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 explaining the relationship between numerators and denominators and equivalent fractions.

And it comes from our unit comparing fractions using equivalents and decimals.

So we're going to look at lots of equivalent fractions in different ways, and we're going to think about the relationship between the numerators and the denominators and how we can use that to help explain and maybe create some equivalent fractions.

So let's get started.

We've got 3 keywords today, and they may well be familiar to you, but they're going to be useful to us today.

So let's just have a practise.

I'll take my turn and then it'll be your turn.

So my turn, numerator, your turn.

My turn denominator, your turn.

My turn, equivalent fraction, your turn.

Well done, as I say, you possibly know those words quite well already, but let's just look at those definitions to remind us.

So the numerator is the top number in a fraction and shows us how many parts we have.

The denominator is the bottom number in a fraction and shows us how many equal parts the whole has been divided into.

And equivalent fractions are fractions which have the same value even though they may look different and they're really important in our work today.

There are 2 parts to our lesson today.

First of all, we're going to be naming equivalent fractions and then we're going to be creating equivalent fractions.

So let's make a start.

And Jun and Sofia are helping us with our work today.

So what fraction of the shape is shaded? And we're going to use a stem sentence that might be very familiar to you.

The whole is divided into hmm equal parts and hmm of these parts is or are shaded.

And Sofia says she's gonna use that stem sentence to help her check what fraction of the shape is shaded.

So what fraction can you see shaded there? The whole has been divided into 5 equal parts and one of these parts is shaded.

So our fraction must be 1/5.

As Jun says, "1/5 of the shape is shaded." And there is our fraction 1/5.

Now what fraction of the shape is shaded? Sofia says, "It's the same." Jun says, "No it isn't." It's got more parts now." Hmm what is the same and what is different? Sofia says, "But the shaded area hasn't changed.

We've just added another line." Jun says, "Let's look at it again." Let's do that.

So there's our original shape and there's our new shape.

Sofia says, "I can use the stem sentence to check." The whole is divided into 10 equal parts and 2 of these parts are shaded.

"Oh", Jun says.

"So 2/10 is equivalent to 1/5." Our whole shape and our shaded area haven't changed, have they? We've just divided the whole into a different number of equal parts.

We can now describe the shaded area in 2 different ways.

1/2 or 2/10.

And those fractions are equivalent.

They represent the same value.

Okay, so what do you notice this time? Can you use the stem sentence to think about what you can see there? What's stayed the same and what's changed? Sofia says, "The whole is divided into a different number of equal parts.

I can use the stem sentence again." So this time the whole is divided into 15 equal parts and 3 of these parts are shaded.

Jun says, "The whole and the shaded area have stayed the same." So what does that mean for our fractions? "This shows 3/15 of the whole is shaded, but we can say that 3/15 is equal to 1/5." And Sofia says, "We can also say that 3/15 is equal to 2/10." Time to check your understanding.

What fraction of the shape is shaded now? Can you use the stem sentence to help you? Sofia's advising you.

And Jun says, "What other fractions are equivalent to this fraction?" So we've got the same whole and the same shaded area.

How can you describe the fraction shown here? And what do you think it will also be equivalent to? Pause the video and have a go.

How did you get on? Did you spot that this time the whole is divided into 20 equal parts and 4 of these parts are shaded.

So our fraction is 4/20.

But we can say that 4/20 is equal to 3/15, which is equal to 2/10 and is equal to 1/5 because the whole and the shaded area have not changed.

We've just described it in a different way by dividing the whole into a different number of equal parts.

So all of those fractions are equivalent.

They are equivalent fractions because the same proportion of the shape is shaded and that proportion meant the same part of the hole.

So what fraction of the shape is shaded now? 1/5, 2/10 which are equal, 3/15 equal to 2/10, 4/20 and 5/25.

And we can say that all of those fractions are equivalent and we can put an equal sign between them all because they have exactly the same value.

What do you notice about the digits in the fractions? The numerator and the denominators? Jun says, "The numerator increases by 1 each time." We've got 1/5, 2/10, 3/15, 4/20 and 5/25.

And Sofia says, "The denominator increases by 5 each time." 5, 10, 15, 20, 25.

Ooh, there's a times table there isn't there? Let's have a look at the number line.

