Lesson video

Hi, my name's Mr. Peters, and welcome to today's lesson.

In this lesson, we're gonna be thinking about finding a unit fraction of an amount using representations.

I can't stress how many times I use this skill within my everyday life without even realising I'm using it.

So hopefully you'll find this useful for you today going forward.

If you're ready to get started, let's get going.

So, by the end of this this session today, you should be able to say that I can use representations to find a unit fraction of an amount.

In this session today, we've got one key word we're gonna be referring to throughout.

I'll have a good saying it and then you can repeat it after me.

The word is representation.

Your turn.

To describe what we mean by representation.

A representation is a way of showing an idea or a concept.

One concept can be shown using multiple representations.

So throughout the session today, we've got two cycles.

The first cycle we're thinking about showing a unit fraction of an amount, and the second cycle will be finding the value of a unit fraction.

Let's get started with the first cycle.

Throughout the session, we'll be joined by both Lucas and Jun.

They'll be sharing their thinking as well as any questions that they have as we go throughout the lesson.

Okay, so let's start our lesson here today, then.

We're gonna recap how we can describe what we can see in this bar model.

Have a look at the bar model, and have a look at the stem sentence below underneath that.

How could you have a go at describing that? Can you use the stem sentence to help you? I'll give you a moment to have a think.

That's right.

We could say that the whole has been divided into four equal parts and each part is 1/4 of the whole.

Well done if you've got that.

We can write 1/4 into each one of the parts to show that that part has a value of 1/4.

And what about this time? Have a look at the bar model and use your stem sentence to help you again.

That's right.

The whole this time has been divided into six equal parts, and each part is 1/6 of the whole.

Well done if you've got that as well.

Let's write 1/6 as a fraction into each one of our parts to show that that part has a value of 1/6.

Okay, so I wonder how we could start thinking about applying what we've just looked at with the bar models to this representation here.

We've got a row of 12 oranges here, and we're wondering how could we share these oranges into equal parts? I'll give you a moment to have a think about it.

How would you share them into equal parts? You might like to use your stem sentence below to help you think that through as well.

Let's have a look what Jun's come up with.

Jun said, "We can share them into two equal parts." There we go, Jun, you're right.

We could share them into two equal parts.

And so if we've shared all of these oranges into two equal parts, then what could we say about each part in relation to the whole? That's right.

We can say that each part is 1/2 of the whole, isn't it? Lucas has joined us now.

How are you gonna share them out, Lucas? Can you think of another way of sharing the oranges out? Ah, you've decided to share them into three equal parts.

Should we have a look at what that might look like? There we go.

Our whole has now been divided into three equal parts and each part is one.

That's right.

Each part is 1/3 of the whole, isn't it? Fantastic.

Jun's still going.

He thinks he's found another way.

Maybe you did too.

This time, he's gonna share it into four equal parts.

Let's have a look.

Here's our whole of 12 oranges.

And this time, that's right, we shared it now into four equal parts.

So we can say this time that the whole has been divided into four equal parts and each part is.

Yep, that's right.

1/4 of the whole, isn't it? So, so far, we've shared it into two, three, and four equal parts.

Do you think there's any other ways that we could have done it? That's right, Lucas.

You're right.

We could have also done it as six equal parts.

So have a look at our whole, maybe you might like to imagine what that might look like as six equal parts if you haven't done that already.

There we go.

Our whole now has been divided into six equal parts, and each part represents, yep, 1/6 of the whole, doesn't it? Well done If you've got that.

Jun, still one more way, you think? Fantastic.

Let's see how you've done it this time, then.

You've decided that it could be done as 12 equal parts.

Of course it can.

We've got 12 oranges altogether, so that could be 12 separate parts, couldn't it? Let's have a look.

The whole has been divided into 12 equal parts now, and each part is.

Yep, that's right.

1/12 of the whole, isn't it? Okay, time for you to check your understanding now.

What fraction of the whole is shaded? Take a moment to have a think.

That's right.

The whole has been divided into nine equal parts, isn't it? And therefore each part is 1/9 of the whole.

Well done if you've got that.

Here's another example for us to think about.

Can you show 1/3 of the whole? Have look at our image.

Well, there's an example of 1/3, isn't it? Or there is another example of what 1/3 could have been.

Or finally, that last segment could also have been 1/3 of the whole.

So we could say that each part represents 1/3 of the whole.

So we could have chosen any of the parts, couldn't we? Well done if you got that too.

Okay, time for us to have a go at our first task for today now, then.

Have a look at the counters.

I'd like you to have a think about the different ways you could represent these counters using the stem sentence below.

If you don't have counters to hand, you could use cubes or something else to represent each one of the counters.

