Lesson video

Hello, my name's Mrs. Hopper and I'm really looking forward to working with you in our maths lesson today.

I hope you're ready to work hard and have lots of fun.

It's fractions and I love fractions.

So let's make a start.

Welcome to this lesson from our unit, comparing fractions using equivalents and decimals.

This lesson is all about using representations to describe and compare fractions in a continuous context.

So we'll be finding out more about what that means as we go on.

So let's make a start.

We've got two key words today.

One is continuous and the other is equal.

I'm sure you've come across equal before.

I wonder about continuous.

Let's practise them and then have a look at what they mean.

So my turn, continuous, your turn.

My turn, equal, your turn.

Now, as I say, I know you'll know what equal means, but it's always worth going back and really focusing on it.

It's an important word in our learning today.

So let's have a look at what these words mean.

So continuous means that every position on a line or a scale has a value.

So we're going to be looking a lot at number lines today and thinking about measurement scales as well.

Every position on that line has a value, however closely you look at it.

So continuous scales can be found in measurement, in the axes, on a line graph, or on any number line.

And we are going to be looking at measurement and number lines today.

Equal means that something has exactly the same amount or the same value and things being equal are really important to us today.

There are two parts to our lesson today.

In the first part, we're going to be estimating fractions.

And in the second part, we're going to be looking at fractions with the same value on a number line.

So let's make a start, estimating some fractions.

We've got Jun and Safia helping us out again today.

So Jun is pouring juice into the glass and he asks Safia to shout stop when the glass is 1/5 full.

And Safia's gonna ask for our help.

She says, can you help me please? So can you do that as well? We're gonna watch the juice pour in and you're gonna shout stop when you think the glass is 1/5 full.

Are you ready? Are you watching? Okay, let's go.

Stop, says Safia.

Did you shout it about the same time as Safia did? Okay, so Safia shouted stop.

You may well have shouted stop as well.

Let's have a think.

Jun says, how do you know that is 1/5? What made you think it was 1/5? I wonder what Safia thought.

Ah, Safia says, I think five of those parts would fill the glass.

So she spotted that 1/5 means that the whole has been divided into five equal parts and we've got one of them.

Or we filled it up to one of those parts.

So the glass would have five equal amounts of that liquid in it.

And that's what Safia used.

I wonder what you used to decide when to shout stop.

Ah, Safia's pouring the juice now and she's gonna ask Jun this time to shout stop when the glass is 4/5 full.

So she says it's your turn now, Jun.

Oh, Jun's asking for your help again, so can you help Jun? So watch the juice fill up and shout stop when you think it's got to about 4/5 full.

Stop, says Jun.

Did you shout stop at about the same time? Juice went in a bit faster that time, didn't it? Okay, so Safia's asking the question, how do you know that's 4/5? How did you know when to shout stop? So Jun says 4/5 is close to one.

There would be one more part to fill the glass.

So four outta the five parts of the glass are full now and Jun estimated that there's about one of those parts left to go.

It's almost full, but there's 1/5 left to go.

Over to you now, check your understanding.

So can you estimate where the juice will come up to when the glass is 3/8 full and explain whether A, B, or C marks that level.

Pause the video and have a go and we'll come back and think about it together.

How did you get on? Which did you think it was? A, B, or C, to show that the glass was 3/8 full? Let's have a look.

Aha, B.

So why is B a good estimate? I wonder how you explained your choice.

Let's have a look at this explanation.

So B is a good estimate.

3/8 is just less than 1/2.

As we know that in fractions, equal to a half, the numerator is half the denominator.

So that would be 4/8, wouldn't it? So 3/8 is just less than 1/2 and B is close to, but less than 1/2 full.

C's too far away from 1/2 and A is a bit too close to 1/2.

So B is a good estimate for 3/8 full.

So Safia is pouring water into three glasses.

She has to make them 1/3, 8/12, and 5/6 full.

