Lesson video

Hi.

Welcome to today's lesson.

My name is Mr. Peters, and in this lesson today, we're gonna be extending our knowledge and understanding of the decimal place value system, thinking about how we can record decimal numbers up to three decimal places.

When you're ready, let's get started! So by the end of this lesson today, you should be able to say that you can read and write decimal numbers up to three decimal places.

Throughout this lesson, we've got some key vocabulary we're gonna be referring to.

I'm gonna have a go at saying it first, and then you can have a go afterwards.

Are you ready? My turn.

Thousandth.

Your turn.

My turn.

One thousandth the size.

Your turn.

My turn.

Thousandths column.

Your turn.

My turn.

Millimetre.

Your turn.

So when we think about one thousandth, we think about one part of a whole that's been divided into 1000 equal parts.

When a whole has been divided into 1000 equal parts, we can say that one of those parts is one thousandth the size of the whole.

The thousandths column places the number of thousandths a given number has.

And finally, a millimetre is a measure of length that can also be recorded as "mm".

This lesson today will be broken down into three parts.

The first part will think about identifying thousandths.

The second part will be thinking about thousandths as decimal numbers.

And then finally the last part will be relating thousandths to length.

Let's get started with the first part.

Throughout this lesson today, both Lucas and Jacob will be here to share their thinking and ask any questions that they have as we go along.

So we're gonna start this lesson by looking at these three numbers here.

We've got one, one tenth, and one hundredth.

And I'm asking you, what relationships do you know between each of these numbers? Take a moment to have a think.

Lucas is saying that we could describe them in relation to one another.

So each number is one tenth the size of the number to its left hand side.

Let's have a look.

One tenth is one tenth the size of one, and one hundredth is one tenth the size of one tenth.

We could also say that each number is 10 times larger or 10 times bigger than the number immediately to the right hand side of it.

So for example, one tenth is 10 times the size or 10 times bigger than one hundredth, and one is 10 times the size or 10 times larger than one tenth.

We could also describe them in relation to the whole, couldn't we? We know that when a whole is divided into 10 equal parts, each one of those parts represents one tenth.

So one divided by 10 is equal to one tenth.

And therefore we also know that 10 tenths are equal to one whole.

And here we could say that when a whole is divided into 100 equal parts, each part has a value of one hundredth.

Therefore we can also say that 100 hundredths are equal to one whole.

So this is where we extend our thinking a little bit further now.

And Lucas is asking, "Well, what would happen if we divided our whole into 1000 equal parts?" Let's have a look.

Here, you can see one whole.

When one whole is divided into 10 equal parts, each part has a value of one tenth.

When one whole is divided into 100 equal parts, each one of these parts has a value of one hundredth.

And so finally, when we have one whole and we divide it into 1000 equal parts, each part would represent one thousandth.

That's right, Lucas.

Can you see how small one thousandth is in comparison to one hundredth or one tenth or even one whole? Jacob's quite rightly saying that 1000 thousandths would be equal to one whole.

And we can also say that one thousandth is one thousandth the size of one whole.

Could you have a go at saying that with me? One thousandth is one thousandth the size of one whole.

Well done.

So Lucas has got a great question now.

He's wondering, how does one thousandth relate to both hundredths and tenths then? Well, let's have a look.

Hopefully you can see here the relative sizes of each one of these values.

And each time, as we move to the right hand side, each value becomes one tenth the size, isn't it? Or 10 times smaller.

So we could say that one thousandth is one tenth the size of one hundredth, or 10 times smaller than one hundredth.

We could also say that one hundredth is 10 times the size of one thousandth or 10 times bigger than one thousandth.

And if we think about this really carefully, have a look at our one hundredth now.

What's happened to it? That's right.

Our hundredth has been divided into 10 equal parts.

So we can see here that 10 thousandths would be the equivalent of one hundredth.

And that's exactly what Jacob is pointing out to us.

Now let's compare one thousandth to one tenth.

We know that when you make something one tenth the size, and then make it one tenth the size again, that's the same as saying one hundredth the size.

So we can say that one thousandth is one hundredth the size of one tenth.

