# Lesson video

In progress...

Hi guys, welcome to today's maths lesson with me, Miss Jones.

Hope you're ready to get started.

Let's have a look at what we're doing today.

In this lesson, we'll be looking at recognising equivalent fractions.

To help us do that we're going to be looking at fraction bars where you're going to identify the equivalents.

Then you're going to have a go at a Talk Task.

Then we'll think about creating a number line to show equivalents.

You'll need for this lesson a pencil and a ruler, if you've got one, to help you draw your number lines.

If not, you'll have to sketch them, and some paper.

If you've got squared paper that will make it easier to draw your number lines, don't worry if not.

if you haven't got what you need, pause the video now and go and get it.

Okay, let's get started.

Before we crack on with our equivalent fractions, I thought it'd be fun to do a starter.

This one's called Explanation station.

And in order to complete this starter, you need to do a really good mathematical explanation and convince me.

You can do that out loud, or you can write something down.

So let's look at the question.

Which triangle has been split into quarters? Explain how you know and convince me.

Pause the video now to have a go.

How did you do? Did you manage to come up with an explanation? Let's look at each triangle.

Is this first one split into quarters? Well, first of all, hopefully you had a think about what quarters meant.

If something's split into quarters, it needs to be split into four equal parts.

Now, I can see that this triangle, the parts are not equal size, so it's not this one.

This one looks like they are equal size.

So this one is split into quarters.

The third one, the parts are not equal.

The fourth one, they are though.

So the answers were the second and the fourth.

And in order to get that correct you need to mention that quarter's mean four equal parts.

Okay, let's move on to recognising equivalent fractions.

Here we've got some fraction bars.

How can we use these to help us find equivalents to 1/3? Well, if we are splitting something into thirds we split it into three equal parts.

So my green bar, which is split into three equal parts can be used to show thirds.

Let's put them in, with a one of these parts representing 1/3.

Now, I've got two other bars here.

This one's split into six parts.

So each part represents 1/6.

And this one's split into how many equal parts? While you can see the 1/6 is split into half.

So they're half the size and it would make sense that each one is representing 1/12.

There are 12 equal parts there.

So now that we've used our fraction bars and labelled them, how can we look for an equivalent fraction to 1/3? Well, if we look at 1/3 here, we can see on this bar that 1/3 is equivalent to 2/6.

It's also equivalent to one, two, three, four, 4/12.

Okay, if 1/3 is equal to 2/6, how many 1/6 is equal to 2/3? Let's look back at our fraction bars.

So this time we're looking at 2/3, so two parts out of my three equal parts.

And let's mark those in.

Now, on my bottom bar, I've got sixths, six equal parts.

And we can see here that 2/3 is equivalent to 4/6.

Let's write that as an equation: 2/3 is equal to 4/6.

Now let's have a look at our numerators and denominators here.

We can see that to get from 2/3 to 4/6, our numerator's been multiplied by two and our denominator has also been multiplied by two.

Remember, if two fractions are equivalent, the numerator and denominator would have been multiplied by the same thing to get to the other fraction.

Or if we started with this fraction we could say it's been divided by two.

And the denominator has also been divided by two.

Here, my second bar has got 12 equal parts.

So I want to see how many twelfths are equivalent to 2/3.

So again, I'm going to highlight 2/3, two, and now I'm going to see how many twelfths that's equal to.

I know that 1/3 is equivalent to 4/12, 2/3 it's equivalent to 8/12.

And again, let's have a look at the relationship between the numerator and denominator.

Our numerator has been multiplied by four and our denominator has been multiplied by four.

If we started with 8/12 and we wanted to find out how many thirds, we could divide our numerator and denominator by four.

I want you to use the fraction bars on the screen to help you explain what fractions are equivalent to 9/12.

Make sure you explain your answer by using the sentence: Something is equivalent to something because.

I want you to talk about equal parts and refer back to your fraction bar diagram.

You might also want to mention numerator and denominator and how they relate to each other with multiplication and division.

