Lesson video

Hello, I'm Mr. Coward.

And welcome to today's lesson about fair shares.

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, including turning off any notifications.

And if you can, please 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.

So here we've got one chocolate bar.

How many ways could you share the chocolate bar between these three? Sketch How you could share the bar.

And I want you to be creative when you're doing this.

I want you to just try and find as many different ways as you can.

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

Pausing.

Three.

Two.

One.

Okay.

Welcome back.

Here are some of the ways that I managed to find.

Now, these ones are all correct.

Okay? And I can use diagonals.

And I could do that in a few different ways.

But over here.

This one, this one is not correct.

Why isn't this correct? Well, it's not one of three equal parts.

These parts aren't equal.

If you imagine having two more lines, in fact, let me draw them in.

If you imagine me having this line here.

And this line here.

Oops, well then, and this bit here where you can see that, that bottom bit is kind of like a quarter.

Can you see how that's quarter? Or can you see how that's two, two eighths? Whereas that is three eighths.

So they are not equal in size.

So that is not shared evenly between the three of them.

How come some of these are? Well in this one, for instance, the pieces are equal and they all get four parts.

In this one the pieces are equal and they all get two parts.

So that's why I know that these are shared equally, but this one is not because those parts aren't the same.

So it doesn't matter how many parts we split it into.

As long as they all get the same amount of parts and those parts are equal.

Okay.

Two chocolate bars are shared equally between three children.

How much does each child get? Now I'm just going to draw a little sketch here of this.

Of what this would look like.

So I'm going to split this up.

Like this, into thirds and imagine they're the same size.

Okay.

It doesn't, it doesn't have to be accurate, but just pretend that they are the same size.

So one person would get this, and one person would get this.

So everyone would get two thirds because the six, six pieces in total or six thirds in total.

So everyone would get two thirds.

So we can say this: two divided by three, two shared between three people, gives us two thirds.

And this is super important, this idea.

So let's, let's do another one to highlight this.

So say we had five chocolate bars shared between 11 people.

That definitely looks like the word people.

And I hope your handwriting is better than mine.

Okay? So we've got five shared between 11 people.

And that would be five elevenths each.

Or, if we had 11 chocolate bars shared between five people, we'd have 11 shared between five.

The number we're dividing by will tell us what our denominator is.

So how many people were sharing it between? Whereas how many things we have will tell us what our numerator is.

So we can, we can view a fraction as a division.

And that's a really important idea.

Okay? So I'd like you to have a go.

So pause the video and have a go at this.

Okay.

Welcome back.

Now, I've just drawn a little sketch here of my answers, and you could have sketched it in different ways, but here I've got three out of four equal parts.

So three shared between four equals three divided by four.

Three quarters.

They get three quarters of a bar each.

So I hope you understand that.

And you understand the idea that three divided by four gives us the answer of three quarters.

And it's kind of like, we don't have to work anything out.

Our answer's here.

Which I think is really nice.

Okay.

Five bars of chocolate are shared equally between two children.

Seven bars of chocolate are shared equally by three children.

Who gets more chocolate? Explain how you know which group gets more.

So when we get a problem like this, I want to draw it straight away.

Because drawing it reveals a lot of structure here.

So we've got five chocolate bars and this is a little bit tricky with this pen.

And imagine they're all the same size.

Definitely the same size, aren't they? So, if I'm going to split each one, between two people, I can split each one in two.

Now that would mean each person gets five out of 10 total pieces.

All right.

Five.

So that's two and a half of a chocolate bar.

Well, what about this person? Right.

So just pause the video and draw a diagram for this.

So pause in three.

Two.

One.

Okay.

Welcome back.

Now, hopefully your diagram looks something like this.

Or maybe nicer than mine.

So seven chocolate bars.

Six.

Perfect fit.

And each one is split into thirds.

So how many pieces are there in total? Well, there's 21 pieces in total.

So how many pieces would each person get? Each person would get seven.

Pieces.

