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.

So this lesson is all about using the language of equivalent fractions correctly, and it comes from our unit comparing fractions using equivalence and decimals.

So we're going to explore fractions that have the same value in different ways and use the language of equivalent fractions.

We've got some keywords in our lessons today.

So I'm going to say them.

Then it'll be your turn.

So my turn, equivalent fractions.

Your turn.

My turn, proportion.

Your turn.

I wonder if you've come across those words before.

Let's have a look at what they mean 'cause they're going to be really important in our lesson.

So equivalent fractions are fractions which have the same value even though they may look different.

Now you may have been exploring fractions that have the same value.

We're going to think about them as equivalent fractions and use that language today.

The proportion of a number, a shape, or a group of objects is a part of the whole.

And we're using that word because equivalent fractions describe the same part or proportion of the whole.

There are two parts to our lesson today.

In the first part, we're going to be representing equivalent fractions, and in the second part, we're going to be recognising equivalent fractions.

So let's get on with part one, and we've got Jun and Sofia helping us with our learning today.

So Jun and Sofia each take some conkers.

You may have seen them doing this before.

Let's have a look at it again and use some different language today.

Jun takes 1/4, and Sofia takes 3/12 of the conkers.

So there's Jun's 1/4 and Sofia's 3/12.

Jun says, "How can we have the same number of conkers when we have a different fraction?" Ah, Sofia says, "They are equivalent fractions.

They have the same value." You may have explored quarters and different fractions that represent the same as a quarter, and the difference today is we're going to really talk about them as equivalent fractions, fractions which have the same value.

So we can say that 1/4 and 3/12 are equivalent fractions.

They have equal value.

1 out of 4 equal parts is the same proportion of the whole as 3 out of 12 equal parts.

Let's just take a moment to look at that and say that again.

So have a look at it, read it to yourself.

And then let's say it together.

That's going to be a really important stem sentence in our lesson, so let's say it together.

1 out of 4 equal parts is the same proportion of the whole as 3 out of 12 equal parts.

Let's have a look at that.

There's our 1 out of 4 equal parts.

So those conkers represent 1 out of 4 equal parts.

We can divide the whole into equal parts, and they will all look like that part with 3 conkers in.

But now we've circled 3 out of the 12 that we have, and we can see that that 1 part out of 4 is the same proportion of the whole as 3 parts out of 12.

It represents the same part.

And we can use an equal sign between those fractions because they are equivalent fractions.

They have equal value.

They are worth the same.

1/4 is equal to 3/12.

So we know that 1/4 is equal to 3/12, and we can represent these equivalent fractions in bars.

So there is 1/4.

And there is 3/12.

I wonder if you noticed something about the bars.

Hmm, let's see.

Jun says, "This shows that the proportion shaded is the same for both bars." There's that keyword, meaning a part of the whole.

So the proportion of each bar, the part shaded, is the same.

Ah, Sofia spotted something really important.

"The whole has to be the same," when we're talking about equivalent fractions.

"The bar represents the whole," and those two bars are the same.

So Sofia says, "They are equivalent fractions.

They have the same value." Time to check your understanding now.

Which equivalent fractions can you see in the bars? Complete the stem sentence in as many different ways as you can.

So our stem sentence has two gaps.

We haven't put lines in them this time.

So our stem sentence is, hmm and hmm are equivalent fractions.

So your job is to find as many different pairs of equivalent fractions as you can in the bars that you can see.

So pause the video and have a go.

How did you get on? Did you spot that 4/8 and 1/2 are equivalent fractions? That same amount of the bar, the same proportion of the bar is shaded for both of those fractions, so we can say that they are equivalent.

What else did you spot? Did you spot that 5/10 and 15/30 are also equivalent fractions? That same proportion of the bar is shaded.

And we can also say that 4/8 and 5/30 are equivalent fractions.

At the beginning we said equivalent fractions represent the same value, even though they look different.

4/8 and 15/30 look really quite different, don't they? But they both represent the same proportion of the whole.

So they are equivalent fractions.

And Sofia says, "All these fractions are equivalent to 1/2," and we can see that in the bars.

1/2 of each of those bars is shaded in purple, the same proportion for each bar.

So let's explain the equivalent fractions using the idea of proportion in our stem sentence.

So we're still going to identify pairs of equivalent fractions.

Hmm and hmm are equivalent fractions.

But we're now going to use the stem sentence to say that hmm is the same proportion of hmm as hmm is of hmm.

I wonder what's gonna go in those gaps.

We're gonna relate those gaps to the fractions.

So let's have a go.

