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Hello again guys and welcome to lesson four in our unit on fractions.

Today's lesson is all about finding unit fractions of a given quantity.

So we're going to have to remember all of the things we've done our previous lessons to help us with this lesson today.

Okay are we ready? Great, let's get started.

So things will need today just like yesterday you need a pencil and some paper and that's about it.

Before we get started make sure that you've completed that knowledge quiz cause that's going to help inform the lesson today.

Now, in that knowledge quiz you would have had a look at some of the things that we learned yesterday.

So let's have a bit of a recap.

There is a really important bits of vocabulary that we looked at yesterday.

What do we call this line in the middle of our fractions? What do we call this? It's called a vinculum.

Great, well done if you've got that.

Then after we've drawn our vinculum we then think about this.

The wall the part that shows us how many parts there are.

We call it our denominator.

And lastly once you've got that we want to know how many parts we are interested in.

That is called our numerator.

Well done if you got all of these.

Let's go through our star words.

So my turn your turn.

Quantity, fraction, whole equal parts, multiplication, division.

Right guys if you're not sure of any of those words pause and maybe practise some of them now.

We might not have come across the word quantity before.

This is a number.

Its an amount of something.

So in today's lesson we're going to be finding fractions of a quantity.

So we're going to be finding fractions of an amount of a number.

Nice simple stuff for us.

But this helps us to be able to think about representations and how we'll be able to show our learning.

What is one half of four? Now in order to be able to solve this I need to think carefully about my knowledge of fractions.

Now I know that the denominator shows me how many parts I need to split my whole into.

The first thing is what is my whole? Well my whole is four.

One, two, three, four.

I need to split this into two different parts.

I could do it by there or I could do it by sharing.

Now you might have some biscuits at home to do it with or you might have some counters that you could use or you might just want to draw it on a piece of paper.

But can we try and represent this in two groups? So trying to split our whole into the different groups.

So I know that the denominator is two so I'm going to split my four into two equal groups.

Hey that's my representation.

Maybe yours is different or similar.

And then I need to think about my numerator.

This is how many of these parts I want.

So because the numerator is one I know I want one of these parts.

So in this case what is one half of four? One half of four is equal to two.

Now I'm quite aware you probably already knew that but we want to see the representation that we're using during this lesson.

So we started with a nice simple example.

So let's make it a little bit more complicated.

I've got two more questions now.

What is one third of 15? What is one quarter of 16? Now just like before I want us to focus on the representations we're using to be able to show and prove that we know the answer.

Not just giving numbers as answers.

So if you're feeling confident you might want to pause the video and have a go at this on your own now.

If you're not feeling as confident then watch along with me to see exactly how we're going to represent this accurately.

Now remember these prompts are going to help us at the top.

So let's really use these to make sure we follow this clear steps.

The first thing I need to think about is what is my whole? Well my whole is 15.

I need to split this into how many equal parts? What tells us the equal parts we're going to use? That's right the denominator does.

So I use my denominator and that tells me I need to split 15 into three equal parts.

I do that by sharing things out or drawing it.

Okay there we go.

I've got 15 and I flipped into three equal parts.

But I'm not finished yet.

Cause my last question says how many parts do we want? Well we know that the numerator is one.

So we know we want one of these parts.

Okay so let's have a look.

So my answer is one, two, three, four, five.

One third of 15 is equal to five.

Great, well let's have a look at the second example.

One quarter of 16.

First off, what's the whole? Okay, great the whole is 16.

How many equal parts are there? So how many equal parts do I want to share into? That's our denominator.

So I need to share this into four equal parts.

Okay let's do that and pictorially represent it.

Okay that's my picture to represent this.

So I can see I've got 16 as my whole and I've shared it into four equal parts.

But I'm not done yet cause remember that numerator.

How many parts do we want? We want one of those parts.

So I can say that there are one, two, three, four.

So one quarter of 16 is equal to four.

Okay, you might have had a bit of a go or I've had a go.

Now it's definitely your turn.

So here's three more examples.

I'd like you to pause the video in a second and have a go at some of these.

Remember our prompts there to support you and really think about how you're representing it.

I don't just want the answer.

I want you to think about how you're going to draw it to prove that you know that is the answer.

Okay, cause someone might not believe you.

So you going to have to have some proof of that.

Okay, pause the video now and then play it when you finished.

Right guys, hopefully you've got this pictorial representation is done and you've got your answers.

Let's just double check those answers.

One third of nine is equal to three.

One fifth of 25 is equal to five.

And one quarter of 24 is equal to six.

Well done if we got all of this.

Let's move on our learning slightly then.

Maybe when you looked at these you thought yourself Ooh! I can see some patterns.

Perhaps there's a quicker way than using our arrays.

Our arrays are brilliant because they show us the learning.

But is there a faster way? Can you use a multiplication tables.

Have a look at these numbers.

One half of 12 is equal to six and have a look.

