Lesson video

Hello, my name's Mr. Peters, and today in this lesson we're going to be thinking about extending our understanding of decimals a little bit further, thinking about hundreds and how they relate to a whole.

When you're ready, let's get going.

Okay, in this lesson today, we've put three key words we're gonna be thinking about.

Let's have a go at saying them.

I'll have a go at saying them first and then you can repeat afterwards.

My turn equal, your turn.

My turn, hundredth.

Your turn.

My turn, tenth.

Your turn.

Right, let's have a little bit more of a think, about what these mean.

So, when we think about equal, equal means exactly the same amount or value.

A hundredth is the name that we give to a part from a whole that has been divided into a hundred equal parts and one of them is what we would call 100th.

Similarly, a tenth is the name we give to a part when a whole has been divided into 10 equal parts and then one of those parts would be named one 10th.

Look out for this language throughout our lesson as we're going to be using it regularly.

So, by the end of today's lesson, hopefully you feel confident enough to be able to say that I can identify hundreds as part of a whole.

Let's get going.

Okay, so this lesson has been split into three parts.

The first part of our lesson, we'll be thinking about hundreds and how it relates to tenths and to ones.

The second part of our lesson, we'll be looking at hundreds in a range of different contexts.

And the third part of our lesson, we'll be thinking about multiples of 100th and different examples of how we can look at this.

Let's get started with the first cycle.

Throughout this lesson today, Jean and Laura will be helping us, along our way with our thinking.

Hopefully you can see here that we have one whole.

Now our whole has been divided into lots of different parts, and Jean's asking, well, how many parts has it been divided into? Laura's had a look and she thinks it's roughly about a hundred and she'd be right.

We have divided the whole into 100 equal parts and each one of those parts is named 100th.

I wonder if we could say what Jean has said altogether.

The whole has been divided into 100 equal parts.

Each part is 100th of the whole.

Well done.

Laura's then added that, well, if we have a hundred of these hundredths that is equal to one whole.

So, 100 hundredths is equal to one whole.

Have a look at this.

Now we've got a base 10 block.

This base 10 block is gonna represent our whole.

Laura thinks she can see 100 parts of in it again and she'd be be right.

The whole has been divided into 100 equal parts.

Each part is 100th of the whole.

And if we were to combine them all back together again, then we know that a hundred hundredths, would be equal to one whole.

Let's have a look here.

There is one of our hundredths highlighted now, and look at the way that we say the word.

We say the word as 100th.

You almost need to stick your tongue out to say that bit at the end of the word, the TH.

Let's say it together.

100th.

Well done.

Have a look at our representations now.

One of them is a bar model and one of them was the base 10 blocks.

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

The hundredth part, that shaded is in a different place to where it was before.

And Jean's asking, doesn't matter where it's placed within the whole as to whether it is still 100th.

Well, no, it doesn't Jean, we can highlight any one of those hundredths within the whole.

It still represents 100th.

Okay, let's revisit our whole now.

Watch carefully.

What happens this time? Okay, what's happened so far? That's right.

The whole has been divided into 10 equal parts.

Each one of these parts is one 10th.

Now what do you notice? Look carefully.

Well, you may have noticed that we divided the whole, underneath both of those into 100 equal parts and then we've overlaid those a hundred equal parts over the tenths.

Have a look at one of those tenths.

You can recognise them by the thicker, darker lines.

How many hundredths fit into one tenth? That's right, Jean.

Each temp we could say, has been divided into 10 equal parts, and one of those parts is 100th.

So, we can say that 10 hundredths is equal to one 10th as well.

We can also represent this again with our base 10 blocks.

Have a look at our whole, this time we've got one column shaded.

That one column represents 10 hundredths or it can represent one 10th.

Not only can one column represent 10 hundredths or one 10th, one row could also represent 10 hundredths or one 10th.

Okay, time for you to check your understanding now.

True or false, when a whole is divided into 100 equal parts, each part is 100 of the whole.

Have a think.

That's right.

That's false, isn't it? Well, why is it false? Let's look at our justification, and see if they can help us.

The first justification says 100 hundredths make a whole.

And the second one says, 100 hundreds make a whole.

What do you think? That's right.

It's A, 100 hundredths make a whole, not 100 hundreds.

