Lesson video

Hello, I'm Mr. Coward, and welcome to final lesson of the unit.

Today's lesson is mixed comparisons, where we'll using lots of our methods that we've learned from the unit to compare fractions.

For this 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, please try and find a quiet space to work where you won't be disturbed.

When you're ready, let's begin.

Time for this "Try this task".

You can use any strategy you want, and I want you to decide which is bigger and how much bigger.

So pause the video and have a go.

Pause in three, two, one.

Welcome back.

Now, here are my answers, and I'll talk about how I did them.

This first one, well, we can see that they've got, because they've got the same denominators, we can see that this is 2/10 bigger.

For the second one, we can see that because they've got the same denominators, this is 8/100 bigger.

Now this one.

Well, you could have subtracted them and got 0.

1, which is also the same as 1/10.

So if you wrote 0.

1 or if you wrote a 1/10, that is fine.

And for this one, if you wrote 0.

8, that is also fine.

And 0.

2 for this one.

That's why I've wrote an e.

g because you might have wrote it in a different way, so you might've even wrote 1/5 there.

So 0.

36 or 0.

21.

Well, that's 0.

05 difference or 5/100, so we can write 5/100.

That is 0.

7 difference or 7/10, and this is, if you subtract them from each other you see that there's 35/100 difference or 0.

35, so we can write it like that.

We're going to look at different strategies now for comparing, and the first strategy we're going to look at to compare these is writing these as decimals.

But the denominators aren't a power of 10.

Hmm, well, let's use equivalent fractions to make them a power of 10.

So we can say that that is 6/10.

I times the numerator and the denominator by the same amount so I still have the same proportion or the same ratio.

Now I can see that because that's tenths, I've got 6/10, which we can write like that.

What about this one? Hmm, slightly trickier.

Well, I can't times it to tenths, but could I times it hundredths? You might not be able to see it in one step, but it might have took you two steps, but it would have got you to a total timesing by 25.

If you think 4 X 5 is 20, 5 X 20 is 100, so 5 X 5 is 25.

So I have to times that by 25 and I get 75.

So now I can compare them and I can see that this one is bigger.

And it is 15/100, 15/100 bigger or 0.

15.

I could also compare them by looking at the numerators.

I've got 3/4 or 3/5.

And remember that quarters are bigger than fifths.

So 3/4 is going to be bigger than 3/5, 'cause each piece is bigger.

So you can compare them that way.

Which do you prefer of these? Do you prefer one or does it depend on the question? And for me it depends on the question.

So for instance, you can look at that and see which one's bigger by comparing the denominators.

Sorry, comparing the numerators or the denominators.

But this one, if you want to know exactly how much bigger is, I think this one's maybe more useful.

So it depends what you want.

It depends what you're trying to get out of the question.

How could we compare these ones? Well, I'm just going to talk about two strategies.

If you think 7/15, how does that compare to 1/2? Well, what's half of 15? Half of 15 is 7.

5.

What's half of 20? 10 This one is 1/20 more than 1/2.

Something like that.

This one is half of 1/15.

Half of 1/15 is 1/30 less than 1/2.

So it's going to be there.

But because you can see that this one's bigger than 1/2, and this one's less than 1/2, this one's definitely going to be bigger.

And that's a really nice way to compare them I think.

Oh, you could compare them this way.

Look for a common denominator.

Can you think of a number that they both go into to make them equivalent fractions? Now, last time we just looked at making them the same.

So I could times this by 20, and I could times that by 20, 140.

Times that by 20, 300.

Times that by 15, 300.

Times that by 15, and 11, sorry, 10 times 15 is 150 plus another 15, 165.

So you can see that this one, as we saw before is bigger.

Now, just on that, 'cause some of you were like, "Well, you didn't need to go to 300.

You could have used 60 as your common denominator." Why could we have used 60? Well, because this goes into 60 and this goes into 60.

How many times? Four.

How many times? Three.

So that would have been three times bigger, and that would have been four times bigger.

We must times in both by the same amount to keep our fraction in the same proportion.

So you can see that 33/60 is bigger than 28/60.

Don't worry if that go into 60 rather than 300, was a little bit confusing with you for you.

You work more on common denominators when you are doing some adding fractions.

Well, that's just kind of, it's just a little teaser for you.

It's just a little, you know, to whet your taste buds.

I knew which fraction was greater or smaller because I compared their numerators, wrote them as decimals, compared both fractions to, so like to 1/2 or to one, wrote equivalent fractions with common denominators.

There are four strategies that we've looked at in previous lessons.

We're going to kind of put them together now.

What I want you to do is I want you to choose pairs of fractions from each set and compare them, decide what is greater, decide when is a good time to use one strategy, when is a good time to use another strategy.

So this is kind of a chance for you to decide and choose what method is best.

So I'd like to pause the video and have a go.

Pause in three, two, one.

Okay, welcome back.

Some possible ways that we could have done it.

Well, you can clearly see looking at these two, these are fifths and these are fifths, so 6/5 is bigger.

Looking at this one and this one, 6/4 is bigger.

And this one and this one, 5/6 is bigger.

Then what about if you're going to compare these two? Well, you wouldn't look at the denominators anymore, you could look at the numerators, and here are five out of six pieces, and here's five out of four pieces.

Well, these pieces are bigger, this is bigger.

Or you could compare these to one.

This is less than one, but that is more than one.

There's so many different ways that you could do this.

You could have converted these into decimals to compare them.

Okay, these, compare the numerators.

These two, compare the numerators.

Here we could compare the numerators.

We could write these as equivalent fractions over 20, if we wanted, or we could see that this is more than one, and this is less than one.

This is more than one and this is less than one.

So there's so many different strategies, and I think it's really good that you've got these in your toolkit so that you can use them and you can use them flexibly.

And it'll just make it more efficient, rather than having one method, you've got lots of different methods so you get to decide which method is best for which situation.

Now it's time for the independent task.

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

Here are my answers.

So you may need to pause the video to mark your work.

And now it's just time for the explore task.

So I want you to use each of the number cards once, and only once, to complete the inequality frame.

Repeat to complete the frame in three different ways.

So I want you to try and fill these blanks in with these numbers and try and do it in three different ways.

I have a hint for this.

Well, I want you to have a goal before I give you your hint.

So if you need the hint come back, but I want you to have a goal first.

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

Here is my hint.

I've just cited off a few of them.

Here I've got 2/4, blank, something sevenths.

Here I've got 7, 4.

0 and 2.

So you've got to kind of think, "All right, using this one, what digits do I have left? Well, what's that? What's that about? Well, that's about 1/2, so I need something more than 1/2 here, more than 1/2 here.

Well, which numbers could I use?" Here, you've got that's four point something.

Well, what would have to go on the top to make that bigger than four? Have a think about that.

Is the "more than one" option.

And over here I've just started off with some common denominators.

Ninths are very small and a half so much bigger.

What could our numerators be? What could the decimal be? So just have a goal.

And you might not get at it first time, but just try lots of different numbers.

Every time you try, even if you don't get it correct, that's more practise if you comparing them.

So you're just getting, if you get it right on the first go, you're getting very little practise.

Wherever it's taking you quite a few attempts, you're getting loads of practise of comparing decimals and fractions, which is awesome.

So pause the video and come back once you've finished.

And here are three example answers that I have chosen, and there are so many.

I can't even comprehend how many there are, but hopefully you found a few and hopefully you found it an interesting task.

So that is all for this lesson and that is all for the unit.

If you'd like, please ask your parent or carer to share your work on Twitter, tagging @OakNational and #LearnwithOak.

Thank you very much for all your hard work over these lessons and yes, thank you very much.