Lesson video

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

Shawrick and I'm really excited to be learning with you today.

You've made a great choice to learn maths with me, and I know that we are going to be successful as we move through the learning.

Welcome to today's lesson.

This lesson is from our unit Calculating with Decimal Fractions.

The lesson is called Convert Units of Mass and Capacity.

As we move through the learning today, we will deepen our understanding of multiplying and dividing by 10, 100 and 1,000 and apply this in the context of measures, in this case, mass and capacity.

Now, sometimes new learning can be a little bit tricky, but I am here to guide you and I know if we work really hard together, then we can be successful.

Should we get started then? How can we use our knowledge of multiplication and division by 10, 100 and 1,000 to convert units of mass and capacity? Our key words for the lesson today are mass and capacity.

You might have heard them before, but it's always good to practise.

Let's have a go.

My turn, mass.

Your turn.

Nice.

My turn, capacity.

Your turn.

Fantastic.

So mass is a measure of how much matter there is in an object, and we usually measure in kilogrammes or grammes.

And capacity is a measure of the amount that something can hold, commonly measured in litres or millilitres.

We're going to start at the lesson today looking at how we convert units of mass.

And in today's lesson we have Lucas and Sofia to help us.

Lucas wants to measure the mass of his adorable kitten.

So he's got some scales there that say zero grammes at the moment because there's nothing on them.

He places the kitten on his electronic scales.

Watch what happens.

Mm.

The mass of my kitten is 500 grammes and it's a very adorable kitten, isn't it? Lucas changes the unit of measurement.

You might have done some cooking at home and notice that you can do that.

He presses the button and changes it to kilogrammes.

What do you notice? Well, the matter of the kitten hasn't changed, has it? But the unit has changed.

It's now showing 0.

5 kilogrammes.

What does that mean, what can we say? That's right, we can say that 500 grammes must be equivalent to 0.

5 kilogrammes.

And do we remember anything else about mass conversion? Sofia is asking us.

Well, do we remember that one kilogramme is equal to 1,000 grammes? And if we know one kilogramme is equal to 1,000 grammes, what else do we know? Well, we know that one-tenth of a kilogramme or 0.

1 of a kilogramme must be equal to 100 grammes.

one-hundredth of a kilogramme or 0.

01 of a kilogramme is equal to 10 grammes.

And we can also say then that one-thousandth of a kilogramme is equal to one gramme.

Can you spot a pattern there? Did you notice that 0.

1 kilogrammes is one-tenth the size of one kilogramme.

So 100 grammes is one-tenth the size of 1,000 grammes, 0.

1 kilogrammes and 100 grammes are equivalent masses.

And the same can be said for 0.

01 kilogrammes.

It's one-hundredth the size of one kilogramme and 10 grammes is one-hundredth times the size of 1,000 grammes.

0.

01 kilogrammes and 10 grammes are equivalent masses.

And the same can be said for one-thousandth times the size of one kilogramme, which is 0.

001 and one gramme is one-thousandth times the size of 1,000 grammes.

So we can say that 0.

001 kilogramme and one gramme are equivalent masses.

We can also write this as a fraction 0.

001 kilogramme, well that is equivalent to one-thousandth.

So one-thousandth of a kilogramme is equal to one gramme.

Why is that? Well, that's because we need 1,000 grammes to make that one kilogramme.

Now I wonder if you have managed to make a connection with the conversions between kilogrammes and grammes with any other conversions? Ah, it's similar to converting units of length where one kilometre is equivalent to 1,000 metres.

Can you see the similarities between kilogrammes and grammes and kilometres and metres? That's because one kilogramme is 1,000 grammes and one kilometre is 1,000 metres.

Let's have a look at this problem.

Sofia has a 2.

5 kilogramme bag of potatoes.

Lucas has a 725 gramme cake.

Lucas is saying that his cake has a greater mass because 725 is greater than 2.

5.

What do you think, do you agree or would you challenge him? Sofia is challenging him.

"I respectfully disagree.

The units are different, so we cannot compare them by just looking at the numbers." So what do they need to do? That's right, Sofia.

They need to convert the units so that they are the same.

We could convert the 2.

5 kilogrammes into grammes or the 725 grammes into kilogrammes, it doesn't matter.

As long as we then have the same unit, we can then compare.

Let's look at the 2.

5 kilogramme bag of potatoes.

We can use the known fact that one kilogramme is equivalent to 1,000 grammes.

So there are 1,000 grammes in one kilogramme.

So we need to multiply the mass in kilogrammes by 1,000 and that will tell us the mass in grammes.

So 2.

5 kilogrammes multiplied by 1,000.

Well, we know that when we multiply by 1,000 the digits move three place value places to the left.

2.

5 kilogrammes is equivalent to 2,500 grammes.

