Lesson video

Hiya, my name's Miss Lambell.

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 Part.

And this is within the unit: Understanding Multiplicative Relationships of Ratio and Fractions.

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

Two words that we'll be using and considering in today's lesson are proportion and ratio.

Remember, variables are in proportion if they have a constant multiplicative relationship.

And we'll be using that word a lot this lesson, multiplicative relationship.

A ratio shows the relative sizes of two or more values and allows you to compare a part with another part in a whole.

I've decided today to divide our lesson into two separate learning cycles.

In the first one, we will concentrate on using a bar model to solve problems where we know one part in the ratio and we need to find other parts.

And in the second learning cycle, we will consider exactly the same thing, but we will look at using a ratio table to do this.

Let's get going on that first learning cycle.

Like I said, in this one we are going to be concentrating on using a bar model, which you are super good at.

Here we go.

Sofia is making some bracelets.

She will use white and black beads in the ratio of 1 : 6.

She says that she's going to use three white beads.

And Jacob says, "How many black beads will be on each bracelet then?" Then let's represent this with a bar model.

Here's our bar model, so we've got the ratio of white to black is 1 : 6.

So we've got one part for white and six parts for black.

Remember, each part has to be equal in size.

If you're drawing it out, it doesn't matter too much, just as long as you remember they should be equal in size.

Sofia says that she's going to use three white beads, so we need to assign the three to the correct place in the bar model, which is for the white.

There's only one box, so therefore it's got one part, and we know that that part is equal to three.

Each part in the bar model represents an equal part.

This means that three needs to go in all of the parts of the ratio.

We wanted to find out, or Jake wanted us to find out, how many black beads we were going to be using.

Well, we've got six parts.

Three in each part would be six multiplied by three, which is 18.

So we're going to use 18 black beads.

Do we need to find the total number of beads? No, you are right, we don't.

The question didn't ask us to find the total number of beads.

Jacob just wanted to know how many black beads there will be.

And the answer to that is that each necklace will have a total of 18 black beads.

We'll now look at another problem, we've got flowers here.

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

There are six red flowers, how many yellow flowers are in the bunch? Let's represent that with a bar model again.

And we know that red is three parts, looking at the ratio, and the yellow is five parts.

So remember the order in which those colours come in the question is the same as the order in the ratio.

So red is three and yellow is five.

There are six red flowers, where do I need to put that six? Yes, you're right, above the bars that represent the red.

We need to take that six and divide it by three, meaning it's two in each part.

The parts are the same, remember, so therefore it's gonna be two in all the parts.

The question says, how many yellow flowers are there in the bunch? The total number of yellow flowers is going to be five multiplied by two, so there are 10 yellow flour in the bunch.

Now let's move on to looking at this problem with a cookie recipe.

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

You use 60 grammes of flour, how much butter is used? So that's what we need to work out.

If I'm using 60 grammes of flour, and I want my cookie to turn out correctly, how many grammes of butter do I need? Here's my bar model, flour, butter, sugar, 3 : 2 : 1.

I know that I'm using 60 grammes of flour.

I need to take my 60 and divide it by 3, because we are using three parts of flour, that's 20 grammes, and then remembering it's the same for all of them.

And the question wanted to know how much butter we were going to use? So we've got here 2 parts, each with 20 grammes of butter, we're going to be using 40 grammes of butter.

Each cookie will have 40 grammes of butter.

Now you are gonna have a go at this check for understanding.

I'd like you please to spot the mistake.

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

There are 100 blue cars, how many red cars are there? Here's my bar model.

You are gonna pause the video, you are going to spot the mistake, and once you've spotted it, you can come back to me, and then we'll check and see if you've got it right.

But we know you will, because you're super good at bar models.

You can pause the video now.

Okay, so what was the mistake? The mistake was the hundred had been put in the wrong place.

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

And also, they found the total number and not the number of red cars.

So there are actually two mistakes in there.

Did you spot two? I didn't tell you there were two, but I'm sure you did.

It's really, really important to make sure that we assign the number or the value given in the question to the correct part of the bar model.

Otherwise we're gonna end up with answers that aren't right.

Here is another common mistake that's made with ratio problems. Can you spot it? We've got the ratio of red to blue cars in a car park is 5 : 3.

There are 120 red cars, how many blue cars are there? So this person here, and I think it's Sofia, has shown her working out.

