Lesson video

Hiya, my name's Miss Lambele.

I'm really pleased that you've decided to join me today to do some maths.

I'm really looking forward to working alongside you.

Welcome to today's lesson.

The title of today's lesson is determining the whole, and this is within our unit: understanding multiplicative relationships with fractions and ratios.

By the end of this lesson, you'll be able to determine the whole, given 1 part and the ratio.

Here are some keywords that we'll be using in today's lesson and they are proportion and ratio.

If you need a quick recap of what those are, I suggest you pause the video and have a read through them.

And then when you are ready, you can come back and we'll get going with today's lesson.

Today's lesson, I split into two separate learning cycles.

In the first one, we are going to look at using a bar model to solve some ratio problems. And in the second learning cycle, we will look at using ratio tables to solve some problems. We can get going now then on that first learning cycle: using bar models to solve ratio problems. Now we know we love bar models because they're really useful for helping us to solve lots and lots of different problems. Let's get going on this first learning cycle.

Here we've got Lucas and Aisha.

Lucas is making some necklaces.

He will use black and white beads in the ratio of 4:1.

We know what that means.

It means every time he puts 4 black beads onto the necklace, he's going to put 1 white bead.

He says he's going to use 4 white beads and Aisha says, "How many beads will be on each necklace?" Let's take a look at that.

We're gonna draw bar model.

We've got our black beads and our white beads in the ratio of 4:1.

Now remember, each of the parts must be the same size.

We know that Lucas is going to use 4 white beads.

So I need to put my 4 alongside the white bar.

Each part of the bar model represents an equal part, remember.

So therefore, 4 needs to go in all parts of my bar model and there they are.

Do you need to find the total number of black beads? Well, no, we don't because we want to know how many beads are gonna be on each necklace.

The whole necklace is going to be 5 parts and each part has 4 beads.

So therefore, that is a total of 20 beads.

Each necklace will have a total of 20 beads.

A bunch of flowers contains red and yellow flowers in the ratio of 3:5.

There are 9 red flowers.

How many flowers are there in the bunch? Let's draw our bar model.

So we need to represent a ratio of 3:5: 3 for the red and 5 for the yellow.

Remember, they are equal parts.

We know that there are 9 red flowers.

Where do I need to put that 9? I need to put it over the red bar because that's 9 red flowers.

I'm now going to divide that by 3 because I've put the 9 over 3 parts, meaning that 3 is gonna go in each part.

All parts are equal.

So 3 will also go into the yellow parts.

I want to know how many flowers are in the bunch.

So that's the total number of flowers.

Therefore, it's 3 multiplied by 8, which is 24.

There are 8 boxes, each containing 3.

There are 24 flowers in total in the bunch.

Now we'll take a look at a different example.

The ratio of flour to butter to sugar in a cookie recipe is 3:2:1.

You use 45 grammes of flour.

How heavy will the cookie be? Here's our bar model.

So we've got flour, 3 parts; butter, 2 parts; sugar, 1.

We know that we are using 45 grammes of flour.

So we need to assign the 45 grammes to the flour bar.

We now need to divide that into 3 equal parts, giving us 15, so 15 in each part for flour.

But remember, each part in the ratio is also equal in size, so 15 in each of the other boxes.

We want the w8 of the whole cookie and the whole cookie is represented by 5 parts.

So we multiply 5 by 15 grammes.

The cookie will weigh 90 grammes.

Your turn now.

I'd like you to spot the mistake.

The ratio of red to blue cars in a car park is 5:2.

There are 30 blue cars.

How many red and blue cars are there in total? Here's the bar model.

Pause the video.

Decide what you think the mistake is.

And then, come back when you're ready.

What did you come up with? 30 has been put in the wrong place.

It was the number of blue cars and not the number of red cars.

It's super important that that value is assigned to the correct part of the bar model.

We are gonna have a go at question together on the left.

And then, you'll be ready to have a go at 1 independently on the right hand side.

