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Welcome back to Lesson 2 of your unit on volume.

I'm Mr. Barton and the way I remember eight multiplied by eight is by singing the theme tune to the children's TV programme 64 Zoo Lane.

So, every time I do it, I go,.

It's silly, but it's the way I've remembered it since I was about eight.

So, I hope that helps you.

This is your second lesson on our unit of volume.

In today's lesson we're going to be doing something a little different.

We're going to explore cubed numbers, which will be really important in our future lessons.

Make sure that you've taken the pre-lesson quiz, that you've got your pencil and your paper ready, and your work area is free from distractions.

All right then, let's get started.

We're going to start with some definitions.

Volume is the amount of space taken up by an object.

So, it's how much space that water takes up, that cube takes up, that chocolate bar takes up.

And volume is measured in cubic units.

And cubic units are what we're really going to explore today.

Before we do anything though, I'd like you to find all the factors for each of these numbers.

Now, I've put them inside factor bugs in case this is how you've found factors in the past.

And if you're not sure how a factor bug works, you make sure you find pairs of legs by multiplying numbers together.

Working systematically, I know that nine multiplied by one is equal to nine.

I then know two multiplied by, oh no, doesn't get me anywhere.

And then I know three multiplied by three equals nine.

Four multiplied by, mm, no.

Nothing multiplied by four.

Nothing multiplied by five, because all multiples of five end in a zero or a five and so on.

I know six, seven, eight and then I'm already back to nine there.

Nine multiplied one.

I then move on to 25.

What I'd like you to do is pause the video and find all the factors for 25, 12, and 16.

Pause the video there.

Let's have a look at your answers.

So, here we have all four factor bugs completed.

I'd like you to pause the video here and write down any patterns or anything that you see that's different or the same.

Pause the video now.

One of the patterns you may have noticed is that nine, 25, and 16 are all squared numbers.

This means that they are the product of two equal factors.

So, nine is the product of three and three.

Five is the product.

25 is the product of five and five.

12 is not a squared number, because it's not got two factors that are the same, but 16 is, because it has four and four.

Therefore, you may say that 12 was the odd one out for that reason.

I've created an array above each of the squared numbers.

The product of nine shows us three groups of three and these make a square when we do our array.

Their length is the same as their height.

I want to delve into this a little bit more.

Here we have three multiplied by three is equal to nine.

We know that three is a factor and nine is the product.

In this example, the factor three is repeated twice to make the product.

We also have the array there.

Another way to write this squared number is three squared.

The three represents the factor, which we repeatedly multiply, and the two represents how many times we multiply it.

We call these squared numbers.

When we create squared numbers, they have an array which is got a height and has got a length that are equal.

So, a question for you.

If three multiplied by three can be written as three squared, because it has two equal factors of three, how could we record three equal factors of three? Pause your video.

Maybe you wrote it like this.

Three equal factors of three, three times, is equal to three cubed.

We call these cubed numbers and we're going to really investigate that now, because volume is measured in cubic units.

Another way to write three cubed is three multiplied by three multiplied by three.

We've got the factor three, three times.

The first two factors show us three multiplied by three, just like the array we've just looked at.

But what about the third factor of three? The final multiple of three shows us that nine, the nine in the array, another three times.

So, we have one group of nine, two groups of nine, three groups of nine.

So, that array of nine is repeated three times.

This time you'll notice that we have a height, a length, and a width.

We have three dimensions.

So, whereas a squared number has two dimensions, a cubed number has three dimensions, a height, a length, and a width.

And our product is 27.

Three cubed is equal to 27.

Three multiplied by three multiplied by three is equal to 27.

It's got three dimensions, a height, a width, and a length.

Here we have the first five cubed numbers in picture form.

We are going to fill out the table to really delve into what cubed numbers are.

So, I'm going to start with one cubed here.

One cubed has one height, one width, and one length.

Three dimensions.

One height, one width, and one length.

Three dimensions.

One cubed is equal to one, because one multiplied by one multiplied by one is still equal to one.

One group of one is one is equal to one.

Let's have a look at two cubed now.

Two cubed has a height of two, it has a width of two, and it has a length of two.

Two cubed is equal to two, multiplied by two, multiplied by two.

Two multiplied by two is equal to four.

Four multiplied by two is equal to eight.

My total number of two cubed is eight.

If I use my picture to help me, I could see one, two, three, four cubes.

Five, six, seven, and there's another one hiding here, eight.

So, eight cubes make up that cubed number.

Eight lots of my one cube.

I'm going to pause there.

What I'd like you to do is fill in the rest of this table.

Use the pictures to help you.

Use my work to help you.

Off you go.

And let's check your answers.

How did you do? Those times tables are getting quite tricky now, so it's important that you make notes as you go.

Okay, it's okay to jot down things before you get the correct answer.

It's time for your independent task now.

And you're going to carry on doing exactly what you've just done.

You will need to use some formal multiplication as you move through the table.

It's all things you can do.

And if you're not sure, take it in steps and chunk it.

Pause your video now.

And here are your answers.

Well done.

These cubed numbers relate really closely to those cubic units that volume is measured in.

It's one of my favourite lessons.

So, well done if you nailed it.

Don't forget to do your end of lesson quiz.

I'll see you next time where we're going to relate these cubed numbers to our volume.

Well done.