We need to remember that a hundred and a hundredth are very, very different things and a hundredth is a lot smaller than a hundred.

Okay, one more for you now.

10 hundredths are equal to A, one whole.

B, one 10th, or C, 10 tenths.

Have a think for yourself.

That's right.

We know that 10 hundredths are equal to one 10th.

And if you think back to our bar model, we can see that I'm visualising that in my head.

I can see the hole and I can see that divided into 10 equal parts.

And then each one of those 10 parts, I'm gonna divide again up into 10 parts, which would make the hundredths.

And we know that 10 hundredths is equal to one 10th.

Okay, our first task for you today then.

Here I've given you two shapes.

What I'd like you to do is choose one of these shapes and treat that as your whole.

I'd like you to cut up that shape into 100 equal parts and then I want you to recombine it to make the whole again.

It's really important for us to get a sense of what making a hundredth and recombining those hundredths together looks like to make the whole.

Okay, so let's have a look at an example that Laura did then.

So, on the left hand side you can see our whole, can't you? And then in the middle picture, we've cut up this whole into 10 equal parts.

Each one of those parts represents one 10th.

We've recombined all those parts then to remake the whole.

Then on the right hand side you can see that the whole has been divided into 100 equal parts and each one of those parts represents 100th of the whole.

10 of those hundredths is equal to one 10th.

And when we've recombined all of those parts back together, we can see that it remakes the whole.

Well done, Laura, for showing that really clearly.

Okay, well done.

Let's move on to cycle two of our lesson.

Here you can see I have one metre and we can also represent one metre using a number line, which I've now placed directly underneath the metre.

You can see on the left hand side of our number line, it starts at zero metres and on the right hand side of the number line, it ends at one metre.

We're gonna be using this in a little bit more detail throughout this section.

So, the whole of our number line, which is one whole because it starts at zero and ends at one, has now been divided into 100 equal parts.

And each one of these parts represents 100th of the whole.

And as you can see, I've coloured 100th, right at the beginning of our number line.

This is 100th of a metre and it's a really tiny part, isn't it? We can also find hundredths in different contexts as well.

Now, you can see my number line is no longer horizontal.

It's laid out vertically and it's on a jug of water.

Again, the bottom of the number line, starts at the bottom of the jug where it would be zero.

And at the top of the number line we would represent one.

And because we're now working with liquid, we're gonna be working with litres.

So, at the top of the number line, we have one litre.

Because we've got the number line, we can say that the whole has been divided into a hundred equal parts again, and each one of those parts would represent 100th.

And let's have a look at 100th.

Gosh, that's a really small part, isn't it? 100th of that litre has been poured into the jug, and you can see that at the very bottom of the jug.

It's a tiny, tiny sliver, isn't it? We can also think about this as kilogrammes.

We use kilogrammes, don't we? As a unit when we're weighing items. So, on my scales here on the left hand side, I've got one kilogramme, and on the right hand side I've got another kilogramme.

And this time it's been divided into 100 equal parts.

And I've shaded in one of those parts for you.

So, you can see that the one shaded part of that kilogramme on the right hand side would represent 100th of a kilogramme.

This time, look at the way I've recorded it on the right hand side.

I've written it as a fraction, haven't I? I've written it as one with the vinculum for the fraction bar.

And then underneath that, the 100, and we can say that the one represents the one whole that has then been divided with the vinculum into with hundred, a hundred underneath equal parts.

This represents 100th of a kilogramme, 100th of the whole.

It's really important to get a sense of what 100th looks like and feels like.

And we're gonna do exactly that now with some rice.

Okay, so we're gonna start here with a kilogramme of rice, which I've poured into this plastic see-through container, so you can get a sense of how much a kilogramme of rice is.

We are now gonna partition this kilogramme of rice into 10 equal parts.

Each one of these parts will represent one 10th of a kilogramme.

Let's do that now.

Okay, so let's start partitioning then.

Here we go.

One 10th of a kilogramme, Two tenths of a kilogramme, three tenths of a kilogramme, four tenths of a kilogramme, five tenths of a kilogramme, six tenths of a kilogramme, seven tenths of a kilogramme, eight tenths of a kilogramme, nine tenths of a kilogramme.

