Lesson video

Hello, how are you today? My name is Dr.

Shorrock, and I'm here to guide you through your learning today.

You have made a great choice to learn maths with me, and I know we are gonna work really hard together.

Today's lesson is from our unit calculating with decimal fractions.

This lesson is called Converting Units of Length.

Throughout the learning today, we will be deepening our understanding of multiplying by 10, 100, and 1,000, and we will be applying this to the context of measures, thinking about length and height.

Sometimes new learning can be a little bit tricky, but don't worry, I'm here to guide you, and I know if we work really hard together, then we can be successful.

So shall we get started then? How do we use knowledge in multiplication and division to convert units of length? Our key words for this lesson are decimeter and convert.

Now they may be new words to you, so let's practise them together.

My turn, decimeter.

Your turn.

Nice.

My turn, convert.

Your turn.

Fantastic.

Decimeter may be a new word to you.

It's just another metric unit of length, like metre or centimetre, and it's equivalent to 1/10 of a metre.

We abbreviate it to dm, like centimeter's cm, decimeter is dm.

So look out for that in today's lesson.

To convert, well, that just means to change a value or expression from one form to another.

In this context of the lesson today, it means to change from one unit of measurement to another, such as centimetres to millimetres.

We're going to start our learning today by looking at how we convert between metres, decimeters, centimetres, and millimetres.

And we have Lucas and Sofia to help us in our learning.

Let's start by looking at this ruler.

Is there anything that you notice about it? Ah, Sofia has noticed that this ruler can measure in centimetres or millimetres.

You can see the cm on the top part of the ruler and mm for millimetre on the bottom part of the ruler.

Have you noticed anything else? Lucas has noticed that one centimetre and 10 millimetres are the same length.

They're in the same place on the ruler, aren't they? One centimeter's equal to 10 millimetres.

And that's because one centimetre is composed of 10 millimetres.

Two centimetres is equal to 20 millimetres, three centimetres is equal to 30 millimetres.

Have you spotted a pattern? That's right.

If we multiply the number of centimetres by 10, this gives us the number of millimetres that are equivalent in length.

So the number of centimetres multiplied by 10 will give us the number of millimetres, and that's because 10 millimetres make up one centimetre.

So Sofia and Lucas measure the length of a toy car.

Sofia is measuring the length of the toy car to be 30 centimetres, and Lucas measures the length of the toy car to be 300 millimetres.

What do you notice? "Why are our measures different?" Lucas is saying.

Ah, thank you for clarifying, Sofia.

They used different units, didn't they? Lucas and Sofia, well, Sofia used centimetres and Lucas used millimetres.

Let's convert Sofia's 30 centimetre measurement into millimetres using known facts.

We know one centimetre is equal to 10 millimetres, and we know that if we multiply the centimetres by 10, we get the amount in millimetres.

So 30 centimetres multiplied by 10 is 300 millimetres.

So both quantities are actually the same length as each other.

There are 10 times as many millimetres as there are centimetres.

They both measured it to be the same length, but the unit they used was different.

Next, Sofia and Lucas measured the height of a flower.

What do you notice about this? So Sofia measures the height of the flower to be 20.

5 centimetres and Lucas to be 205 millimetres.

Anything you've noticed? The measures are different again, aren't they? Why is that? Why has one measured 20.

5 and the other 205? Ah, thank you, Sofia, for reminding us.

That's because they used different units again.

We know one centimetre is equivalent to 10 millimetres and we know that we can multiply the value of centimetres by 10 to get the value of millimetres.

20 centimetres multiplied by 10 is 200 millimetres, and that 0.

5 centimetres, while it's half a centimetre, that must be equal to five millimetres.

So Sofia is a value of 20.

5 centimetres is equal to 205 millimetres, both quantities were the same length as each other.

And we know there are 10 times as many millimetres as there are centimetres because one centimetre is composed of 10 millimetres.

So Sofia and Lucas both measured the height of that flower to be the same length, but they used different units, so it looked like they were different, but they weren't really because when we convert the centimetre measurement into millimetres, they wear the same.

Now Lucas and Sofia are going to play a converting game.

Lucas measures the length or height of an object in millimetres, and Sofia has to convert it to centimetres.

Lucas has measured the length of a book and is saying that it is 310 millimetres, so Sofia has to convert it to centimetres, and Sofia can use known facts to help her.

We know 10 millimetres is equal to one centimetre, so 300 millimetres must be equal to 30 centimetres.