Can you see any patterns there? If you can try and explain them to the person with you.

What do you notice? Okay, hopefully you've noticed that we can see some of these multiplication and division patterns in our fractions.

So you can see that two multiplied by six is equal to 12.

And we can see that 12 when we divide it into six parts is equal to two or we could see that 12 divided by two is equal to six.

So this shows us in all of these examples that we can use our multiplication facts to help us when we're doing fractions.

And we're finding fractions of amounts or fractions of quantities.

We still need our pictorial representations but these can really support us.

So do use those to help you when you're working these out.

Now, I've got a real challenge for you now.

These numbers I've taken the whole away.

So if you got some problems where the whole is no longer there.

Now let's have a look.

I'm going to do the one which says my turn now.

I'm thinking of a number.

I don't know the number.

But I have been given one of the parts.

One quarter of the number is four.

What number am I thinking about of? So what is the whole? So if I know that one quarter of a number is four can I work out what the whole is.

Okay, well I'm going to try and use my pictorial arrays to help me with that.

So I know that because the denominator is four there are going to be four equal parts.

Okay that is my four equal parts.

And I know that one of those parts is equal to four.

So I put in four counters.

Now we find though that one of these parts is equal to four.

I also can then say well, all the other parts cause I know in fractions all the parts are equal.

All the other parts must also equal four.

So therefore, can you work out what my number is going to be? What number was I thinking of? Well, that's another four and another and another.

So one quarter of my number is four then my number must be four eight, 12, 16.

So my number must've been 16.

What else can you tell me? So can you tell me anything else that perhaps that might give you some creatives? So if I've got two as my quarters I know that two quarters of my number is equal to four eight.

It's three quarters of my number.

I can see as equal to 12.

So we can use our pictorial representation not just to find out the answer but to find out lots more as well.

Okay then its your turn.

So thinking about the same way that I've just done it using our pictorial representation.

I know that one fifth of the number is three.

If I know that one fifth of the number is three can I work out what number it was to start with.

Pause the video now and have a go at that.

Okay guys how did you do? Hopefully you're feeling very happy with that and you should have got that one fifth of the number is equal to three and there are five equal parts.

So you should have had five lots of three.

So we should have had an answer of 15.

So a number I was thinking of was 15.

Well done if you got that guys.

Okay I've got another problem for you.

This is different sorts of representation.

True or false? This time I'm going to let you go first and then I'm going to have a go.

So I have shaded one quarter of this shape.

Am I true or false? And can you prove it? Can you explain really clearly why it is true or if it's false.

Pause that then when you're ready and you've got your explanation play again.

Okay how did we do? Well, what I've done first is I thought to myself well, this is kind of useful but I can't really see it really clearly.

Now to see a bit more clearly I'm going to move these two over to here.

So I can see nice and clearly the representation that I've got.

Now this helps me to see that although there were four shaded that isn't necessarily one quarter.

In fact it isn't one quarter.

And I can see here that actually now I've got one two, three groups.

So I've only shaded one out of three.

Okay, so one out of three.

One out of three.

One out of three.

One out of three.

Not one out of four.

Okay so this one is actually false.

Well done if you've got that but I'm really interested in is how you're able to explain it to the person sat next to you.

Okay guys along the same lines as this I've got some further problems for you to have a look at.

So have a look at these different activities and think.

Firstly, this shows one quarter.

Is that true or false? And just like before can you explain why and how you know.

Once you've done that can you shade the same shape so that it shows one third.

Maybe can do that in more than one way.

And I've got some problems here saying who has more? So these people are finding fractions of quantities and who has more and then Eva has a problem here.

And can you explain why that.

So lots of explaining but keep on using those pictorial representations to help you.

Pause the video now and have a go.

Okay how did we do guys? Hopefully we're able to solve lots of those problems and give really detailed explanations using our knowledge of fractions well done.

Lets have a look at the answers.

Now true or false? This shows is one quarter does it? Well, we can see that if we moved this over then we would have our quarters.

So in fact it is true.

Hopefully you've got a shape which shows now one-third.

Could look a little bit like that but it might look a little bit different if you did it differently make sure you can explain it to the person who is with you.

Who has more? Well Rosie has one quarter of eight pounds.

Hopefully with our representations we found that that was two pounds.

And Whitney has one half of six so she would have three pounds.

Okay then with your explanations I can't really give you a good thing on this display.

But Eva said that she has one quarter because she has four marbles.

Now do we think that's true? Is that one quarter or is she got a little bit confused? Hopefully you're able to explain that actually she's not got one quarter she has one fifth of that.

So one out of five not one out of four.

Okay so we've used our knowledge of fractions all the way through from numbers to also using it in shapes and different representations.

Really well done today guys that wasn't an easy lesson.

If you're not sure about anything please do go back and practise those things again.

Now before you leave just to make sure that you finish the final quiz.

How you have fun guys keep on practising on fractions and I will see you soon bye bye.