Once you've done that, I'd like you to have a go at task two here, and I'd like to have a go at shading or circling 1/3 of each of these different wholes.

Good luck with those two tasks and I'll see you back here shortly.

Okay, welcome back.

Let's see how you got on.

So I wonder how many different ways you were able to divide up these counters to make equal parts.

Well, you could have said that the whole was divided into two equal parts, and therefore, each part is 1/2 of the whole, couldn't you? You could have divided the whole up into three equal parts, and each part would represent 1/3 of the whole.

You could have also divided it up into six equal parts, and each part would represent 1/6 of the whole.

And look here, you could have also divided it up into nine equal parts, and each part would've been 1/9 of the whole.

Were there any other ways you could have done it? That's right.

You could have divided them all up individually as well, couldn't you? Into eighteenths, couldn't you? So we could have said that the whole was divided into 18 equal parts and each part is 1/18 of the whole.

Well done if you managed to get that one as well.

Okay, and on to task two then.

Let's have a look here.

Can we circle or shade 1/3 of the following wholes? Well, let's have a look at a.

We can see our whole here.

Now, our whole of counters isn't actually in one long line here, is it? It's in an array.

How could we divide our whole up into three equal parts so that we could show 1/3? Well, there you go.

There's an example.

There's one group there.

And if I had another of those two groups, altogether, we would have 3/3 'cause those groups would be equal in size.

And now you can see we've just circled one of those groups, haven't we? And for task two, have a look at that.

How could we divide that into three equal parts? You may have done it in many different ways, but here's an example of what you could have done.

We've shaded in three of these here, and hopefully you can see that we've got three parts that would have the same value.

Three columns of three rectangles.

And then for the last one, have a look.

Well, we need to divide our whole into three equal parts, don't we? So there we go.

Hopefully you can see from the dotted lines that I've now divided the whole into three equal parts and we've shaded one of those parts.

Okay, that's the end of our first cycle.

Well done if you managed to get all of that.

Let's move on to our second cycle now, finding the value of a unit fraction.

So let's revisit our representation of the oranges.

How could we describe what we can see so far? Well, that's right.

The whole is 12 oranges altogether, isn't it? And so we can draw a bar around the oranges to represent the 12.

Watch now how I place those oranges underneath, and the oranges that were in the top bar are now represented by the number 12.

That bar of 12 at the top is equal to the 12 oranges underneath.

Now have a look at what we've done to the oranges.

The oranges, this time, have been divided into six equal parts, haven't they? What's the value of each one of the parts here? Well, we could describe each one of the parts as 1/6 of the whole, couldn't we? But what's the value of oranges in each part? That's right.

There are two oranges in each part, aren't there? So we can say that each part has a value of two.

And there we go.

We've replaced the oranges now with the number two to represent the number of oranges in each one of the parts.

So let's use our stem sentence now to help us describe what we've just seen.

We can say that the whole has been divided into six equal parts, and there are two oranges in each part.

Let's have a look at it again this time.

This time we've got our 12 oranges as the whole again, haven't we? We can represent that here using the 12 at the top to represent the 12 oranges.

And our oranges, again, have been divided into six equal parts.

We know that the value of each one of those parts is two oranges, but we also know that each part represents 1/6 of the whole, doesn't it? So let's have a go at using our stem sentence now to describe how this all links together.

We can say that each part is 1/6 of the whole, and therefore, 1/6 of 12 oranges is equal to two oranges.

Could you have a go at saying that again for yourself? Well done.

Each part is 1/6 of the whole.

1/6 of 12 oranges is equal to two oranges.

Let's have a look at a different example now.

So come on, then, Jun and Lucas, I wonder, can you help me out here? Can you hand me 1/6 of the oranges please? Have a little think for yourself.

If it was you, what would you try to do here? Jun says that, "Every two oranges are equivalent to 1/6 of the whole." So he says, "I could choose this pair of oranges to hand to you." That's right.

Thanks, Jun.

If you handed me those two oranges, you would've handed me 1/6 of the whole or 1/6 of the total amount of oranges.

Lucas is saying it didn't have to be the first pair though, it could have been any of the pairs, couldn't it? "I could have handed you this pair instead." He says.

And that's right.

Each part is 1/6 of the whole.

So you can hand me any one of these parts, can't you? And you would've handed me 1/6 of the whole.

Let's have a look at another example now.

We've still got our 12 oranges that make up the whole.

There we go.

So we're gonna re-represent our bar model to show this.

The 12 at the top represents the 12 oranges, and now we've got another bar underneath which shows the 12 oranges are equal to the bar at the top.