And 310 millimetres, well, that must be equal to 31 centimetres.

Converting from millimetres to centimetres is equivalent to dividing by 10, because we have 10 millimetres equivalent to one centimetre.

There are 10 times as many millimetres as there are centimetres.

All the digits will move one place value place to the right because we are dividing by 10.

This time it is Lucas's turn.

Sofia measures the height of an object in centimetres, and Lucas has to convert it to millimetres.

"The height of my apple is 8.

3 centimetres." And Lucas knows that he can use known facts to help convert.

We know our known fact is one centimetre is equal to 10 millimetres, so eight centimetres must be equal to 80 millimetres.

And 0.

1 of a centimetre is one millimetre, so 0.

3 centimetres must be equal to three millimetres.

So the height of the apple at 8.

3 centimetres must be equal to 83 millimetres.

The units are different, but the length or the heights were the same.

Converting from centimetres to millimetres is equivalent to multiplying by 10, because there are 10 millimetres in one centimetre.

Millimetres are smaller, aren't they? So there must be more of them.

All the digits move one place value placed to the left when we multiply by 10.

Let's check your understanding.

30.

5 centimetres, is that equal to 350 millimetres? True or false? Pause the video, and when you are ready, press play.

Did you work out that that was false? But why is it false? Is it because A, when we convert from centimetres to millimetres, we need to multiply by 10.

So all the digits move one place to the left, the answer should be 305 millimetres.

Or is it B? When we convert from centimetres to millimetres, we need to multiply by 10, so we need to place a zero at the end of the number.

The answer should be 30.

50.

Pause the video, maybe chat to somebody about this, and when you are ready for the answers, press play.

How did you get on? Did you realise that it must be A.

It can't be B because we don't just place a zero at the end of a number, especially decimal numbers.

So we needed to move the digits one place to the left, so the answer should be 305 millimetres.

30.

5 centimetres is equal to 305 millimetres.

How did you get on with that? Well done.

Now let's look at this ruler.

What do you notice? Remember what we noticed about the other ruler? What do you notice here? Lucas is noticing that this ruler is measuring in the unit dm.

Can you remember what that stands for? Dm stands for decimeter.

Deci means 1/10th.

So one dm, one decimeter, is 1/10 of one metre.

It's 10 centimetres.

And here we can see on our ruler that one metre is equivalent to 10 decimeters.

Let's look at these two different rulers.

What do you notice? Do you notice that one metre is equivalent in length to 10 decimeters and to 100 centimetres? They are all the same length, they're just different units.

One metre is equal to 10 decimeters, which is equal to 100 centimetres.

Let's revisit the measurement for the height of a flower.

The height of the flower was 20.

5 centimetres, but we could give the measurement in decimeters or in metres.

It's your choice, really.

And we know there are 10 times as many centimetres as there are decimeters.

Centimetres are smaller than decimeters, so to convert from centimetres to decimeters, we need to divide by 10.

20.

5 divided by 10.

Well, we know when we divide by 10, the digits move one place to the right.

So 20.

5 divided by 10 is equal to 2.

05 decimeters.

We know also that there are 100 times as many centimetres as there are metres.

Centimetres are smaller than metres, so there must be more of them.

So to convert from centimetres to metres, we need to divide by 100.

20.

5 centimetres divided by 100, well, we know when we divide by 100, the digits move two places to the right.

20.

5 centimetres divided by 100, well, that's equal to 0.

205 metres.

So we can say that 205 millimetres is equal to 20.

5 centimetres, which is equal to 2.

05 decimeters, which is equal to 0.

205 metres.

All the units are different.

Now we've got millimetres, centimetres, decimeters, and metres, but all the length are equivalent, and you can measure in whichever length you choose.

Let's check your understanding.

Look at these rulers and use them to complete the equation.

0.

3 metres equals decimeters, equals centimetres, equals millimetres.

So you're looking to complete the equation.

Pause the video while you do that, and when you're ready for the answers, press play.

How did you get on? Did you work out that 0.

3 metres is equal to three decimeters, which is equal to 30 centimetres, which is equal to 300 millimetres? Did you notice a pattern there or spot a connection? That's right.

Each measure given is 10 times bigger than the previous measure, and that's because the measures are getting 10 times smaller than each other.

So a decimeter is 10 times smaller than a metre, a centimetre is 10 times smaller than a decimeter, and a millimetre is 10 times smaller than a centimetre, so you need more of them each time.

