Lesson video

Hello, how are you today? My name is Dr.

Shark.

I am so excited to be learning with you.

You have made a great choice to learn maths with me today.

I am here to guide you as we move through the learning.

Welcome to today's lesson.

This lesson is from our unit: Measures: mass and capacity.

The lesson is called Solve Problems Involving Volume.

We are going to look at lots of different scenarios related to volume and think about how we can use the bar model to help us solve the problems. Sometimes new learning can be a little bit tricky, but I am here to guide you and I know that if we work really hard together, we will be successful in our learning.

In our learning today, we will start by looking at solving problems which involve the additive relationship.

In the lesson today, we have these characters who will help us, Aisha, Sophia, Jacob, and Andeep.

When we are given a word problem to solve, first of all, it's really important that we visualise it so we think of a picture of it to show where we can see the maths in the real world.

After we have done that, we then need to represent the word problem mathematically.

So this is where the bar model comes in and this will support us to solve the problem.

Let's look at this problem.

Jacob drinks a glass of juice.

He also drinks a cup of tea.

Can you visualise that? What do you see? In your head, can you see a glass of juice? Can you see a cup of tea? I can see something that looks like this.

I wonder what the question might be.

Have you got any thoughts? The question is: What volume of liquid has he drunk in total? So Jacob is asking what further information we need to be able to answer this.

Do you know? That's right.

We will need to know the volume of juice in the glass and we will need to know the volume of tea in the cup before we can then find the total volume.

To find the volume of juice, Jacob could pause it into a measuring jug.

What do you notice? Could you tell me what the volume of the juice is? That's right.

Jacob is telling us the juice reaches the 250 millilitre mark.

So the volume of juice in the glass is 250 millilitres.

Jacob pours the tea from the cup into a different jug that will help him measure its volume.

There we go.

What do you notice this time? That's right.

We're gonna have to work out the value of the unmarked parts.

So Jacob is telling us there are 10 equal parts in between that marked interval of 100.

So each part must be worth 10 millilitres.

The tea reaches the end of that ninth part.

So the volume of tea in the cup is 90 millilitres.

So let's remind ourselves of the problem.

Jacob drinks a glass of juice.

He also drinks a cup of tea.

What volume of liquid has he drunk in total? So now we know the volume of liquid in both containers, so what do we need to do? Ah, thank you Sophia.

Yes, we need to represent this mathematically.

One of the ways that we can represent problems is to use a bar model.

A bar model is made up of a whole and parts.

And depends on the problem, the parts may be the same or different and there may be two or more parts.

And if we can identify the parts and wholes in our problem, it helps us to understand the structure of the problem and then it helps us know how to solve it.

Let's represent our problem in a bar model.

If you can remember, our problem is about Jacob drinking a glass of juice.

Well, we're not sure at the moment with that piece of information if the glass of juice is the whole or a part.

We need to read on.

He also drinks a cup of tea.

So now we've got two objects, but again, we need a little bit more information.

What volume of liquid has he drunk in total? Ah, that tells us, doesn't it? That word total, it tells us we need to find the whole.

So the glass of juice will be a part, and 'cause he also drinks a cup of tea, that word also tells us that we have another part.

Whilst we've got our bar model, we can use it to help us know what to calculate and how.

We can see that we've got two parts, the volume of juice and the volume of tea.

And we need to find the total volume drunk.

We know from measuring the volume that the volume of juice is 250 millilitres and the volume of tea is 90 millilitres and we need to find the whole.

Let's check your understanding.

I wonder if you can represent this problem in a bar model.

Jacob drinks 350 mls of orange squash.

He then drinks 225 mls of water.

What is the total volume of liquid that he has drunk? Remember, try and visualise this first.

What picture do you see in your head? Pause the video.

When you're ready to look at the answer, press play.

How did you get on? This is how I represented it.

I've got two parts, the orange squash and the water, 350 millilitres and 225 millilitres.

