Lesson video

Hi, my name's Mr. Peters.

Welcome to today's lesson.

In this lesson today, we're gonna be extending our understanding of the word volume and starting to think about how we can measure volume in different ways.

If you're ready, let's get started.

So by the end of this lesson today, you should be able to say that I can describe the units used when measuring volume.

Throughout this lesson we've got a number of keywords we're gonna be referring to.

I'll have a go at saying them first and then you repeat them after me.

Are you ready? First one, volume.

Your turn.

The second one, cubic centimetre.

Your turn.

And the last one, cubic metre.

Your turn.

So thinking about what these mean in a bit more detail, the amount of three-dimensional space something takes up is known as its volume.

A cubic centimetre is the volume that is taken up by a cube that has one centimetre on each edge.

And a cubic metre is the volume taken up by a cube that has one metre on each edge.

Let's see if we can apply these words into our learning throughout the rest of the lesson.

This lesson today is broken down into three cycles.

The first cycle is thinking about standard units of measure.

The second cycle will be exploring smaller volumes, and the third cycle will be exploring larger volumes.

If you're ready, let's get started.

Throughout this lesson today, we've got Laura and Izzy and they're gonna be telling us their stories to help us understand volume and how we can measure this as best we can.

Okay, so our lesson starts here with Laura's dad.

Laura's dad works for MEI delivery partners.

In the factory where he works, his job is to package up items that have been bought into boxes ready to be delivered.

He has lots of different size boxes to put the items into as you can see below.

Laura's saying that her dad has said that it's useful to know the volume that each box takes up so when packing them onto the vans, he knows how much space it's going to take up.

The amount of space an object takes up is known as its volume.

So Laura's asking, "How could we work out the volume of this box then?" Izzy suggests that we fill it up with something and count how many items there are in there.

Laura thinks it might be best to use cubes.

Izzy is suggesting that maybe we could use marbles.

So, let's start with Laura then.

Laura starts off using those cubes.

She starts stacking them vertically and then stacks them in rows.

And then completes the rest of the space by stacking in the columns as well.

Laura thinks that the box has a volume of 180 cubes.

So Izzy's thinking, "Well, in that case then, if you have 180 cubes, maybe the box should be filled up with 180 marbles as well then." Well, let's have a look then.

Izzy starts stacking the marbles into the box.

"Hmm, I can only fit 60 marbles into the box," Izzy's saying.

"So why have we got different volumes then?" She says that the marbles are larger than the cubes, so they're taking up more space within the box, aren't they? And also the cubes didn't leave any gaps from being stacked in the boxes.

Compared to the marbles if you look carefully, there's lots of little gaps in amongst each marble where they're sat next to each other.

Hmm.

So Izzy then comes to the conclusion that maybe it's better to use the cubes, isn't it? To measure the volume of the box as the marbles themselves have left some of the volume unaccounted for because they have the gaps in between each of the marbles.

Whilst using the same shape is gonna be important when measuring the volume of the boxes, actually the same size would also really be important, wouldn't it? Let's have a look here for example.

If we were to use the cubes like Laura had, we could see for this box there would be 150 cubes that make it up.

Whereas if we use slightly bigger cubes to measure the volume of the box, the volume of the box is now 8 cubes.

So we've got 150 cubes and we've got 8 cubes.

This isn't a consistent measure, is it? So we can't compare the volumes here because we've measured the boxes with different sized objects, haven't we? Okay, so all around the world people use what's called a standard unit of measure to measure the volume of items. Here is one cubic centimetre.

It has a length of one centimetre, it has a height of one centimetre, and it has a width of one centimetre.

We write one cubic centimetre as 1 C-M with a little 3 in the air next to the M.

This represents the volume of the cuboid, one centimetre by one centimetre by one centimetre.

It's important to note that at this point here, what you can see on the screen is not actually what we call to scale.

That's not the actual size of one cubic centimetre.

One cubic centimetre would be the same size as often the blocks that you use with your maths lesson to represent ones.

So we can use cubic centimetres to measure the volume of items or shapes, can't we? Have a look at this shape here then.

Have a think.

What's the volume of this shape? That's right.