So where do you think the water will come up to in each glass? You might want to have a little think about that before we see Safia's water going in.

Where do you think the water will come up to? Safia's going to say she's going to think about which fraction is nearest to zero, a half or one.

That's an interesting way of thinking about it, isn't it? So of 1/3, is that nearest to zero, 1/2 or one? What about 8/12, what about 5/6? So it's easy to imagine empty of zero.

Full is our one whole.

And then half is that halfway up the glass.

So I wonder if we can use those sort of benchmarks, those points of reference to help us to decide.

So let's see how Safia got on.

Safia's filled this one up to 1/3.

So it's less than half and it's kind of close to one 'cause one outta three is not that many parts outta three.

8/12.

Well, it's more than half, isn't it? 6/12 would be half.

So it's more than half, but there's still quite a way to go till we get to the glass being full of water.

What about the last one, 5/6? Or five outta six parts is almost all of it.

So we're going to be close to full here, aren't we? So Safia has poured her water into the three glasses.

Do you think she's got it about right? Do you think her reasoning, thinking about which fraction was nearest to zero, a half or one has helped her? Time for you to check.

Can you use that way of thinking to check Jun's work? Jun has to make the glasses 2/3, 3/9 and 20/24 full.

Has he filled and labelled them correctly? So pause the video and check whether you think Jun has got this right or not.

What did you think? How's Jun got on? Hmm, I'm not sure he has got this right, has he? So did you think that this glass should be labelled as 2/3? It's more than half, but there's still a whole 1/3 to go before it's full.

Hmm, I think that's about right.

This glass is half full, not three out of nine equal parts full.

So I don't think he's got either the amount of water in the glass or the fraction right for this one.

And the missing part in this one is smaller than 1/3.

If we look at that first last, which we reckon should be 2/3, this one can't be 2/3 as well.

So this one probably ought to be 20/24.

It's almost full, but there's still a little way to go.

So the middle one, which should be 3/9, it's got too much water in it, so we needed to lessen the amount of water in that glass.

Ah, there we go.

Jun's corrected his glasses of water now.

So his first one, as we said, was 2/3.

The middle one, he's changed the amount of water.

He had too much water, he had it half full.

So he's now got it three out of nine parts full.

And for his last one, he's relabeled that with 20/24 full.

So Jun and Safia are looking at the glasses of water that they've both filled.

What do you think they have noticed? Have a look at the glasses.

What do you notice? Let's see what Jun and Safia have noticed.

Jun says some of the glasses have the same amount of water, but Safia says the fractions are different though.

Aha, so they've rearranged them now.

So what do you notice about the glasses of water? Jun says different fractions can represent the same level of water in the glass.

So we can see in those first two, we've got 3/9 and 1/3, but they're representing the same amount of water in the glass.

So Safia says we can say that 3/9 is equal to 1/3.

And you might have learned about 1/3, that the numerator multiplied by three equals the denominator.

The denominator is three times the value of a numerator in a fraction equal to 1/3.

So three times three is equal to nine and one times three is equal to three.

So that shows us that 3/9 is equal to 1/3.

And Jun says, and we can also say that 2/3, it must be equal to 8/12 because that shows the same amount of water and that 20/24 must be equal to 5/6 because it's the same level of water in the glass.

Hmm.

Can you see a relationship between those fractions? I wonder.

Okay, so time for you to do some practise.

Which of the fractions could be used to label the glasses of water? And can you think of any other fractions which you could use? So we've given you some markings on the side of the glasses to show you how much water there is, but there are lots of different fractions there.

Can you write all the fractions that could be used to label that first glass in the box underneath and all the fractions that could be used to label the second glass in the box underneath there? And can you add extra fractions in that would represent the same amount of water in those glasses? Pause the video, have a go and then we'll look at it together.

How did you get on? Now, not all the fractions could be used, could they? So 2/4, 12/24, 3/5 and 8/9 couldn't be used to label those levels of water in the glasses.