Can you spot a pair of equivalent fractions here? I spotted that 4/8 and 1/2 are equivalent fractions.

So let's think about how we can use the stem sentence to think about the proportion.

We can see in the bar models the same proportion of each bar is shaded in purple for 1/2 and 4/8, even though our whole is divided into a different number of equal parts.

So let's have a look.

So 4 is the same proportion of 8 as 1 is of 2.

So 4 out of 8, 4 is the same proportion of 8.

So 4 shaded parts out of 8 is the same proportion as 1 shaded part out of 2.

So our 1 out of 2 represents our 1/2, and our 4 out of 8 represents our 4/8.

And we can only say that because the bars are the same length.

The whole is the same.

So let's say that stem sentence together.

4 is the same proportion of 8 as 1 is of 2.

We're going to be using that stem sentence a lot in the rest of this lesson.

Let's have a look at another pair of fractions.

Ah, so 4/8 and 15/30 are equivalent fractions as well.

Can you complete the stem sentence? Let's have a look at it.

So 4 is the same proportion of 8 as 15 is of 30.

When we look at those two bars, 4 out of 8 represents the same part of the whole as 15 out of 30.

And Sofia reminded us these are all equivalent to 1/2.

Time to check your understanding now.

You've got a different set of bars.

So first of all, what fraction of each bar is shaded? And then complete the stem sentences in as many ways as possible.

They're the stem sentences we've just been using.

So you're going to identify a pair of equivalent fractions, and then you're going to fill in the stem sentence to identify the proportion shaded in each case.

So pause the video and have a go.

How did you get on? So did you spot that we've got 1/4, 2/8, 4/16, and 5/20 were the fractions that each bar represented? So what pairs of equivalent fractions did you find? Let's have a look at a couple of examples.

So we found that 1/4 and 5/20 are equivalent fractions.

We know they are, we can see that.

The shaded part represents the same proportion of the whole for 1/4 and for 5/20.

So let's look at that stem sentence.

1 is the same proportion of 4 as 5 is of 20.

1 part out of 4 in the whole is the same proportion as 5 parts out of 20, as long as the whole is the same.

Let's have a look at one more.

2/8 and 4/16 are equivalent fractions.

They are equal in value.

So what will the stem sentence look like for those fractions? 2 is the same proportion of 8 as 4 is of 16.

So if we look at the two bars, 2 out of 8 equal parts is the same proportion of the whole as 4 out of 16 equal parts, as long as the whole is the same.

And as Sofia says, "There are lots of other possible answers." I'm sure you worked out lots of different ways of completing those stem sentences.

So well done.

So we've got some counters here.

Some are white and some are red, and the red ones we've put inside a sort of hoop.

So how could we write the fraction of counters that are red in different ways? So what fractions can we use to describe those red counters out of the whole set, and how can we use the stem sentence of proportion to describe those fractions as well? So you might want to have a little think about that before we go through the answers.

So let's have a look together.

So what can we say? We can say that 2/10 of the counters are red or 1/5 of the counters are red.

There are 10 counters in all and 2 of them are red, but you can see that we've arranged them into pairs, into groups of 2, and we've got 5 groups of 2, and one of those groups of 2 is red.

So 2/10 of the counters are red, or 1/5 of the counters are red.

So we can say that 2/10 and 1/5 are equivalent fractions, and we could use the equal sign to say 2/10 is equal to 1/5.

So let's think about those proportions.

So we've got 2 red counters out of 10 or 1 pair out of 5 pairs, but it represents the same fraction of the whole.

So let's use that stem sentence.

2 is the same proportion of 10 as 1 is of five.

2 red counters out of 10 is the same proportion of the whole as 1 pair of red counters out of 5 pairs.

So we can see that 2/10 is equal to 1/5.

Slightly different thing here.

We've got an area of a shape.

How could we write the fraction of the shaded part in different ways? We can think of the whole shape, and we can think of the shape as a collection of individual squares.

Can you see something in the shape there that might help you think of a fraction? So you might want to have a little think, and then we'll look at the answers together.

So how can we describe the shaded squares? So we could say that 3/4 of the squares are shaded 'cause we can sort of see that pattern.

If we draw a line down the middle vertically and a line across the middle horizontally, we divide that shape into 4 quarters, and 3 of them are shaded.

So we can say that 3 quarters of the shape is shaded.

If we count the individual squares though, there are 16 squares, and 12 of those squares are shaded.

So 3/4 of the squares are shaded, or 12/16 of the squares are shaded.

So we can say that 3/4 and 12/16 are equivalent fractions.

And when we look at our stem sentence, we can say that 3 is the same proportion of 4 as 12 is of 16.