And finally 10 tenths of a kilogramme.

So, hopefully you can see here that we've now partitioned our one kilogramme into 10 equal parts, and each one of these parts represents, one 10th of a kilogramme.

We also know that 10 tenths is equal to one whole.

So as we can see here, 10 tenths of a kilogramme is equal to one whole kilogramme.

You can see that my kilogramme container is now empty as we have partitioned it into these 10 equal parts.

Now, if we were to take each one of these parts and partition this into another 10 equal parts, altogether, we would have 100 equal parts.

We'd have 10 here, 10 parts here, 10 parts here, another 10 parts, and another 10 parts.

Each one would represent 10 parts, and altogether that would be 100 equal parts, which if we recombined altogether, would make our whole again.

What we're going to do this time is we're going to take one of our tenths and we're gonna partition this into 10 equal parts to show you the size of what 100th of a kilogramme, would look like.

Okay, so here we go again then.

Here is our one 10th of a kilogramme and we're gonna divide this into 10 equal parts.

And each one of these parts, will represent 100th of a kilogramme.

100th of a kilogramme, two hundredths of a kilogramme, three hundredths of a kilogramme, four hundredths of a kilogramme, five hundredths of a kilogramme, six hundredths of a kilogramme, seven hundredths of a kilogramme, eight hundredths of a kilogramme, Nine hundredths of a kilogramme, and finally 10 hundredths of a kilogramme.

10 hundredths of a kilogramme is the equivalent of one 10th of a kilogramme.

So, now we have ten one hundredths of a kilogramme, one 100th, two one hundredths, three one hundredths, four one hundredths, five one hundredths, six one hundredths, seven one hundredths, eight one hundredths, nine one hundredths, ten one hundredths.

And we know that ten one hundredths is equal to one 10th.

So, ten one hundredths of a kilogramme is equal to one 10th of a kilogramme.

Now, let's compare a kilogramme against one 10th of a kilogramme and against 100th of a kilogramme.

Okay, so hopefully you can see now that here we've got our one kilogramme of rice and I'm just gonna rotate that around so you can get a sense for the size of one kilogramme of rice.

And then here we've got one 10th of a kilogramme of rice.

We would need to recombine 10 lots of this amount here to create our one kilogramme.

So, this is one 10th of a kilogramme of rice.

And then this here, as you can hopefully see is 100th of a kilogramme.

Can you see how much less rice there is in comparison to the other two amounts? We would need 10 lots of 100th of a kilogramme here to make one 10th of a kilogramme.

And we would need 100 lots of this amount to make one whole.

So, we would need 100 hundredths of a kilogramme to make one whole kilogramme again.

Hopefully that enabled you to get a really good sense of the size of a kilogramme in comparison to a 10th of a kilogramme and to a hundredth of a kilogramme.

Okay, time for you now to check your understanding again.

Have a look at my number line, look at where it starts and look at where it ends and think about what the whole is.

The highlighted section represents what? Is it A, one 10th of a metre.

B, 100th of a metre or C, 10 hundredths of a metre.

It might be more than one solution.

Have a think.

Well done.

It was both A and C, wasn't it? We know that when a whole is divided into 10 equal parts, each one of those parts represents one 10th.

And if you think about the longer lines that have separated our number line, each one of those represents the dividing of the whole into 10 parts.

So, the distance between those two longer lines, would represent 100th.

We also know that when a whole is divided into 100 equal parts, then one of those parts represents one 10th.

And we can see that again with the smaller lines that are demarcating the hundredths.

In the image, we can see that 10 of those hundreds have been shaded.

So, one 10th of the whole has been shaded, but also 10 hundredths of the whole have been shaded.

And we know that one 10th is equal to 10 hundredths.

Okay, now it's your turn.

We're gonna start thinking, about some more practical examples of creating tenths and hundredths.

So, what I'd like you to do is you can choose, you can either create a metre long piece of paper that fits the length of your metre stick and then cut that piece of paper into 10 equal parts.

Then I'd like to take one of those parts and cut that again into another 10 equal parts.

Each one of those parts should then represent 100th.

You might like to do it in a different context here, using water.

You might like to measure out a litre of water and divide that up into 10 equal parts, using 10 different cups.