Let's summarise what we know.

We know one metre is equal to 10 decimeters, it's also equal to 100 centimetres, and it's also equal to 1000 millimetres.

And we can represent our conversions in a table, and you can use this table whenever you want to help you convert from any of the measurements that we've looked at, millimetres, centimetres, decimeters, and metres and to convert to millimetres, centimetres, decimeters, or metres.

So, for example, we can see that to convert from centimetres to millimetres, we need to multiply by 10 because one centimetre is composed of 10 millimetres.

It's your turn to practise now.

For question one, I'd like you to find some objects that can be measured with a class ruler.

Use the table to record your measurements.

Part A, could you measure the length of at least two objects in millimetres? For part B, measure the length of at least two different objects in centimetres.

And for part C, could you convert your measures from the previous questions A and B to complete the table? For question two, could you complete these equations converting between measures? Have a go at both questions, pause the video, and when you are ready to go through the answers, press play.

How did you get on? Let's have a look.

So you might have measured the length of some objects like this and then converted your measures to complete the table.

So I measured the length of a book as 290 millimetres, I converted it to centimetres by divided by 10.

I divided by 10 again to get the length in decimeters, 2.

9, and divided that by 10 to get the length in metres, 0.

29.

I wonder what you measured? For question two, you were asked to complete these equations converting between measures.

So three metres is equal to 30 decimeters, which is equal to 300 centimetres, which is equal to 3000 millimetres.

Each time, the unit of measure is getting 10 times smaller, so we need 10 times more of them.

Six metres is equal to 60 decimeters, which is equal to 600 centimetres, which is equal to 6,000 millimetres.

So 2.

6 metres is equal to 26 decimeters, which is equal to 260 centimetres, which is equal to 2,600 millimetres.

8.

7 metres is equal to 87 decimeters, which is equal to 870 centimetres, which is equal to 8,700 millimetres.

6.

4 metres equals 6,400 millimetres, 0.

3 metres equals 430 millimetres, 540 centimetres equals 54 decimeters, 930 millimetres equals 0.

93 metres, 45 decimeters is equal to 4.

5 metres, and 63 centimetres is equal to 6.

3 decimeters.

How did you get on with those? Well done.

Fantastic learning so far.

I can see you're trying really hard.

We're gonna move on now and look at how we convert between kilometres and metres.

Sofia says she can run 1.

75 kilometres.

I wonder if any of you do any running? And Lucas wants to know how far that is in metres.

And we know that one kilometre is equal to 1000 metres, and we can use that to help us.

To convert 1.

75 kilometres into metres, we need to multiply 1.

75 by 1000, and that's because there are 1000 metres in one kilometre.

So we know we need to multiply 1.

75 by 1000, and when a number is multiplied by 1000, the digits move three places to the left.

So the distance in metres is 1,750.

1.

75 kilometres is equivalent in length to 1,750 metres.

They are just different units.

And Lucas supports Sofia.

Metres are smaller than kilometres, so there must be more of them in 1.

75 kilometres.

1.

75 kilometres, we now know, is equal to 1,750 metres.

And we know we need to multiply the distance in kilometres by 1000 to get the distance in metres.

They are equivalent lengths.

The length of the school field is 346 metres.

"How far is that in kilometres?" Lucas is wondering.

We know that one kilometre is equivalent to 1000 metres.

That's our known fact.

To convert 346 metres into kilometres, this time we need to divide by 1000.

The distance in kilometres is the distance in metres divided by 1000, so it's 346 divided by 1000.

Can you remember what we do when we divide by 1000? That's right.

The digits move three places to the right, that's equivalent to 0.

346.

So, 346 metres.

Well, that's equivalent to 0.

346 kilometres.

And Lucas supports Sofia.

Kilometres are larger than metres, so there must be fewer of them.

In fact, 346 metres, that's not even 1000 metres, so it's not even one kilometre.

We've got 0.

346 of a kilometre, so part of a kilometre.

Let's summarise what we know so far.

One kilometre is equal to 1000 metres, and we are multiply by 1000 to convert between kilometres and metres.

Kilometres are larger, so there must be fewer of them, and metres are smaller, so there must be more of them.

That's why we multiply by 1000.

We then could also work out that 0.

1 kilometre is 100 metres because it's a 10th of size.

A 10th of that is 0.

