Lesson video

Hi, everyone, welcome to today's math lesson with me, Miss Jones.

As usual, make sure you've got your thinking caps on, your brains ready, hope you're raring to go, let's get started and see what we're doing today.

In today's lesson, we're going to be recognising equivalent fractions.

We're going to start off by looking at creating fraction bars, we're then going to use those fraction bars to help us find equivalent fractions.

Then later on, you've got a task, and the usual quiz.

You'll need for this lesson, a pencil and a piece of paper or something else to write on and write with.

You might also want to get a ruler because we are going to be drawing bars and it'll help you make them a little bit more neat if you have one, but don't worry if you don't.

Okay, so here is a bar.

Now this bar represents one or one whole, and you can see I've labelled it for you.

Now, if we introduce a second bar, and I've split this bar into two equal parts.

The value of each part would be 1/2.

My denominator is two because there are two equal parts.

And if we're just looking at one of those parts on their own, that would be worth 1/2, okay? So let's create another bar, this time I've split it into four equal parts.

So what would the value of each part be? The value of each part would be 1/4.

The bar has been split into quarters, and if we're looking at one of these, after one of these each one would be worth 1/4.

Okay, next one, we've got another bar this time it's been split into eight equal parts.

What would the value of one part be? That's right, it would be 1/8.

So each of these is worth 1/8.

Now we can use these fraction bars to help us identify which fractions are equivalent to which fractions.

Let me show you what I mean.

So, if we zoom in here to 1/2 and our bar that shows quarters, we can see that 1/2 is the same size as 2/4.

Can you see that? Or we can write that as an equation, 1/2 is equal to 2/4.

Let's look at the eighths.

We can also see that 2/4 is equivalent to 4/8, and it's also equivalent to 1/2.

All three of these areas, if you like, are equal.

So we can write 1/2 is equivalent to 2/4 and equivalent to 4/8.

We can also write 1/2 is equal to 4/8 if we wanted to.

I want you to look closely at the equations that we've written down below.

What do you notice? If you're not sure what to look for, have a look at the numerators and the denominators.

What's happening to the numerator? What's happening to the denominator? Can you spot any patterns? Okay, let me help you out in a little bit.

So if you notice very carefully, our numerator here has been doubled one, two, then four.

And the same has happened to our denominator, two times two is four times two is eight.

If we were starting with 4/8, it's been harmed or divided by two, interesting.

So we might say in order to find equivalent fractions, you can multiply the numerator and the denominator by two.

But we also know these are equivalent and one hasn't been multiplied by two it's been multiplied by four, but the same as happened with the denominators.

So actually it's not just multiplying by two, halving and doubling, as long as we multiply or divide the numerators by the same number as the denominators, our fractions are equivalent.

Okay, I want you to look back at our fraction bars now and think about, are there any other equivalents you can come up with? What equivalent fractions are represented here? Well, we could say 1/4 is equal to or equivalent to 2/8.

What's happened to our numerators and denominators this time? Well, if we started with 1/4, they've been multiplied by two.

Although if we started with 2/8, you could say that the numerators had been divided by two.

The denominator has also been divided by two.

What about this one? We can say that one whole is equal to two halves.

Whenever our numerator and denominator are the same number, the fraction is equivalent to one or one whole.

If you look closely, we can also see that one whole is equivalent to 4/4.

Our numerator and denominator are the same.

And that makes sense, because if we divide four into four equal parts, and you can see it here, it's going to equal one whole.

Okay, this time I've divided my fraction bars up slightly differently.

You can see here on this bar that I've got three equal parts.

So what's each part worth? 1/3, what about here, how many equal parts do I have? I have six equal parts.

So therefore, each part is worth 1/6.

Are you starting to spot any equivalent fractions already? What about this last bar? I've got three, three, three, so there are nine equal parts each part is worth 1/9.

Now let's see if we can spot some equivalents.

Okay, 1/3 is equal to 2/6.

If I look closely at my 1/3 here, I can see it's the same size as two of these parts which are divided into sixths.

What other equivalent fractions can you spot? You might have spotted that one whole is the same as 3/3.

Remember when our numerator and denominator are the same number, it's equivalent to one whole.

You might have spotted that 3/9 is equivalent to 1/3.

Let's look at that on our fraction bar.

3/9 is here, now we could say that's equivalent to 2/6 as well, or 1/3.

The bars don't have to be directly next to each other to see that it's equal to.

So my ninths here are the same size as my 1/3 here.

Okay, for your task today, you're going to have some questions about finding equivalents.

Here, we've got an example question.

So we know the numerator here is one, but we don't know the denominator but we know this fraction is equivalent to 2/6.

So what can we do to help us? Well, we can either use our fraction bars.

So hopefully you've got a copy of your own fraction bars or you can draw some of your own similar to this, or we can use our multiplication and division facts.

Now I'm going to do a bit of both because I want to make sure that I'm confident in my answer.

So what do I know? I know that we're looking at 2/6, so I need to find 2/6, I can look over here and identify 2/6 and see what it's equivalent to.