We also know then, if you make something 10 times bigger and then 10 times bigger again, that's the same as making it 100 times bigger or 100 times the size.

So we could say that one tenth is 100 times the size of one thousandth.

And look carefully at our one tenth now.

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

Our one tenth has been divided up into thousandths, and we can see here that 100 thousandths would be equal to one tenth.

And finally, let's have a look at it in relation to the whole.

We know that if you make a number one tenth the size and then one tenth the size again, that's the same as making it one hundredth the size.

But if we make it one tenth the size again, that would be the same as making it one thousandth the size.

So we can say that one thousandth is one thousandth the size of one whole, which is what we said earlier on.

Similarly, we can apply that to making numbers slightly larger, can't we? If we multiplied one thousandth by 10 and made it 10 times larger, and then made it 10 times larger again, and then made it 10 times larger again, that would be the same as making a number a thousand times the size.

So we can say that one is 1000 times the size, or a thousand times larger, than one thousandth.

And finally, let's have a look at our one whole, and breaking that down into thousandths again.

What do you notice? That's right, exactly what Jacob is saying.

There are 1000 thousandths that make up one whole.

Okay, time for you to check your understanding now.

When a whole has been divided into 1000 equal parts, each part has a value of, A, B or C? Take a moment to have a think.

That's right.

It's C, isn't it? Each part has a value of one thousandth.

And then secondly, have a go at describing the relationship between these two values.

That's right.

We can say that one thousandth is one hundredth the size of one tenth.

Or we could say that one tenth is 100 times the size of one thousandth, or 100 times bigger.

Jacob's also pointing out that 100 thousandths would be equivalent to one tenth.

Have a look at that one tenth and think about it being broken down into those tiny thousandths.

That's right, there would be 100 of them.

Well remembered, Jacob.

Okay, onto our first task for today.

What I'd like you to do is have a go at describing the relationships between each number that has been written.

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

Okay, let's go through that together then.

One is 1000 times larger than one thousandth.

One tenth is 100 times larger than one thousandth.

One hundredth is 10 times larger than one thousandth.

One thousandth is one thousandth the size of one.

One thousandth is one hundredth the size of one tenth.

And finally, one thousandth is one tenth the size of one hundredth.

Well done if you managed to get all of those.

Let's move on to cycle two, then.

Thousandths as decimal numbers.

So we should by now be able to represent one tenth and one hundredth as a decimal number.

Let's have a look at this to remind us.

One is divided into 10 equal parts.

Each part has a value of one tenth.

And we record this as 0.

1.

We can say that one tenth is one tenth the size of one.

If we have one whole and we divide it into 100 equal parts, each part has a value of one hundredth, and therefore one hundredth is one hundredth the size of one.

And you can see here that we need to place our placeholders in place here.

So we can write one hundredth as 0.

01.

And we know that 0.

01 is one hundredth the size of one.

So let's think about what that means for thousandths, then.

Well, if we have one, and we divide this into 1000 equal parts, each part would be one thousandth, wouldn't it? And you can see here that it would become one thousandth the size.

And we're going to need another column here, aren't we, to be able to represent this? So we call this the thousandths column.

We can record this using our place value holders in the ones, tenths, and hundredths.

We write this as 0.

001, and we can say that one thousandth is one thousandth the size of one, can't we? Okay, quick check.

Which numeral represents one thousandth? A, B, C, or D? That's right.

It's D, isn't it? One thousandth can be written as 0.

001.

We now know how to write one thousandth, but we can now extend this to multiples of one thousandth.

We can say that one thousandth can be written as 0.

001, So two thousandths can be written as 0.

002.

Let's extend this further.

One thousandth can be written as 0.

001.

So six thousandths can be written as 0.

006.

And again, repeat the same sentence with me as well as you go.

One thousandth can be written as 0.

001.

So 10 thousandths can be written as 0.

010.

Hmm, what do you notice? That's right.

We've actually moved the ones digit into the hundredths column, because we know that 10 thousandths is equivalent to one hundredth.

Well done if you notice that.

Here's another example.

One thousandth can be written as 0.

001.

So 21 thousandths can be written as 0.

021.

Again, 10 thousandths is equal to one hundredth.