I need to find the total volume.

So that is the whole.

So let's revisit our problem.

As a reminder, Jacob drinks a glass of juice, he also drinks a cup of tea and we want to know what volume of liquid he's drunk in total.

We're gonna use the bar model to identify the calculation we need to solve it.

We know we've got two parts.

We've got the 250 millilitres and the 90 millilitres, and we have to find the total.

So we need to find the whole.

The parts are different.

So when the parts are different, we can use our additive relationships to find the whole.

So to find the whole, we need to add the known parts together.

250 millilitres add 90 millilitres.

I'm going to partition my 90 millilitres into 50 and 40 because 250 add 50, I know makes 300.

Then I can add the other 40 on.

So it's 340 millilitres.

So the total volume of liquid that Jacob drinks is 340 millilitres.

Let's check your understanding.

Look at the bar model.

What is the total volume drunk? Pause the video, maybe find someone to discuss this with.

Have a go at working it out.

And when you are ready, press play.

How did you get on? Did you notice the parts are different? So to find the whole, we need to add the known parts together.

350 millilitres and 225 millilitres, I'm going to partition that 225 into 200 and 20 and 5.

So 350 add 200, is 550.

Then I've got another 20, so 570, and another 5.

575 millilitres.

The total volume drunk was 575 millilitres.

How did you get on with that? Well done.

Time for you to practise now.

For question one, could you solve these problems by drawing them so that it helps you visualise the maths? Also represent them as a bar model and then identify the calculation.

So part a, Sophia has a tin of paint with 3 litres 150 millilitres in it.

Jacob's tin of paint has 650 millilitres in it.

What volume of paint do they have in total? And for part b, Aisha's bottle of water contains 750 millilitres.

This volume is 250 millilitres more than that in Andeep's bottle.

What volume of water is in Andeep's bottle? For question two, I'd like you to write your own problem related to volume that involves additive relationships.

Then solve it by drawing it to help you visualise the maths, representing it as a bar model and identifying the calculation.

You have two questions to have a go at.

Pause the video and when you are ready to see the answers, press play.

How did you get on? Let's have a look.

So the first question you were asked to look at was about Sophia and Jacob's paint and you might have drawn a picture of two paint tins, one for Sophia and one for Jacob.

And Sophia's would've been larger than Jacob's.

You might have drawn a bar model like this and then solved the problem.

I could see that I had two parts and so I added the parts together so that I could find the whole.

To help me add, I partitioned the 650 millilitres.

I added the 50 millilitres on first.

So I had 3 litres 200 millilitres, and then I added the remaining 600 millilitres to give me 3 litres 800 millilitres.

So they had 3 litres 800 millilitres volume of paint in total.

How did you get on? Well done.

For question two, you had a problem about two bottles of water.

I drew a picture of two bottles to help me.

Andeep's bottle was slightly smaller than Aisha's bottle.

I then drew a bar model like this to help me solve the problem.

I could see I had the whole and a part.

So to find the missing part, I needed to subtract the part we know from the whole.

750 subtract 250, well, I partitioned the 250, so I subtracted 200 first to get 550, and then I took off that 50 millilitres to get 500 millilitres.

So the volume of water in Andeep's bottle is 500 millilitres.

How did you get on? Well done.

So for question two, you were asked to write your own problem.

You might have written a problem like this.

Andeep has a paddling pool, which he has filled with 10 litres 500 millilitres of water.

Izzy pours in another two litres 300 millilitres.

What volume of water is in the paddling pool now? You might have then drawn a bar model to support you to solve the problem.

I could see I had two parts.

And so to find the whole, we needed to add the parts together.

If I added my parts together, I got 12 litres 800 millilitres.

So I found out that there is 12 litres 800 millilitres of water in the paddling pool now.

I wonder how you got on with your problems. Fantastic learning so far today.

You are really deepening your understanding of how we can use this bar model to solve problems. We're going to move on now and look at some problems that involve the multiplicative relationship.

