Lesson video

Hi there.

Nice to see you.

My name is Mr. Tilstone.

I'm a teacher and I'm feeling very lucky today 'cause I get to spend this math lesson with you.

I can't wait to get started.

So if you are ready, I'm ready.

Let's begin.

The outcome of today's lesson is I can identify equal parts when they do not look the same.

You might have had some recent experience of dealing with parts and wholes.

Let's see if we can apply that today.

And we've got some keywords, so I'll say it first and you say it back.

So my turn, equal.

Your turn.

My turn, unequal.

Your turn.

I think you've probably heard those words before, but let's have a reminder about what they actually mean.

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

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

So they're kind of opposites.

Our lesson today is split into two cycles, two parts.

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

So if you're ready, let's start thinking about the difference between equal and unequal parts.

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

Have you met them before? They're here today to give us a helping hand with our maths.

Izzy and Jun are given some counters and asked to put them into groups.

Now maybe, hopefully, you've got some counters in front of you too, and you could do something very similar.

So these are their counters.

What has happened? What do you notice? How would you describe Izzy's grouping? How has she grouped her counters? There were 12 counters.

How has she grouped them? Izzy says, "Even though the counters look different, the parts are equal." So what's different about the counters? Well, the colours are different, but what's the same about them? They're the same size.

She says, "I know this because the number of counters in each group or part is the same: four." So if you don't think about the colours and just think about the number, and the shape and size, you could say they're equal groups.

How would you describe Jun's grouping? So let's have a look at this.

He's got some counters, he's grouped them differently.

What could you say about how Jun has grouped his counters? He says, "Even though the counters look the same, the parts are unequal." So they do look the same, don't they? They're the same size, shape, and even colour.

But the groups are not equal.

The groups are unequal.

There's a different number in each group.

And that's where he says, "I know this because the number of counters in each group is not the same," so therefore it's unequal.

Let's have a little check.

Let's see how much you've understood about equal and unequal.

Complete the sentences to describe the grouping of these cars.

So the parts are (hums).

What's the missing word? I know this because the number of cars in each group is (hums) the same.

So we're looking for two missing words.

Pause the video and see if you can find them.

Well, let's have a look.

The groups are not the same, are they? You can't say they're equal because they haven't got the same number and the middle one's got one more car in.

So the parts are unequal.

I know this because the number of cars in each group is not the same.

So they were the two words we were looking for, unequal and not.

And if you got those words, you're on track and you're ready for the next part of the learning.

So it's time for some practise.

"Rearrange the counters so that the parts become equal." And if you've got some real counters in front of you, I highly recommend you using those.

"Justify how you know the parts are now equal." So see if you can explain that.

And can you find more than one way to do it? I can think of more than one way.

See if you can find them too.

Number two, "If this is possible and you've got your teacher's permission, go for a walk and look for equal and unequal parts in nature.

If it's not possible to go for a walk, look for equal and unequal parts in your current environment, which may be a classroom.

Make drawings of what you spot." Have fun with that and I'll see you soon for some feedback.

Welcome back.

If you had the chance to go for a walk, I hope you enjoyed that.

I hope you saw lots of equal and unequal groups.

So rearrange the counters, and hopefully you had some real counters, but don't worry if not, so that they become equal.

They're not equal at the minute, they're unequal at the minute but you could make them equal.

You could do this.

You could move one counter from this group to this group, and now they're equal.

Each group's got three counters in.

You might have reasoned that the parts are now equal because there are now the same number of counters in each group: three.

Did you have another way to do it? I wonder.

What about this? Now I can see nine equal groups of one.

That's the only other way to make equal groups.

Nine groups of one counter.

And then maybe you had the chance to go for a walk, or if not, you use your current environment.

So you might have seen, for example, some birds on a fence and draw a representation like this.

So you might have made a drawing a little bit like this.

And in this case, we can see that the birds are in equal groups.

Each group has got two birds in.

You might have spotted some unequal groups too, and maybe that's what you drew.

Time to move on to our next cycle.

You're doing really well.

You're ready for this.

This is equal parts.

Let's look at these same size squares that have been divided into parts.

So you can see we've got four squares.

So you can say we've got four of the same whole, and each one has been divided into parts.

What do you notice? What can you see? Think about the number of parts.

Think about the type of parts.

All the squares have been divided into four equal parts.

You could say that about each of those squares have been divided into four equal parts.

That's what's the same about them, but what's different? Let's look at one part from each of the squares.

What is different about each part? Each of these was one of four equal parts.

The parts are all different shapes.