The volume of this shape is 10 cubic centimetres.

We can write this as 10 C-M for centimetres with the 3 to represent the cubic centimetre.

So if that shape was filled with something, we would say that the shape has a volume of 10 cubic centimetres or 10 centimetres cubed.

Okay, time to check your understanding now.

Always, sometimes, or never? A shape that is made up of fewer cubes will always have a smaller volume than a shape that is made up with more cubes.

Take a moment to have a think.

Laura is saying it is true for these shapes.

The shape on the left hand side has fewer cubes than the shape on the right hand side.

And the shape on the right hand side therefore has a greater volume than the shape on the left hand side.

However, Izzy thinks it's false for these examples.

The shape on the left hand side has more cubes.

It's got three cubes.

However, each of those cubes is smaller than the cubes on the right hand side.

So the shape on the right hand side actually has a greater volume than the shape on the left hand side, even though it has fewer cubes.

Okay, another check for understanding now.

Can you estimate the volume of these shapes? I've given you an example of what one cubic centimetre might look like in this context of the page.

Okay, let's see how you got on.

The first shape would measure at 4 cubic centimetres.

The second shape would measure at 5 cubic centimetres, and the last shape would measure again at 4 cubic centimetres.

Notice how the first and the last shape both have the same volume of 4 cubic centimetres, but they're different in shape, aren't they? Okay, time for you to check your understanding now.

Can you estimate the volume of these shapes? Once again, be aware that these are not to scale.

So this is not exactly what one cubic centimetre would look like each time.

Once you've done that, I'd like you to have a go at making one cubic centimetre with a malleable object, maybe some plasticine or some Play-Doh.

And then I'd like you to change the shape of your cubic centimetre into lots of different shapes, and I want you to think which one of these shapes would be best for measuring the volume of different items. Good luck with that and I'll see you again shortly.

Okay, welcome back.

So estimate the volumes of these shapes then.

The first one is 6 cubic centimetres, the second one was 8 cubic centimetres, and the last one was also again, 8 cubic centimetres.

Here's some examples we came up with for different shapes of a cubic centimetre.

All of these shapes have the same volume as one cubic centimetre, although they've just been sliced up or moulded into different ways.

Which ones do you think would be the best for measuring the volume of different objects? That's right.

It's probably best to use these three here, isn't it? These three generally could form a cuboid shape, whether it's already in a cuboid or a cube or in the bottom example, they could be joined together to create a cuboid or a cube, couldn't they? So in doing so, using cuboid-style shapes are often best for measuring the volume of different objects.

And we can see that here, Laura's pointing out that these three shapes would be best because they would create a cuboid-like shape.

And Izzy is saying that these would not be so good as they would leave gaps if lots of them would join together in order to try and measure the volume of a shape.

Okay, let's move on to our second cycle now, exploring smaller volumes.

Have a look at these shapes here.

Again, it's not to scale and we've given an example of what one cubic centimetre would look like in this context.

How can we work out the volume of each of these shapes? Take a moment to have a think.

Laura's saying that the first one is easy to work out.

She can see that there's 4 cubes and each cube represents one cubic centimetre, therefore there are 4 cubic centimetres.

So it was easy to count the first 4 cubic centimetres on that one there wasn't it? However, she's now saying that on the other shapes it's not as easy to count how many there are because we can't see all of the cubes, can we? We need to get a real understanding for how these shapes have been built up.

So let's have a look.

What did you notice about each of these shapes then? If each cube again represents one cubic centimetre, what did you notice? Take a moment to have a think.

Well, that's right.

Each one of the cubes was the same size, wasn't it? So again, each one of those cubes represents one cubic centimetre.

However, what changed with the shapes was that each shape added on one layer of 4 cubic centimetres, didn't it? So we could use on multiples of 4 to find out how many cubes are in each shape, couldn't we? The first one was 4 cubic centimetres.

This one had a second layer of 4 cubic centimetres added to it, so that would be 8 cubic centimetres, and then another 4 cubic centimetres would make 12 cubic centimetres.

And then finally the last one would be 16 cubic centimetres.

Have a look at this example now.