So let's look at a different problem.

A jug holds 420 millilitres of juice.

All the juice in the jug is shared equally between 10 cups.

So let's try visualising that.

What do you see? Ah, yes, I see something like this.

I've got my jug and I've got 10 cups.

And what might the question be, do you think? The question is, what volume of juice is in each cup? I wonder if you guessed that question.

What do we need to do now now that we visualise it? That's right.

We need to represent this information as a bar model.

So first we need to identify the whole and the parts.

So we've got a jug holds 420 millilitres of juice.

That's tricky, we don't know if that's a whole or a part just yet.

All the juice in the jug is shared equally between 10 cups.

Ah, yes.

That tells us that there are 10 equal parts.

There's my 10 equal parts.

So the jug of 420 ml of juice is the whole.

There's my whole.

And the question, what volume of juice is in each cup? Well, this is the part that we need to find.

So from the bar model, we can see we have the whole 420 millilitres and 10 equal parts.

And we need to find the value of one of those parts.

And because the parts are equal, we can use our known multiplicative relationships.

The whole is 420 millilitres and there are 10 equal parts.

420 is composed of forty-two 10s.

Ten 42s are equal to 420.

So the volume of juice in one cup is 42 millilitres.

Let's check your understanding.

Could you look at this bar model? The whole is 240 millilitres and there are 10 equal parts.

What is the value of one part? I'm giving you some sentences to help you.

240 is composed of hmm 10s.

10 hmm are equal to 240.

The volume of one part is hmm millilitres.

Pause the video, have a go.

And when you are ready to go to the answers, press play.

How did you get on? That's right.

240 is composed of twenty-four 10s.

So ten 24s are equal to 240.

The volume of one part is 24 millilitres.

So the liquid in one cup is 24 millilitres.

Let's revisit our question.

If you remember, we've got a jug that holds 420 millilitres of juice and all that juice is shared equally between 10 cups and we found out the volume of juice in each cup.

Aisha is just helping us to remember, what did we know? Well, we know the volume of juice in one cup is 42 millilitres.

Let's do it, Aisha.

Let's add another part to our question.

Sophia has a bottle that has half the volume of water that is in the jug.

What volume of water is in Sophia's bottle? What do we need to do first? That's right.

We need to visualise this.

Can you see that? Can you see a bottle? Can you see that jug? That's what it looks like in my head.

So now we need to represent this in a bar model.

If we can remember our bar model, the whole is 420 and the juice has been shared between 10 cups.

So this part of the bar remains unchanged.

That part of the question is still there.

But our new part: Sophia has a bottle that has half the volume of water that is in the jug.

So we now need to add that to our bar model.

There we go.

This is a new part.

The word "half" tells us that it is one of two equal parts and I've now added that to my bar model.

And we need to know what volume of water is in Sophia's bottle.

So that's the part that we need to find - one of those two equal parts.

So I'm going to use the bar model now to help us find the volume of water in Sophia's bottle.

And Aisha is telling us the volume of juice in the 10 cups is 420 millilitres and is the whole.

The volume of water in the bottle is one of two equal parts of the whole.

420 is composed of two equal parts of 210.

So the volume of water in Sophia's bottle is 210 millilitres.

Let's check your understanding.

Look at this bar model.

The volume of liquid in a jug is 240 millilitres.

This is the whole and I've added that to the bar model for you.

The volume of liquid in the glass is half of that in the jug.

So I'd like you to find out what the volume of liquid in the glass is.

I've given you some sentences to help.

240 is composed of two equal parts of hmm.

The volume of liquid in the glass is hmm millilitres.

Pause the video, maybe find someone to talk to about this.

And when you are ready, press play.

How did you get on? Did you manage to work out that 240 is composed of two equal parts of 120? The volume of liquid in the glass is 120 millilitres.

Well done.

Let's revisit our question.

If we can remember, a jug holds 420 millilitres of juice.