So 20 thousandths would be equal to two hundredths.

And we've got an additional one thousandth, so we record that as 0.

021.

And one more for us to think about.

One thousandth can be written as 0.

001.

So 321 thousandths can be written as 0.

321.

We know that 100 thousandths is equal to one tenth.

So 300 thousandths would be equal to three tenths.

And we know that 10 thousandths is equal to one hundredth.

So 20 thousandths would be equal to two hundredths.

And again, we have one additional thousandth this time, so we can write this number as 0.

321.

We can also represent decimal numbers with thousandths using place value counters.

Have a look at the place value counters provided.

What number do you think it represents? That's right.

We can write this number as 0.

234.

That's right.

We've got two tenths, we've got three additional hundredths, and we've got four additional thousandths, haven't we? So we can record this number as 0.

234.

Here's another example.

How would we record this one? What did you notice this time? That's right.

We don't have any hundredths this time, do we? So how are we gonna record this? Well, we would record this as 0.

204.

We have two tenths, don't we? We have zero additional hundredths, but we do have four additional thousandths, don't we? So we record this as 0.

204.

Here's another example.

What'd you notice this time? That's right, we don't have any additional tenths, do we? Or any additional hundredths.

But we do have a one count, don't we? So we would record this as 1.

004.

We've got one whole, zero additional tenths, zero additional hundredths, and four additional thousandths.

Okay, time for you to check your understanding again.

Which image represents 0.

305? That's right.

It's C, isn't it? Hopefully you can see that there are zero ones.

We've got three tenths, we've got zero additional hundredths, but we have got five additional thousandths as well.

So C represents 0.

305.

And the next one.

38 thousandths can be written as, A, B, C, or D? That's right.

It's C, isn't it? 38 thousandths can be written as 0.

038.

Lucas is asking, "Can you explain how you know?" Well, we could use that stem sentence we had from earlier on.

I know that one thousandth can be written as 0.

001.

So 38 thousandths can be written as 0.

038.

10 thousandths is equal to one hundredth.

So 30 thousandths would be equal to three hundredths.

So that's why we've got a three in the hundredths column, and then we've got eight additional thousandths, So that would be represented as 0.

038.

Time for you to check your understanding now.

What I'd like you to do is have a look at the place value charts on the left hand side, and fill in the gaps on the right hand side for each place value chart.

And then once you've done that, what I'd like you to do is either use place value counters, or you could draw the counters to represent each number on the left hand side.

Good luck with that, and I'll see you back here shortly.

Okay, let's go through these together then.

So the first one represents four thousandths.

So we can write this as 0.

004.

The second one represents 31 thousandths.

So we can write this as 0.

031.

And the last one represents 254 thousandths.

So we can write this as 0.

254.

And here we go.

You can see how I've recorded each one using a place value counter now.

I'll let you have a moment to have a look through those and tick them off.

Well done if you managed to get all of those.

Right, moving on to our last cycle for today now, then.

Relating thousandths to length.

Okay, so previously we were looking at one being our whole, weren't we? Whereas now we're gonna look at one metre being our whole.

One metre can be divided into 10, 100, or 1000 equal parts.

Let's have a look here.

Here you can see one metre, and if I divide that one metre into 10 equal parts, each one of those parts would be one tenth of a metre.

If I then divided our one metre into 100 equal parts, each one of those parts would represent one hundredth of a metre.

Now let's take a moment to zoom in on that one hundredth of a metre.

If I had taken that whole metre we had previously and divided it into 1000 equal parts, each one of those parts would look like one of these.

This would be one thousandth of a metre.

You can see here that we have ten one thousandths of a metre, because we know that 10 thousandths is equivalent to one hundredth of a metre or one centimetre.

So let's have a look at the comparative sizes of each of these, then.

Here we have one metre.

Then we have one tenth of a metre.

Then we have one hundredth of a metre.

And then we have one thousandth of a metre.

Can you see how each time they're getting 10 times smaller as they move down? So when we take one metre and we divide it into 1000 equal parts, we would say that each part is called one millimetre.

Can you see, I've tried to represent this here on our metre stick.