She's not drawn a bar model, she's worked out the steps.

I'd like you please to pause the video and come back when you've worked out what mistakes Sofia has made.

Pause the video now and come back when you're ready.

What did you come up with? 120 is not the total number of cars.

Always using the given number, so the number given in the question, as the total is a common mistake.

Drawing and labelling a bar model correctly can help you to check you are working out the correct part.

So here Sofia decided to add together the numbers in the ratio to do the division and then to do the multiplication.

But she'd assumed that the 120 was the total number of cars.

But if we read the question carefully, we know that 120 was actually the red cars.

It's really important you take care when reading the question and then assigning the value to the correct part of the bar model.

Now we can have a go at one together and then you independently can have a go at the one on the right hand side.

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

Aisha has 25 sweets, how many sweets does Lucas have? Our bar model, representing Lucas with seven parts and Aisha with five parts.

We know Asia has 25, so we know that we need to represent the 25 Aisha's bars.

Aisha has five parts, we're gonna divide that by five, meaning we put five into all of them.

And the question wanted us to know how many Lucas had? Lucas has seven lots of five, Lucas has 35 sweets.

Now it's your turn.

Lucas and Aisha share a packet of sweets in the ratio 4 :7, so the ratio has changed.

Lucas has 16 sweets.

How many sweets does Aisha have? Please now pause the video and come back.

I'll be waiting here to check your answer when you get back.

Great work, how did you get on with that? You drew a beautiful bar model and made sure that you assigned the 16 to Lucas, I hope? 16 was for Lucas, Lucas was 4 parts.

16 divided by 4 is 4, 4 in each part.

Aisha had seven parts, so seven lots of four, 7 multiplied by four is 28.

I'm sure you got that right.

Aisha has 28 sweets.

You are now ready to have a go at the first question of task A.

Here I have given you a ratio and I have given you one part, and what I'd like you to do is to draw out a bar model, make sure to take care that you are assigning the value given for A or B in the correct place.

And then I'd like you to find the missing one.

So if I've given you A, I want you to find B.

And if I've given you B, I'd like you to find A, you are ready now to have a go at these.

I have every confidence you're gonna get all of these right.

Pause the video now and I'll be here when you get back.

Great work.

Now we'll have a look at question number two.

Question number two, again, I'd like you to use a bar model to answer these.

We've got a question about sharing sweets, a question about a triangle, and then the good old cookie question at the end.

Pause the video now and when you come back we can check those answers.

Good luck.

Great work, now let's check the answers.

1st in the table B was 18, the second one, B was nine.

The 3rd you were missing A, and that was 12.

The 4th, A was 52, the 5th, A was 12.

The 6th you were missing B, and that was 36.

The 7th you were missing B, and that was 432.

And then in the last line you were missing A and that was 100.

Well done if you got all those right, I'm sure you did.

And then onto question number two.

We wanted to know how many do Andeep and Sam get? We were given how many Sofia had.

Andeep had 9 sweets and Sam had 24 sweets.

In B, we were wanting to work out the length of the other two sides.

We were given the shortest side and we wanted to find the length of the other two.

And they were 21 centimetres and 18 centimetres.

And then C, we wanted to know how much butter and sugar, we were given the amount of flour.

We needed 300 grammes of butter and 150 grammes of sugar.

Did you get those right? Super.

Now we'll move on to looking at using a ratio table to find one part.

So same questions or similar questions to the ones we've been doing in that first learning cycle, but using a ratio table.

So thinking about efficiency, because drawing out a bar model sometimes may take a lot of time, and also, if there are lots of parts in the ratio, it can be quite inefficient and time consuming.

Let's go then.

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

Sofia wants to make a jug of the drink.

She has 600 millilitres of orange juice.

How much lemonade does she need? Here's my ratio table, we've got our orange juice and lemonade in the ratio of 3 : 7.

We know that we've got 600 millilitres of orange juice.

Where's that 600 going to go? That's right, underneath the three, 'cause that's the orange juice column.

We are then looking for the multiplicative relationship, so remember I said when we looked at those keywords we were gonna be considering that a lot? The multiplicative relationship between 3 and 600.

And that's multiplied by 200.

So we need to also multiply the lemonade by 200, which is 1,400.

We need 1,400 millilitres of lemonade.

