Lesson video

Hello again, it's Mrs. Holmes.

I'm here again to teach you about equivalent fractions.

Now, this is the task that I left you with at the end of the last lesson, isn't it? I just want to see how some of you got on.

There's a few bits there to sort of make it a little bit more tricky, wasn't there? Let's see if we can work out.

So, let's look at the square at the top there.

What can you do to help you to work out one of those fractions, using all of the skills we used last lesson? I wonder what you did.

Did anyone count individually? Did anyone count in rows? So, if I was doing this, I would've looked at it in two ways.

The first one would have been to say, "Well, how many squares are there in total?" Because this would give me my denominator.

And then, how many of those squares were shaded? And that would give me my numerator.

That would be one of the fractions I would have worked out.

So, counting along in the columns, I would have said four, eight, 12, 16.

So, my denominator is 16, and I can see that four, eight, 12, three of those columns are shaded.

So, one of the fractions could be 12/16.

The other way I look at it, if I took a step back, I could see that there were four columns.

If I counted each of those as one part, just like we did with the teddy bears last lesson, then I could say that it's divided into quarters, too, and 3/4 is shaded.

There you are, 12/16 and 3/4.

Okay.

The next one along is also a square, isn't it? But that one's a little bit more tricky because you have only parts of four of the shared squares on there shaded.

Did you work out that if you put the smaller part with the bigger part, that would make a complete square? So, what would that mean? How many would then be shaded in total out of that 16? We know it's 16 because it's the same size as the previous square that we looked at.

That's right, two.

Well done, you.

So, two out of 16.

How else could you look at that? Couldn't do the same as we did last time and have a complete row, could we? No, it would be half of a row.

How many parts would there be then? Hmm, that's a tricky question.

Let's see if you've got that right.

1/8.

Okay, so 2/16 and 1/8 are equivalent.

And moving on to our other two shapes, now these have been put there definitely to test you.

One of them's not complete, so you can't see how many parts there are.

And the other one, it's all different sized parts.

But did you notice in the rectangle shape, there is definitely three parts you could see? And two of those parts have only got half of them shaded, just in different orientations.

Like I was talking about last time with the number line, the orientation doesn't always matter, if the part is equally divided.

So, that means if you were able to put those two halves together, squish them back together, that, that would mean 2/3 of that shape would be shaded, wouldn't it? Can you think of another equivalent fraction for that? There you go, 4/6, because we can divide them each into half again, which will give you six equal parts, and then four of those would be shaded.

The final shape, thinking again, you've got two there.

If you can see the type of shape it is, you'd notice that it's a, that's right.

It's a hexagon, isn't it? The hexagon has how many sides? Six.

Yeah, I heard you, well done.

So, two out of six could be one of your starting fractions, but what else could we have it equivalent to? There's more than one answer, but using that shape there might help you.

Let's see.

Did you get it, 1/3? Because you could have used those two parts that are shaded as being equivalent size to one part, and you've now to fit two more in, wouldn't you? Well done, you, if you've got those right.

Okay, let's move on to today's lesson then.

As I said, we are still looking at equivalent fractions.

We're going to try and understand how equivalent fractions work so that when you come across them, it's a little bit easier to understand.

This is our stem sentence for today.

The whole is divided into so many equal parts, and so many of these parts are shaded.

So, looking at the shape I've got there, how would we complete that stem sentence? The whole is divided into three equal parts.

Well done.

Yes.

And one of these parts of shaded.

Excellent.

We know that, that's 1/3.

What about if we have it divided again into more parts? So, how many have we got this time? The whole is divided into, well done.

Six equal parts, yes.

And of those six parts, how many are shaded? And two of these parts are shaded, aren't they? So, that means 1/3 and 2/6 are equivalent.

Let's try again.

The whole is divided into? Yeah, well done, nine equal parts, and three of these parts are shaded, aren't they? Three out of nine, 3/9.

And then here's another one.

Whole is divided into 12 equal parts, and four of them are shaded, aren't they? Finally, this one we've definitely come across before.

1/3 is the same as, if you can remember our teddy bears, that will tell you this one is 5/15.

Well done.

And finally, ooh, there's lots of parts now, aren't there? What we can do is count how many there is in one part, and multiply them, if we need to, can't we? There's six of them in that shaded part.

And there's three lots of six, six, 12, 18.

So, the whole is divided into 18 equal parts, and six of these parts of shaded.

So again, 6/18 is equivalent to 1/3.

Okay.

Here we are, so it shows us our fractions.

It means that they represent the same proportion.

Proportion being the size or part of the whole.

Okay, so let's have a look on a number line.

So, we've discussed that they're the same proportion, the same size as 1/3.

