Lesson video

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

I hope you're doing okay and you're having a good week.

In this lesson today, we're gonna be thinking about how we can find the size of a unit fraction if the size of the non-unit fraction is known.

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

So by the end of this lesson today, you should be able to say that I can find a unit fraction when the size of the non unit-fraction is known.

In this lesson today, we've got three keywords we're gonna be referring to throughout.

I'll have a go at saying them first and then you can repeat them after me.

Are you ready? The first one is represent.

Your turn.

The second word is unit fraction.

Your turn.

And the third word is non-unit fraction.

Your turn.

Let's have a think about what these mean then.

To represent something means to show something in a different way.

The same thing can be shown using multiple representations.

A unit fraction is a fraction that has a numerator of one, and a non-unit fraction is a fraction which has a numerator that is greater than one.

For today's lesson, we've got two cycles we're gonna be working through.

The first one is about finding the unit fraction of a non-unit fraction, and the second cycle is about finding a unit fraction of a set.

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

Throughout this lesson today, we've got four pupils who are gonna be joining us.

We've got Andeep, Laura, Izzy, and Jun.

And as always, they'll be sharing their thinking as well as any questions that they have throughout the lesson.

So let's start here.

We've got Laura who's been eating some pizza.

At the moment, Laura has 3/8 of her pizza left.

What would the size of 1/8 of her pizza be? Take a moment to have a think.

So Laura's saying that she has 3/8 of pizza, and that's represented by the three slices.

She can say that each slice has a value of 1/8, and we've represented that here by writing the fraction on each slice.

So we can say that one slice would represent 1/8 of the whole.

This is the unit fraction of the whole.

Let's have a look at a different example.

Izzy has been drawing a shape.

The part that you can see represents 3/7 of the whole shape.

I wonder what 1/7 of the shape would look like? Take a moment again to have a think for yourself.

Well, there we go.

3/7 of the shape is represented so far, and this has been represented by the three pentagons, hasn't it? Each one pentagon represents 1/7 of the whole.

So the unit fraction of the whole, or in this case 1/7, would be equal to one pentagon, wouldn't it? Here's a slightly different example this time.

Andeep walked 6/10 of a mile to get to the park at the weekend.

What would 1/10 of the whole distance look like that he walked? Well, we can see on our number line here that Andeep has walked 6/10 of the whole, can't we? And this is represented by his position on the number line and where he's moved from zero to 6/10 with the arrow.

If each one of those intervals represents 1/10, we can say that he's walked six 1/10 of the distance to the park, can't we? And therefore, the unit fraction, or 1/10 of the whole, would be represented by just the one interval, wouldn't it? Here's another example from Jun and his gaming.

Jun has 4/5 of his lives left on the game.

How would you represent it if he had 1/5 of his lives left? Well again, we can see here that we have four hearts, don't we? And each one of these hearts would represent 1/5.

So if each heart has a value of 1/5, we can say that the unit fraction of the whole, in this case 1/5, would be one heart, wouldn't it? So you would have to draw one heart to represent 1/5 of the whole.

Okay, time for you to check your understanding now.

This image shows 3/4 of the whole.

Tick the image that represents 1/4 of the whole.

Take a moment to have a think.

That's right.

It's a, isn't it? And why is it a? Well, at the moment, this bar represents 3/4 of the whole.

So it's three parts of the whole, isn't it? We know that each one of those parts would represent 1/4.

So we can see that 1/4 would be one of three of those parts, which is what a represents.

Well done if you've got that.

And the next one, true or false? The image represents 3/6 of the whole.

So one circle would represent 1/3 of the whole.

Take a moment to have a think.

Okay, and that's false, isn't it? And use one of these justifications to help you reason why.

And that's right.

You can use justification a here, can't you? The whole has been divided into six equal parts, hasn't it? Not three equal parts.

So if the whole has been divided into six equal parts and we have three of those parts, then one of those parts would represent 1/6, so one circle would represent 1/6.

Okay, time for you to have a go at practising now.

What I'd like you to do is draw and write the unit fraction for each example.

And for task two, what I'd like you to do is draw the non-unit fraction for each example.

