Lesson video

Hello there.

My name is Mr. Tilstone.

I'm a teacher and I really love maths, so I'm very excited to spend this maths lesson with you.

You may have had some recent experience talking about parts and wholes, and we're going to apply that knowledge today.

So if you're ready, I'm ready.

Let's begin the lesson.

The outcome of today's lesson is: I can identify the number of equal or unequal parts in a whole.

And our keywords are, my turn, equal.

Your turn.

My turn, unequal.

Your turn.

You may have heard those words before.

Hopefully you have.

What do they mean? Let's have a little reminder.

We can say that two or more things are equal if they have the same quantity or value.

So equal, same.

We can say that two or more things are unequal if they do not have the same quantity or value.

So unequal is the opposite to equal.

Our lesson today is split into two parts.

The first will be wholes and their parts and the second, equal and unequal parts.

So if you are ready, let's begin by thinking about wholes and their parts.

And like I say, maybe you've already got some knowledge about this.

Let's see if we can take that even further.

In this lesson, you're going to meet Izzy and Jun.

They're here today to give us a helping hand with our maths.

Have you met them before? They're very helpful.

Izzy and Jun have both been given a square piece of paper, and the squares are the same size as each other.

"This," says Izzy, "is our whole." So it's all of it.

Izzy and Jun are asked to cut their square into parts.

Izzy cuts her square like this.

Hmm.

Can you think of a different way to cut it? Well, Jun can because he cuts his square like this.

So you can see they've cut them in different ways.

What do you notice? There's lots of things you can notice here.

What do you notice? Well, Izzy says, "I cut my square into three parts." Was that the same with Jun as well? Here's one, here's two, here's three different parts.

What about Jun? Let's have a look.

No.

Jun cut his square into four parts.

One, two, three, and four different parts.

So the same whole, because remember, the pieces of paper were the same size as each other, so you can say they've got the same whole as each other.

The same whole can be made up of a different number of parts.

So one of these is made of three parts, and one of those is made of four parts.

A whole is made of many parts, and many parts make one whole.

That's a really important sentence, so I'd like to say that together.

Are you ready? Let's go.

A whole is made of many parts.

Many parts make one whole.

Fabulous.

Now can just you say it on your own? Are you ready? Go.

Very good.

Let's have a quick check.

Can you think of a different way to cut a square into parts? So you've seen two different ways with two different numbers.

Can you think of a different way, and then maybe a different way again, and maybe a different way again? And maybe you've got some square paper in front of you.

Maybe you could sketch that square any way you like to cut that square into parts.

Pause the video, and off you go.

How did you cut your square into parts? Well, like Izzy says, there are many ways to cut a square into parts.

Many, many ways.

You may have cut your square like this.

That's one way.

That square is now in parts.

Izzy cuts another square so that her square has the same number of parts as Jun's square.

So can you see? So Izzy's got one, two, three, four, and Jun's got one, two, three, four.

Hmm.

What do you notice? Something unusual.

What's the same about those squares, those wholes, those parts? And what is different do you think? Well, both whole squares are made of four parts.

You can see that, one, two, three, four, one, two, three, four.

But are they the same? Hmm.

The parts are different shapes, yeah.

So the one on the left has been cut into square parts and the one on the right has been cut into triangular parts.

So we've got four squares, they're the parts, four triangles, they're the parts.

Let's have a check.

Can you think of a different way to divide a square into four parts? Pause the video and have a think.

What did you come up with this time? Hmm.

Well, like Izzy says, there are many ways to divide a square into four parts.

You may have divided your square like this.

So that's one possible way that's different to the way that we've seen before from Jun and Izzy.

It's time for some practise.

Use a paper shape such as a circle.

Maybe you've got like a paper plate, something like that, or a regular triangle or a rhombus.

It can be any paper shape at all.

Cut each shape into different number of parts, then stick the parts back together to form the whole.

Complete the stem sentence for each shape.

The whole is made of mm parts.

Mm parts make the whole.

Can you remember earlier on when we were saying the whole is made of many parts, many parts make the whole.

Let's see if you can put some numbers into those.

And when you've investigated one shape, maybe you can move on to a different shape and repeat that activity.

So many possibilities here.

So have fun exploring and I'll see you soon.

Welcome back.

How did you get on exploring the parts and wholes there? Let's have a look at some possible feedback.

But there are thousands, tens of thousands of ways that you could have done this.

Might have done something like this though.

Here's a circle.

The whole is made of three parts.

Three parts make the whole.

So you could cut that circle into three parts and take the parts apart.

And then you could put the parts back together.

And in this case, the whole is made of five parts.