All the juice had been shared equally between 10 cups.

Sophia has a bottle that's half the volume of water that is in the jug.

And Aisha is prompting us to remember what we know now and Andeep is reminding us we know the volume of juice in one cup is 42 millilitres and that in Sophia's bottle is 210 millilitres.

Okay, let's do it one last time, Aisha.

Let's add another part to the question.

Are you ready? How much more water does Sophia's bottle hold than a cup? What do we need to do first? That's right.

We need to visualise it.

What do you see? There I see a cup and a bottle and I need to know how much more.

So that's why I've got a question mark there.

How much more water would need to be added to my cup to make it the same as Sophia's bottle? So now let's represent this as a bar model.

The question tells us that Sophia's bottle contains a greater volume, but we need to find out how much more.

We need to compare the volume of liquid in Sophia's bottle to that in a cup.

So I've drawn a new bar model to help us here.

We can see we need to find the difference between the volume of water in Sophia's bottle and that in the cup.

So this time the water in Sophia's bottle is the whole and we have a part that is 90 millilitres and we need to find an unknown part.

To find the missing part, we need to subtract the part we know from the whole.

210 subtract 90, I'm going to subtract 10 first because I know that takes me to 200.

Then I can subtract the other 80, which is 120.

So Sophia's bottle contains 120 millilitres more water than the cup.

Let's check your understanding.

Could you represent this as a bar model, then solve it? A glass holds 120 millilitres of liquid.

A cup holds 24 millilitres of liquid.

How much more liquid does the glass contain than the cup? Pause the video.

Have a go at drawing a bar model.

And when you are ready, press play.

How did you get on? This is what I thought.

My glass holds 120 millilitres.

That is the whole.

It's the larger amount.

And my cup holds 24 millilitres.

That was a part.

And I needed to find that missing part.

To find a missing part, we need to subtract the known part from the whole.

120 subtract 24.

I partitioned my 24 into 20 and 4 because 120 subtract 20 is 100.

And then I could just subtract the 4, which was 96.

The glass contains 96 millilitres more liquid than the cup.

Your turn to practise now.

Could you solve these problems by drawing them to help you visualise the maths, representing them in a bar model and identifying the calculation? For part a, you've got a jug containing 480 millilitres of water.

All of the water is poured equally into 10 identical glasses.

What volume of water is in each glass? We're going to build on that for part b.

A bottle contains half as much water as the jug.

What volume of water does the bottle contain? And taking that even further for part c, how much more water is in the bottle than in one glass? Pause a video.

Have a go.

And when you are ready to go through the answers, press play.

Did you get on? Let's have a look.

So for part a, this is how I visualised it.

I've got my 10 glasses and my jug containing 480 millilitres of water.

I then drew a bar model.

My whole was 480 millilitres and there were 10 equal parts.

I then worked out the volume of water in each glass to be 48 millilitres.

For part b, I extended my bar model to look like this because my bottle contained half as much water as my jug.

I then worked out the volume of water in the bottle to be 240 millilitres.

Then I drew a new bar model to represent how much more water was in the bottle than the glass.

And I knew I had to find a missing part.

So to find a missing part, we have to subtract the known part from the whole.

So 240 subtract 48.

I subtracted the 40 first, then the 8.

So that was 200 subtract the 8 was 192.

So the bottle contains 192 millilitres more liquid than one glass did.

How did you get on? Fantastic.

Fantastic learning today everybody.

I can see you really deepened your understanding at solving problems involving volume.

We have learned that when we are given a word problem, we need to visualise it first.

We need to see it in our head, don't we? We can then represent word problems as a bar model by identifying the parts and the whole.

The bar model helps us to understand the structure of the maths and then to form a calculation to help us solve the problem.

We know that if the parts are unequal, we can use additive relationships and if the parts are equal, we can use multiplicative relationships to solve the problem.

Really impressed with how hard you have tried today.

Really well done.

I look forward to learning with you again soon.