Now I know that I'm looking for a unit fraction with a numerator of one.

So 2/6 is not the same as just 1/9.

And I can see it's not the same as looking at my top bars, it's not the same as an 1/8 or 1/4 or 1/2, but I can see right next to it, that it is equal to 1/3.

2/6 is equal to 1/3.

So here, my denominator has to be three.

Now, if I was using my multiplication and division to help me work this out, I need to look at the relationship between the numerators and the relationship between the denominators, and make sure the same thing is happening in terms of multiplication or division.

Now here, my numerator had been halved, divided by two.

So I would have needed to do the same with my denominator.

Six divided by two would have got me three.

Let's look at another example question.

So this question asks what fractions are equivalent to 1/2.

So I know I'm looking for 1/2.

I could use my multiplication and division, but first I'm going to look at my fraction bars.

So I'm identifying 1/2, I can see it's up here.

Straight away, I can see that it's equivalent to 2/4, or one, two, three, 4/8.

Is there any other fractions that are equivalent to 1/2 that you can see? You might've noticed if we look down here that actually 3/6 is also equivalent to 1/2.

Now if we write these equivalents down, we can see 1/2 is equal to 2/4, 4/8, or 3/6.

Interestingly, we were following a bit of a pattern with these multiplying by two, multiplying by two, but here 3/6, which was on our different diagram and slightly different, but if we go back to 1/2 and we think about 3/6, we can see that both the numerator and denominator have been multiplied by the same thing.

They've both been multiplied by three.

Okay, so you can see that actually these are equivalent.

What's interesting when you're looking at 1/2 is that the denominator is always double the numerator for equivalence for 1/2.

Two is half a four, four is half of eight.

Okay, it's time to go off and complete those equivalent questions.

When you're finished, come back to this video and we can go over the answers together.

Okay, hopefully you've had a chance to complete your independent task.

Let's look at the answers together.

So question one, hopefully you should recognise this kind of question from our examples.

So we know that our missing denominator has to be three.

1/3 is equivalent to 2/6.

You can see both the numerator and the denominator have been multiplied by two.

Question two, what fraction is equivalent to 1/4? And show me using your own bar diagram.

Well, 1/4 could be equivalent to 2/8.

Here's my bar diagram, which shows that 1/4 the same size is 2/8 here.

I've got all of my parts in the rest of the bar.

You might have chosen a different fraction such as 3/12.

Question three, 1/2 is equal to so many sixths.

What's our missing numerator? Well, two has been multiplied by three so I need to do the same with my numerator.

I would've got 3/6.

You might have used a bar diagram to help you with that one as well, or to prove that you were right.

Question four, this one's in words, two thirds is equivalent to hmm ninths.

Well, I know that 2/3 here it's equivalent to 6/9.

How did I know that? Well, my denominator has been multiplied by three so my numerator needs to be multiplied by three.

Let's look at question five.

We've got here, a missing numerator.

Let's look at what's happening with our denominators, that's been multiplied by two again.

So my missing numerator needs to be half of two.

So we're going from six to three, we're dividing by two, two to our numerator we're dividing by two as well.

1/3 is equal to 2/6.

You might've remembered that from question one as well.

Question six, what fractions are equivalent to 1/3? Create a fraction family, and show me using your own fraction bar diagram.

Now you might've had even more than this, but I know that 1/3 is equivalent to 2/6 or 3/9.

You might've kept going and gone on to 4/12 and kept the pattern going, well done if you did.

Question seven, what's our missing denominator? 2/8 now let's use division to work from two over to our numerator, we know that that's been halved so the denominator needs to be halved.

Eight divided by two is equal to four so 1/4 is equivalent to 2/8.

And question eight, 4/6 is equivalent to hmm thirds.

Let's write out again, 4/6 is equal to something thirds.

Let's look what's happening.

Six has been halved to get to three so I need to half my numerator, four divided by two is equal to two.

Here come our answers, there we are.

Question nine, this one asks you for an explanation.

Derek says that 1/3 is equivalent to 2/9.

Explain why he is not correct.

Okay, so here's my explanation, let's see if it's similar to yours.

I said that 1/3 cannot be equivalent 2/9 because 1/3 has the same value as 3/9.

And then I did a small fraction bar diagram to show my thinking.

So you can see here that 1/3 is actually equivalent to 3/9, and 2/9 would have a smaller value.

You might have also written that out, 1/3 is equivalent to 3/9 where the numerator and the denominator have both been multiplied by three.

Question 10, true or false, 5/10 is equivalent to 1/2.

Convince me using your own fraction bar.

Okay, so this is true.

5/10 is half of 10/10, which would be one whole.

5/10 is equivalent to 1/2.

You can see in my diagram here, I've got my one whole, I've got my halves, and here I've got my tenths.

5/10, which you can see here, is equivalent to 1/2.

Hope you enjoyed today's lesson.

It's now the end of the lesson so time to go and complete the quiz.

Thank you, bye-bye.