Time to check your understanding now.

How could we write the fraction of the part of the line in different ways, and can you use the stem sentences to describe that shaded part of the line? Pause the video now and have a go.

How did you get on? Did you spot that the shaded part of the number line can be described as 2/8 or 1/4? So 2/8 of the number line or 1/4 of the number line is shaded.

2/8 and 1/4 are equivalent fractions.

They are equal in value.

And 2 is the same proportion of 8 as 1 is of 4.

Time for you to do some practise.

Got lots of shapes there with different bits shaded or some collections of objects and things ringed.

So find different ways to label the fraction of the shape or quantity that is shaded or ringed, and use the stem sentence to think about what that means in terms of the proportion.

So pause the video now, have a go, and then we'll look through the answers together.

How did you get on? There are lots of different ways to label the shaded or circled fractions, but here are some examples that you might have used.

So for A, we can say that 1/2 of the shape is shaded or 4/8 or 8/16, if you count the squares and realise that we can combine the half squares to make full squares.

What about B? B was interesting 'cause we didn't give all the divisions, so you had to think about how those shapes worked together.

But again, 1/2 of the shape was shaded or 3/6.

What about C? Lots of different shapes here within our rectangle.

If you went down and thought about it all in the smallest squares, it might help you, or you could combine the squares together.

However you decided to think about the shape, 2/3 or 4/6 or 8/12 perhaps, you could describe the shaded part.

And for D, the part of the number line shaded is 4/10, or we could say 2/5.

Let's look at the stem sentence for that one.

So we can say that 4 is the same proportion of 10 as 2 is of 5.

If there are 4 out of 10 parts shaded, it's the same as having 2 parts out of 5 shaded as long as the whole is the same.

And E was a bit different.

We had a collection of hats.

And we can say that 1/4 of the hats are ringed, 1 out of 4 of those pairs, or 2/8, 2 out of 8 of the hats in total.

1/4 is equal to 2/8.

Well done, we've come to the end of the first part of our lesson.

So we're going to move on and look at recognising equivalent fractions.

So here are some fractions.

How can we identify pairs of equivalent fractions? Jun says, "I'm visualising the bars.

The proportion shaded is the same for both fractions." And Sofia says, "I'm looking at the numerator and denominator." Hmm, I wonder what Sofia's looking at.

What do you notice about the pairs of equivalent fractions? Jun says he's still visualising those bars and that the proportion shaded would be the same for both fractions.

Oh, that's interesting.

He says if the whole is divided into twice as many parts, we will need to shade twice as many.

Hmm, that's an interesting thought, isn't it? If you imagine a bar divided into two equal parts and we've got one of them shaded, if we divided the same bar into twice as many parts, four parts, we'd have two of them shaded to keep the proportion shaded the same.

And Sofia is reminding us that in fractions equivalent to 1/2, the denominator is two times the numerator, hmm.

And in fractions equivalent to 1/3, the denominator is three times the numerator.

And in fractions equivalent to 1/4, the denominator is four times the numerator.

Can you see that in the fractions we've got on the screen there? 1 if half of 2, and 2 is half of 4.

1 times 3 equals 3, and 2 times 3 equals 6.

1 times 4 equals 4, and 2 times 4 is equal to 8.

So that works, doesn't it? Time to check your understanding.

Jun says that these are all pairs of equivalent fractions.

Is he correct? Can you use the stem sentence thinking about the proportions to decide whether he's correct And Jun says, "Visualise objects or bar models.

Is the same proportion shaded?" And Sofia says, "Can you see a common link between the numerator and the denominator?" Pause the video, have a think.

Which of these are pairs of equivalent fractions? How did you get on? Did you spot that it was only C that was a pair of equivalent fractions? And we can use the stem sentence.

1 is the same proportion of 4 as 3 is of 12.

1/4 is equal to 3/12.

We could imagine the bar shaded in.

But we could also think about what Sofia talked about, the numerator and the denominator.

1 times 4 is equal to 4, and 3 times 4 is equal to 12.

Let's see if we can position these fractions on the number line.

Jun says, "Equivalent fractions are equal in value," and Sofia says, "They must be in the same position on the number line." We can complete that stem sentence for all the pairs that we make.

So we can see here that 1/2 is equal to 5/10.

They sit at the same position on the number line.

1/2 and 5/10 represent the same proportion of the whole.

1 part out of 2 is the same proportion of the whole as 5 parts out of 10.

What about 1/10? Can we find a fraction that's equivalent to 1/10? 1 part out of 10 would be the same proportion of the whole as? That's right, 2 parts out of 20.

