Lesson video

Hello everybody, my name is Mr Kelsall.

And welcome to today's lesson on fractions of quantities within measures.

Now, before we start, you will need a pen and a piece of paper, and also please try and find somewhere quiet that you're not going to get disturbed, and don't forget to remove any sorts of distractions.

For example, put your mobile phone on silent or move it away completely.

Pause the video, and then when you're ready, let's begin.

Today's lesson is all about fractions of quantities.

We're going to start by reminding ourselves about fractions and looking about measures.

We'll then look at quantities within measures.

We'll then look at multi-step fraction questions.

And then it's our quiz time.

As I mentioned, you'll need a pencil and a piece of paper.

Now, star words for today are fraction, denominator, numerator and vinculum.

A proper fraction, improper fraction, mixed number fraction, and we'll be talking a lot how to multiply.

In order to access this lesson, you need to understand that a fraction is part of a whole.

A denominator is the number of parts the whole is split into.

A numerator is the number of parts of the whole.

The vinculum is the line between the numerator and the denominator.

A proper fraction is where the numerator is less than the denominator.

And an improper fraction is where the numerator is greater than the denominator.

A mixed number fraction is a whole and a fraction together.

Equivalent fractions are fractions that represent the same number and to simplify a fraction, we look at reducing the numerator and denominator at the same time.

To multiply fraction, we will multiply the numerator by the whole number.

A little bit of revision.

There are five facts and we call these base facts that you need to learn.

The reason we call them base facts is you can use these facts to answer other questions about measures.

So fact number one is one kilogramme is a 1000 grammes.

When I say you can use this, if I ask you what two kilogrammes is, you know, that one kilogramme was a 1000 grammes.

Therefore, two kilogrammes is 2000 grammes.

Fact number two is one litre is a 1000 millilitres.

Fact number three, one kilometre is a 1000 metres.

Fact four, a metre is a 100 centimetres.

And fact, five, a centimetre is 10 millimetres.

Now that's great just to learn that, but actually we need to understand it a little bit.

So one kilogramme, a 1000 grammes.

Imagine a bag of sugar, you've got two general types of bags of sugar.

Quite a big one, and then a small one.

The big one is 1000 grammes.

So, when you're talking about a kilogramme, one big bag of sugar is a kilogramme.

When we're talking about a litre, if you think of cans of Coke, a can of Coke is 330 millilitres.

If you think of a big two litre, a big bottle of Coke, that's two litres.

And then you've got one half the size, which is still a big bottle, but it's not the biggest bottle.

And that's one litre, that's a 1000 millilitres.

I'm just going to jump to centimetres next.

And let's start with the smallest unit of measurement of length, one centimetre is 10 millimetres.

If I look at my little finger, the width of my little finger is about one centimetre.

When talking about one metre, most adults are less than two metres to think of one metre.

One metre is a 100 centimetres.

So if I put my little finger next to each other a 100 times, that would add up to be one metre.

Okay, these five facts you need to know, you need to be able to use.

If I said to you, how big is five centimetres? You should be able to think of one centimetre is 10 millimetres.

Two centimetres is 20 millimetres, three centimetres is 30, four centimetres 40, five centimetres is 50 millimetres.

These are the facts you need to able to use for this lesson.

Pause the video and spend a couple of minutes just learning these facts.

So for our new learning today, we're looking at fractions of quantities in a context, so, in real life situations.

So our starting point, the question says, "in the long jump Jessica Ennis jumped a distance of six metres and 40 centimetres." Now, straightaway before you even look at the question, and the possible answers, I'm thinking about what is six metres? Well, I know one metre is 100 centimetres, so six metres is 600 centimetres.

So six metres, 40, 640 centimetres.

I'm going to keep that in my mind for the moment, and then I'm going to carry on reading the question.

So, in the long jump, Jessica Ennis jumped a distance of six metres, 40 centimetres, which is 640 centimetres.

The first person said, "I can jump a quarter of that distance." The next person said that, "I can jump three fifths of that distance." And the final person said, "I can jump half of that distance." Pause the video, take a moment to think about these.

See if you can start working out what distance these three people can jump.

So the first person said, "I can jump a quarter of that distance." Well, how do we represent this? So first thing that I've done is on the left hand side here, I've drawn a bar model and that bar model is 640 centimetres.

Now I've split it into four parts because we're talking about quarters.

So, I'm interested in what is one of these parts.

And there's a few different ways that we can find a quarter.

So, I've give you one example here.

And I know that I've got six metres and 40 centimetres or 640 centimetres.

Well, I'm thinking multiples of four.

So I've just taken four metres and I've split those into four parts.

So I know each one of these is one metre.

So that's one metre, one metre, one metre, one metre.

That leaves me with two metres, 40 or 240 centimetres.

and I need to divide this by four parts.

Well, I know 24 divided by four is six.

So 240 divided by four is 60, so each one of these parts is 60 centimetres.

So I'm thinking I've got one metre and 60 centimetres.

So a quarter of six metres, 40 is one metre 60 centimetres.

You might think that that's quite a slow way to do it, and you might use a different way.

An alternative way is you can divide 640 by four.

So how many fours go into six? Well, there's just one and that leaves me two leftover.

How many fours go into 24? Four, eight, 12, 16, 20, 24, that's six.

How many fours into zero? Zero, so I know that's 160 centimetres or one metre 60 centimetres.

Or I could say 1.

6 metres.

Then the second person said "I can jump half of that distance." So I've modelled the question in the same way, I've drawn a bar model, it's 640 centimetres, and I've split it into two equal parts because we're talking about halves.