You then might like to take one of those cups and divide that again into 10 equal parts.

That might be a bit of a challenge, but it should hopefully help you get a feel and a sense of how big 100th is of the measure that you have decided to look at.

Good luck and I'll see you shortly.

Okay, welcome back.

Have a look here.

As you can see, I chose to use the water and I've got a measuring jug here, which I filled initially on the left hand side with water up to the one litre mark.

Have a look carefully at that.

I then decided to pour that and divide that into 10 equal parts.

And then as you can see in the middle, I left one of those parts in the jug.

So, we can see that that part there represents one 10th of a litre of water.

You can see how much smaller it is, compared to the first one, can't you? Then again, I decided to pour out that one 10th into 10 equal parts and left one of those parts in the jug again.

That part there on the right hand side, represents 100th of a litre.

Look really carefully at that.

It's really small, isn't it? Hopefully you can compare that to the size of the litre on the left hand side now and get a real sense for how much one litre of water, actually looks and feels like.

Well done if you manage to do that as well.

Okay, now we're moving into the final cycle of our lesson.

We're gonna be thinking about describing examples of multiples of 100th.

Let's have a look.

So, we've gone back to our image of the base 10 block.

Have a look.

What do you notice this time? That's right, the whole has again been divided into 100 equal parts, but we don't actually just have one that's been shaded this time.

Do we? We have two of those parts that have shaded.

The two parts shaded represents two hundredths of the whole.

What do you notice this time? Again, that's right.

The whole has still been divided into a hundred equal parts and there are still only two parts that have been shaded, but those are two different parts that have been shaded this time.

Does it still represent two hundredths of the whole? That's right, it does.

It doesn't matter where they're placed, does it? It still represents two hundredths of the whole.

Have a look this time.

How do you think we could describe this? Well, once again, the whole has been divided into a hundred equal parts, isn't it? How many have been shaded? That's right.

10 parts have been shaded.

So, this represents 10 hundredths of the whole, doesn't it? Laura's asking, "How else could we describe this?" Have a think.

That's right.

10 hundredths is also equal to one 10th, isn't it? So, we could also describe this as one 10th of the whole, having been shaded.

Now, we've moved on to our bar model as a representation.

Look carefully.

Can you see where the whole has been divided into 10 equal parts and a hundred equal parts? Can you use that to help you identify how much of our bar model has been shaded? Have a look.

That's right.

The whole has been divided into 100 equal parts, and we can see that 24 of those hundredths have been shaded.

So, we can say that 24 parts is 24 hundredths.

Jean's then thinking, "Well, can we describe this in another way?" Well, yes we can, can't we? 'Cause we know that 10 hundreds is equal to one 10th and there are two lots of 10 hundredths that have been shaded, aren't there? And an additional four hundredths.

So, we've got two tenths instead of 20 hundredths and then the additional four hundredths.

So, we could say together that we've got two tenths and four hundredths.

Have a look this time.

What do you notice? That's right.

It's not starting on the left hand side of our bar model, is it? It's right in the middle.

Doesn't matter though.

No, it doesn't matter, does it? I wonder how many we've got shaded.

Can you have a think.

Laura's pointed out that instead of counting them in ones, it might be quicker to count them in tens, wouldn't it? Let's have a look.

We know that between each thick bar is 10 hundredths, so let's see if we can count them together.

10 hundredths, 20 hundredths, 30 hundredths, 40 hundredths, 50 hundredths and an additional two hundredths.

So, altogether that's 52 hundredths.

And as Jean is saying, we can describe that in two ways, can't we? We can either say that's 52 hundredths or it's five tenths and two additional hundredths.

Here's another example.

Look carefully this time with our measuring jug.

Can you work out how much water is in our jug? Laura is saying that it's 100th less than three tenths, isn't it? So, what we could say is that three tenths is actually the same as 30 hundredths and we know if we take 100th away from 30 hundredths, that would leave us with 29 hundredths, which is exactly how much water there is in the jug.

There are 29 hundredths of a litre in the jug.

Okay, our final checks for understanding today, the first one.

Which image represents eight hundredths? Take a moment to have a think.

That's right, it's C.

Laura's asking, can we explain why it isn't A or B? Well, let's have a look at A.