1 times 10 is equal to 10, and 2 times 10 is equal to 20.

We've divided our whole into twice as many parts, and we need twice as many of them to keep the proportion the same.

What about 9/10 of the whole, almost all of it? Well, we can have a look there and see which fraction we think represents almost all of the whole.

And it will be 90/100.

We've got 10 times as many pieces in the whole.

10 times 10 is equal to 100.

So we will need 10 times as many of them to create the same proportion, and 9 times 10 is equal to 90.

And what about 4/10 then? Well, we can see there's one fraction there.

4/10 and 2/5 are equivalent.

And if you think about it, if we've got 2/5 of the whole, if we divide that whole into twice as many parts as you can see on the number line there, 10 parts, 2 jumps out of 5 along the number line will be the same as 4 jumps out of 10.

They represent the same proportion of the whole.

And Sofia says, "1 jump out of 10 is the same proportion of the number line as 2 jumps out of 20." And we could complete that stem sentence for all the other pairs of equivalent fractions that we've just found.

Now then, if we know that fractions have the same value, we could perhaps use them to help us with some calculations.

So how can we use this fact to complete these equations? We know that 1/3 is equal to 4/12.

So can we use that fact to help us to work out 1/3 subtract 4/12 and 1/3 add 4/12? Hmm.

Jun says, "Equivalent fractions have the same value." They are equal.

I can use this to help." And Sofia says, "We could replace 4/12 with 1/3 in each equation." So 1/3 subtract 4/12 would become 1/3 subtract 1/3.

Well, 1/3 subtract 1/3 must be equal to 0 because when we subtract the same number from itself, we get to 0.

What about the second one then? Let's do Sofia's trick and replace 4/12 with 1/3.

So 1/3 plus 4/12 is equal to 1/3 plus 1/3.

And if I've got one lot of 1/3 and another lot of 1/3, I must have 2/3 altogether.

So we can use that idea of equivalent fractions to help us to complete equations, and that's gonna be really useful in the future.

Time for you to do some practise.

Can you match each pair of equivalent fractions and complete the stem sentence for each pair? And then in part two, you're going to use this fact, 2/5 is equal to 4/10, to complete the three equations.

And remember Jun's advice.

"Equivalent fractions have the same value.

They are equal.

I can use this to help." I wonder if you can do that too.

Pause the video, have a go, and we'll look at the answers together.

How did you get on? Did you spot that 1/4 was equal to 3/12, 1/5 is equal to 3/15, and 1/3 is equal to 3/9? Did you spot that the numerators were all 3 there? Let's have a look at those stem sentences.

So we can say that 1 is the same proportion of 4 as 3 is of 12.

1/4 is equal to 3/12.

1 times 4 is 4, and 3 times 4 is equal to 12.

So we can see that equivalence there as well.

1 is the same proportion of 5 as 3 is of 15.

1/5 is equal to 3/15.

And 1 is the same proportion of 3 as 3 is of 9.

So in part two, you were asked to use this fact to complete the equations, 2/5 is equal to 4/10.

Jun was reminding us that equivalent fractions have the same value.

They're equal.

So we can use that to help.

And Sofia says, "We could replace 2/5 with 4/10 in each equation or the other way round." Or you may just have chosen to think about the equivalence and not actually rewrite the equations.

So 2/5 plus 4/10 is equal to 4 somethings.

Well, we know that 4/10 is equal to 2/5.

So 2/5 plus another 2/5 will give us 4/5.

In B, 2/5 plus 4/10 is equal to 8 somethings.

Ah, so this time we could replace the 2/5 with 4/10, and then we've got 4/10 and another 4/10, which gives us 8/10.

And then for C, 4/10 subtract 2/5.

Well, we know that those are equivalent fractions.

They have the same value.

And if I subtract something of the same value from itself, I will get an answer of 0.

So 4/10 subtract 2/5 is equal to 0.

And we've come to the end of our lesson.

Thank you for working hard today.

I hope you've been using that language of equivalent fractions and thinking about all the other things you've learned about fractions with the same value.

So let's think about what we've learned today.

We've said that the proportion of a number is a part compared in relation to the whole, and we can use fractions to describe the proportion of the whole.

That might be a new word that you've used today, using proportion to think of a part of the whole.

Different fractions can be used to describe the same proportion of the whole, and these fractions are called equivalent fractions.

And we've also found out that equivalent fractions appear in the same position on the number line, as they are equal in value.

Well, what you've learned today is gonna be really useful in the future.

So I hope you've enjoyed it, and I look forward to seeing you in a lesson again soon.

Bye-bye.