Lesson video

Hi there! My name is Mr. Tilstone.

I'm a teacher and I really love teaching maths, so it's a really great honour, pleasure, privilege, and delight to be here with you today teaching you this lesson which is all about perimeter.

You might have had lots of recent experience with perimeter.

You might be becoming quite the perimeter expert.

Let's see if we can teach you even more today.

If you're ready, I'm ready, let's begin.

The outcome of today's lesson is I can calculate the side length of a regular polygon by division where the perimeter is known.

You might have had some recent experience using multiplication and a known side length to work out perimeter.

Well, we're gonna flip that around today.

Our keywords are, my turn, perimeter.

Your turn.

My turn, regular.

Your turn.

Well, hopefully you've not got this far without knowing what perimeter means, so let's have a little check.

The distance around a two-dimensional shape is called the perimeter.

Here's a rectangle, and that's the perimeter of the rectangle.

And a regular polygon has all sides equal and all angles equal, and recently you might have explored that in terms of perimeter.

Here's some examples.

Our lesson today is split into two cycles.

The first will be squares and the second will be other regular polygons.

So for now though, let's focus on squares.

In today's lesson, you're going to meet Laura and Lucas.

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

Got a road sign here, it's a parking sign and it's square.

This square road sign has a perimeter of 32 units.

What is the length of one side? So, we know it's square.

Squares are regular.

What does that mean? All of the side lengths must be the same.

This time we know the total perimeter.

Is it possible, is there enough information to work out what one of the side lengths is? Hmm.

Could we use multiplication? Not really.

This time we know the perimeter.

Multiplication won't help.

Lucas says, "I know that squares are regular.

All of the sides must be the same," yes.

"I could use division to work this out." Yes, that's a great idea, Lucas.

In this case, look, 32 divided by 4, because there are four equal parts.

What's that? If you know your times tables, you might be able to use this to automatically work out 4 times something is 32.

Let's have a look.

32 divided into 4 parts.

There is another way to do it as well and that's to think of halving and halving again.

So let's have a look at that.

This is a bar model.

That's 32 split into 4 equal parts and each of them represents one of those sides.

So we can halve and halve again.

Half of 32 is 16, and then half of 16 is 8.

So that means that each of the side lengths is eight, eight units long.

There we go.

And then we can check that using the inverse.

8 times 4, one of our times tables facts, is 32.

It works.

Laura sees it differently.

She's using multiplication.

Hmm.

Okay, let's have a look at this.

"I can see a times tables fact," yes.

4 times something equals 32.

That's how I saw it initially as well.

"I know that 4 groups of 8 is equal to 32." Laura clearly knows her times tables.

So it's four times eight.

So you can use division or you can think of it as a missing times tables fact.

"Each side is eight units long." They've both got to the same answer but in different ways.

This square, and it is a square, it's in a different orientation but it's a square, has a perimeter of 320 units.

What's the length of one side? Hmm.

Is that number 320 ringing a bell? Has it reminded you of what we've just done? We looked at 32 for the perimeter.

This time it's 320.

Lucas has spotted it.

He said, "This is similar to the last one." So we can halve 320, and we can do that by thinking about halving 32.

"If half of 32 is 16, half of 320 is 160.

If half of 16 is 8, then half of 160 is 80." So that means that each of the side lengths is 80.

"Each side is 80 units long." So that's using that halving and halving again strategy.

Laura is once again thinking about times tables facts, good for you, Laura, they're very useful, and facts that relate to them, and this one is a related fact.

She says, "If 4 times 8 equals 32," which we know, we've established that, she knew that, "then 32 divided by 4 equals 8.

So 4 times 80 equals 320 and 320 divided by 4 equals 80.

So each side is 80 units long." So she did it slightly differently.

She used her times tables knowledge.

Let's have a quick check.

If you know the perimeter of a square, divide it by four to find the length of one of its sides.

That's true, that's what we've just done.

These shapes all have a perimeter of 48 units.

Which ones have side lengths that can be worked out using that rule? Give the side length.

Okay, have a look at that, have a go.

If you've got a partner to work with, work with them and check your answers, swap your answers.

Pause the video.

Welcome back.

Which ones did that rule work for? Well, this one is, and if it's got a perimeter of 48 units, 48 divided by 4 is 12.

And you can move it out by halving and halving again, maybe you did that, or you can think of it as a missing times tables fact.

4 times something equals 48, 4 times 12 equals 48.

So each of those sides is 12 units long.

What about B? Is B a square? Yes, it is.

It is.

It's the same square, in fact, but in a different orientation.

So we already know the answer to that.

12 units.

What about C? Is C a square? No, it's not.

That is not a regular shape.

It's got two longer sides and two shorter sides.