The line is divided into 5 equal parts.

What fraction would go here on the line? Jun says 1/5 is at this position, let's put it in.

What do you notice about the number line now? It's not divided into 1 equal parts now is it? The line is divided into 10 equal parts? Do we need to change the fraction then Sofia? No, it's still 1/5.

It's still 1 out of 5 equal jumps along the line, but it is also 2/10.

So we can put 2/10 at the same place on the line.

That proportion is the same, 1 jump out of 5 is the same proportion of the whole as 2 jumps out of 10.

And our whole this time is 1.

And Sofia's reminding us, "1 is the same proportion of 5 as 2 is of 10." So 1/5 and 2/10 are equivalent fractions.

So they sit at the same position on the number line.

And that's a really important thing to know about equivalent fractions.

What do you notice about the number line now? Well the arrow's still in the same place, that's right.

This time the whole is divided into 15 equal parts and the arrow is 3 out of 15 jumps along the number line.

So this must be 3/15.

But can you spot the arrow's not moved, has it? So how else could we label that point? Ah Jun says, "3/15 is equivalent to 1/5 and 2/10." So we can put those fractions at the same point on the number line.

Time to check your understanding now.

What do you notice about the number line now? How could you label the position shown by the arrow? And Jun says, "Can you label the point with more than one fraction?" Think about what's the same and what's different from the number lines we've just been looking at.

Pause the video and have a go.

So did you spot that this time it was 4 out of 20 jumps along the number line? So this point represents 4/20.

But what else does it also represent? That's right, all those fractions we've looked at before can still be used to label the same point because the proportion of the distance along the number line is the same.

So it can be labelled with 1/5, 2/10, 3/15 and now 4/20.

And Sofia says "1/5, 2/10, 3/15, and 4/20 are all equivalent fractions." They sit at the same point on the number line.

Okay, so we know that those are all equivalent fractions.

How could we label this point with these divisions on the number line? Have a moment to have a look, what can you see now? Do you need to count all the divisions? Well we know that that point marks 1/5 of the distance along the number line and we've now got 5 equal parts leading up to that.

So we must have 25 parts in our whole.

And as Jun says, "The arrow is in the same place." But the whole is divided into a different number of equal parts.

The arrow is 5 jumps out of 25 along the number line.

So we can label the point with the fraction 5/25.

But we also know that that is equivalent to all of those other fractions which label that same point on the line, the same proportion of the line between 0 and 1.

Time for you to do some practise.

You're going to add horizontal lines to these images to show equivalent fractions and name those fractions like we saw in the lesson with the fractions equivalent to 1/5.

So what do you notice about the fractions that you've created and the box's there for you to write down what you've noticed.

And then for the second part, you're going to estimate where the fractions that you've just drawn would sit on this number line.

So use the fractions you created in part 1 and then position them on the number line.

And remember, Jun says the whole stays the same and the shaded area stays the same each time.

And the whole is divided into a different number of equal parts.

So can you use that knowledge to help you with putting the numbers on the number line? Pause the video, have a go, and then we'll have a look together.

How did you get on? Did you spot that it was 1/3 and then when we added one more horizontal line, we divided the whole into 6 equal parts so it was 2/6.

When we added a second line, we divided it into 9 equal parts so we have 3/9.

When we divided it into 12 equal parts with a third line, we had 4/12.

And when we added the 4th line to divide it into 15 equal parts, we have 5/15 as our shaded area.

There's different ways you might have described what you found out or things that you noticed.

But here's one idea from Jun.

He says, "I noticed that the denominators of all the fractions are in the 3 times table and the numerator increase by 1 each time you add another line.

So we've got 1/3, 2/6, 3/9, 4/12 and 5/15.

And our denominator is 3, 6, 9, 12 and 15.

I wonder what you spotted.

Did you spot that as well? So in part 2 you were going to estimate where the fractions you drew would sit on the number line.

And what did you notice again? Well they're all equivalent fractions, so they all must sit at the same position on the number line.

1 jump out of 3 along the number line, and that also can be represented as 2 out of 6, 3 out of 9, 4 out of 12 or 5 out of 15 equal jumps along the number line.

Well done.

Okay, so part 2 of our lesson we're going to be creating equivalent fractions.

