Lesson video

Hi, welcome to today's maths lesson.

You're with me, Ms. Jones.

Hope you're all feeling well today and ready to get started.

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

In this lesson, we're going to look at equivalent fractions.

Have you heard of the word equivalent before? Well, it sounds a little bit like equals and has a similar meaning.

If two numbers or fractions are equivalent, it means they have the same value.

For example, one half is equivalent to two quarters.

And we're going to start by having a closer look at the denominators and how that affects equivalent fractions.

Then we're going to do an activity called always, sometimes, never.

Then you've got your independent task and a challenge question.

And finally, the lesson quiz.

You'll need today something to write with and something to write on such as a pencil and piece of paper.

If you haven't got that already, go and grab one now and then come back to the video.

Okay, if you've got everything you need, let's get started.

Here we've got a problem and three statements.

Now, I like the look of this problem because it's about chocolate.

Now, looking at each of these statements, we need to work out if we agree with them or not.

Jo, Bill and Sarah are sharing a bar of chocolate.

They can either have one third each, eight twenty-fourths or four-twelfths.

Let's have a look at what they say.

Jo says, "I would rather have one third "because thirds are bigger than twelfths or twenty-fourths." Hmm, do you agree with Jo? Sarah would rather have eight twenty-fourths.

She says eight is the highest numerator, so it must mean the most pieces.

Is that correct? Bill says, "I would rather have four twelfths "because twelfths is fun to say." Hmm, I'm not sure about Bill's reasoning there, but I wonder if you agree with him.

How could we explore this further? Well, we could use representations.

I wonder if you could draw something on your piece of paper that might help us explore each of these fractions and compare them.

Pause the video now to have a go at that.

Hopefully you've had a chance at drawing some representations for each of these fractions.

Did you work out if any of them are greater or less than, or are they equivalent? Hmm, let's have a look at this representation.

Here I've tried to use counters to represent each fraction.

I've got Jo representing a third, Bill representing four twelfths, and Sarah representing eight twenty-fourths here.

Is my representation or are my representations here, helpful or useful? Hmm, they're actually not very useful because it's really difficult to compare.

Jo has showing a third, but we can't show twenty-fourths or twelfths using this same representation of three counters.

What we could do is use this representation of 24 counters to show each fraction.

Remember, the bar of chocolate they're sharing is the same bar of chocolate and the same size and these representations because they're all using different amounts of counters aren't really showing that we're sharing something of the same size.

So using 24 counters and representing each fraction using that same representation might be more sensible.

So I'm just going to use 24 counters this time.

We can split that into thirds.

You can see how much chocolate we get here.

Here it's already in 24 parts, you can see how much chocolate we get here.

And I've split it here into 12 parts, and you can see how much chocolate we get here.

Now, you might notice that actually we're getting the same amounts of chocolate no matter which way we split it out of Bill's way, Sarah's way or Jo's way.

And that's because all of those fractions are equivalent.

They're the same value.

Okay, so here I've got my representations showing my equivalents and this time I've chosen the chocolate bar divided into 24 pieces.

I wonder if you chose something similar when you were representing.

And up here, I've got my equivalents.

I know that one third is equivalent to four twelfths, and that's equivalent to eight twenty-fourths as well.

Now, what we'll need to think about is, is there any patterns here? Is there a relationship between the numerator and denominator for each of these? Is there any pattern you can spot between the denominators? Pause the video now to have a quick reflection.

Hmm, what do I notice? Well, I notice that we're looking at thirds here and interestingly, I know that one is a third of three and four is a third of 12.

I wonder if that's always the case.

Well, let's look at this one, is eight a third of 24? Yes, it is.

I'm going to start recording this.

So one is a third of three, and we can write that as three divided by three is equal to one or one times by three is equal to three, four times by three is equal to 12.

Interestingly, so hopefully we've spotted a bit of a generalisation between equivalence to one third.

I also asked you, did you spot a pattern between the denominators? Hmm, well, you might think all of these are in the three times table, and certainly 12 is a multiple of three and 24 is a multiple of 12.

Did you spot anything else? I wonder if this is always sometimes or never true.

In equivalent fractions, denominators are multiples of the same number.

Hmm, pause the video now and see if you can explore that.

Hopefully you've had a chance to think about that statement and decide whether it was always true, sometimes true or never true.

You might've used some representations to help you.

I did, and I thought about a different fraction.

I stuck with one third and I thought, what else is it equivalent to? Hmm, well, we've already looked at eight twenty-fourths, and we've looked at four twelfths, but I also know that one third is equivalent to three ninths, and I know that because if we look at a representation that's split into nine parts, we can see that one third would be the same as three parts out of nine.

Now, I also know that one third is equivalent to eight twenty-fourths for example, which means that three ninths is also equivalent to eight twenty-fourths.

But 24 isn't a multiple of nine or nine isn't a factor of 24, but these are equivalent.

So, I think because of this example and other examples which you might've explored, that this is sometimes true.

Sometimes they are multiples, such as 24 is a multiple of three, but sometimes they're not, 24 is not a multiple of nine.

How did you deal with that? If you didn't get the answer, sometimes, perhaps you could do some further exploration looking at some different fractions.

Okay, on the screen I've listed some other fractions that are equivalent to one third here.

Now, we've already looked at this statement saying that equivalent fractions have denominators that are multiples of the same number.

And we decided that was sometimes true.

Six is a multiple of three, but we know nine isn't a multiple of six.

So sometimes that's true and sometimes that's not.

I wonder if we could think about what's always true here.