01 kilometres, or 100th of a kilometre is equal to 10 metres, so 1000th of a kilometre is equal to one metre.

And we can write that as a fraction.

1000th of a kilometre is one metre, or 0.

001 kilometre is one metre.

And we know to convert from metres to kilometres, we can divide by 1000 because there are fewer kilometres than there are metres.

Let's check your understanding on this.

Which of these is the correct conversion of 402 metres into kilometres? Is it A, B, C, or D? Pause the video while you think about that.

Maybe have a chat to someone, see if you agree, and when you are ready to go through the answers, press play.

How did you get on? Did you realise it can't be A because we really need to be dividing.

We're converting metres into kilometres, and there are more metres than there are kilometres, so we need to be dividing.

It can't be B because we are dividing by 1000 and we've just removed the zero, and we know we can't do that.

All the digits have to move three places to the right.

C is correct.

402 divided by 1000 is 0.

402.

And it can't be D because there we are dividing by 100 and we know there are 1000 metres in a kilometre, so we should be dividing by 1000.

How did you get on with that? Brilliant.

It's your turn to practise now.

For question one, can you solve these problems? A family needs to travel 23 kilometres from Didcot to Oxford.

After travelling 5,700 metres, they stop to get petrol.

How much further do they have to travel? Give your answers in metres and in kilometres.

For question B, the width of a farmer's rectangular field is 305 metres and the length is 0.

46 kilometres.

What's the perimeter of the field? And for part C, an aeroplane travels 150 metres in one second.

How many kilometres will it travel in one hour? Pause the video while you have a go at those questions, and when you're ready for the answers, press play.

How did you get on? Should we have a look? So our first question about the family travelling, well, they need to travel 23 kilometres, but they stop after 5,700 metres.

My units are different, so I'm going to convert them.

I'm going to choose first to convert metres into kilometres.

5,700 metres, well, I need to divide by 1000 to convert to kilometres, which is 5.

7.

And then I can subtract 5.

7 from 23 to work out how much further they have to travel.

I'm going to partition the 5.

7 into five and 0.

7 to make it easier for me, and I get 17.

3.

Now you might have chosen to convert the other way and to convert the kilometres into metres by multiplying by 1000, so 23,000 metres, and then subtract the amount in metres, 5,700, which is 17,300 metres.

The families still have 17.

3 kilometres, or 17,300 metres, to travel.

Both of those are correct, the units are just different.

For part B, you were asked to find out the perimeter of a field.

I drew it just to help me, a sketch.

I knew the length is 0.

46 kilometres and the width is 305 metres.

I can see straight away there that my units are different, so I'm going to need to convert.

To find the perimeter, it's the distance all the way around the shape, so I needed to add up the 305 twice 'cause there are two widths and the 0.

46 twice 'cause there are two lengths.

And then I decided that I would convert my 0.

46 to metres by multiplying by 1000 to get 460.

When I add those together, I get 1,530 metres, or that is the same as 1.

53 kilometres.

For part C, an aeroplane travels 150 metres in one second.

How many kilometres will it travel in one hour? Hmm.

So here I wrote down the key information, 150 metres in one second, and then I found out how much it would travel in 60 seconds, or one minute, and I multiplied by 60, and I did 15 sixes on 90, so 150 sixties are 9,000, but that's in one minute.

I need to know one hour, so I need to multiply by another 60.

And I know nine sixes are 54, so 9,000 sixties must be 540,000.

So the aeroplane will fly 540,000 metres, or 540 kilometres, in one hour.

How did you get on with those questions? Well done.

For the last part of the lesson today, we are going to look at comparing and ordering units of length.

Let's have a look at this.

The children in Lucas's class have been growing some sunflowers.

These are their results.

So you can see the child and the height of the plant.

Is there anything you notice in that table? There's something I've noticed.

Yes, that's right.

The unit given are different.

We've got some centimetres and some metres, and Sofia wants to know whose sunflower was the tallest.

Lucas is saying, "Mine is the tallest, 286 is the largest number in the table, so it must be the tallest." Do you agree with him? Ah, Sofia doesn't.

She's saying she respectfully disagrees.

The units of measure are different, so we cannot compare by just looking at the numbers.

We need to convert them to the same unit, and then we can compare.

We could convert the units in metres to centimetres or vice versa.

It doesn't matter as long as you convert them all to the same.

Sofia prefers to multiply, so she's going to convert the units given in metres to centimetres.