And have a look now, what's our whole been divided into this time? That's right.

Our whole has been divided into three equal parts, hasn't it? Take a moment to have a think.

How many oranges make up each part? And what is each part in relation to the whole? That's right.

Each part has a value of four, doesn't it? So when we take this a little bit further and we can use our stem sentences again to help us describe this, we can say that when 12 oranges are divided into three equal parts, there are four oranges in each part.

Linking this to the size of the part in relation to the whole, we can say that each part is 1/3 of the whole.

And 1/3 of 12 oranges is equal to four oranges.

Well done if you managed to get that too and say that along with me.

Here's one more example.

Once again, we've got 12 oranges that make up the whole this time.

There we go.

And look, how many equal parts has the whole been divided into? Great.

And what's the value of each one of those parts? That's right.

The whole has been divided into four equal parts and the value of each part is three.

There are three oranges in each part of the whole.

Okay, so let's use our stem sentence below to help us link this together, then.

We can say that when 12 oranges are divided into four equal parts, we can say that there are three oranges in each part.

Take a moment now to have a look at the stem sentence below and think how might you answer this stem sentence now based on what we've just seen so far? Take a moment to have a think.

The first bit's been done for you, isn't it? Each part is 1/4 of the whole.

So we can say that 1/4 of 12 oranges is equal to three oranges.

Brilliant, well done if you've managed to say that for yourself.

Okay, time for you to check your understanding again now, then.

1/3 of the whole is equal to four.

Can you tick the representation that represents this? Take a moment to have a think.

That's right.

It's b, isn't it? We can see here that the whole has been divided into three equal parts.

So each part is 1/3 of the whole.

And within each one of those parts, the value of that part is four.

And on for the second check now, then.

Tick the statement that matches the representation.

Is it a, 1/4 of 20 is equal to five? Is it b, 1/5 of 20 is equal to four, or is it c, 1/20 of four is equal to five? Take a moment to have a think.

And that's right.

It was a, wasn't it? The whole, which was 20, was divided into four equal parts, and each part is therefore 1/4, and the value of 1/4 is five.

So we can say that 1/4 of 20 is equal to five.

Okay, time for you to practise now, then.

What I'd like you to do is look at the images on the left hand side and complete the stem sentences for each image.

Once you've done that, I'd like you to have a go at ticking the statements here that are true and drawing a bar model for each one that is true to represent that.

Good luck with that, and I'll see you back here shortly.

All right, let's go through these stem sentences together then.

When nine strawberries are divided into three equal parts, there are three strawberries in each part.

Each part is 1/3 of the whole.

1/3 of nine is equal to three strawberries.

Well done if you got that one.

So for the second one, when 10 counters are divided into five equal parts, we can say that there are two counters in each part.

Each part is 1/5 of the whole.

So 1/5 of 10 counters is two counters.

And the last one, when 24 is divided into eight equal parts, there is three in each part.

Each part is 1/8 of the whole.

So we can say that 1/8 of 24 is three.

Well done if you managed to get all of those.

If you've got some extra time, you might like to create your own one for a friend to have a go at tackling.

And then for task two, then, can you tick the statements that are true? Draw a bar model for each one.

Okay, the first one.

1/3 of 15 is equal to five.

Is that true? Yeah, it is true.

And we can see, here's our bar model divided into three equal parts and each one is 1/3 and then, therefore, 1/3 has a value of five each time.

The second one, 1/5 of 15 is three.

Again, that's also true.

This time, the whole has been divided into five equal parts.

So each part is 1/5 of the whole and the value of each 1/5 is three.

For the third one, 1/7 of 21 is four.

Ah, that's not right, is it? Actually, that should be that 1/7 of 21 is equal to three.

We know that three sevens makes 21.

So 21 divided into seven equal parts gives you a value of three for each one.

The next one, 1/10 of 100 is 10.

That is also true.

We know that.

And here we go, 100 divided into 10 equal parts.

Each part has a value of 10.

And the last one.

1/9 of 81 is nine.

Yeah, that is also true.

If the whole was 81 and we divided that into nine equal parts, each part would have a value of nine or 1/9 of 81 is equal to nine.

Okay, that's the end of our lesson for today.

Hopefully, you're feeling a lot more confident in the representations that we can use to find a unit fraction of an amount.

So to summarise our learning today, we can say when a whole is divided into equal parts, one of those parts is known as a unit fraction.

Where the whole is an integer that has been divided equally, each of the parts will have the same value.

And we can help to find the value of a unit fraction by representing the maths using a bar model.

Okay, that's the end of our lesson.

I've really enjoyed that one today.

Hopefully, you have too.

Take care, and I'll see you again soon.