So if this is one millimetre, we would need 1000 of these to make one metre.

So we can say that one millimetre is one thousandth of a metre, and we can write one millimetre as 0.

001 metres.

I say 0.

001, but I think zero wholes and one thousandth.

We have zero whole metres, and one thousandth of a metre.

Let's have a look at how we could represent this using our place value chart.

Look carefully at what's just happened to our place value headings.

We've replaced the headings with the sizes of each one of those parts, haven't we? We've got one metre on the left, and then we've got our tenths of a metre, and then we've got our hundredths of a metre, and then we've got our thousandths of a metre.

So I say 0.

001, but I think zero wholes and one thousandth.

We can change this to, I say 0.

001 metres, but I think zero wholes and one thousandth of a metre, or one millimetre.

Okay, here we're back at our metre stick.

Let's take a moment to zoom in on one tenth of a metre or 10 centimetres.

Here we are.

We can see that we've got 10 centimetres, and each one of these centimetres have been divided into 10 equal parts.

So each one of these parts would represent one millimetre.

One millimetre can be written as 0.

001 metres.

So 10 millimetres can be written as 0.

010 metres.

And we know that because 10 thousandths is equivalent to one hundredth, and therefore 10 thousandths of a metre, or 10 millimetres, is equivalent to one hundredth of a metre, or one centimetre.

Okay, let's take this a little bit further.

Have a look this time.

How many millimetres do we have shaded in? That's right.

There are 32 millimetres shaded in.

So say this with me.

If one millimetre can be written as 0.

001, then 32 millimetres can be written as 0.

032.

We know that 30 millimetres is equivalent to three centimetres, and two millimetres is equivalent to two tenths of a centimetre.

So we can write this as 3.

2 centimetres.

Right, time for you to check your understanding.

10 millimetres is equivalent to, A, B, or C? That's right.

It's B, isn't it? 10 millimetres is equal to one centimetre.

And 48 millimetres can be written as, A, B, C, or D? That's right.

It's B, C, and D, isn't it? 48 millimetres can be written as 48 mm for millimetres, it can be written as 0.

048 of a metre, or it can be written as 4.

8 centimetres, because 40 millimetres is the same as four centimetres, and eight millimetres is the same as eight tenths of a centimetre.

And so why isn't it option A? Well, option A says 0.

48 centimetres.

So this isn't even the size of one centimetre, is it? And we know that one centimetre is equivalent to 10 millimetres, so therefore in order for it to be 48 millimetres, it would need to be 4.

8 centimetres, which is what we've got recorded for option D.

Okay, onto our final task for today then.

Can you fill in the missing values for metres, centimetres, or millimetres? On the left hand side, I've told you where to put the metres and the centimetres.

On the right hand side, I haven't.

So that's entirely up to you to decide where you record the missing either metre, centimetre, or millimetre values required.

Once you've had a go at that, come back, and we'll go through it all together.

Good luck.

I'll see you shortly.

Okay, welcome back.

Hopefully you're feeling a bit more confident having gone through those now.

And here are the answers, just for you to check your understanding as you went through.

Was there anything in particular that you noticed or that helped you? I spent some time thinking about how any number with three decimal places can just be referred to as the number of thousandths that there are, aren't there? It also helped me to think about how I know that 10 millimetres is equal to one centimetre, and how I know that 100 millimetres is equal to one tenth of a metre, or 1000 millimetres is equal to one metre.

Well done if you managed to get all of those.

Okay, just to summarise our learning from today then.

We can say that a thousandth is one thousandth the size of one.

We can say that a thousandth is one hundredth the size of one tenth.

And we can also say that one thousandth is one tenth the size of one hundredth.

We now know that the thousandths column is placed immediately to the right hand side of the hundredths column.

And we're now becoming more confident with writing thousandths as decimal numbers, and how we can refer to this as a unit of measure.

So for example, one thousandth is equal to 0.

001 metres, or is equal to 0.

1 centimetres, or again, it is equal to one millimetre.

Hopefully, again, you're feeling more confident about the relationships between decimal numbers with three decimal places, and how they can be applied to metres, centimetres, and millimetres.

Take care, and I'll see you again soon.