So we can see a square, which is a kind of rectangle, we can see a rectangle that's not a square, and we can see two different kinds of triangles.

The wholes were all divided into four equal parts, and because the wholes are the same size, each part must represent the same amount of the whole.

Each of these parts, even though they look different to each other, is one of four equal parts of the whole.

Izzy says, "Equal-sized parts do not have to look the same." But how can we prove she wonders that these parts are equally-sized? Hmm, what do you think? Any good ideas? How can you prove, for example, that that rectangle and one of those triangles is the same size? Well, you could do this.

You could recombine the different parts to form the original whole square.

So if you look at that first example, look, that's the same whole as before, but it's made up of four different parts.

Two of them squares, two of them rectangles.

So that must mean that the square is the same size as a rectangle.

And the middle one, we've got two squares and two triangles that make up that whole again.

And on the other one, we've got two triangles again and two rectangles.

So there's lots of different ways to do that, but when you recompose those shapes, it makes the hull.

So each of those four parts was the same size.

We've proved that parts must be equal.

So remember, different equal-sized parts can look different.

Equal-sized parts do not have to look the same, but they must take up the same space.

Let's have a little check.

Let's see if you've understood that.

Are these parts of this rectangle? So the rectangle as a whole this time, are these parts equal or are they unequal? Pause the video, have a think and have a chat.

What do you think? Are they equal parts or unequal parts? Well, the first thing that you can notice is that they're different, aren't they, to each other? Two of them are the same, the triangles, and a different two are the same, the rectangles.

But are they all equal? Hmm, the whole is divided into four equal parts.

Each part must represent the same amount of the whole.

Each of these parts is one of the four equal parts of the whole.

So although they look different, they're actually equal parts.

Equal size parts do not have to look the same, remember.

Time for some more practise.

Look at these shapes.

Has each shape been divided into equal or unequal parts? Hmm, and explain how you now have a good think about that.

And number two, can you divide these shapes into A, unequal size parts? B, equal size parts that look the same? Or C, equal size parts that do not look the same? And here are those shapes that you're going to be working with and thinking about.

Pause the video.

Good luck with that, and I will see you soon for some answers.

Welcome back.

How did you get on with that? Let's give you some answers, shall we? So number one, look at these shapes.

Has each shape been divided into equal or unequal parts? And explain how you know.

Well, let's have a look here at A and B.

These rectangles have both been divided into equal size parts.

So even though the parts look different and are different shapes, they are equal to each other.

Each whole is divided into four equal parts.

Each part must represent the same amount of the whole.

Each of these parts is one of four equal parts of the whole.

So both shape A and shape B have been divided into four equal parts even though they look different.

Equal size parts do not have to look the same.

And for C, this rectangle has been divided into unequal parts.

The whole is divided into four, in fact, unequal parts, The parts are not all the same size, so they're unequal.

Number two, you might have done something like this.

So you might have divided this shape into unequal size parts like that.

There's lots of ways to do that though.

There's different numbers of parts.

You could divide it into different ways you could do it, you could do it with straight lines.

They don't have to be straight lines, all sorts.

And here's another example.

So that's an equal size part that looks the same.

So we've taken that square, and we've divided it into four squares.

So they're all equal to each other.

And what about this one? Equal size parts that do not look the same.

That's a little bit trickier, isn't it? But here's an example.

So this has been divided into eight equals size parts.

Some of them look the same, the rectangles look the same as each other.

Some of them look the same as each other, but different to the rectangle.

So those triangles all look the same as each other but there are eight equal-sized parts.

And another unequal-sized part, again, this has been divided into three unequal parts.

And this is another one that's been divided into equal-sized parts that's been divided into four equal-sized rectangles.

They're all the same.

And here's another one that's an example of equal-sized parts that do not look the same.

So how many parts has this been split into? Divided into eight, and they're equal-sized even though they look different.

We can see some triangles that are the same as each other and we can see some squares that are the same as each other.

But there are eight equal-sized parts.

We've come to the end of the lesson.

Today, we've been looking at identifying equal parts when they do not look the same.

Equal parts of the same-sized whole may not look the same, and we've seen plenty of examples of that today.

They can be different shapes.

So we've seen examples where you could split, for example, a square into rectangles and triangles, but they're all equal-sized.

A whole can be made from equal-sized parts that are different shapes.

And each equal part of a whole must represent the same amount of the whole for it to be equal-sized.

Have a great fun working with you today, and I hope I get the chance to work with you in the near future with another maths lesson.

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

Take care and goodbye.