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Welcome back to year five math lessons on volume.

I'm Mr. Barton, I'm going to be working with you today.

Over the last couple of lessons, I've given you my tips and tricks for remembering those tricky multiplication tables.

I've got another one for you today.

Now I remember 56 is equal to seven times eight because we can go five, six, seven, eight 56 is equal to seven multiplied by eight five, six, seven, eight.

I quite like that one coz I can never remember seven multiply by eight off the top of my head.

This is your fourth lesson on volume.

We're going to be building on the knowledge from lesson two and lesson three, especially today.

So make sure you've done those lessons.

You should have also started our pre-lesson quiz, and you should have a workspace free from distractions, with a pencil and paper, ready to go.

If you've got all those things, let's get started.

So my question to you, is the volume at this cube seven centimetres cubed? I think this, because I can count seven cubes, one, two, three, four, five, six, seven.

And we worked from the premise that one cube is equal to, one centimetre cubed.

Pause your video, and let me know if you agree, or if you disagree.

And again, it's important to note that this is not to scale, pause your video now.

Right then, let's break this down a little bit.

I've broken the cube up and separated each of the unit cubes a little.

I know that the length is two.

I know that the width is two, and I know that the height is two.

So that would leave me to going, two multiply by two two multiply by two or two cubed.

So why does it appear that there was only seven centimetres cubed.

I've made each of the centimetre cube transparent, and we can see that our missing cubic centimetre is at the back in the bottom left corner, but when they're all filled in, we just can't see it.

It is still there, because when we do two multiplied by two multiplied by two, two times two is four times two is eight.

We know that we have eight cubic centimetres, eight centimetres cubed.

And it takes up that amount of space just coz you can't see it, it doesn't mean it's not there.

But let's explore this a little further.

So I'd like to tell me, what's the volume of this shape? Pause your video now.

What was the quickest way to find the volume? You may have counted the cubes and that's fine, but there's not always going to be cubes to count.

You might find the length and the width and the height.

Here, I have my length, one, two, three, four, five.

I have a length of five centimetres.

I have a width of one, two, three centimetres and I've got a height of just one centimetre.

My width times my height times my length would be five multiplied by three multiplied by one.

Five multiplied by three is 15 multiplied by one is equal to 15.

Remember that's not to scale, is a representation to help us understand.

Let's make it a bit trickier now.

We've got that same length and the same width, but this time we've got double the height.

We've got two of have the heights.

Pause your video now, and find me the volume of this shape.

So, as I said the length and the width are the same as our previous example.

However, this time the height is doubled.

So we've still got five centimetres.

We've still got three centimetres for our width, but this time we've got two centimetres for our heights, which leads me to be doing five multiplied by three multiplied by two.

If I do five multiplied by three is 15.

That tells me that, this whole bottom chunk is 15.

But I've got two of those chunks, which is equal to 30 and their centimetre cubes.

There are 30 centimetre cubes in this shape.

Now you could have counted the cubes.

But it would've been harder for this one coz there's more cubes that we can't see.

So here are those eight cubes that we can't see.

I've let them in two different shades of green.

We've got one group of four there, and one group of four there light green and dark green.

So they all there, but we can't see them because they're obscured.

Here with two more cuboids for you.

In a second, I'd like you to pause the video and work out the volume of each of the cuboid.

You've got one here and one here.

Remember they are not to scale.

And we're presuming that all our units is one blue box is equal to one centimetre cubed.

Can you challenge yourself by writing a height multiplied by length, multiplied by width equation for each of them.

Pause your video now, and have a goal of finding the volume of these two shapes.

Let's see how you did.

So was it harder to find the volume of this shape? Pause your video and jot down your answer.

Can we write a height, times length, times width, the equation for it? Well I can do, a length here three.

I can do a width three, but then we've got two different heights.

I can't multiply by two because there's not any here, so, because this is not a cuboid.

I can't do it that way.

So I'm going to have to use my known facts, so I can use this part here, three and three.

And I can use this part here, knowing that that's one, three multiplied by three is equal to nine times by one is equal to nine centimetres cubed.

Then I've still got this one on top.

So it will be nine centimetres cubed and one more centimetre cubed.

And that will give me 10 centimetres cubed.

That was just like what you were doing at the very start of this lesson.

How about this one? Again, you'll be able to use your groups to help you, but it's got a different height, length and width as to normal.

Pause your video and work out the volume.

But what do we know about the shape? We've got one group of four, two groups of four.

And what we presume and can just about see three groups of four, three groups of four centimetres cubed is equal to 12 centimetres cubed.

So we can still work out our volume of the shapes, even if they're not a perfect cuboid.

Because everything has a volume.

Everything it's solid takes up room.

I've made those boxes transparent for you.

So you can see those three that we couldn't quite see.

Time for your independent task now.

You've split this task into task one and task two.

Task one can be completed by using our height times length, times width, multiplication equation.

But as task two, is going to require you to use your powers of deduction of counting boxes and imagining where they may be.

If you can not see the shapes clearly keep watching this video where task one and then task two will come up.

If that's still not big enough for you, that's absolutely fine, exit this page and move on to the task side where we'll put two tasks or two shapes per page.

If you need to do that, exit the video now and click the next button or pick the pause button.

Again remembering that these shapes are not to scale and each cube we are using one centimetre cubed form.

Pause your video now.

Here's task one, Here's task two.

Here are your answers.

Here are your answers for task two.

A great lesson today, a real great skill to have.

And for your use for the rest of your life.

Don't forget to complete the end of lesson quiz well done for today.