What patterns do you notice? Looking at our fractions, what's the same and what's different? Have a moment to think about that.

If you want to, you might want to pause the video and write some things down.

Let's have a look together.

You might've noticed that the numerator is always one third of the denominator.

Let's have a look.

One is a third of three.

Two is a third of six, three is a third of nine.

So when we're looking at fractions that are equivalent to one third, the numerator is always one third of the denominator.

Did you find that? I wonder if that works for other fractions.

For example, we know that one half is equivalent to two quarters.

And in this instance, the numerator is half of the denominator, and the numerator is half of the denominator.

This would be a really interesting one to investigate further, which is it? This person says, "I've noticed that the denominator "is always a multiple of three." Let's check, three, six, nine, 12.

This is a bit like our three times table, isn't it? I wonder if you could use that pattern to help you find other equivalent fractions.

This person says, I've noticed that the numerator and the denominator can be multiplied by the same number to find an equivalent fraction.

That's really interesting.

So if we look at one third and two sixths we can see one's being multiplied by two, and three has also been multiplied by two.

This is a really key statement to be noticing.

And actually this is true for all equivalent fractions.

Let's have a look at another example here.

Here we've got one third and four twelfths.

We can see that these are equivalent because the numerator, to go from one third to four twelfths has been multiplied by four and the denominator has also be multiplied by four.

If we were starting with four twelfths, we could say that the numerator has been divided by four and the denominator has also been divided by four.

This is how we can tell these fractions are equivalent.

Here's my pictorial representation.

One third is equivalent to four twelfths.

For your independent task today, I'm going to give you some pairs of equivalent fractions.

For example, one-third is equivalent to two sixths.

I'd like you to think about how you might show that pictorially.

You'll need to match the pair of equivalent fractions of the correct pictorial representation, or you might want to draw some of your own pictorial representations.

Make sure you're explaining how you know by referring to the amounts of parts.

For example, here, I can see that one third and two sixths.

What do I know about these? When I know that one third represents one part out of a total of three parts and two sixths represents two parts out of a total of six parts.

I can see that this matches this pictorial representation, one part out of a total of three parts.

We can see it's equivalent to two parts out of a total of six parts.

Here I've got another one, one half, and that's equivalent to four eighths.

Now I can see that one half is the same as one part identified out of two parts, and four parts identified out of a total of eight parts.

So I can see this matches this pictorial representation.

Make sure you're explaining as you're working through the task.

You might want to explain out loud, or you might want to have a go at some written explanations and perhaps link that to your pictorial representations.

Okay, once you've finished your task, come back to the video.

How did you do with your independent task? Let's go over some of these together.

Okay, so here we've got one quarter is equivalent to three twelfths.

Which picture does that match with? Can you point to it? I can see that it matches with this one, B, because we've got one part out of four representing one quarter, and here we've got three parts out of 12.

We know that these are equivalent, which therefore these fractions must also be equivalent to.

Let's have a look at the next one, one fifth.

So one part out of a total of five parts is equivalent to three fifteenths.

I can see this matches picture A.

We've got one part out of total of five is equivalent to three parts out of a total of 15 parts.

Then we've got one sixth is equivalent to two twelfths.

Hmm, we've got these two left.

It doesn't look like it's this one, because we can see that half is identified here.

So it looks like it must be C.

Let's just double-check.

One part out of a total of one, two, three, four, five, six, perfect.

And two parts out of a total of 12 parts.

So that means that this one must match with D.

One half is represented here and six twelfths which is equivalent is represented below.

How did you get on? Hopefully you had a really good go at explanations doing that, referring to the amount of parts, referring back to your numerator and denominator.

To finish off, I've got a final question for us to have a look at.

These are pairs of equivalent fractions but all of them have a mistake.

Can we spot the mistake and correct them so that they are equivalent? Let's do the first one together.

Here we have one half is equivalent to four ninths.

Well, we know that fractions are equivalent when the numerator and denominators have been multiplied by the same number or divided.

So starting with a half.

We know that one, our numerator has been multiplied by four, has the same happens on the bottom.

Hmm, doesn't look like it, so these are not equivalent.

We need to make sure our denominator has also been multiplied by four.

So our denominator, to make these equivalent needs to be eight.

One half is equivalent to four eighths.

Okay, I'd like you to have a go at the others.

Pause the video now and then come back and we'll do the others together.

Okay, hopefully you've had an opportunity to explore some of those.

Let's have a look.

Here we've got two quarters is equivalent to two eighths.

Well, our numerators here are the same, but our denominators are different.

So these cannot be equivalent.

We can see that four has been multiplied by two, so let's do the same with our numerator.

Two quarters is actually equivalent to four eighths.

Might've noticed these are equivalent to one half.

Three quarters is equivalent to eight twelfths.

Is that correct? Or four, our denominator has been multiplied by three.

So actually, we need to do the same on the top.

This should say nine-twelfths.

Here, two twelfths is equivalent to one half.

That doesn't make sense.

I know that equivalents to one half need to have the numerator being half of the denominator.

Let's think about 12 has been divided by six.

So we need our numerator to have been divided by six.

If we change this to a number six, six twelfths, I can make these equivalent.

And finally, two eighths is equivalent to four twelfths.

My numerator here has been multiplied by two, so my denominator needs to do the same.

I'm going to change this to sixteenths.

Two eighths is equivalent to four sixteenths.

That's the end of the lesson today.

If you'd like to share your work, please ask your parent or carer to do so.

It's time to complete your quiz.

Thanks very much, bye bye.