But for the first glass, we could use 3/4, which we can see quite clearly on the scale there.

We've got three outta four equal parts, 3/4, but we can also label that using 6/8, 18/24, and 30/40.

Hmm, can you see the relationship between some of those numbers? 3/4 and 30/40 is definitely something there, isn't there? And the second last was 1/4.

So we could also label that with 10/40, 6/24 and 2/8.

And I wonder if you added in any extra fractions.

I thought about hundredths.

So I labelled the first one as 75 out of 100 and the second one as 25/100.

So 25 parts out of 100.

I'm sure you found some other ones as well.

So onto part two of our lesson.

So we're going to look at fractions with the same value on a number line.

So we're going to thinking about our measuring jugs, but we're also going to think about the scale on the measuring jug as a number line.

So Safia is imagining the scale on the measuring jug as a number line.

So in our jug, we've filled it up to 1/5.

So a number line is a continuous scale, one of our key words, all the points have a value.

So wherever we put a mark on that number line, we'd be able to give it a value.

So where would she record 1/5 on this number line? Let's have a think.

Jun says, imagine the whole divided into five equal parts, and our whole is one in this case, zero to one is our whole, so one is our whole.

So if we imagine that whole divided into five equal parts, our 1/5 would be one of those equal parts along the line.

So let's have a look and see if we can estimate where 1/5 would go.

Safia says 1/5 is a small part of the hole, so it will be close to zero.

Ah, and there's our arrow flying in up to 1/5 of the way between zero and one.

So marking that point is 1/5 on the number line.

Oh, now what have we done this time? This time, we've got a continuous horizontal number line.

So we're going in this direction horizontally, rather than this direction vertically.

So where would she record 1/5 on this continuous horizontal number line? So Jun says, it's the same thing but horizontal.

And Safia says the arrow will be one part outta five along the line again.

So let's have a look.

There is our 1/5 on the number line.

So that point marks 1/5 of the way between zero and one.

Time to check your understanding.

Jun is imagining the scale on the measuring jug as a number line, a vertical one this time, where would he record 4/5 on his number line? So pause the video, have a think.

And where would you put 4/5 on this number line? How did you get on? What thinking did you use? Let's have a think about what Jun and Safia thought about.

Jun says, imagine the whole divided into five equal parts, 'cause we're thinking about 1/5 here.

And Safia says 4/5 is a large part of the whole, so it's close to one.

So there's our arrow going up to 4/5 of the way.

So that point marks 4/5 of the distance between zero and one, 4/5 of the way along the number line.

I wonder if you used that same thinking, really useful thinking about the number of equal parts and then thinking about whether that fraction is a large part of the whole or a small part of the whole.

So will it be closer to one or closer to zero? So the second part of your check, where would you record 4/5 on this horizontal number line? Pause the video and have a go.

How did you get on? Did you remember that this is just the same as the one we did before, but lying down horizontally rather than up vertically? And there goes our arrow, 4/5 of the way along the line.

So that point marks 4/5 on our zero-to-one number line.

We could imagine the number line divided into five equal parts and 4/5 is closer to one and it's almost all of the whole.

Okay, so which fractions fit at which position on the number line? We've got two points marked on our number line and we've got some measuring jugs there with a number line scale on as well.

So which fractions fit at which position on the number line and how can we decide? I wonder, have a think about it.

What do you think will go at, that first position, the one closer to zero, and what will go at the position closer to one? I wonder how Jun and Safia are going to think about this.

Let's have a think with them.

Jun says, I'm going to think about the whole line divided into parts.

Okay.

So he says I think 1/4 and 3/4 go here.

So what's he imagined? How many parts has he imagined the whole divided into? Safia says, I agree, I can see the line divided into four equal parts and she's put that extra division in at halfway along the line.

So we can clearly see that 1/4 and 3/4 mark those two points.

