Lesson video

Hello, everybody.

It's Mrs. Holmes here, and this is lesson nine in a series on equivalent fractions, so let's get started.

I'm very excited because fractions is one of my favourite topics in maths.

I will confess though, when I was younger I didn't like it very much 'cause I found it a bit confusing.

I really hope that these lessons will help you to understand it better.

Okay, so I know last lesson Mrs. Perry left you with a task, but before we go on to that, I just want to make sure that you're really, really solid and clear on a couple of things, so just bear with me.

Okay.

Now, I know five take away five equals zero is a really easy calculation for you to do.

And it's not really about that, that I'm drawing the attention, okay? It's more to help you understand how we know that fractions are equivalent, so bear with me as we go through this.

So, as you can see there is a fraction calculation there.

So, we have 1/5, one part out of the five, and we take that part away, the difference is zero.

We've taken the same amount away, haven't we? And the same on the final equation at the bottom there.

1,274, if you take away the 1,274, we have zero.

Okay, you with me so far? Brilliant.

So, this is the stem sentence that was introduced to you last time by Mrs. Perry.

If the difference is zero, then the minuend and the subtrahend have the same value.

Have you remembered which is which? Okay, I'll just recap.

So, in any calculation where there is a subtraction, the first number is the minuend.

And the second number is the subtrahend, okay? So, you can see that this stem sentence matches up with what we just talked about.

Five take away five equals zero, so five being the minuend, take away five, the subtrahend, gives a value of zero, because there's no difference between the values of those two numbers.

All right, okay.

Let's have a look at this one here, moving on to our fractions.

What do you notice about this equation? Yeah, you might have spotted that the result is zero.

That's brilliant.

So, what does that actually mean, based on what we've just talked about? What was that? Yeah, you're absolutely right.

They must be worth the same value, so that means that they must be equivalent fractions, okay? Now, to check that, that's what we're going to look at this lesson, really.

Trying to understand the relationships and making sure that we know how we can see whether or not fractions are equivalent.

So, looking at this one here, what would you use, then, to help you, do you think? If you did the homework, you might have a clue.

You can see a relationship? Yeah, I can see one, as well.

What relationship can you see? Yeah, I was looking at the 28 and the 14, as well.

So, 28 divide by, yeah, two, well done, is 14.

Okay, so what does that mean we need to do to our numerator then? Yeah, you've guessed it.

Well done.

You also need to divide by two, don't you? So, we end up with 11/14.

So, that's looking at our horizontal relationship there because we compared the two denominators to help us to work out the relationship.

In this case, that was probably easier to do 'cause it's harder to look at how many times, say, 22 and 28, looking at that relationship, the vertical one is a little bit more tricky.

Okay.

So, this was the task, wasn't it, that Mrs. Perry left you with? So, when we look at these in a second, we are going to start with the middle one, but that doesn't really matter if you've got them written down in a different order.

Now, most of you hopefully, would have a go at this task, but if you haven't, it's okay.

Pause the video now, and then have a go and see if you can work out what you think the answers are.

Remember what we've just looked at, 'cause it's really important to help you understand, and then when you're ready, come back to me.

You're back already? Wow, you're super speedy.

Okay, so as I said, we're going to look at the middle one first.

Let's have a look at that.

Okay, so this is our first one to look at.

Got 6/12 take away something over six, gives zero.

Did you notice that zero? So, what does that tell us? Hmm, do you remember what we said? Yes, you're right.

It means that the missing fraction is equivalent, the same size, as the first fraction that we've already got the 6/12.

So, what we're going to do is think about how we could work out that missing value.

Now, there are two ways to look at missing values in fractions.

There's the horizontal relationship, and I tend to think of a sailor looking on the horizon to help me remember that.

And there's also the vertical relationship, and for that, I tend to think about Roman and Greek buildings with the columns.

That's what helps me remember.

In this one, we're going to look at the horizontal relationship, so that's this part here.

Now, the two values we have are the denominators.

We have the twelfths and the sixths.

So, we need to work out their relationship, and once we do, we can then find the missing value.

That's what I mean by fractions.

If you understand how it works, it's so much easier.

So, can you see the relationship? Well done, you.

Absolutely, it's divide by two, isn't it? 12 divided by two equals six, so what does that mean for our missing value? Well remembered, yes.

Whatever we do to the denominators we must also do the same thing to the numerators to keep the values proportionate, mustn't we? So, we must also divide that by two, and that gives us, yes, well done.

3/6.

So, 6/12 an 3/6 are equivalent.

So, when we take one away from the other, we are left with zero, because they are of the same size.

Ah, what do we notice about this one? Has anything changed? Yes, the zero's in a different position, isn't it? Does that make any difference, though? No, it doesn't, does it? The orientation of our equation doesn't make a difference.

We can see that we still have a difference of zero, so what does that tell us? Fantastic, yes, you're right.