It's not a square, so that rule won't work for that.

It's a rectangle but it isn't a square.

It's time for some practise.

Always, sometimes, or never? If you know the perimeter of a quadrilateral, divide it by four to get the length of one of its sides.

Is that always true, sometimes true, or never true? And can you prove it, can you explain it? Number two, Lucas has measured the perimeter of his classroom, which is square-shaped.

Its perimeter is 28 metres.

What's the length of one side of the classroom? See if you can use that rule to work that one out.

Number three, give the side length of each of these squares.

So you've got some information about these squares, you've got the perimeter, in fact, of the squares.

Can you work out the side lengths? And we've got some more square shapes here.

Number four, complete the table, which is about squares.

So we know that squares have got four sides.

The perimeter's given.

What must the length of each side be? Use that rule that we've explored in this cycle.

Very best of luck with that.

Work with somebody if you can.

I'll see you soon for some feedback.

How did you get on? So always, sometimes, or never? If you know the perimeter of a quadrilateral, that's a four-sided shape, divide it by four to get the length of one of its sides.

Only sometimes.

That's only true of squares, one particular kind of quadrilateral, because all the sides are equal.

But there are many four-sided shapes that do not have all equal side lengths and that rule won't work for them.

It's got to be equal sides.

So here's an example of one that will, the square, and here's an example of one that won't, the trapezium.

Lucas has measured the perimeter of his classroom, which is square-shaped.

Its perimeter is 28 metres.

What's the length of one side of the classroom? Maybe you did a little sketch to help you to work that one out and drew a square maybe.

But it could be worked out by considering the times tables fact something times 4 equals 28, and that's 7 times 4 is 28.

There are other ways to do that as well.

You might have halved and halved again, but the length of each side is seven metres.

Well done if you got that.

And these signs, we've been given the perimeter.

So in the first one it's given you what to do.

So 20 units divided by 4, think of your times tables facts or halve and halve again, doesn't matter which.

That's five units.

And here, look, 28 units.

What are we dividing it by? By four, because there's four sides.

28 divided by 4, use your times tables knowledge or halve and halve again, seven units.

And for C, this is 48 units.

Right, so, that's 48 units, that's the perimeter.

Divided by how many sides? Four sides.

48 divided by 4, hmm.

It's a times tables fact but you can halve and halve again.

12, 4 times 12 equals 48.

So it's 12.

Each side is 12 units.

For D, the total perimeter is 100 centimetres.

100 divided by 4.

That's not a times tables fact.

Halving and haling again would work with that, I think.

And that is 25 centimetres.

And for E, that's 12 centimetres divided by 4, so three centimetres.

That's our starting times tables fact.

And then we can apply that to 120 centimetres divided by 4 is 30 centimetres.

And for F, 280 metres.

Well, if we know 28 divided by 4 is 7, therefore 280 divided by 4 equals 70.

So the side length is 70 metres.

Well done if you got those.

And number four, complete the table.

It's all about squares.

They've all got four sides.

You could use division, halving and halving again, you could think of it as times tables facts and what's the missing number there.

But if the perimeter's four, the length of the side is one.

If the perimeter's eight, it's two, 12, it's 3; 40, it's 10; 80, it's 20; and 120, it's 30.

And you might see, you could think of it as multiplication as well because 4 times 1 is 4, 4 times 2 is 8, 4 times 3 is 12.

So these are the missing times tables facts.

Did you notice, by the way, that if the perimeter doubled, the length of the side doubled? Hmm.

Did you notice the last three perimeters were 10 times the size of the first three? So you could use the first three to help you with the last three.

Let's move on to other regular polygons.

Let's see if something similar will work there.

So the square is an example of a regular polygon.

This square, let's not call it a square, let's call it a regular polygon, and then we can look at other regular polygons as well.

So this regular polygon has how many sides? Four sides.

It has a perimeter, that's been given, of 32 units.

So four, because that's the number of sides, times something equals 32.

Or you could look at it as 32 divided by 4 equals something.

So a missing times tables fact there either way.

And that's eight.

So 4 times 8 equals 32 or 32 divided by 4 equals 8.

The length of each side is eight units.

So there we go, each of the sides is eight units long.

Let's use that same stem sentence, but this time let's change the shape.

This triangle has equal side lengths.

It's also a regular polygon.

So let's keep that part of the stem sentence fixed.

So this regular polygon has mm sides.

It has a perimeter of mm units, mm times mm equals mm, or mm divided by mm equals mm.

The length of each side is mm units.

You might want to have a go at that before we explore it together.

Let's have a look.

This regular polygon has this time three sides and it's got a perimeter of 30 units.

So we can add that information into our stem sentence.

