Lesson video

Hello there.

My name is Mr. Tilston.

I'm a teacher and a maths specialist.

So it's my great pleasure to be with you today teaching you a lesson all about unit conversions.

Units of measure can be seen everywhere, every day.

Let me give you an example.

I've got some water here and you might see that's measured in millilitres.

And I've got a bottle of soft drink here and you can see that's measured in litres.

It would be helpful then if we had a way to convert from one unit to another, and that's what we're going to do today.

So if you are ready, I'm ready.

Let's begin.

The outcome of today's lesson is I can convert to and from fraction and decimal quantities of larger units.

You might have had some very recent experience of converting whole numbers.

Today we're going to look at fractions and decimals.

Our keywords for today, my turn equivalent, your turn, and my turn, convert, your turn.

Again, you might have had some very recent experience using these words, but it's worth a reminder because they're very important words that are going to come up a lot today.

So let's have a look.

If two or more things have the same value, they are equivalent and convert means to change a value or expression from one form to another.

Our lesson today is split into two parts or two cycles.

The first will be unit fractions and their decimal equivalents.

And the second one-unit fractions and their decimal equivalents.

If you're ready, let's start by looking at unit fractions and their decimal equivalents.

In this lesson, you're going to meet Izzy and Lucas.

Have you met them before? They're here today to give us a helping hand with our maths.

Lucas knows that one kilogramme is equivalent to 1000 grammes, and I bet you know that as well.

I bet that fact is locked and loaded and ready to go.

He's been writing these facts on two coloured counters to help him with conversions.

You might have seen him doing this.

You might have done it yourself even.

Here we go.

So he's got some red and yellow counters, on one side, he is written one kilogramme, on the other side, 1000 grammes.

Izzy's he's been doing something very similar but not quite the same.

She's been drawing on circles and writing those equivalent facts onto the circles.

So one kilogramme in one circle and 1000 grammes in a circle underneath it.

And that's something good that you can do if you don't have the counters.

It's nice and quick and simple.

Now Izzy is exploring what would happen if her circle was split into two equal parts.

So she's drawn that circle a few times and she's split it into two equal parts.

Can you see? So she's still got that one kilogramme written in her circle.

She's applying her knowledge of fractions and decimals, and I'm confident that you've got lots of knowledge about fractions in decimals too.

So here's a fraction, a decimal, and in grammes that fraction is half.

And again, I think you knew that already.

That's half, half a kilogramme to be exact in this case.

As a decimal, half is 0.

5 or five tenths.

I bet you knew that too.

So that's five tenths of a kilogramme or 0.

5 kilogrammes.

And in grammes, half of one kilogramme is half of a thousand grammes and half of a thousand is 500.

So we can see that showing half a kilogramme, 0.

5 kilogrammes or 500 grammes, they are all equivalent to each other.

And that can be shown on a double number line.

So we've still got her circles as a reminder is a double number line.

We can see look his half, which is the same as 0.

5, which is the same as 500.

So 500 grammes.

Okay, so we've got a key fact.

We've got half a kilogramme equals 0.

5 kilogrammes equals 500 grammes.

Okay, you're going to shout it.

Say it quickly, say it slowly and whisper it.

I'll start.

Okay, ready.

Half a kilogramme equals 0.

5 kilogrammes equals 500 grammes.

Can you do that? Go.

That was nice and loud.

Good, right.

We're going to say it very quickly.

I'll have a go and then you do it.

Here we go.

Half a kilogramme equals 0.

5 kilogrammes equals 500 grammes.

Can you do that? Off you go.

That was quick.

Right, we're gonna say it slowly.

I'll go first.

Half a kilogramme equals 0.

5 kilogrammes equals 500 grammes.

Can you do it slowly too? Off you go.

Very good.

And now we're going to whisper it.

Half a kilogramme equals 0.

5 kilogrammes equals 500 grammes.

You do it.

Very good.

That's a key factor.

See if you can remember that.

That would be helpful.

Now Izzy is exploring what would happen if her circle was split into four equal parts.

So it was two before and now it's four.

And again, she's looking at what the fraction and decimal and grammes would be.

So that is a quarter.

You knew that, didn't you? That's a quarter.

And in this case it's a quarter of a kilogramme.

What's quarter is a decimal is 0.

25.

So 0.

25 kilogrammes is equivalent to one quarter of a kilogramme.

And what about grammes? Now remembering that one kilogramme is 1000 grammes, what's a quarter of a thousand? Halve and Halve again, and you've got 250 grammes.