Five parts make the whole.

So that's a different shape and it's been cut into different kinds of parts.

In this case, they're all triangles.

Let's move on to cycle two, because you're doing really well.

Let's look at equal and unequal parts.

Let's revisit the squares from earlier on.

You might recognise these squares, you might remember them.

They were cut into different parts.

What do you notice? Anything at all? Have a good look at them.

What do you notice about the squares and the parts of the squares? Well, you could have said this.

The first square is made of unequal parts.

That's one of our keywords today.

The parts look different.

They're not the same as each other, are they? There are two triangles and a hexagon.

A hexagon is much bigger than the triangle, so you can see very clearly they're not the same.

I always think of it in terms of food.

So if that was like a square pizza, you wouldn't say that you're getting an equal part if you get the triangle, would you, compared to the hexagon part.

The second and third squares are made of equal parts.

So let's focus on one at a time.

Let's look at the middle one.

What equal parts can we see there? They're equal triangles.

And the one on the right, let's have a look at that one.

They're made of equal rectangles.

They are the parts.

So these two wholes have been divided into equal parts.

Each of the parts from the same whole is the same shape and takes up the same amount of space.

Izzy and Jun play a game of equal or unequal parts.

You can join in here.

See if you can help them out.

Let's help them.

So can you say each time whether they are made of equal parts or unequal parts? Let's have a look.

Equal or unequal parts? What about this first one? What do you think? Get ready to say in three, two, one, go.

Well, Jun says, "The parts look like they are the same." Yes, they do.

"The whole has been divided into four equal parts." Yeah, it's four triangles.

Now one of them is in a different orientation to the other three, but they're still equal.

Right, what about this one? Don't say it yet.

Ready? Equal or unequal? Three, two, one, go.

Jun says, "The parts look like they are the same." Yes, they do.

"The whole has been divided into four equal parts." And again, thinking back to food, if that was a cake, for example, you could say that cake's been split into four equal parts.

I would be happy to have any of those four parts because they're all the same.

Have a look at this one.

Equal or unequal parts? Don't say it yet.

Hold your horses.

Say it in three, two, one, go.

"The parts do not look like they're the same," says Jun.

No, they don't, do they? The middle one takes up more space or the middle ones do.

Yeah, that's right.

So again, if that was a pizza or a cake, I'd rather have the middle parts.

They take up more space.

That's a bigger part of the whole cake or pizza.

The whole has been divided into four unequal parts.

Right, get ready.

Don't say it yet.

Are these equal or unequal parts? Three, two, one, go.

Jun says, "The parts do not look like they are the same.

The top part is much smaller than the bottom part." Yes, it is, isn't it? Much smaller.

So they're not equal parts, they're unequal parts.

"The whole has been divided into four unequal parts." Have a look at this one.

Don't say it yet, hold on.

Are these equal or unequal parts? Three, two, one, go.

"The parts do not look like they are the same," says Jun.

No, they don't.

"Two parts look bigger than the other two parts." Definitely.

"The whole has been divided into four unequal parts." Let's have a quick check for understanding.

Have a look at the square.

It's been cut into parts, but are they equal parts or are they unequal parts? Complete the sentences below.

So there you go, the whole has been divided into mm parts.

So how many? And the parts are mm.

Can you think of the word to describe the parts? Okay, work with a partner if you can, compare answers, pause the video, and I'll give you some feedback very shortly.

Let's have a look.

So the whole has been divided into four parts.

One, two, three, four, you can see them there, but the parts are unequal.

I think the top and bottom parts are equal to each other, the two middle parts are equal to each other, but the four parts are not equal to each other.

They are unequal.

So well done if you said that.

You're on track.

Jun and Izzy have been given a strip of paper each.

What do you notice about the paper? The paper's the same size, so they've got the same whole as each other.

Jun and Izzy fold their strip of paper.

Now, if somebody said to you, fold your strip of paper, you might even have one in front of you, there's lots of ways you could do that, isn't there? Let's see what Jun and Izzy do.

That's how Jun has folded his and then unfolded it again.

And that's how Izzy has folded hers and then unfolded it again.

You can still see the fold marks.

What's the same and what's different? Hmm.

Can you think of at least one thing that's the same about how they folded it and at least one thing that's different? Well, Jun has folded his whole length of paper into four equal parts.

They're exactly the same as each other.

They're equal parts.

Izzy has folded her whole length of paper into four parts, so that's what is the same about them.

But these are four unequal parts.

They are not the same as each other.

They're unequal.

Look at this line.

What do you notice about the line? The line has some divisions marked on it to divide it into parts.