Firstly, the whole looks like it's been divided into 10 equal parts.

So, we know that each one of those parts represents one 10th and eight of them are shaded, so that would represent eight tenths and not eight hundredths.

Let's have a look at B.

Well, we know that with this number line today, we've been looking at, we've divided the hold into 100 equal parts and that's exactly what's happened in this middle number line.

How much has been shaded? It looks like the 80 hundredths have been shaded, therefore we know that does not represent eight hundredths.

If we have a look at C, we can see that eight parts have been shaded of the whole that has been divided into a hundred equal parts.

So, therefore C has to represent eight hundredths.

Well done if you've got that.

Okay, onto our task for today then.

First of all, it says, can you fill in the missing numbers? I've given you the stem sentences on the right hand side, so you need to have a look at the number with the arrow next to it and then next to the same sentence with the same number and arrow.

What I'd like you to do is fill in those missing numbers.

You need to represent it as hundreds and also as tenths and hundredths.

You also then need to do the same here.

So as you can see here, B has a number line.

C has a whole divided up into triangles and D has an oval with a hundred circles drawn into it that representing the whole.

And for task two, I'd like you to have a little bit of a think, about how you could create your own examples of 25 hundredths.

You could use a square, a rectangle, a number line or complete your own example.

I'll be really interested to see what you can come up with.

Good luck and I'll see you shortly.

Okay, welcome back.

Let's see how you got on.

So, number one is pointing at 78 hundredths.

So, we can also write that as seven tenths and eight hundredths.

Number two is halfway, so that's pointing to 50 hundredths of a litre.

And again, we can write that as five tenths and zero hundredths.

Number three is 19 hundredths, and we can write that as well as one 10th and nine hundredths.

And finally number four is four hundredths.

We can write that as zero tenths and four hundredths.

Let's have a look at B.

B is one less than 20 hundredths, so we can record that as 19 hundredths.

And again, we know that 10 hundredths is equal to one 10th, so we can record that as one 10th and an additional nine hundreds.

C the whole, all of those triangles has been divided into 100 equal parts.

There are a hundred triangles there.

And we actually have one part that's not shaded in blue, don't we? So, that would mean that all of them together shaded, would be a hundred hundredths, but we've only got 9,900 shaded.

Again, we can record that as nine tenths and nine additional hundreds.

And finally, the last model here, we've got a hundred circles in our oval here.

Can you see that they've been grouped into groups of 10? Let's count up in groups of 10 hundreds again.

10 hundredths, 20 hundredths, 30 hundredths, 40 hundredths.

How many more have been shaded? An additional eight, isn't it? So, we can describe this as 48 hundredths, having been shaded and we can write that, can't we? As four tenths and an additional eight hundredths? Well done if you've got those.

Okay, I'm sure you came out with lots of different creative ways of making 25 hundredths and it's good not just to stop at one, try making lots of different ways to represent 25 hundredths.

Here's one that Jean has created.

Have a look.

What do you notice about it? Well, he's used a square and the square's been divided into a hundred equal parts and he shaded in 25 of them.

But look at the shape of the 25 that he shaded again.

That's another square, isn't it? That's really interesting.

I wonder how that relates to our square numbers.

Also, look carefully.

How many of those blue shaded areas do you think it would take to make the whole? That's right.

It would take four of them, wouldn't it? We can see that here, can't we? Actually, if we divided the whole into four equal parts and shaded one of them like the blue that we've got here, then that would represent one quarter.

So, we can see here that maybe 25 hundredths is also equal to one quarter of a whole, which is exactly what Laura's pointing out here.

She's saying that I noticed it looked like one quarter of the shape is shaded blue.

Great spot Laura, and well done if you managed to spot that too.

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

Well done.

And hopefully you feel a lot more confident, thinking about hundredths now, don't you? Let's summarise our learning for today.

First things first, when a whole is divided into 100 equal parts, each part is 100th of the whole.

10 one hundredths is equal to one 10th.

And finally, if you shade in more than 100th, then you could say that you've shaded in multiple one hundredths of the whole.

Thanks for learning with me today.

I've really enjoyed teaching you that lesson.

Hopefully you feel confident too.

Take care and I'll see you again soon.