I think Jun was correct, wasn't he? What about the other fractions though? Safia says if the line is divided into eight equal parts, then 2/8 and 6/8 will go at the same points.

So she's going to put 2/8 and 6/8 at those same points on the number line.

Do you agree with her? I think she's right, isn't she? If you imagined eight marks on the number line, you could see that it'd be two jumps out of eight and six jumps out of eight.

Oh, this is an interesting one.

Jun says, I think 10/40 and 30/40 look like 1/4 and 3/4.

So instead of one part out of four, we've got 10 times as many parts out of 10 times as many parts in the whole.

So if we imagined our line divided into 40 equal parts, then 10/40 would be where 1/4 is and 30/40 would be where 3/4 is.

Safia says, yes, 40 parts is 10 times four parts and the numerators are also 10 times the size.

She says, let's look at the numerators and denominators of the last two.

So we've got 6/24 and 18/24.

Oh, now, I wonder if we can think about how much of the whole we've got in each case as to where each one might sit on the number line or whether we can think about this in another way as well.

Well, that's interesting.

Jun says six times four is equal to 24.

So 6/24 could be equal to 1/4.

6/24 is not much of the whole, so it's quite a small proportion of the whole.

So 6/24 could be equal to 1/4.

So that would mean that 18/24 would be equal to 3/4.

And Safia says six times three is equal to 18, so the numerator times three is equal to 18, and six times four, we know is 24.

So 18/24 could be equal to 3/4 and 18/24 is quite a lot of the whole, so that would work as well in our thinking.

Okay, time to check your understanding.

Where do you think 20/100 and 75/100 will fit on the number line? And can you explain how you know? So pause the video and have a go.

How did you get on? how did you think about those fractions? So we've put 25/100 at the same place as 1/4 and 75/100 at the same place as 3/4.

I wonder how we know that.

Jun says 25 times four is equal to 100.

So 25/100 is equal to 1/4.

So he spotted that 25 times four is equal to 100, so it's four times, so the denominator is four times the size of the numerator and that's the same as it is in 1/4 as well.

And also, 25/100 is quite close to zero.

It's not very much of the whole.

And Safia says that 25 times three is equal to 75.

So 75/100 must be equal to 3/4.

That's an interesting way of thinking about it.

If 1/4 is 25/100, then 3/4 must be three of those.

So three lots of 25 is equal to 75.

And it also fits with our thinking that 75 out of 100 is almost all of it.

So it'll be closer to one.

Well done if you use that thinking to help you position those numbers.

Time for you to do some practise.

So we've got a number line with three points marked on it.

So first thing to do is to estimate which fractions would be at these points on the number line.

And can you then label each point with two or more different fractions? And then part C, can you add another point to label it with two different fractions? So pause the video, have a go, and then we'll look through the tasks together.

How did you get on? So those original points were labelled as 1/8, 1/2, and 7/8.

So could you find some other fractions that would also be able to be used to label those points? Well, we came up with 3/24 and 2/16 to label 1/8.

2/4 and 4/8 to label 1/2.

And then thinking about those 1/16 and 1/24 again, 21/24 and 14/16 to label 7/8.

And for the final part, you were asked to add another point and label it with two different fractions.

Well, we've chosen 1/4 and we've labelled it with 2/8 and 20/80, and there were lots of different possibilities.

But can you see how 20/80 looks a bit like 2/8? And we've come to the end of our lesson.

So we've been using representations to describe and compare fractions in a continuous context.

So we've learned that fractions have positions on a continuous scale such as a measuring jug or a number line, and that that fraction marks a particular point on that scale or number line.

And we've also learned that fractions that look different can represent the same part of a whole or the same position on a continuous scale or number line, and that these fractions are equal in value.

And you can see there we've got fractions equal to 1/4 and fractions equal to 3/4.

I hope you've enjoyed exploring our fractions today in a continuous context and I hope I'll get to work with you on some more fractions very soon.

Bye-bye.