Let's take a look at this first 1 together.

Lucas and Aisha share a packet of sweets in the ratio of 7:5.

Aisha has 30 sweets.

How many sweets were in the bag? So here's my bar model, representing Lucas and Aisha.

Notice because Lucas was mentioned first, then he is the first part shown in the ratio.

So Lucas has 7 parts and Aisha has 5 parts.

Aisha has 30 sweets.

So we need to put the 30 with Aisha.

We need to take that and we need to divide it by 5 because Aisha has 5 equal parts, giving us 6.

6 goes into all of the boxes and we want to know how many sweets were in the bag.

So we can see that we've got 12 parts in total with 6.

So therefore, the bag contains 72 sweets.

You are ready now to have a go at this one.

Lucas and Aisha share a packet of sweets in the ratio of 4:7.

Lucas has 28 sweets.

How many sweets were in the bag? Off you go.

Come back when you're ready.

You can pause the video now.

Great work, let's check and see if you've got it right.

I'm sure you did.

This time, we knew that Lucas had 28 sweets.

So we've assigned the 28 to Lucas.

We divided that by 4 because Lucas had 4 parts.

That gave us 7, 7 in each part.

And then in total, there were 11 parts.

So 11 multiplied by 7, there were 77 sweets in the bag.

Now you are ready to have a go at some independent tasks.

You're going to use the bar model to find the total amount.

Pause the video and when you are done, I'll be here waiting for you to move on to the next set of questions, good luck.

And now let's move on then to the next set of questions.

Again, pause the video and when you're done, come on back.

Okay, so in those 1s, I was super kind and I gave you the bar models.

You're on your own now.

I'd like you to draw your own bar models to answer these questions.

Pause the video and I'll be here when you come back to check all those wonderful answers that you've got.

Great work, now let's check our answers.

Number one, a, was 24; b, 27; c, 44; and d, 117; e, 42; f, 120; g, 528; and h, 275.

And then, how did you get on it drawing your own bar models? A was 64 sweets, b was 119 centimetres, and c was 270 grammes.

Well d1 if you've got all those right.

But like I said, I'm sure you did because you're super good at using bar models.

We're now gonna look at the same type of problems, but how we would use a ratio table to solve the problem.

The ratio of orange juice to lemonade in a drink is 3:7.

Sophia wants to make a jug of the drink.

She has 750 millilitres of orange juice.

How much drink will she make? So we've assuming here that she's got as much lemonade as she needs and we want to make sure that the drink tastes just right.

So we need to make sure that it stays in the ratio of 3:7.

Here's my ratio table.

We've got our orange juice and we've got our lemonade.

The total is 10.

We know that we've got 750 millilitres of orange juice.

So I need to put my 750 in the orange juice column.

No surprises there.

We are then looking for that multiplicative relationship between those.

What is the multiplicative relationship between 3 and 750? Remember, if you're not sure, we can just do 750 divided by 3 and we get that the multiplicative relationship is 250, means we need to multiply.

To get from the top line to the bottom line, we need to multiply by 250, giving us 2,500.

She'll make 2,500 millilitres of the drink.

Different problem now: Lucas and Aisha raised some m1y doing a sponsored silence.

Very good, Lucas and Aisha.

They split the m1y between two charities in the ratio of 4:5.

Charity A gets 60 pounds.

How much money did they raise in total? So we are looking for how much money did they raise in total and we know the value of one of the parts of the ratio.

We've got Charity A, Charity B in the ratio of 4:5.

That gives us a total of 9.

Charity A gets 60 pounds, so I need to put my 60 here.

Remember, we're then looking for that multiplicative relationship between these.

Now I know that that is multiplied by 15.

If I wasn't sure though, I could do 60 divided by 4 and that would give me 15.

So to go from the top line to the bottom line, I need to multiply by 15, giving 135 pounds.

Lucas and Aisha raise 135 pounds.