So how many parts has that been divided into? Can you see? Let's describe the line.

Jun says, "The whole line has been divided into three equal parts." What do you think? Do you agree with that? Can you see three equal parts there? And Izzy says, "I respectfully challenge you." That's a lovely way to say that you disagree with somebody.

Why don't you try that one day? It's very polite.

What do you think? Why has Izzy challenged Jun? Was she right to challenge him or was Jun right? What do you think? She says, "Can you prove that the parts are equal?" Hmm.

What would you do if somebody said that to you? If they said, can you prove that these parts are equal, how would you do that? What could he do? Well, he's got an idea.

Jun says, "I know.

Let's measure each part." Yes.

Yeah, that's a good idea.

So he's done that and this part's 28 centimetres, and this part's 45 centimetres, and this part is 39 centimetres.

Hmm.

Are they all the same number as each other? He says, "I was wrong.

The whole line has been divided into.

." What could he say here? "Three unequal parts.

The parts are different lengths." So he was right to say it's been divided into three parts, but just not three equal parts, three unequal parts.

Let's have another check.

Look at the line and complete the given sentence.

So the stem sentence is this.

The whole line has been divided into mm mm parts.

So we're looking for a number and a word.

Pause the video and off you go.

Well, the answer is: the whole line has been divided into five unequal parts.

So there's five different parts there, but they're not the same as each other.

They are unequal.

It's time for some final practise.

I think you are ready.

Number one, sort the shapes according to whether they are made of equal or unequal parts.

Number two, do you agree or disagree with the following statement? Are you ready? Give reasons for your answer.

You may like to use shapes made of paper and cut them into parts to help you.

And this is the statement.

It is only possible to divide a whole into equal parts using straight lines.

Hmm.

Is that true or not? Investigate that.

That's quite tricky, so good luck with that.

Have a good think.

Number three, Izzy, Jun, and Jacob have folded their paper strips in different ways.

Which strip is the odd one out? Now there's more than one possible answer to this.

So give reasons for your choice if you can justify it.

And then can you find a way to make each of the strips the odd one out? So is there a reason why Izzy's is the odd one out? Is there a reason why Jun's is the odd one out? Is there a reason why Jacob's is the odd one out? Pause the video and good luck with exploring that.

I'll see you soon.

Welcome back.

I hope you had fun exploring all of that.

Let's give you some answers.

So number one here were the shapes with equal parts.

It's got equal parts, all triangles, all the same size.

This one's got unequal parts, so it's been cut into four parts, but they're not the same size as each other.

They're unequal.

This has got equal parts.

Again, all triangles, all the same size.

And this has got unequal parts.

Not the same size.

This one's got two equal parts.

Again, they're triangles.

And this one's got four parts, but they're unequal parts.

They're not the same size.

And this one's got four parts.

Again, they're unequal.

This one's got three parts, but they're not the same size.

They're unequal.

And number two, you might have said that you disagreed with this statement that it's only possible to divide a whole into equal parts using straight lines.

Hopefully you did disagree.

You might have proved your answer, that was the hard part, by cutting or folding shapes something like this.

So think about those curved lines.

Here we go.

So we can divide that shape, first of all maybe in half using a curved line and then divide it in half again using another curved line.

So that's split into four equal parts.

What about this one? Even more complicated.

This has got four parts.

And even though they're not straight lines, that's four equal parts.

The wholes have been divided into equal parts.

Each of the parts from the same whole is the same shape and so must take up the same space.

Number three, you might have said that Jacob's folded strip was the odd one out because he folded it into unequal parts.

Yes, he did.

So Izzy and Jun folded theirs into equal parts and Jacob folded his into unequal parts.

You might have said that Jun's folded strip was the odd one out because he folded it into five parts, whereas Izzy and Jacob folded theirs into three parts.

And finally you might have said that Izzy's folded strip was the odd one out because it was a shorter strip of paper, and the other strips were equal in length and longer.

So you could say that Jun and Jacob's wholes were the same.

We've come to the end of the lesson.

I've had really great fun exploring parts and wholes today.

Today's lesson has been identifying the number of equal or unequal parts in the whole.

The whole can be made of many parts.

Many parts can make the whole.

The parts that make up a whole can be equal or they can be unequal in size, and you've explored both today.

We can describe the parts in the whole using this stem sentence.

There are mm equal or unequal parts in the whole.

This is key language that's going to come up again and again as you explore fractions, so make sure you're really confident with it.

I've thoroughly enjoyed spending this math lesson with you and hope to get the chance to do the same in the near future.

But until then, enjoy the rest of your day whatever you've got in store.

Take care and goodbye.