However, this time I thought it might be easier to start and do a written method to solve this.

So I'm doing 640 and I'm splitting it into two equal parts.

How many twos go into six? Which is the 600, is three, which is 300.

How many twos go in to the four? which is 40, two which is 20.

How many twos go into zero? Zero, so I know each half is 320 centimetres, or I could say three metres, 20 centimetres, or I could say 3.

2 metres.

If you wanted to do it mentally, you might consider looking at it like this.

So I've taken my six metres and I've split off my 40 centimetres.

I'm thinking six metres, what's half of that? Three metres, 40 centimetres, what's half of that? Well, a half four is two, so a half of 40 is 20.

So again, each part is worth three metres and 20 centimetres.

Finally, the last person said, "I can jump three fifths of that distance." Again, I represented my question using a bar model and I split it into five equal parts this time, because we're talking about fifths.

And I'm interested in three of those five parts.

If I wanted to do it mentally, I'm going to chunk my six metres 40, I'm going to chunk it into five metres and one metre 40.

The reason I've done five metres, is because we're talking about five parts.

So five metres divided by five means each part is one metre.

I think 140 centimetres and I need to divide them by five.

I'm thinking can I do that mentally? Well, I know a 100 centimetres divided by five is 20 and 40 centimetres divided by five is eight.

So, that means that each one of these parts is 28 centimetres.

So when I split six metres 40 centimetres into five parts, each part is one metre 28 centimetres.

However, I don't want one part, I want three parts.

So I need to do three lots of one metre and 28 centimetres.

So, three lots of one metre is three metres, three lots of 20 is 60 centimetres, and I'm going to remember that, three lots of eight centimetres, eight, 16, 24.

I'm going to remember that, and now to the sixty.

So 24 and 60 is 84.

So three fifths of six metres, 40 is three metres 84 centimetres.

Again, I could say that's 3.

84 metres, or I could say 384 centimetres.

Now that I have the three answers of the three different people I can compare, who's jumped the furthest, who's jumped the least furthest.

So while the first person could only jump a quarter of six metres, 40, which was one metre 60.

However, the second person could jump the furthest.

They could jump three fifths of six metres 40, which was three metres, 84.

And the last person could jump a half of six metres 40, which was three metres, 20.

Now look at the question on the screen and have a go with it.

In an Olympic high jumping event, an athlete cleared the height of two metres, 28 centimetres.

The first person said, "I can jump a third of that height." The second person said, "I can jump three quarters of that height." And the third person said, "I can jump a half the height he jumped," Pause the video, have a go at this, when you're ready, press play to continue.

So I know a third of two metres, 28, is 76 centimetres, which was the shortest height.

Number two, three quarters of two metres, 28 was 171 centimetres which was the highest of the three heights.

And the third one, a half of two metres, 28 was one metre, 14 centimetres or 114 centimetres.

That brings us to the develop learning for today.

Some problems there.

On his first throw, Alfie threw the javelin 38 metres, after working hard on his throw, he was able to throw half of that distance again.

How far did he manage to throw the javelin? Pause the video, have a go.

So, I started off when I drew a bar model and this 38 metres represented the whole first time Alfie threw his javelin.

I then thought, well, what is half of that 38 metres? I could use a written method, but actually I know half of 40 is 20, so half of 38 must be 19.

So I split this 38 into two halves, and then I reread the question and it said, "after working hard in his throw, he was able to throw half that distance again." So, I needed to add on half of that to my 38 metres.

So there's two ways to do this.

I can think of 38 at 19, or I can think of three lots of 19.

Well, let's check and see if they give the same answer.

So 38 at 19, I can think 38 and 20 is 58, and takeaway one is 57, or I can think of three 19s.

Now, some people might remember from arts that treble 20, three times 20 is sixty and treble 19 is 57.

So I also know three times 19 is 57 metres.

So Alfie was able to throw 57 metres on a second try.

And here's a question for you to try.

On his first try Sven threw the shot put 10 metres 50 centimetres.

After weeks of training, he could throw a further three fifths of this distance.

How far did he throw the shot put? Pause the video and when you're ready, press play for the answers.

So, Sven was able to throw it 10.

5 metres first time, three fifths of that is 6.

3 metres, which gives a total of 16.

8 metres that he was able to throw after that.

That brings us to our independent task for today.

Solve these questions, pause the video and when you're ready, press play for the answers.

For question, one, one six of 24 is four, so five sixth is 20, add to the original 24 is 44 metres.

Question two, one tenth of 50 is five metres, three tenths is 15 metres.

Question three, a third of five metres 10 centimetres is one metre 70, add that to the five metres 10 centimetres gives us six metres 80.

Question four, a quarter of six metres is 1.

5 metres or one half metres.

And for question two, one quarter of 4.

12 metres is 1.

03 metres.

Therefore, three quarters is 3.

09 metres.

The second part asks for two fifths of 10.

5 kilometres or one fifth is 2.

1 kilometres, so two fifths is 4.

2 kilometres.

Congratulations on completing your task.

If you'd like to please ask your parent or carer to share you work on Twitter, tagging @OakNational, and also #LearnwithOak.

And before we go, please complete the quiz.

So that brings us to the end of today's lesson on fractions of quantities within measure.

A really big well done on all the fantastic learning that you've achieved.

Now, before you finish bounce, quickly, review your notes and try to identify the most important part of your learning from today.

Well, all that's left for me to say is thank you, take care and enjoy the rest of your learning for this day.