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

Okay, welcome back.

Let's see how you got on.

So for example a, we've got four stars, which represents 4/6 of the whole, so one star would represent one six of the whole.

For b, we've got a whole that's been divided to 10 equal parts, and we've got three of those parts.

So 3/10 would be three shaded squares, so 1/10 would be one shaded square.

For part c, we've got a length of string here, which represents 2/3 of the whole.

Therefore, if that's 2/3 of the whole, then 1/3 of the whole would be half of that.

So there's 1/3 of the whole.

And finally, the penguins at the bottom.

We've got four penguins, and these four penguins represent 4/7 of the whole.

If these are 4/7, then 1/7 would be one penguin, wouldn't it? So one penguin be equal to 1/7.

Okay, and onto question two then.

Can you draw the non-unit fraction for each one of these examples? Well, if this parallelogram represents 1/3 of the whole, then we know this is one of three equal parts.

And how many parts do we need? And that's right, we need two of those parts, don't we, because the numerator on the non-fraction is two, so we can represent it like this.

The next one is 1/4 of the whole.

How many parts do we need? We need three parts, don't we? So we're gonna need 3/4 of the whole.

The example after that is 1/5 of the whole.

If we need 3/5, how many of those parts will we need? That's right.

We'll need three of the dots, won't we? And the last one.

We've got a number line here which represents 1/6 of the whole.

What would 5/6 of the whole look like? That's right, we would need to cover five of the intervals, wouldn't we? One interval is 1/6, so five intervals would be 5/6 of the whole.

Well done if you've got all of those too.

Okay, that's the end of cycle one.

Moving on to cycle two now.

We're gonna extend our thinking a bit more to start thinking about unit fractions of a set.

So let's have a look here then.

Izzy received some money for her birthday.

The image shows 2/5 of the total amount of money that she received.

If she spends 1/5 of the money that she received, how much money does she spend? Hmm, take a moment to have a think for yourself.

Well, Izzy is saying that she has four 1 pound coins, which represents 2/5 of the total amount that she received, or in this case the whole.

We can therefore say that two 1 pound coins represents 1/5 of the whole.

We've got two lots of 1/5, and each 1/5 is represented by two 1 pound coins.

So if Izzy was to spend 1/5 of the money that she received, then we could say that she'd have spent two pounds.

Here's a different example now.

Let's see what Andeep's been up to.

Andeep says that he's read 3/4 of the books on his bookshelf.

He said that he read 1/4 of the books in five days.

How many books did he read in five days? Andeep's saying that 3/4 of the books on his bookshelf is actually 15 books.

And there we go.

We can see those 15 books here.

So if 15 books is equal to 3/4, then we can say that 1/4 of those books would be equal to five books.

1/4 would be five books, 2/4 would be 10 books, 3/4 would be 15 books.

So how many books did he read in five days? That's right, he read five books in five days.

That's good going, isn't it? Fantastic reading.

That's really gonna help you with your learning going forward, Andeep.

Keep it up.

Okay, and here's another example then.

Let's find out what Laura's been up to.

It took Laura 4/6 of an hour to finish her homework.

She spent 1/6 of the hour doing her spellings.

How long did she spend on her spellings in minutes? Well, let's take a closer look at this, shall we? If it took 4/6 of an hour to complete all of her homework, then we could divide our hour up into six equal parts, couldn't we, and shade in four of them.

So we've got 4/6.

Now we're looking for the size of one of those sixths, aren't we? So hopefully you can now see that 1/6 can be represented by this one segment here.

And how much time is that one segment worth then? That's right.

1/6 of an hour is equal to 10 minutes, isn't it? Okay, time for you to check your understanding again now then.

This image shows 4/5 of the whole.

Can you circle one fifth? Take a moment to have think.

That's right.

This here could represent 1/5 of the whole, couldn't it? And why is that? Well, 1/5 is equivalent to three counters.

And the numerator here, as Laura is pointing out, is helping us to identify how many groups we have at the moment.

We have four groups, and we want one of those groups.

Here's another example.

This is 1/3 of the whole.