What do you notice this time? What's the same and what's different? Again, each one of the cubes is exactly the same size, isn't it? Each one represents one cubic centimetre.

And again, each shape is growing in volume, isn't it? By adding another layer of 4 cubic centimetres each time.

However, this time it's going vertically, isn't it? We're adding one on top of the other rather than in front of the other.

So once again, we can count in multiples of 4 to work out the volume of each one of these shapes.

Laura was mentioning that we need to put C-M with the little 3, cubic centimetres, after each one of the numbers.

This helps us to understand what we've measured the volume of the shapes in.

So if anybody else wants to find out the volume of the shape, they've got an understanding of the size of the measure that was used to measure the volume of each of the shapes.

And because we're measuring the volume of each of these shapes here, we can write it as V is equal to blank centimetre cubed or cubic centimetres.

This is how we would record it in an equation.

Okay, time for you to check your understanding.

What is the volume of this shape? Take a moment to have a think.

That's right.

The volume is 24 cubic centimetres.

And why is it not option B or option C? Well, hopefully you can see that each layer has 8 cubic centimetres in it, and therefore we have 3 layers of 8 cubic centimetres, which would represent 24 cubic centimetres.

It cannot be 18 or 28 as neither of these are a multiple of 8.

Okay, time to practise then.

Can you give the volume for each of these shapes? You can record this on the blank lines under each shape.

And for your second task, what I'd like to do is create as many different shapes as you possibly can using just 5 cubic centimetres.

Good luck with that and I'll see you again shortly.

Okay, here are the answers to the first task.

I'll let you go through these and tick them off if you've got them correct.

I was particularly interested in example F and how you work that out.

If the whole cuboid was full, then we could see that there's 3 layers of 6 cubic centimetres.

So 3 layers of 6 cubic centimetres would be 18 cubic centimetres.

However, we're missing 2 cubes in the middle, aren't we? So that's why it is 16 cubic centimetres.

Well done if you got those.

And for task two, here's some examples of what you could have created using 5 cubic centimetres.

Did you manage to get them all or find a different way of doing it completely? Well done with that.

Okay, and onto our last cycle now, exploring greater volumes.

Okay, so once Laura's dad has packaged the items into the boxes, he then stacks the boxes into a large cube-like shape.

This helps when it comes to stacking the boxes onto the vans to be able to get the most boxes into the vans.

So therefore, knowing the volume of this pile of boxes would be really useful to know how many of these piles of boxes they would be able to fit into each van.

So let's have a think about this.

This pile of boxes is obviously quite large, and now you can see the size of one cubic centimetre.

Again, this is not to scale, but this is an example of what one cubic centimetre would look like in comparison to these boxes.

Would this be large enough for us to measure the volume of this pile of boxes? Laura doesn't think so.

She thinks it's a bit small and therefore we could do something slightly larger, couldn't we, to measure the volume of this pile of boxes? Okay, so let's see if we can make something slightly larger then.

Well, Izzy is suggesting, "If we multiplied the length, the width, and the height of our cubic centimetre, each one of those by 10, then the length, the width, and the height of our cube would all be 10 centimetres.

Therefore we could create a cube that looks like this." How many cubic centimetres do you think are making up this cube now? That's right, it'd be 1000 cubic centimetres would be making up this cube here.

Instead of drawing all of those individual cubes, we can draw a rough outline of the cube just like this.

So whereas before we had one cubic centimetre and we could say that was one centimetre multiplied by one centimetre multiplied by one centimetre, we can say this is 1000 cubic centimetres and we can represent this as 10 centimetres multiplied by 10 centimetres multiplied by 10 centimetres.

Let's see.

Is this now gonna be big enough to measure the volume of this pile of boxes? Izzy's unsure.

She thinks we can go even bigger here.

Let's have a look and see if we can manage that.

So far we've got one cubic centimetre and we've got a 1000 cubic centimetre cube, haven't we? I wonder what would happen if we made each one of the dimensions of our cubic centimetre, so the length by the width, by the height, if we made each one of those actually 100 times larger than the original one centimetre and it was.

Well, there we go.

It might look something like this, wouldn't it? The length would be 100 centimetres, the height would be 100 centimetres and the width would be 100 centimetres.