So which group gets more? How can we tell from our diagram? Which group would you rather be in? Well, every person gets two.

But in this group, they get two and a third.

And this group, they get two and a half.

And you can see that a third of a chocolate bar is smaller than half of a chocolate bar because the chocolate bars are the same size.

So you, this group gets less and this group gets more.

And we know that because we can see that visually this group gets two whole ones, and a half.

This group gets two whole ones and a third.

And a half is bigger than a third.

Okay.

So now I'd like you to have a go at the independent task.

So there are one, two, three questions that I'd like you to have a go at.

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

Okay.

So here are my answers.

You may need to pause the video to mark your work.

Now this one, this last one was quite tricky.

And drawing a picture, I don't really think it helps that much for this because our pictures might not be that accurate.

However, what I think is quite useful is comparing it to something.

So if you imagined that a half would be this, okay.

2.

5, over five.

Top is half of the bottom What would a half be of a seven? It'd be 3.

5 over seven.

Now this one is not 0.

5 or half of a fifth.

Okay.

So half of a fifth over a half.

And this one is a half of a seventh over a half.

And a fifth, a fifth is bigger than a seventh.

So this is going to be bigger than this.

Now don't worry if that went a bit over your head here.

It's something that you might be able to use to help you on the explore task.

But, more importantly than that, is it something we're going to be spending a lot of time on and quite a few lessons on to really get you to understand how to compare fractions.

And for the explore task, which is bigger? What do you notice? And I definitely recommend drawing a picture to try and support your answer.

Okay.

So pause the video and have a go.

Pause in three.

Two.

One.

Okay.

So here are my answers.

Now I don't know exactly what strategy you used to work them out.

I think drawing them is a good strategy.

So if you imagine now, I've got two thirds and here I've got quarters.

This is one third away from the whole.

And that is one quarter away from the whole.

And we can see that one quarter away from the whole will mean that that number, three quarters, is bigger than two quarters.

Sorry, bigger than three, two thirds, bigger than two thirds.

On this one, similar logic.

All right.

The third with each piece is bigger than if we split into four pieces.

This one, well, that's four whole ones.

So four whole ones is bigger than three whole ones.

What about this one over here? Well, that is one and a half.

And that is one and one third.

Well a half, split into two pieces will mean each piece is bigger than where we split into three pieces.

So we can see that this one is bigger.

Okay.

What about this one? This one is a bit trickier.

Well, what if we compare them to a half? Which one's closer to a half? Well, they're both less than a half, but this one's closer to a half.

Can you see that? Cause what would a half be? A half would be 3.

5 over seven.

And here we'd have a half as 2.

5 over five.

Now this is not 0.

5 away from a half.

And this is not 0.

5 away from the half.

So if they're both not 0.

5 pieces, sorry, not 0.

5 pieces from a half and not 0.

5 pieces from a half, but each of these pieces are smaller.

So that means this one is closer to a half.

So it's bigger.

That was a bit tricky that wasn't it? Okay.

What about this one? Well, that's five pieces that split into two.

So that's two and a half.

So we've got two full ones and a half.

Whereas this one is two full ones and a third.

So that's kind of similar to this one that we've got a half is bigger than the third.

So drawing pictures of these things, what these would look like.

Two whole ones and a half of one.

We'd be able to see that that is bigger than, Oh, I will go and draw that back in a second.

Once the pen size stops being silly.

So we can see that two and a half of one is bigger than two and a third of one.

So it is quite tricky, this.

And this was more, you know, I don't expect you to, to fully have all these methods that I kind of described them to work out.

Because that's what we're going to look up.

This is just to give you a sense of size.

So don't worry if you found this tricky.

I just, I kind of wanted you to, just to get you thinking about size with this task and we'll explore more about how to work each one out in future lessons.

Okay.

So that is all for today.

Thank you very much for all your hard work.

I really hope I see you in the next lesson because we've got a lot of exciting things to learn about fractions.

So thank you very much and I'll see you next time.