Let's check your understanding with that.

Which of these is the correct conversion of 0.

31 kilogrammes into grammes.

Is it A, B, C, or D? Pause the video while you have a think about it.

Maybe chat to somebody about this.

When you're ready for the answers, press play.

How did you get on? Did you work out that it can't be A? We can't just put three zeros on the end.

It can't be 3.

1 grammes because that's only 10 times larger than 0.

31.

It can't be 31 grammes because that's only 100 times larger than 0.

31.

It must be D, 310 grammes.

When we convert from kilogrammes into grammes, we need to multiply by 1,000.

When we multiply by 1,000, all the digits move three places to the left.

How did you get on? Well done.

But let's look at the 725 gramme cake.

We could convert grammes to kilogrammes using the known fact that one kilogramme is equal to 1,000 grammes.

There are 1,000 grammes in one kilogramme, so we need to find one-thousandth of 725.

To find one-thousandth, we need to divide by 1,000.

This is the same as multiplying by 0.

001.

So we can take the mass of the cake and divide it by 1,000 or multiply it by 0.

001.

Can you remember how to do that? That's right.

When we multiply by 0.

001, the digits move three places to the right.

725 grammes is equivalent to 0.

725 kilogrammes.

Let's check your understanding.

Which of these is the correct conversion of 403 grammes into kilogrammes? Is it A, B, C, or D? Pause the video while you take a look at those and when you are ready to go through the answer, press play.

How did you get on? Did you realise it can't be A? For A, we've just removed zero and we know we can't do that when we are dividing, all the digits have to move.

B, we've multiplied by 1,000, haven't we? And grammes are smaller, so there must be more of them.

So for kilogrammes we must divide.

So when we convert from grammes to kilogrammes, we need to divide by 1,000.

That's the same as multiplying by 0.

001 or one-thousandth.

And when we multiply by that one-thousandth, all the digits move three places to the right.

So C is our only option.

D, we have multiplied by or we've divided by 10,000.

We've done 10 times too many.

Let's summarise.

Lucas has a 725 gramme cake.

We know that's equivalent to 0.

725 kilogrammes.

We know Sofia has a 2.

5 kilogramme bag of potatoes, which is equivalent to 2,500 grammes and we can see then that Sofia was correct after they converted the units, we could then compare the masses.

We can see 0.

725 kilogrammes is smaller than 2.

5 kilogrammes or we could compare the grammes.

725 grammes is smaller than 2,500 grammes.

So the bag of potatoes has the greater mass and we can summarise what we have been converting.

We can convert from kilogrammes or grammes to kilogrammes or grammes.

And we can see converting from grammes to kilogrammes we divide by 1,000 and converting from kilogrammes to grammes, we multiply by 1,000.

That's because there are 1,000 grammes in one kilogramme.

It's your turn to practise now.

For question one, starting with the smallest, could you put these units of mass in order and give reasons for your ordering? For question two, could you solve these problems? Sofia needs 10 kilogrammes of flour.

She already has 3,200 grammes.

How much more flour does she need? And for part B, Lucas's dad bought 850 kilogrammes of sand to build a wall.

He used 75,000 grammes on Monday and 250,000 grammes on Tuesday.

How much sand does he have left? Pause the video while you have go at both of those questions.

When you are ready to go through the answers, press play.

Shall we see how you got on? For question one, you had to start with the smallest putting the units of mass in order.

You might have reasoned that you converted the units, so they were all either in kilogrammes or grammes.

You could then compare them.

So I converted into grammes, 0.

45 kilogrammes.

I had to multiply it by 1,000.

There are 1,000 grammes in one kilogramme and that's 450 grammes.

Four kilogrammes multiplied by 1,000 is 4,000 grammes.

0.

404 kilogrammes multiplied by 1,000 is 404 grammes.

Once the units were the same, I could compare them.

Starting with the smallest 0.

404 kilogrammes, 405 grammes, 0.

45 kilogrammes, four kilogrammes, and then 4,050 grammes.

For question two, you had some problems to solve.

I represented this in a bar model.

Sofia needs 10 kilogrammes of flour, so that is my whole.

She already has 3,200 grammes, that's my part and we need to find the unknown part.

First of all, I noticed that the units were different, so I converted kilogrammes into grammes by multiplying by 1,000, and then I could subtract to find the unknown part, which was 6,800 grammes.

Sofia needs 6,800 grammes more flour, and that's equivalent to 6.

8 kilogrammes.

For part B, I could represent this in a bar model.

850 kilogrammes is our whole, and we have three parts, two that are known and one that is unknown.

First we find the sum of the known parts, then we can subtract from the whole to find the unknown part.

750,000 plus 250,000, I can partition the 75,000 and that gives us 325,000.

But then I've noticed that my units are different, so I need to convert.