Lucas and Aisha raised some money doing a sponsored silence.

Well done, Lucas and Aisha.

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

Charity A gets £80 pounds.

How much money did charity B get? So we'll draw our ratio table.

With charity A and charity B in the ratio of 4 : 5.

Charity A gets £80, so we're gonna put 80 in the charity A column.

And again, that multiplicative relationship between 4 and 80.

Yes, that's right, you've got it.

It's multiplied by 20, well done.

If we multiply charity A by 20, we also need to multiply charity B by 20.

And 5 multiplied by 20 is 100.

Charity B got £100.

We're back to Sofia now, and she's making some different bracelets.

So she was making bracelets earlier, I think it was black and white beads.

We're now making bracelets with red, blue, and white beads, and those beads are in the ratio of 2 : 7 : 5.

She uses 14 blue beads.

How many red and white beads does she use? Let's set our ratio table up.

We've got red, blue, white, and we know that there are 14 blue beads.

So let's get that 14 in the right place.

What's that multiplicative relationship? Multiply by two.

So I multiply the red by two and the white by two as well.

So 4 red and 10 white.

Each necklace will have 4 red and 10 white beads, including, obviously, the 14 blue beads as well.

Now we're ready to have a go at some questions.

We'll do the one together on the left hand side and then I'll know you be ready to do the one on the right hand side independently.

Let's do this first one together.

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

There are 48 black cars.

How many red and blue cars are in the car park? We'll set this up the ratio table with our ratio of 8 : 5 : 12, making sure that we've got the order correct, and that is a total of 25.

We know that there are 48 black cars, so we need to put the 48 underneath the 12, because that's the part of the ratio that is showing us the black cars.

Now we need to look for that multiplier.

What is our multiplicative relationship between 12 and 48? And that is multiplied by four.

So to go from the top row to the bottom row, we multiply everything by four.

Now we know that there would be 32 red cars and 20 blue cars.

So in the carpark in total there are 32 red cars and 20 blue cars.

Now why didn't I find the total number of cars? That's right, because the question didn't ask me to find the total.

Here I could find the total by adding together this total number of red, blue, and black cars or I could have used that multiplicative relationship.

Now you are ready to have a go at one of these independently.

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

This time though there are 35 blue cars.

How many red and black cars are in the carpark? Pause the video, come back when you've got your answer.

Good luck.

And let's check, we make sure that we are putting the 35 in the correct place, that needed to go in under the blue cars.

So our multiplicative relationship between 5 and 35 was multiplied by 7.

So I multiply the others by seven, meaning there are 56 red cars and 84 black cars in the car park.

Well done on that.

Now you can have a go at this task.

You are going to use a ratio table to find either A or B given the ratio.

So if I've given you A, I'd like you to find B and vice versa.

Good luck with these.

You may use the calculator.

I'll be here waiting when you get back, you can pause the video now.

Great work, now we can move on to question number two.

And here it is.

So we've got some sweets, we've got a triangle, and we've also got the good old cookie recipe question.

Pause the video, have a go at these, and then when you get back I'll be ready.

Remember to try and use your ratio table to answer these questions.

Good luck.

You can pause that video now.

Great work, let's check those answers.

Question 1, B was 27, 2, B was 18, and the 3rd, A was 48.

The 4th, A was 180.

And the 5th, A was 600.

The 7th, B was 36.

And the 2nd to last 1, B was 3802.

5.

And in the final 1, A was 27.

2.

How did you get on with those? Great work.

And now the answers to question number two.

Part A, Andeep got 15 sweets and Sofia got 25 sweets.

Part B, the other sides were 12 centimetres and eight centimetres.

And then our cookie question, we needed 189 grammes of flour and 63 grammes of sugar.

Well done if you've got all of those right.

I'm sure you did.

You've worked really, really well today.

And now we're ready to summarise our learning.

During this lesson we have been looking at, given the ratio and one part determining the other part or parts.

We firstly looked at using a bar model to do this.

Remember, the most important thing is that you make sure you assign the value in the question to the correct part of the bar model.

And there's an example there, the example we went through, about the red and the yellow flowers.

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

And remember, when we're using a ratio table, we are looking for that multiplicative relationship between the two rows in the ratio table.

Really enjoyed working through this with you today and I'm so glad that you decided to join me.

I look forward to seeing you again soon, bye.