We could record that as 100 centimetres multiplied by 100 centimetres multiplied by 100 centimetres.

How many cubic centimetres do you think would fit in the whole of this? Well, you might have got that.

It's 1 million.

It would take 1 million of those tiny cubic centimetres to fit into the size of this unit here.

This is a big unit that we're looking at.

So whilst we know that each dimension here has a length of 100 centimetres, we know that 100 centimetres is also equivalent to one metre.

So we could replace the dimensions of 100 centimetres with one metre.

How would that change our equation then? Well, our equation would become one metre multiplied by one metre multiplied by one metre.

And then what would we call this unit do you think? That's right.

We would call it one cubic metre.

Could you have a go at saying that? One cubic metre can be represented like this.

The one represents how many units there are, and the M with a little 3 in the air represents the cubic metre.

So we can use cubic metres to measure greater volumes, can't we? Let's have a look at our pile of boxes then.

Do we think one cubic metre is gonna be big enough? Look at that.

It looks like it's gonna be roughly the same size.

So we can say that the pile of boxes was roughly one cubic metre in volume.

So Izzy's uncle is the van driver who delivers all the parcels to the houses who have purchased them.

Izzy says it would be useful to know what is the capacity of the back of her uncle's van, and therefore they can identify how many piles of boxes can fit into the back of the van.

Let's have a look.

We're gonna represent the back of the van here with the cubic metres that we can fit in.

So we've got 8 cubic metres so far, and there's another 8 cubic metres.

So we can fit 16 cubic metres into the back of Izzy's uncle's van.

That must mean we can fit 16 of those piles of boxes into the back of Izzy's uncle's van.

Izzy says, "No wonder he's tired at the end of the day.

That's a lot of parcels to deliver, isn't it?" Okay, time for you to check your understanding now.

True or false? 100 cubic centimetres is equal to one cubic metre.

Take a moment to have a think.

Ah, that's right.

It's false, isn't it? And which justification did you use to help you? That's right, it's A, isn't it? One cubic metre is equivalent to 1 million cubic centimetres.

It's an easy one to confuse that that 100 centimetres is equal to one metre.

However, when you think about how many of those smaller cubic centimetres would fit into one cubic metre, the larger unit is 1 million of them that would fit into that.

Okay, and another check for understanding.

What units of volume would be the most appropriate to measure the volume of a teacher's cupboard? Take a moment to have a think.

That's right.

It would be B or D in this case.

Why would it be B or D? Well, a teacher's cupboard is quite large, isn't it? So I think a cubic metre would be the most appropriate to measure that in.

And we know that one cubic metre is the equivalent of 1 million cubic centimetres, so that is why it's B or D.

Okay, time for us to have some practise now.

What I'd like you to do is to tick the unit of measure that you would use to measure each one of the objects on the left hand side.

And then at the bottom I've put a tick in the cubic centimetre column and I've put a tick in the cubic metre column.

And you need to come up with an object that you would use either cubic centimetres or cubic metres to measure the volume of.

Good luck with that task and I'll see you again shortly.

Okay, let's go through the answers then.

So a box that a ring might be bought in would probably be best measured with cubic centimetres.

And so with also a pencil case, they're relatively small, aren't they? However, a bookcase and a bus shelter would definitely need cubic metres.

And then a school hall as well.

When you think about the size of your school hall, yep, definitely gonna need cubic metres to measure the capacity or the volume of that.

Two examples that I've come up with myself are a pad of Post-It notes.

The size of a pad of Post-It notes would be ideal to measure in cubic centimetres.

And then finally a greenhouse, something that you might grow your vegetables in, in your garden.

That would certainly be something that would be measured in cubic metres.

Okay, that's the end of our learning for today.

Hopefully you've enjoyed yourself and you're becoming a lot more familiar with the units of measure that we can use to measure volume.

So to summarise our learning today, we can say that volume can be measured using three-dimensional units of measure.

The volume of smaller spaces can be measured using cubic centimetres, and the volume of large spaces can be measured using cubic metres.

Thanks for joining me today.

I've enjoyed myself.

Hopefully you have too.

Take care and I'll see you again soon.