What do you notice about these fractions? You might recognise them from the first part of our lesson.

What do you notice about the numerator? Jun says, "The numerator increases by 1 each time." Sofia says, "I don't think it's all about adding 1.

We need to look at the denominator." So what do you notice about the denominators? Jun says, "The denominators increase by 5 each time and they're all multiples of 5." That's interesting to spot.

And Sofia says, "Every time we add 1 to the numerator, we add 5 to the denominator." So time for a quick check.

What do you notice about the numerator and denominators in these equivalent fractions? Can you complete the stem sentences? And Jun says you could imagine adding lines to create those equivalent fractions.

So pause the video, have a go, and then we'll look at the stem sentences together.

Did you spot that the denominators increase by 4 each time and they're all multiples of 4, and that every time we add 1 to the numerator, we add 4 to the denominator.

Did you imagine the lines being added to that shape at the bottom of the screen as Jun suggested? I wonder if you did.

Or are you starting to see those proportions being the same? 1 out of 4 is the same proportion of 2 out of 8 and even a 5 out of 20, and that's why they are equivalent fractions.

So let's focus on 1/5.

What do you notice about the numerator and the denominator, just in 1/5? Jun says, "The denominator is 4 more than the numerator." Hmm, well he's right.

1 plus 4 is equal to 5.

That's right.

Is the same true for 2/10? We know that 1/5 and 2/10 are equivalent fractions.

So is the same true? And Sofia says, "No, it isn't true for 2/10." 2 plus 8 is equal to 10, not 2 plus 4.

She says, "I don't think this is about adding and subtracting." So what else can we notice about the numerator and the denominator? Sofia says, "Let's try using multiplication and division to explain the relationship." So Jun says, "The denominator is 5 times the numerator." 1 times 5 is equal to 5.

And Sofia says, "If you divide the denominator by 5, you get the numerator.

5 divided by 5 is equal to 1.

Is the same true for 2/10, then let's try.

The denominator is still 5 times the numerator.

2 times 5 is equal to 10.

And if you divide the denominator by 5, you still get the numerator.

10 divided by 5 is equal to 2.

So that does work.

Over to you to check.

Is the same true for all fractions equivalent to 1/5? We've got some more there for you to try out.

So the generalisations we come to were that the denominator is 5 times the numerator.

And if you divide the denominator by 5, you will get the numerator.

Is that true for 3/15, 4/20 and 5/25? Pause the video and have a look.

How did you get on? Well it is true, isn't it for 3/15? 3 times 5 is equal to 15, 15 divided by 5 is equal to 3.

And it's true for 4/20 and it's true for 5/25.

So for all the fractions we've tried, we can say this, in fractions equivalent to 1/5, the denominator is always 5 times the numerator.

And if you think about how we've been dividing up shapes and bars and number lines, we can probably say that that is true for all fractions equal to 1/5.

So how can you explain that these are all equivalent fractions to 1/4.

We've got 1/4 equals 2/8 equals 3/12 and we can prove it by drawing bars.

But let's think about the relationship between the numerator and the denominator.

And Jun reminds us it's all about multiplication and division and not addition and subtraction.

And Sofia says, The relationship between the numerator and the denominator is the same for all the fractions." So let's have a think about that.

In all fractions equivalent to a 1/4, the denominator is always hmm times the numerator.

Have a look at the fractions we've got there.

What is the missing number there? What do we multiply 1 by to equal 4? 2 multiply by what equals 8 and 3 multiplied by what equals 12.

Have you spotted it? That's right, it's 4 times.

And if you think about it 1 part out of 4, we're always going to have 4 times as many parts in the whole as we have shaded if our fraction is equivalent to 1/4.

1 times 4 is 4, 2 times 4 is 8, 3 times 4 is 12.

And we could say the same is true for those division relationships as well.

So use the stem sentence to decide which of these fractions are equivalent to 1/4.

So we've got lots of fractions there.

Which ones are equivalent to 1/4? Remember, in all fractions equivalent to 1/4, the denominator is always 4 times the numerator.

So let's have a look.

So yes, 10/40 is equal to 1/4.

10 times 4 is equal to 40.

What about 25/100? Yep, 25 times 4 is equal to a 100.

So 25/100 is equal to a 1/4.