So it's got three sides, so 3 times something equals 30 or 30 divided by something equals 3.

Times tables facts again, 10.

So the length of each side is 10 units.

Here we go.

Let's try a different regular polygon.

Have a look at this one.

How many sides has it got? We've been given the perimeter, it's 48 units.

So this regular polygon's got eight sides.

It's a regular octagon, and it's got a perimeter of 48 units.

So let's use that information in our stem sentence.

So something times something equals 48, or 48 divided by something equals something.

We've got one bit of information to add to those calculations, haven't we? And that is the number of sides.

So 8 times something is 48, or 48 divided by 8 equals something.

Again, if you know those times tables facts, this should be pretty straightforward.

So 8 times 6 equals 48, or 48 divided by 8 equals 6.

So therefore, the length of each side is six units.

And we can see that in the bar model.

To find the length of each side of a regular polygon, divide the perimeter by the number of sides.

That is our rule.

Can we say that together? That's an important rule.

Are you ready? To find the length of each side of a regular polygon, divide the perimeter by the number of sides.

Right, I just want you to say it now.

You ready? Go.

And you can see some regular polygons there.

That rule would work for all of those if we knew the perimeter.

Let's have a check.

Which of these shapes have side lengths that can be determined using that rule: to find the length of each side of a regular polygon, divide the perimeter by the number of sides.

Which would that work for? Pause the video.

Well, really we're just looking for the regular one here, and there's only one.

The only regular shape is C, that pentagon, so that's the only one that would follow that rule.

It wouldn't work with the other ones.

So well done if you said C.

Time for some final practise.

This regular pentagon has a perimeter of 40 centimetres.

What's the length of each side? So think about how you can use division there.

This regular octagon has a perimeter of 40 centimetres.

What's the length of each side, and what do you notice? Are these statements always true, sometimes true, or never true? Explain why, prove it.

A, if you know the perimeter of a regular shape, divide it by the number of sides to give the length of each side.

Always, sometimes, or never? B, if you know the perimeter of a regular pentagon, divide it by four to give the length of each side.

C, if a regular hexagon and a regular octagon have the same perimeter, they will also have the same side lengths.

And D, if you know the perimeter of a hexagon, divide it by six to give the length of each side.

See what you think.

See if you can explain that really clearly.

Best of luck with that and I'll see you soon for some feedback.

Welcome back.

How did you get on? Number one, this regular pentagon has a perimeter of 40 centimetres.

So, it's a pentagon, it's got five sides, they're regular.

40 divided by 5 equals 8.

So that's eight centimetres.

You might have thought of it as a missing times tables fact, just like that, 5 times 8 equals 40.

This regular octagon has a perimeter of 40 centimetres.

So it's an octagon, it's got eight sides.

So what are we doing this time? We're doing 40 divided by 8, which is 5, or 8 times 5 equals 40.

It's five centimetres, however you look at it.

Our times tables were useful there once again.

Did you notice the same multiplication fact on both of those examples? Well done if you did.

And these statements, always, sometimes, or never.

If you know the perimeter of a regular shape, divide it by the number of sides to get the length of each side.

That's always true.

Regular shapes have equal side lengths, so that's why that rule works.

B, if you know the perimeter of a regular pentagon, five sides, divide it by four, hmm, to give the length of each side.

That's never true.

Pentagons have got five sides, so you need to divide by five.

If a regular hexagon and regular octagon have the same perimeter, they will also have the same side lengths.

No, that's never true.

The hexagon has fewer sides, so each side will be longer, so never.

And D, if you know the perimeter of a hexagon, divide it by six to give the length of each side.

Always, sometimes, or never? Sometimes.

It didn't say regular, did it? Did you spot that? Hexagon must be regular for that rule to work.

It is possible for hexagons to have unequal side lengths, to be irregular hexagons.

Got to be regular.

We've come to the end of the lesson.

You've done so well today, brilliant! Our lesson has been calculating the side length of a regular polygon by division where the perimeter is known.

Because the sides in a regular polygon are all the same, the following rule can be used: divide the perimeter by the number of sides to give the length of each side.

That works with regular polygons.

Often this can be done by considering the missing value in a times tables fact, as the example shows.

So I cannot stress this enough to you, learn those times tables and learn them off by heart.

They're so important.

So in this case, 30 centimetres divided by 5 equals 6 centimetres.

It's a pentagon so we're dividing by five.

Or 5 times 6 centimetres equals 30 centimetres.

Well, congratulations, you've completed the lesson.

Why don't give yourself a little pat on the back? It's deserved.

I would love to spend another math lesson with you in the near future.

Hopefully I get that chance.

But in the meantime, have a great day whatever it is you've got coming up for the rest of your day.

Take care of yourself and goodbye.