I'm going to convert my 325,000 grammes into kilogrammes by dividing by 1,000, which is 325.

I can then subtract the 325 from the 850, which gives me 525 kilogramme.

He has 525 kilogrammes of sand left.

This is equivalent to 525,000 grammes.

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

Fantastic learning so far.

Shall we move on? Let's have a look at how we convert units of capacity.

Lucas fills a jug with water.

Can you imagine that? Can you visualise filling a jug with water? There you go.

What do you notice about my jug? Ah, Lucas has noticed that the capacity of this jug is one litre or 1,000 millilitres.

1,000 millilitres must be equivalent to one litre.

They are just different units.

The units are different, but they are the same capacity.

He then pours all that water into another jug of the same size.

Hmm, what do you notice this time? That's right, the capacity has remained the same, but the unit has changed.

We've got DL, haven't we? One litre is equivalent to 10 DL and then he pours all of the water into another jug.

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

The capacity has remained the same, but the unit has changed again.

This time we know that 10 DL is equivalent to 100 CL.

Let's look at the jugs altogether.

What do you notice? The capacity is the same for each jug, but the unit is different, isn't it? We can see that one litre is equivalent to 10 DL, which is equivalent to a hundred CL, which is equivalent to 1,000 ML.

Hmm, I wonder if you noticed this.

Sofia remembers that L stands for litre and ML stands for millilitre.

But what about DL and CL? What do they stand for? I wonder if you know.

Thank you, Lucas.

DL stands for deciliter.

The prefix deci means one-tenth.

So one DL must be one-tenth of one litre.

What about CL then? Well, CL stands for centilitre.

The prefix centi means one-hundredth.

So one CL is one-hundredth of one litre.

And we can use these known facts to convert between any of these measures of capacity and we can use a table to help us convert from any of these measures to any of the measures.

So for example, if I want to convert from litres to centilitres, I can see I need to multiply by 100.

Let's have a look at this problem.

Lucas and Sofia both have a bottle of water.

Lucas' bottle has a capacity of 1.

575 litres.

Sofia's bottle has a capacity of 175 millilitres.

"My bottle has a greater capacity," Sofia is saying, "because 175 is greater than 1.

575." What do you think? Do you agree with her or would you respectfully challenge her? Ah, Lucas is respectfully disagreeing.

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

We've got litres, our millilitres, haven't we? What do we need to do? That's right, we need to convert the units so that they are the same.

We could convert litres to millilitres or millilitres to litres.

It doesn't matter.

So let's look at Lucas's bottle.

Lucas's bottle has a capacity of 1.

75 litres.

We know one litre is 1,000 millilitres and we can use that known fact to convert 1.

575 litres into millilitres.

To find the capacity of millilitres, we need to multiply the amount in litres by 1,000 because there are more millilitres in the same amount.

So the capacity millilitres is the capacity litres multiplied by 1,000.

So we need to multiply 1.

575 by 1,000.

When we multiply by 1,000, the digits will move three places to the left.

We can say 1.

575 litres is an equivalent capacity to 1,575 millilitres.

Let's check your understanding on this.

Which of these equations correctly represents converting 0.

406 litres into millilitres? A, B, C, or D? Pause the video while you have a look and work it out.

And when you are ready for the answers, press play.

How did you get on? Did you realise it must be D? It can't be A because when we multiply by 1,000, we don't just place three zeros at the end.

That means the value of the number has not changed.

What about B? Well, we know we can't be dividing because there are more millilitres in the same amount than there are litres, so we must be multiplying.

C, well, we are multiplying by 1,000 but we've only moved the digits two places.

So C can't be correct.

It must be D.

When we convert from litres into millilitres, we need to multiply by 1,000.

When we multiply by 1,000, all the digits move three places to the left.

How did you get on with that? Well done.

Let's look at Sofia's bottle.

We could have converted this bottle from millilitres into litres.

We can use that known fact that one litre is 1,000 millilitres.

So to find the capacity in millilitres, we need to divide the amount in millilitres by 1,000 because there will be fewer litres.

So the capacity in litres is the capacity in millilitres divided by 1,000.

So we need to divide 175 by 1,000.

When we divide by 1,000, it is the same as multiplying by 0.

001.

And when we multiply by 0.

001, the digits move three places to the right.

So we can say that 175 millilitres is equivalent to 0.

175 litres.

Let's check your understanding on that.

Which of these equations correctly represents converting 540 millilitres into litres? Pause the video while you have a think about this.

Maybe chat to someone about it and compare your answers.

And when you are ready to go through it, press play.

How did you get on? Did you realise it must be B? It can't be A because we are multiplying by 1,000 and there will be fewer litres than there are millilitres.

So we need to divide by 1,000.