What about 2/10? 2 times 4 is equal to 8 not 10.

So that's not equal to a 1/4.

What about 8/36? They're nice numbers with the 4 times table, aren't they? Perhaps that's a 1/4.

8 times 4 is equal to 32.

So no, that's not equal to a 1/4.

What about 9 times 4? Well, yep, 9 times 4 is equal to 36.

So 9/36 is equal to 1/4.

And if 9/36 is equal to a 1/4, what do we know about 9/36 or 9/32.

No, it's not, is it? 'Cause 9 times 4 is not equal to 32.

If 9 times 4 is equal to 36, it can't be equal to 32.

So those 3 fractions are equivalent to 1/4.

We've used our statement that in fractions equal to a 1/4, the denominator is always 4 times the numerator to help us decide.

Time to check your understanding.

Can you find some pairs of equivalent fractions in here? And can you use the idea of in all fractions equivalent to hmm, the denominator is always hmm times the numerator.

So you've got some unit fractions in there and some non unit fractions.

Can you create some pairs of equivalent fractions? Pause the video and have a go.

How did you get on? So did you spot that in for 1/6 we're looking for another fraction where the denominator is 6 times the numerator.

So 1 times 6 is 6, and 4 times 6 is equal to 24.

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

1/2, well we always know in a 1/2 that the numerator is half the denominator or the denominator is double the numerator.

So 3/6 is equal to 1/2.

We've got that times 2 relationship.

In infractions equal to 1/5, the denominator is 5 times the numerator.

So 6/30 is equal to 1/5 and in fractions equal to a 1/3 the denominator is 3 times the numerator.

So 3/15 must be equal to 1/3.

I hope you found all those pairs of equivalent fractions.

Time for you to do some practise.

Now for the first part, we want you to go back to the fractions that you created in task A and think about what you notice about the numerators and the denominators in those fractions.

For 2, you're going to describe the relationship between the numerators and the denominators in your equivalent fractions.

And for part 3, you're going to choose a different unit fraction.

So where the numerator is 1, and create equivalent fractions with numerator of 2, 3, 5 and 10.

And explain how you know they're equivalent using our stem sentence.

So enjoy having fun with the fractions you created in task A.

And I will see you soon for some answers.

Pause the video now.

So how did you get on? For the fractions you created in part A did you complete those stem sentences thinking about the denominators increasing by hmm each time and all being multiples of hmm.

And every time we add hmm to the numerator, we add hmm to the denominator.

So we can think about describing equivalent fractions in that way, but it's really useful to think about the relationship between the numerator and the denominator, and to think about that using multiplication and division.

So in those fractions, could you also complete the sentence.

In all fractions equivalent to hmm, the denominator is always hmm times the numerator.

You may have used a 1/3.

So in that case, in all fractions equivalent to a 1/3, the denominator is always 3 times the numerator.

And Sofia's saying she hopes you use the stem sentences to help.

And part 3, you were asked to choose a different unit fraction with a numerator of 1 and create equivalent fractions with numerators of 2, 3, 5 and 10.

And explain how you know they're equivalent fractions.

So I chose 1/7, so my equivalent fractions were 2/14.

1 times 7 is 7, 2 times 7 is 14.

3/21, 3 times 7 is equal to 21.

5/35, 5 times 7 is equal to 35.

And 10/70, 10 times 7 is equal to 70.

And I could check all of those by using the stem sentence in all fractions equal to 1/7 the denominator is always 7 times the numerator.

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

You've worked really hard today, and I hope that you've started to understand more about the relationship between the numerator and the denominator in equivalent fractions, especially where we're thinking about fractions equivalent to a unit fraction where 1 is the numerator.

So what have we learned about today? We've learned that in equivalent fractions, there is a relationship between the numerator and the denominator.

And that links to that proportion of the whole that we talked about earlier.

And we can use the stem sentence to decide whether fractions are equivalent to a given unit fraction.

So we can create a generalisation from our stem sentence and use that to test our fractions.

So here we've got fractions equivalent to a 1/5.

So our sentence would become in all fractions equivalent to 1/5.

The denominator is always 5 times the numerator.

And we can then change that stem sentence to match the fraction that we're looking at at the time.

Thank you for your hard work today, and I hope I get to work with you again soon.

Bye bye.