working this out gives me 6,336.

Now that means I know 6,336 times 0.

01 is going to be my answer.

So working this out, I've got a final answer of 63.

36.

So increasing 48 by 32% is 63.

36.

Notice how I did this entire calculation using multipliers and that associative law.

Now what I want you to do is your task.

I want you to match the calculation with the question.

See if you can give it a go.

Press pause if you need more time.

Well done.

Let's move on to question two.

Question two wants you to work out the amount of money when 640 pounds has been increased by 41%.

Question three wants you to work out 138% of 700.

And question four says, "Aisha tries to increase 40 pounds by 5% by working out 40, multiply by 1.

5.

Explain why she's incorrect and correctly work out the answer." See if you can give this a go.

Press pause if you need more time.

Great work.

So let's move on to our last question, question five.

Question five says, "Three of the towers A to F have been made 10% taller.

Three of the towers have been made 10 centimetres taller, which is which and how do you know? Now seventh towers made 10% taller and this also increases the height by 10 centimetres." For B says, "How tall is the tower now? And how about a tower that's made 5% taller and grows by five centimetres or a 17% taller and grows by 17 centimetres.

Can you explain these answers?" This is a great question.

See if you can give it a go.

Press pause if you need more time.

Well done.

So let's go through these answers.

Well, for question one, hopefully, you've matched all of these questions with the corresponding calculations.

Well done.

For question two, increasing 640 by 41% gives you 902 pounds 40.

138% of 700 is 700 multiply by 1.

38, which is 966.

And unfortunately, Aisha has worked out an increase of 50%, not 5%.

And working out that correct answer, you should have had 42 pounds.

Very good if you got those.

And for question five, which is which? Well, A, B, and E have been made 10% taller, C, D, and F have been to made 10 centimetres taller.

All of these 10 centimetre changes are identical.

Whilst the 10% growth varies according to the height of the original tower.

And for B, well, if 10% growth results in a 10 centimetre growth, the original tower must be 100 centimetres tall.

This is true for all the percentages asked and the original tower in each case must be 100 centimetres tall.

Great work, everybody.

So let's summarise what we've done in this lesson.

Understanding the context of the question tells us if we can increase anything beyond 100%.

And if an increase is possible, double number lines, bar models are really helpful visual approaches to work out the increase.

And it is important to remember the same question can be asked but in different ways.

For example, increased 70 by 12% is the same as 112% of 70.

Lastly, we've used a decimal multiplier and using a decimal multiplier can be a good approach to work out a percentage increase.

Fantastic work, everybody.

It was great learning with you.