So one quarter of a kilogramme and 0.

25 kilogrammes and 250 grammes are all equivalent to each other.

And again, we can see that on a number line.

There we go.

Right, again, shout it, say it quickly, say it slowly and whisper it.

I'll let you do it this time.

Off you go.

Now Izzy it is exploring what would happen if her circle was split into five equal parts.

So she split it into two equal parts and then four equal parts, and now five.

Hmm.

So what would that fracture be? What do you think there? What can you see there? Not half, not quarter.

What is it this time? It's one fifth.

So that's one fifth of a kilogramme.

And that's how we write that.

You knew that I'm sure.

What's that as a decimal? Hmm? Can you remember? You worked it out? 0.

2 kilogrammes or two tenths of a kilogramme if you like.

0.

2 kilogrammes and then it's grammes.

What do you think? So that's 1000 grammes divided by five, five equal parts.

What's one part going to be? 200 grammes.

So one fifth of a kilogramme and 0.

2 kilogrammes and 200 grammes are all equivalent.

And again, we can see that on a double number line.

Go and then shout it, say it quickly, say it slowly and whisper it.

Now Izzy is exploring what would happen if her circle was split into 10 equal parts.

She split into two equal parts, four equal parts, five equal parts, and now 10 equal parts.

What fraction can you see to start with? What's that? You've seen this before, I know.

That's one 10th of a kilogramme.

What's that as a decimal? That's 0.

1 kilogrammes.

And again, that can be read as one 10th of a kilogramme as well.

They're worth the same and in grammes.

Okay, a thousand grammes divided by 10.

What does it give? 100 grammes.

So one 10th of a kilogramme and 0.

1 kilogrammes and a hundred grammes are all equivalent.

And once again, we can see that on a number line.

A double number line.

Go on, and shout it.

Say it quickly, say it slowly and whisper it.

So we've got those key facts that one kilogramme equals a thousand grammes.

One kilometre equals 1000 metres.

One litre equals 1000 millilitres and one metre equals 1000 millimetres.

And I'm hoping that by now you've got those memorised because if you've got them memorised you can start to do other things with them, which is what we're going to do today.

So that same skill that we've just looked at can be applied to other unit conversions.

We looked at kilogrammes and grammes, but it works with others too.

So for example, if that was one metre, that would be 500 millimetres, that would be 250 millimetres.

That would be 200 millimetres, and that will be 100 millimetres.

So you can see there a half, a quarter, a fifth and one 10th of a metre.

Okay, over to you for a quick check.

Give the values of those grey sections this time in metres.

So if the circle, the full circle is worth one kilometre, what are the other great parts worth? Pause the video and give that a go.

Let's have a look.

So I can see a half there, which is 500 metres because half of 1000 is 500.

And then what about the next one? It's a quarter, isn't it? Hmm.

So a quarter of a thousand, that would be 250 metres.

And what about the next one? It's split into five equal parts.

So one fifth.

So 1000 divided by five gives you 200.

These numbers hopefully are ringing a bell.

They're the same numbers as before, aren't they? And what about the last one that's split into 10 equal parts? That's one 10th.

1000 divided by 10 equals 100 metres.

Well done if you got those.

You're on track.

A table can be used to list and summarise those conversions.

So half a kilogramme is 0.

5 kilogrammes equals 500 grammes.

One quarter of a kilogramme equals 0.

25 kilogrammes, equals 250 grammes.

One fifth of a kilogramme equals 0.

2 kilogrammes, equals 200 grammes.

And one 10th of a kilogramme equals 0.

1 kilogrammes, equals 100 grammes.

So they're really important facts to know.

Maybe your teacher could write those on a big sheet of paper in the classroom, or maybe you could jot it down somewhere.

It is time for some practise.

Number one, give the values of the grey sections in millilitres.

So this time the full circle is worth one litre.

What are the other grey sections worth? And then we've got a few questions to answer.

Now when you've done that, so 0.

2 litres equals what? One 10th of a litre equals what? And 0.

5 of a litre equals what in millilitres.

And number two, how much liquid is in that container? So you could see it would go to one litre, one full.

It's not at one litre.

Think how many equal parts it's divided into.

Record it as a fraction, as a decimal and in millilitres, please.

Number three, complete the table.

So we've got some information given already.

So the first column is fractions, the second column is decimals, and the third column, conversions to millimetres.

See if you can complete that.

And number four, Lucas says 0.

25 kilometres is equivalent to 25 metres.

Is he correct? Explain.

And number five, express each scale reading in three ways, a fraction, a decimal, and in grammes.