Can you draw the whole? Take a moment to have a think.

Well, we know that the whole needs three equal parts, doesn't it? There we go.

And each one of those parts has four counters in it, so we can say that this image here would represent the whole.

Hmm, I wonder what would 2/3 of the whole look like? That's right, it would just be the first row and the second row, wouldn't it? Well done if you managed to identify that for yourself as well.

And onto our final tasks for today then.

What I'd like to do here is draw the unit fraction for the given non-unit fractions on the left hand side that have been given for you.

And then for task two, I've given you the non-unit fraction of 2/5 in several different representations.

What I'd like you to do is have a go drawing the unit fraction for each of those as well.

And then finally, for task three, what I'd like you to do is draw the unit fraction of 1/5 for each of the non-unit fractions on the left hand side as well.

And once you've been through that, ask yourself what did you notice each time? Good luck with those, and I'll see you back here shortly.

Okay, welcome back.

Let's see how you got on then.

So at the moment, this image here represents 2/3 of the whole.

That means we have two groups, doesn't it? And each group would represent 1/3.

So if this represents two groups, then one of those groups would look like this, wouldn't it? This would be 1/3 of the whole.

And the next one.

We can see here that this arrow represents 3/4 of the whole.

That means we've got three groups again, and we're looking for one of those groups.

So if that distance shown by the arrow was divided into three equal parts, one of those parts would look like this.

So this would represent 1/4 of the whole.

And then finally, we've got 5/7 of the whole here.

So the numerator is telling us the number of parts that we have.

We have five parts, don't we? Each one of those parts would represent 1/7.

So let's find out.

This is five equal parts.

We want one of those parts.

One of those parts would look like this.

Well done if you've got all of those.

Okay, let's have a look here now then.

So we're trying to find 1/5 of these amounts here.

Each of these represents 2/5.

So let's start off with our number line here then.

This number line is 2/5 of the whole, so that means this distance jumped represents two groups, doesn't it? So we want one of those groups.

So that would mean it would look like this.

It'd be equivalent to three intervals.

For the second one, we've got 2/5 here.

We can see quite clearly that the whole has been divided into five equal parts, therefore each one of those parts would represent 1/5.

We have 2/5 though, so we only want one of them, so it would look like this.

You may have shaded in the other part, which would also be equally fine.

And then the last one here, we've got some cupcakes.

These represent 2/5 of the whole, don't they? So we want one of those fifths.

If this represents two groups, how could we divide these cupcakes into two groups? There we go.

We could divide them into two rows, couldn't we? This row here represents 1/5 of the whole.

Well done if you've got all of those.

And then for task three now then.

Can you draw 1/5 of each of the non-unit fractions? The first non-unit fraction is 2/5.

That means it needs to be divided into two parts to find out the size of each one of those parts, so that's 1/5 of the whole.

This time the whole, even though it's the same as before, represents 3/5.

So how many parts are we gonna divide it into? That's right.

We're gonna need to divide it into three parts to find out the size of each one of those fifths.

So this would represent 1/5.

Four dots would represent 1/5 of the whole this time.

And then the next one.

Hmm, what do you notice this time? That's right, the number of dots is the same again, but this time it represents 4/5, doesn't it? So how many equal parts are we going to have to divide it into to find 1/5? That's right.

We're going to need to divide it into four parts, aren't we, to find one of those fifths, and the numerator helps us with that.

And now we can see that 1/5 would also look like this.

So what did you notice then by going through that activity there? That's right.

The same unit fraction can be different in size, can't it? We were finding 1/5 of the same amount, but the number of circles for each amount was different each time, so the unit fraction of 1/5 can differ in size.

Well done if you managed to get all of that too.

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

Let's summarise what we've learned then.

If you know the size of a non-unit fraction, then you can use this to help you find the size of the unit fraction.

You can use the numerator in a non-unit fraction to help us identify how many parts we have.

And finally, unit fractions can look different depending on the size of the non-unit fraction.

Thanks for joining me again today.

I wonder if you can go and find a way to apply this knowledge into your everyday lives? Take care, and I'll see you again soon.