How did you do? You might have found out that 9/12, which I've highlighted here, is equivalent to 3/4 and 6/8.

Did you notice any patterns when you were doing it? Let's have a look at some of those patterns.

So here's our equivalent fractions.

9/12 is equal to 3/4 and it's also equal to 6/8.

Did you notice anything? I noticed that all of my numerators are in the three-times table and all of my denominators are in the four-times table.

I'm going to reorder them so my numerators follow the three-times table and my denominators follow the four-times table.

3/4 is equal to 6/8 and it's also equal to 9/12.

What else might 3/4 be equal to? Can you think of another equivalent fraction? Well, following this pattern I've also noticed that 3/4 is equivalent to 12/16.

And let me do one more, 15/20.

And if we think about it, let's look at 3/4, which is our fraction in the simplest form, and 15/20, we can see that here our numerator's been multiplied by five and the same thing's happened to our denominator.

So they must be equivalent.

Did you manage to spot that pattern? For your task today you're going to be creating number lines that show equivalent fractions.

Let me show you what I mean.

We've got our fraction bars which we've been using here and underneath, I've got a number line.

Now this fraction bar represents one whole and it's split into two equal parts.

Each equal part would be 1/2.

Now on my number line, I need to show where zero is and I know that I'm only using one whole, which I can represent with one.

I then need two equal intervals to show halves.

We've got two equal intervals.

I've got a line in the middle to show exactly where 1/2 would be on the number line.

Okay, two equal jumps or two equal intervals, representing my two equal parts of my fraction bar.

Let's look at quarters.

So this middle one here, we've got four equal parts which we know are quarters.

Again, we're only going up to a whole, which we can represent as one.

So my number line's going to start at zero and it's going to end in one.

Okay, now we know that this bar would be 1/4.

So I'm going to place this first marker as 1/4.

Now on my number line increases each time.

So this would be 1/4 and this would be another 1/4, so altogether 2/4.

Then I'm going to do another jump of 1/4 to end up with 3/4.

Then another jump would be 4/4 which I know is equivalent to one whole.

Now, already I can spot an equivalent fraction.

1/2 is equal to 2/4.

Okay, this time we've got eight intervals, one, two, three four, five, six, seven, eight.

Again, my green fraction bar represents one whole.

So on my number line, I want to indicate zero.

And we'll go up to a maximum of one.

Now one jump, which is one part out of eighth, we can say is the same as 1/8 of the number line.

Two jumps would be 2/8 and then 3/8, and you can count with me if you like, 4/8, 5/8, 6/8, 7/8, and then finally 8/8, which we know is the same as one whole.

Now, can you spot any more equivalents? Well, we've already pointed out that 1/2 is equivalent to 2/4, but now we can see it's also equivalent to 4/8.

What fraction would be equivalent to 3/4? Well, looking down below we can see 3/4 is equivalent to 6/8 and 1/4 is equivalent to 2/8.

Thinking about our whole, we can say that 8/8, which we know is one whole is the same as 4/4, or 2/2.

Now for your task I'd like you to use number lines to investigate equivalent fractions, but instead of doing lots of different number lines, I'd like you to try and create one number line with all your equivalent fractions underneath.

Let me show you what I mean.

Here's an example number line that I've created using the facts I was just exploring.

I've got my zero to show the start of my number line and I go up to one whole.

Here I've got different ways of showing one whole, 2/2, 4/4, 8/8, all equal one whole.

And each jump here is another 1/8.

So I've got eight equal parts.

But when I get to 2/8 you can see I've also put my equivalent fraction.

I know that 1/4 is the same as 2/8.

Then I've got 3/8 and here at the halfway point I've put all the equivalents to 1/2 that I have explored.

Then we've got 5/8.

Then we've got 3/4.

Which is equal to 6/8.

Then we've got 7/8 and this would be 8/8 or 2/2, 4/4 or one whole, hopefully you get the idea.

I'd like you to create your own number line.

You can use ideas from my number line or you can create your own with different fractions such as thirds, sixths and ninths.

Or perhaps you might want to add twelfths.