Lesson video

Hello, I'm Mr. Coward, and welcome to the second lesson on comparing fractions.

For today's lesson, all you'll need is a pen and paper or something to write on and with.

If you could please take a moment to clear away any distractions, that would be brilliant.

And if you can't, try and find a quiet space to work where you won't be disturbed.

Okay, when you're ready, let's begin.

Okay, so time for the try this task, find three ways to shade a 1/4 of a square.

Find three ways to shade 3/8 of a square.

Now, when you're doing this task, I just want you to be really careful the way that you're breaking up the shade is in equal parts.

So for the first one, it should be four equal parts, and you've got to make sure that you can justify why those parts are equal and same for the second one, you've got to try and justify why those are equal.

Okay, so pause the video and have a go.

Pause in three, two, one.

Okay, so here are some possible answers and there is many, many more ways that you could possibly do it.

But these are just three ways that I can think of.

Okay.

Which one is bigger? By how much? Which one is easiest to compare? Well here, the top one, we can quite clearly see there is one piece bigger, 1/7 equal pieces bigger.

So 1/7 bigger.

Whereas on the bottom one, it's kind of hard to work out exactly how much bigger it is.

Why was it easier for this one? Well, it was easier because these were both sevenths.

Whereas over here, they don't have a common denominator.

Okay, they don't have the same denominator down here.

Whereas these ones do have the same denominator.

So when they have the same denominator, it's easier, much easier to compare by how much is one bigger.

So, have a look at this.

Well, here we have 2/5, okay? 2/5 equal parts.

And here we have 1/4, one to four equal parts.

On this diagram, can you see where the 2/5 is? Here.

Can you see where the 1/4 is? Here.

How many equal parts are there here? There's 20 equal parts? So what we've done here is we split apart, shape, we split the shape this way, like in the quarters and this way, like in the fifths, so that we can share the same proportion, but now they have a common denominator.

Now we can compare these.

So you can see that this one, 1/4 is equal to 5/20.

Okay, that's four times bigger.

That's four times bigger.

That's times five, that's times five.

Whereas this, that's 8/20, four times bigger, four times bigger.

So now we can clearly see that 2/5, is 3/20 more than 1/4.

I'm going to rewrite that, 'cause that is awful.

Okay, so 2/5 is 3/20 more than 1/4.

And we can say that we can compare exactly how much bigger 2/5 is because we have the same denominator.

So how are equivalent fractions and common denominator useful? Because we can compare exactly how much bigger one fraction is to the other.

And to do so, we must use a common denominator so that they must have the same denominator and we can find the same denominator by using equivalent fractions.

Okay, so I just want you to have a look at this.

So pause the video and have a look.

Pause in three, two, one.

Okay, what's the same and what's different? Which model do you think is better and why? Well, what's the same? Well, it's still 2/3 and it's still 3/4, 2/3, 2/3, 3/4, 3/4.

Well, and this one you can see, you can see it's bigger, but this one, you can see how much bigger, this one is, 8/12.

Okay, this one is 9/12.

We can see that 3/4 is 1/12 bigger.

So I think that this representation is more useful if we want to see how much bigger something is, and this is still a useful representation, because we don't always need to know how much bigger something is, but if we do, I think that this is superior.

So I'd like you to draw your own model.

Okay, so draw a square and shade 5/6, draw another square and shade 3/4.

So you might want to do one go in and one into columns and one into rows and then try and put those rows and columns together.

And then you should be able to compare them.

So pause the video and have a go.

Pause in three, two, one.

Okay, so here are my answers.

Now what I've done is I've done the six as columns, the quarters as rows, and now I've put them together on my final diagram.

And in this one, we can see this 24 pieces, okay? And that the 3/4 is the same as 18/24 equal pieces.

That's six times bigger.

That's six times bigger.

Here, well, that's 24, four times bigger, so the top is four times bigger.

And you can count them to check if that is true.

So you can see that 5/6 is 2/24 bigger than 3/4.

Now, how, how was this number helpful? Well, this number was helpful.

Where did we get this number from? Well if you think if we're splitting this up into six and then into four, our denominator is actually the six times the four.

So what we're essentially doing is times in this, the numerator and the denominator by four and on this one we're essentially times in the numerator and the denominator by six.

And that, that helps us find, use equivalent fractions to find a common denominator.

And now all the common denominators we can use, and we could actually use 12, but for now, which is what is called the lowest common multiple of these two numbers.

But for now, we're just going to, we're just going to times them together to find our common denominator, okay? And you'll learn more about using the those common multiple in future lessons.

Okay, so we're going to compare the following fractions, which is bigger and how much.

This time we're going to try and do it without our model.

So what could be my common denominator? Well, I'm going to split up one way into fifths, five pieces and one way into quarters.

So that would give me five pieces there, four pieces there, five times four, 20.

So our common denominator is going to be 20.

So that's four times bigger, so that must be four times bigger.

That's five times bigger, so that must be five times bigger.

Well, which is bigger and by how much? This one is bigger by 3/20, okay? The difference between 8/20 and 5/20 is 3/20.

Okay, next one, we've all split into seven and four more common denominator would be 28.

There'll be 28 equal pieces.

So I've times that by four.

So I need to times the top by four.

I've times that by seven, so I need to times that by seven to keep them in the same proportion.

And now I can clearly see that this one is bigger by 5/28.

Okay, 21 takeaway 16, five, so 5/28.

So I would like you to have a go at this one.

So pause the video and have a go.

Pause in three, two, one.

Okay, welcome back.

Now hopefully you made your common denominator.

30, six times five is 30.

And is just a beautiful three.

Okay, now I've made that number five times bigger.

So I need to make that five times bigger.

I've made that six times bigger.

So I need to make that six times bigger.

So we can see the 5/6 is bigger, and how much bigger is it? It is one one, 1/30 bigger.

Okay, so let's just check that.

We've times that by five and we've times that by five.

Good.

So that's in the same proportion, we've times that by six, and we've times that by six, so that's in the same proportion.

Now they've got a common denominator.

We can compare how exactly how much bigger it is.

Okay, so now it's time for the independent task.

There are three questions.

So I would like you to pause the video to complete your task and resume once you're finished.

Okay, welcome back.

Here are my answers on number one, you may have shaded it slightly different.

This is just an example.

Okay, so now it's time for the explore task.

A 1/4 of the circle is shaded blue.

2/5 of the circle is shaded yellow.

What fraction is unshaded? So I'm going to give you a little hint, but I want you to have a go first, okay? So pause the video to complete your task, resume once you're finished and if you need a hint after a bit, come back, okay? Okay, so here's my hint.

I've said that this is 1/4, and I've said that this is 2/5, and the whole thing is equal to a whole.

That's one whole, 1/1 almost.

So you need to use a common denominator to find out what fraction is shaded and then try and find out what fraction is unshaded.

Okay, so pause the video and have a go.

Pause in three, two, one.

Okay, so here are my answers.

Well, this was 5/20 and this was 8/20 using our equivalent fractions and a common denominator of 20.

So in total, five plus eight is 13.

So that means the 7/20 remaining.

Really well done if you've got that correct.

And that is all for today's lesson.

Thank you very much for all your hard work.

And I look forward to seeing you next time.

Thank you.