Pause the video and good luck.

Welcome back.

How did you find that? How did you get on? Are you feeling more confident? Well, let's have a look.

So that is one lead to the circle.

We could say it is 1000 millilitres.

That will be a good helpful starting point, meaning that circle segment is worth 500 millilitres.

That's 250 millilitres.

That's 200 millilitres, and that's 100 millilitres.

So a 0.

2 litres equals 200 millilitres, one 10th of a litre equals 100 millilitres and 0.

5 of a litre, that's half equals 500 millilitres.

Number two, how much liquid is in the container? Well, as a fraction, that's one 10th of a litre, as a decimal, it's 0.

1 metres, and in millilitres, that's 100 millilitres.

And that's the completed table.

Half a metre is 0.

5 metres is 500 millimetres.

One quarter of a metre is 0.

25 metres is 250 millimetres.

One fifth of a metre is 0.

2 metres, that's 200 millimetres and one 10th of a metre is 0.

1 metres is 100 millimetres.

And then Lucas thinks 0.

25 kilometres is equivalent to 25 metres.

Is that correct? No, it's not.

0.

25 is the same as one quarter, which hopefully you knew.

And one quarter of a thousand equals 250.

And number five express each scale reading in three ways, a fraction of decimal and grammes.

So the first one, one fifth of a kilogramme equals 0.

2 kilogrammes equals 200 grammes.

The second one, one 10th of a kilogramme equals 0.

1 kilogrammes equals 100 grammes.

And the third one, half a kilogramme equals 0.

5 kilogrammes equals 500 grammes.

Well done if you've got those.

Well, you're doing really well, really, really well.

Are you ready for cycle two? I think you are.

That's non-unit fractions and their decimal equivalents.

So all of those had one for their numerator.

You had one half, one quarter, one fifth, and one 10th.

Let's explore what would happen if it wasn't one for the numerator.

Izzy is using her knowledge of unit fraction equivalents to give non-unit fraction equivalence.

She's got that one kilogramme again, she'd done this before.

That's one quarter of a kilogramme.

That means that's one quarter of a kilogramme as well.

And so is that, and so is that.

So she's writing the fraction on all of the circle sections.

And as a decimal, that's 0.

25.

So is that, so is that, and so is that, and in terms of grammes, that's 250 grammes or so is that, and so is that, and so is that.

So what have we got here? If I know that one quarter of a kilogramme is 250 grammes, that means three quarters of a kilogramme is 750 grammes.

So can you see the three quarters, first of all in the fraction circle, one quarter, two quarters, three quarters, and then look at the grammes.

Can you see 250 grammes, 500 grammes, 750 grammes? So three quarters of a kilogramme and 750 grammes are the same.

They're equivalent.

If I know that 0.

25 kilogrammes is 250 grammes, 0.

75 kilogrammes is 750 grammes.

So can you see that with a decimal? 0.

25, 0.

5, 0.

75.

So they're all equivalent to each other.

You could calculate 250 plus 250 plus 250, or you could calculate 250 times three, whatever's easier and whatever's more efficient.

Okay, we've got another one here.

So this is fifths.

It's been divided into five equal parts.

So all of those are fifths, and that means all of those are 0.

2 or each of those are, and each of these is 200 grammes.

Now we can use that unit fraction to work out the non-unit fractions and the equivalents.

What have we got here, then? Let's have a look at this.

What can you see? What different things can you see? Can you see three different values? What fraction can you see? What decimal can you see? And how many grammes can you see? Well, if I know that one fifth of a kilogramme is 200 grammes, two fifths of a kilogramme is 400 grammes.

And if I know that 0.

2 kilogrammes is 200 grammes, 0.

4 kilogrammes is 400 grammes.

You could calculate 200 plus 200, or you could calculate 200, multiply by two, whatever's quicker and more efficient.

Let's have a check.

What is three fifths of a kilogramme in grammes? Use the circles to help.

Pause the video.

What do you think? Let's have a look.

So this is three fifths of a kilogramme.

Look at that on the fraction part.

And we can also see that as a decimal.

That's 0.

6, but that's not what it's asking.

It's asking how many grammes that is.

Well, let's see, 200, 400, 600.

So three fifths of a kilogramme in grammes is 600 grammes.

Very well done if you've got that, you are definitely on track.

We've got another one here.

So this is the 10th.

So the fraction is one 10th of a kilogramme.

That's our unit fraction.

We're going to use that as a starting point for other values.

They're all one 10th, that's 0.

1.

So they're all 0.