These fractions are equivalent again.

Instead of looking at the horizontal relationship, as we did last time, we're going to look at the vertical relationship this time.

There we go.

What we can see is that the denominator is five times the value of the numerator, so how could that help us to find our missing value? Fantastic, you're right, yes.

We multiply the numerator four by five, we would get.

I'm getting you to do some work, as well.

20, brilliant.

So, 4/20 take away 1/5 equals zero.

Okay, now this is our last one of these.

This time we have both our values, don't we? So, all we need to do now is just calculate it, don't we? Hang on a minute.

Just stop right there.

I want you to have a look at the two equations and see if we notice something about them.

2/14 and 1/7.

So, we could look at the vertical relationship here, and the horizontal one, if we wanted, couldn't we? So, if we were looking at the vertical relationship, let's check 1/7.

So, the numerator and the denominator, the relationship there is that the denominator is seven times the value of the numerator.

So, let's check on 2/14.

Is that the same? Two times by seven equals 14.

That works.

Okay, now let's look across on the horizontal relationship.

So, we could go either way around, couldn't we? Let's start with the 2/14, so that's first in our equation at the moment.

So, we need to divide that by two, and we get one.

Two divided by two equals one.

And for the denominator, 14 divided by two equals seven.

Yeah, so both of those work.

So, what must the product be? Just checking.

Zero! Brilliant! Course it must be zero because they're equivalent again, aren't they? Well done, you.

Right, okay, so this is a slightly different task.

But pay close attention to this though, because the task at the end might be a little bit similar.

So, what we need to do is to pause the video, and I want you to have a go at working out the equivalent fractions.

So, this means that you will use the four cards I've got there, and arrange them into two fractions.

So, 2/6 equals, and then you'll have one fraction, and then you have another equals sign, and then another fraction, okay? So, you need to work that out using what we have been doing so far, and then we will look at the solutions and discuss after.

So, pause the video, and off you go.

You're back already? Wow, super speedy at this.

So, let's have a look.

I had a go, as well, and I need you to just check I've got this right.

So, here's my solution.

Do you agree? No? Oh, dear, have I made a mistake? Well, let's see if you can help me to work out where I went wrong.

So, the first thing I noticed is our original fractions of 2/6 there.

So, the denominator is three times the value of the numerator, isn't it? That's looking at the vertical relationship.

So, let's see.

So.

Oh, dear.

Doesn't seem to work with either of them, does it? Because 1/8, one times three.

No, that would give me three, so that's wrong.

Oh, dear.

Three times three is nine, so that's not 24 either.

Oh, dear.

Woops.

Yeah, I got that wrong.

Shh.

You're turn.

Let's see if you can help me work it out.

What was that? Okay, I think I heard you.

Is this what you said? All right, well, we just need to check though, don't we? So, 2/6 is our original one, and we worked out that the relationship is that the denominator is three times the value of the numerator.

So, on the second fraction, one times three is three, so that one works.

And eight times three is 24.

Yeah, I think you've worked it out.

Just as well I had you here to help me.

Well done.

Just to reinforce what we just looked at there, let's compare it in a different type of diagram.

So, there's our 2/6 again.

Can you see the six? Yes, the six is the top line, isn't it? And two of those six parts are coloured yellow.

And the bottom part is divided into 24.

I promise you.

You can check, though, if you want.

And the ones that are shaded yellow, there's eight of those.

And you can see that they are of equal size.

Ah, now this is a special challenge for you.

You've been getting so good at these equivalent fractions.

This is one of those many possibility-type challenges.

I want you to take this one away, so you might need to copy it down now, and I want you to see if you could challenge a family member, or maybe a teacher, and then share with them your solutions.

You can show them how fantastic you are at fractions.

There are lots of possibilities.

So, you need to think about what you already know about parts of a whole, and then decide on how many solutions you think there may be.

So, if you look at the denominator, think about how many parts there would be.

And then there are other ways you could look at it, as well, but I'll leave that with you.

Maybe you could share some online solutions with us.

That would be fantastic.

And this is the activity I'm going to leave you with, the practise activity for lesson nine.

So, don't use the one that's on the board 'cause that's obviously, the example we had earlier.

But this time, I want you, as I say in the speech bubble there, to use this as an example to help you to make up your own.

So, I want you to think of a fraction.

Could be one we've covered in the last few lessons, such as 2/5, 3/5, that kind of thing.

Could be eighths.

You could have 6/8, or 7/10.

It's entirely up to you.

But then you have to work out two equivalent fractions and make up some cards for whoever you're going to play it with, to test them.

So again, it might be a mom or dad, or brother or sister.

Can they work out how to reorganise your cards to find the equivalent fractions to your original fraction that you give them? I'm sure you'll be fantastic at it.

Okay, so I'll leave that one with you, and thank you very much, and it's time for me to go now.

So, bye!.