Sofia reminds us that one metre is equivalent to 100 centimetres, so we're going to multiply by 100.

We'll start with the 3.

4 metre measurement multiplied by 100 is 340, so Sofia's height of her plant is 340 centimetres.

Then, if we look at Izzy's, 3.

14 multiplied by 100 is equal to 314 centimetres.

So now the units are the same, and we can then compare the height.

260 is less than 286, which is less than 314, which is less than 340.

We could also put them back into the original unit.

So 260 centimetres is less than 286 centimetres, that's less than 3.

14 metres.

So even three looks like a smaller number than 286 is metres.

So we have to be very careful to look at the units.

3.

14 metres, which is less than 3.

4 metres.

So we can now say that Sofia has grown the tallest sunflower at 340 centimetres.

Let's check your understanding with that.

Starting with the greatest, could you put these heights in order? Pause the video while you have a look and do that, and when you're ready for the answers, press play.

How did you get on? Did you notice that the units were different, so you needed to convert them? I chose to convert them all to centimetres.

So if I start with 2.

31 metres, I need to multiply that by 100 is 231 centimetres.

The other unit given in metres, 2.

03 metres multiplied by 100 is equal to 203 centimetres.

And then we had two units already given in centimetres, and then I had the last one given in millimetres, 2,130 millimetres.

Well, to convert that to centimetres, I need to divide by 10 because there are 10 millimetres in one centimetre, which is 213 centimetres.

Once all the units had been converted, we could then put them in order, starting with the greatest, 2.

31 metres, then 230 centimetres, 214 centimetres, 2,130 millimetres, and then 2.

03 metres.

How did you get on? Well done.

It's your turn to practise now.

For question one, could you complete these equations with the appropriate inequality? So smaller than, greater than, or with the equal sign.

For question two, true or false? A line measuring 120 millimetres is longer than a line measuring 10 centimetres because 120 is greater than 10.

Could you give reasons for your answer? And for question three, could you solve this problem? A bus company has measured the dimensions of its buses.

You can see the height, 3,475 millimetres, width, 250 millimetres, and length, 9,600 millimetres.

There's a mistake here.

Can you spot it and give reasons for your answer? Pause the video while you have a go at those three questions, and when you are ready for the answers, press play.

How did you get on? For question one, you had to complete some equations with the appropriate inequality or equal sign.

240 is greater than 204.

Both units are the same there, so we can just look at the value of the number.

240 centimetres, well, that equals 24 decimeters.

There are 10 times as many centimetres in one decimeter, so we need to divide by 10.

240 centimetres is greater than 2.

04 metres.

240 centimetres would be 2.

4 metres.

240 centimetres, well, that's greater than 240 millimetres.

The number is the same, 240, but centimetres are larger, so 240 centimetres must be larger than 240 millimetres.

240 centimetres, well, that is equivalent to, that equals 2,400 millimetres.

3.

5 metres, well, that's greater than 350 millimetres.

3.

5 metres is less than 350 decimeters.

3.

5 metres is equal to 350 centimetres.

3.

5 metres is less than 3,500 centimetres.

3.

5 metres is equal to 3,500 millimetres.

For question two, you were asked whether this was true or false.

A line measuring 120 millimetres is longer than a line measuring 10 centimetres because 120 is greater than 10.

Well, this is true, but the reason given was false.

You might have reasoned that 120 millimetres is longer than 10 centimetres, but not because 120 is greater than 10, but because the units are different, so we need to convert.

You might have explained that 120 millimetres is equivalent to 12 centimetres.

And this is how we know that the 120-millimeter line is longer.

And for question three, the problem about the bus company, did you spot a mistake? That's right.

You might have spotted that the width must have been given incorrectly.

250 millimetres, well, it's only equivalent to 25 centimetres, and a bus is wider than 25 centimetres, isn't it? You might have reasoned that the measurement should have been 2,500 millimetres, which is equivalent to 2.

5 metres.

How'd you get on with those questions? Fantastic.

I am really impressed with the learning that you have been doing today.

You've worked so hard.

You should be really proud of yourselves.

We know that we can use our knowledge of multiplying and dividing by 10, 100, and 1,000 to convert between units of measure.

We know there are 10 millimetres in one centimetre, 10 decimeters in one metre, 100 centimetres in one metre, 1000 metres in one kilometre, and 1000 millimetres in one metre.

Fantastic learning today.

I have had great fun, and I look forward to learning with you again soon.

Goodbye.