So, where would these other fractions sit on the number line? Whereabouts would you expect them to be? Of course they'd be at exactly the same point on the number line, wouldn't they? Because of the fact they are the same proportion.

So, although they're divided into more parts, they're the same size, the same proportion, so they would be in the same place on the number line, wouldn't they? Can see the same for 3/9, 4/12, 5/15, 6/18, all at the same point on a number line as 1/3, as they are equal in size in the equivalent fractions.

Okay, so hopefully, that's starting to make sense to you, but what we need to look at now is why that is.

We know that they're equivalent, we know that they represent the same proportion, the same size of the shape.

But what can we see? We start with the denominator.

I've got three, six, nine, 12, 15, 18.

What can you see there? What's happening? What do you notice? That's right, it's increasing by three each time, isn't it? And that's to show the proportional relationship there between the fractions.

Each time it's increasing by three.

Denominator, that is.

What about the numerator? Yep, you can see that it's going up one each time, isn't it? What does that mean? When we look at the fraction itself, 1/3, so the one in the numerator times by three is the relationship that's happening there, isn't it? So, this must happen with all fractions are the same value, which is why the 2/6 is the two for the numerator, times by three, that will give you six.

All equivalent fractions work this way.

You multiply by the same value as your original fraction that you're comparing it to.

Okay.

Oh, here's a tricky question for you.

Is 11/33 equivalent to 1/3? So, what did we do, do you remember? Let's see if I can draw this on here for you, so excuse my writing on here 'cause it's a little bit tricky.

So, we do what we did with 1/3, we should do this, shouldn't we? So, there's the 11/33.

Oh, sorry.

Wobbly.

And then we did this, didn't we? Times by three.

Now, using your times table knowledge, does that work? Let's hear your counting.

So, 11, 22, 33.

That's three times 11.

Yes, that means, what does that mean? Absolutely.

Well done.

That means that 11/33 is equivalent to 1/3.

Let's try another one.

This time, we've got 6/8.

I'm just drawing my 6/8.

Sorry, it's moving funny.

Six.

Oh, that's it.

You have to do times by three.

Now, does that work? Six times three is.

Yeah, we've made six, 12.

Yep, you're right, 18.

Well, that can't be right then, can it? So, 6/8 is not equivalent to 1/3.

The other thing that might help you with that, if you think about it, is 1/3 on our number line, if we look at our number line here, is less than a half, isn't it? So, our half is here.

Just draw that on.

The 1/3 is most definitely less than that, isn't it? So, can you think what might be an equivalent fraction in eighths? Some of you might have worked this out to half.

Let's see.

Has anyone guessed? 4/8.

6/8 is more than that, isn't it? So, 6/8 should be more like.

This way, shouldn't it? That's another reason why we know that, that wouldn't be equivalent.

But sometimes you can use what you know about other size fractions to work out whether or not something is equivalent.

And other times, you can use this calculation.

Okay, there are other calculations, too.

So, there's always methods to these ways of working out.

6/8 is not the same proportion as 1/3.

This is a greater proportion.

Okay, so for your first task, I'm going to leave you with this lesson.

I want you to think about 1/5, and I want you to think about, if I write 1/5 on here, woops.

They're a bit of squiggly lines.

Sorry about that.

1/5, can you think about other fractions that would be equivalent? So, if we follow what we did with 1/3, and get a numerator to our denominator, you have to multiply by five, don't we? Hopefully, that will give you a clue of what you might need to do.

I won't say any more.

So, you could show your equivalent fraction in lots of different ways.

You could get some paper and try and fold it.

It's quite tricky.

You could draw some shapes.

A rectangle, like, woops.

It's very squishy.

Sorry about that.

Like this, and try and make sure that it's in equal parts.

Really would recommend using a ruler.

Or another way of doing it might be to use something like this some square paper.

That can help you because you can use the squares to help you make them the same size.

Or you could even use some teddy bears or other things around your house like we've used before, to try and show the equivalent fraction.

I will look forward to seeing that next time.

I'm sure there'll be some that you'll think of that no one else will.

That's my challenge to you.

Can you think of some slightly different ones? Okay, so that's task one.

Task two, woo, look at that! 32/160.

What a big fraction, or is it? That's the question.

The numbers are large, aren't they? But is the proportion? You need to decide which one of the these is not equivalent to 1/5, because one of them isn't, but it may not be that one.

And sometimes people get confused about the size of the numbers.

There you go.

So, next time my colleague, Ms. Heaton, we'll pick up with these two tasks to see how you got on, and I know you'll be fantastic.

Thank you very much for joining me over the last few lessons.

See you, then.

Bye!.