For charity, they've d1 fantastically there, haven't they? I wonder if you've ever done a sponsored silence.

We're back with Lucas now and he's making some different necklaces with red, blue and white beads this time in the ratio of 2:7:5.

He uses 21 blue beads.

How many beads are on each necklace? Let's take a look.

Let's put this into a ratio table.

We've got our red, blue, and white in the ratio of 2:7:5.

That is a total of 14 parts.

I know that Lucas is going to use 21 blue beads.

I need to put the 21 in the correct place and that's blue.

And then looking for that multiplicative relationship.

So I need to multiply the total by 3 as well.

14 multiplied by 3 is 42.

Each necklace will have 42 beads.

Let's do one together and then you can have a go at one independently and if you get that right, you'll be good to go on the next task, let's go.

The ratio of red to blue to black cars in a car park is 8:5:12.

There are 96 black cars.

How many red, blue, and black cars are there in total? Ratio table, red, blue, black, 8:5:15, sorry, 12.

The total of those is 25.

We know that there are 96 black cars, so we need to make sure that 96 goes in.

In the black cars, my multiplier is 8, so I need to multiply 25 by 8 to give me 200.

There are 200 red, blue, and black cars in the car park.

Now you are ready to have a go.

The ratio of red to blue to black cars in a car park is 8:5:12, so exactly the same ratio.

This time I'm telling you that there are 30 blue cars.

I want you pleased to work out how many cars there are in total.

By all means, use a calculator just to speed this up, but do make sure you write down all of the steps that you are putting into your calculator.

Good luck with this.

You can pause the video.

I'll be here waiting when you get back.

Let's take a look.

I'm sure you've got this right.

We've got here.

We've got blue was 30, my multiplier to take me from 5 to 30 was 6, 25 multiplied by 6 is 150.

There were 150 red, blue, and black cars in the car park.

You are now ready to have a go at this task.

What I'd like you to do, please, is to find the total given either A or B.

So you can draw out your ratio table, the ratio is given to you in the first column.

I've given you either A or B, and I want you please to find the total.

Good luck, come back when you're ready.

I'll be here waiting for you.

And onto question two, we're going to use a ratio table to solve these three problems. We've got Andeep, Sam, and Sofia with some sweets.

We've got a triangle and then we've got the cookie recipe back again.

Good luck with these.

I look forward to seeing you when you come back.

Great work.

Let's take a look at the answers.

Here are the answers to question number one.

First one was 36, then 54, 176, 405, 2100, 120, 4647.

5, 74.

8.

How did you get on with those? You got them all right? Of course you did.

You didn't need to find those numbers in grey, but they are here just in case you did.

So you may have decided that you were gonna find all of the missing values in a table, and if you did, those were the missing values, okay? But that was not what I asked you to do.

So it's absolutely fine if you've not done those.

If you have, just pause the video and then come back when you've marked those answers.

And the answers to question number two, a, there were 80 sweets in total; b, the perimeter of the triangle is 34 centimetres; and c, the cookie would be 378 grammes.

We can now summarise our learning from today's lesson.

Firstly, we looked at using a bar model to determine the whole.

Really important, we make sure that we assign the number given to us in the question to the correct part of the bar model.

So in this example, we needed to make sure that we assigned the 45 to the flour bars because we were told we have 45 grammes of flour.

We then looked at maybe a more efficient way to determine the whole is to use a ratio table.

It's really important that you put the value given to you in the question in the correct column, 'cause if you put it in the wrong column, you're going to make a mistake.

So here we were told there were 21 blue beads.

We then looked for that multiplicative relationship between 7 and 21, which was 3.

And then I can multiply the total by 3.

14 multiplied by 3 was 42.

Super work today, well done.

I've really enjoyed looking through solving these problems using the bar models and the ratio tables.

We can now divide in a ratio.

We can also determine the whole.

Fantastic work, well done, like I said.

And goodbye, I look forward to seeing you again really soon.