1 and that's 100 grammes.

So they're all 100 grammes.

What have we got here? What's the fraction? What's the decimal? And how many grammes? Hmm? Knowing that one 10th of a kilogramme is equal to 100 grammes allows you to give other multiples of one 10th of a kilogramme or other multiples of 0.

1 kilogrammes.

This example shows that seven tenths of a kilogramme or 0.

7 kilogrammes are equivalent to 700 grammes.

Can you see that? If one 10th of a kilogramme equals 100 grammes, seven 10th of a kilogramme equals 700 grammes.

We could do that without the circles.

And Izzy thinks she can too.

She thinks she can use that sentence structure to convert from lots of different unit fractions and types.

So if one quarter of a kilogramme equals 250 metres, three quarters of a kilogramme equals what? What do you think? Think about that three times.

I'm picturing that in my mind.

I'm picturing the circle still.

What do you think? 750 metres.

Let's do another one.

If one fifth of a metre equals 200 millimetres, four fifths of a metre equals what? So think about that 204 times.

I'm seeing the circles again in my mind, I'm visualising them.

Well, we got, that's 800 millimetres.

And what about if one fifth of a litre equals 200 millilitres? Three fifths of a litre equals what? Hmm? Picture the circles.

Picture that 200 mils three times and you've got 600 millilitres.

So can you see how starting with a unit fraction is a helpful starting point for working out one-unit fractions and the equivalents.

Let's have a little check.

Complete the stem sentences.

If one quarter of a metre equals mm millimetres, three quarters of a metre equals mm millimetres.

And if 0.

25 litres equals mm millilitres, 0.

75 litres equals mm millilitres.

Pause the video.

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

Well, if one quarter of a metre equals 250 millimetres, which it is, then three quarters of a metre equals 750 millimetres.

And if 0.

25 litres equals 250 millilitres, 0.

75 litres, which is three lots of that equals 750 millilitres.

And very well done if you got that.

Time for some practise.

Number one, fill in all the parts of the circle in millimetres and use it to answer the questions below.

Number two, complete the table.

The first one's been done for you.

So we've got, again, just like before, fractions in one column, decimals in the middle one and conversions to metres at the end.

And then number three, if one fifth of a kilometre equals mm metres, then three fifths of a kilometre equals mm metres.

And number four, how much liquid is in the container.

Record as a fraction, as a decimal and say how many millilitres there are.

And number five, express each scale reading in three ways, as a fraction, as a decimal and in grammes.

Pause the video.

Welcome back.

Well, let's have a look, shall we? Number one, fill in all the parts of the circle in millimetres and use it to answer the questions below.

And you can use mm, instead of writing millimetres.

So that's 500 millimetres, 250 millimetres in all of those parts, 200 millimetres in all of those parts, and 100 millimetres in all of those parts.

Have you noticed these same numbers keep coming up again and again.

So hopefully you're starting to memorise those and get used to them.

Okay, and then for a three quarters of a metre equals 750 millimetres, two fifths of a metre equals 400 millimetres and 0.

9 metres equals 900 millimetres.

Number two, complete the table.

The first one's been done for you.

So four fifths of a kilometre.

That equals 0.

8 kilometres or eight tenths of a kilometre, and that's 800 metres.

0.

75 kilometres as a fraction is three quarters of a kilometre and converted to metres that's 750 metres.

And the 900 metres is the same as nine tenths of a kilometre, which is 0.

9 kilometres, which could also be read as nine tenths of a kilometre.

And number three, if one fifths of a kilometre equals 200 metres, then three fifths of a kilometre equals 600 metres.

And for number four, three fifths of a kilogramme equals 0.

6 kilogrammes, equals 600 grammes.

The second one, that's four tenths of a kilogramme, that's 0.

4 kilogrammes and that's 400 grammes.

And the last one, that's four fifths of a kilogramme or 0.

8 kilogrammes or 800 grammes.

We've come to the end of the lesson.

Today, we've been converting to and from fraction and decimal quantities of larger units, and we've used circles to help us to understand that.

By working out a unit fraction of a metre, litre, kilogramme or kilometre, you have the basis to calculate non-unit fractions.

This example shows how you might use that one 10th of a kilogramme is equivalent to 100 grammes to convert other tenths of a kilogramme.

You've been amazing today.

I've thoroughly enjoyed spending this time with you, and I hope that I get the chance to spend another math lesson with you in the near future.

Give yourself a pat on the back.

You deserve it.

I hope you enjoy the rest of your day, whatever you are doing.

Take care and goodbye.