B is correct because we're dividing by a thousand, which is the same as multiplying by 0.

001.

So the digits will move three places to the right.

The placeholder in the thousandth is not necessary.

So we don't have to write a 0.

540 because it just tells us that there are no thousandths.

C, well, it can't be C.

We've only divided by 100 there.

And what about D? In D we have divided by more than 1,000.

We've divided by 10,000, so that can't be correct.

How did you get on? Well done.

Let's summarise.

So Lucas and Sofia both had a bottle of water and we converted the capacity of both bottles so that we could then compare them.

We know that Lucas's capacity of 1.

575 litres is equal to 1,575 millilitres.

And Sofia's bottle had a capacity of 175 millilitres.

We converted that to litres at 0.

175 litres.

Lucas is then correct.

We can see because we can now compare the capacities because we've got them in the same unit.

We could compare litres.

1.

575 litres is greater than 0.

175 litres or we could compare millilitres.

1,575 millilitres is greater than 175 millilitres.

So if the units are different, it's really important that we convert them to the same.

Lucas's bottle we can see has the greater capacity.

It's your turn to practise now.

For question one, could you tell me which is more 505 millilitres or 0.

5 litres? And could you give some reasons for your answer? For question two, starting with the smallest, could you put these units of capacity in order and give reasons for your ordering? For question three, got some problems to solve.

Lucas fills a bottle with water so it is full to its capacity of three litres.

Lucas and his friends have a 250 millilitre drinks bottle each.

They use all of the water in the three litre bottle to fill their bottles, how many bottles are filled? And B, Lucas and his friends have drinks bottles with different capacities.

Lucas' is 0.

2 litres, Sofia's is 230 millilitres, Izzy's is 25 centilitres and Andeep is 1.

9 deciliters.

What amount of water could they hold in total? Pause the video while you have a go at those questions.

When you are ready to go through the answers, press play.

Shall we see how you got on? For question one, you had to tell me which was more.

You might have said that 505 millilitres is the greater capacity.

The capacities were given in different units.

So to compare, we needed to convert.

When we convert from litres into millilitres, we need to multiply by 1,000 because millilitres are smaller, so there will be more of them.

All the digits move three places to the left.

0.

5 litres is equal to 500 millilitres.

And that is smaller than 505 millilitres.

So we can see that 505 millilitres is greater than 0.

5 litres.

For question two, you had to start with the smallest and put these units in of capacity in order, and you might have said that you converted the units so they were all given the same unit.

We could then compare them.

So I converted to litres 1,330 millilitres.

I'm dividing by 1,000 because there are 1,000 millilitres in one litre and that gives me 1.

33 litres.

The deciliter amount, 13 deciliters, I can divide by 10, which gives me 1.

3 litres.

103 centilitres divided by 100 is 1.

03 litres.

Once I had converted them to all two litres, I could then compare them and put them in order.

The smallest was 0.

13 litres, 0.

3 litres, 103 centilitres, 13 deciliters, and then 1,330 millilitres.

And then for question three, you had some problems to solve.

The first problem was about Lucas filling a bottle of water so it's full to its three litre capacity and then sharing that out between him and his friends.

So I've represented this in a bar model.

The whole amount is three litres and each part is 250 millilitres.

And we had to find out how many parts.

So I'm going to convert first because I've got litres and millilitres.

Three litres multiplied by 1,000 is 3,000 millilitres.

Now I can then use my known fact, 250 multiplied by four is 1,000 millilitres.

So 250 multiplied by 12 would be 3,000 millilitres.

So 12 bottles were filled with 250 millilitres each.

For part B, Lucas and his friends had drinks bottles with different capacities and we had to find the total amount of water they could hold.

I can represent this in a bar model.

The whole is the unknown amount and I've got four different capacities.

The easiest thing for me to do would be to convert the units to the same unit and it doesn't matter which unit we use.

So I'm going to convert to litres.

0.

2 litres is already in litres, so I do not need to convert that one.

230 I need to divide by 1,000, which is 0.

23 litres.

27 centilitres I need to divide by 100, 0.

27 litres and 1.

9 deciliters we need to divide by 10, 0.

19 litres.

Once they're all the same unit, I can add them together to work out the total amount, 0.

89 litres.

But you might have done it differently.

You might have converted differently.

So you could say that the bottles could hold a total of 0.

89 litres or 89 centilitres, or 8.

9 deciliters or 890 millilitres in total.

Any of those are correct.

They are all the same capacity, just different units.

These capacities are all equivalent, but the units of measure are different.

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

Fantastic learning today.

You should be really proud of the progress that you have made.

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

We know to use our known facts, that there are 1,000 millilitres in one litre and there are 1,000 grammes in one kilogramme.

It's been great fun learning with you today and I look forward to learning with you again soon.

Bye for now.