Lesson video

Hello there.

My name is Mr. Tilstone.

I'm a primary school teacher and I teach all of the different subjects, but the one that I enjoy teaching the most of all just has to be maths.

So it's a real pleasure to be with you today, teaching you a lesson all about perimeter.

You may have had some recent experience learning about perimeter.

Let's see if we can learn something new today.

If you're ready, I'm ready.

Let's begin.

The outcome of today's lesson is I know that the perimeter of a regular polygon can be calculated by multiplication.

So what do you know about polygons, and what do you know specifically about regular polygons? Well, they form parts of our keywords.

So my turn, perimeter.

Your turn.

And my turn, regular.

Your turn.

Perimeter.

Hopefully you've been learning about that for quite a while now, and you know a little bit about it by now.

What does it mean? Could you explain it yourself? Don't worry if you can't.

Here's a reminder.

The distance around a two dimensional shape is called the perimeter, is a rectangle, and that's the perimeter of the rectangle.

And a regular polygon has all sides equal and all angles equal.

So see if you can picture a regular polygon in your mind now.

Here's some examples.

Our lesson is split into two cycles.

The first we're going to be looking at the perimeter of squares and the second perimeter of other polygons.

Let's start by looking at the squares.

In this 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 our maths.

Got a roadside here.

Have you seen a roadside like this before? Actually, a parking sign.

I bet you've seen one.

And we've got one of the side lengths.

Can you see? It's eight.

What shape is that road sign? Square.

This square shaped road sign has a side length of eight units.

And Lucas says, "I know that squares are regular." He's right.

Let's think back to that definition.

All the side lengths are the same, all the interior angles are the same, it's regular.

Therefore, all of the sides must be eight units long.

They're not given, but we know them.

There we go.

I could use addition to find the perimeter of the sign and maybe that's something you've had experience of before using addition to find perimeter.

8 + 8 = 16, 16 + 8 is 24.

And then 24 + 8 = 32 is when you add all of those eights together, it gives you 32.

The perimeter of the square is 32 units.

Would you agree? It is.

Well done, Lucas.

But Laura sees it differently.

A square's a rectangle, and I know how to find the perimeter of a rectangle.

Do you? You can add the length and the width and then double it.

Ah, yes.

Have you done that recently? Added the length and width and doubled.

So 8 + 8 = 16, and double 16 is 32.

That seemed a bit more efficient than Lucas's way.

Got to the same answer.

The perimeter of the square is 32 units.

That was even more efficient, Laura.

You're quite right.

Well done.

That's what good mathematicians do.

They keep thinking of more efficient ways to solve problems. Lucas sees it differently again.

"Two can play that game, Laura," he says.

"I think I can do this with just one calculation." Very competitive, isn't he? I can see eight four times.

Oh I can two lot.

One, two, three, four.

Four lots of eight.

So I can use a times table fact that I know.

Of course, Four times eight, four lots of eight, and four times eight, hopefully, you know this off by heart and you don't need to do any thinking about it.

It's a known fact, 32.

Or you might have seen it the other way, 8 x 4 is 32.

The perimeter of the square is 32 units.

Now that was the most efficient way of all, and it was quick, Lucas, you're quite right.

Laura says, "I wonder if using the 4 times table always works for squares." Hmm, what do you think? So here's a square.

Another square.

It's got a side length of 5 centimetres.

Can we use the four times table here? What times table fact would come up here? Five times four, 5 centimetres four times.

So 5 x 4 = 20.

And again, hopefully, if you know your times tables, that's automatic.

The perimeter of the square is 20 centimetres.

Lovely stuff.

It works.

Yeah! So we can use the 4 times table to work out the perimeter of squares.

Oh, look at this shape.

What shape is this? Laura says, "Ooh, this one's trickier.

What is it, a diamond?" Is it a diamond? What do you think? It's got a side length of 5 centimetres.

Lucas says, "No, Laura.

It's got four sides all the same length.

It's a square just in a different orientation, that's all." Can we use our 4 times table again? Yeah, again, 5 centimetres times 4 equals 20.

It's the same as before.

So sometimes the squares that you see might be in different orientations but they're still squares.

What about this one? Have a look at this one.

It's got a side length of 3 centimetres.

Can we use our 4 times table here? There's four sides.

Laura says, "This one must be a square too.

3 centimetres x 4 = 12 centimetres.

What do you think? Do you agree with Laura there or not? "No Laura," says Lucas.

"The side lengths aren't equal.

It's got long sides and short sides.

It doesn't follow the rule about regular shapes." It's a rectangle.

The actual length of one side of the parking sign is now given.

Can you see? 80 centimetres? What's the perimeter? Can we use our 4 times table here? Laura says, "80 x 4 isn't one of my known times tables facts." Hmm, but Lucas says, "We can still use our four times table.

One of the factors is 10 times the size." Can you see which one? So eight has been made 10 times the size to be 80.

So the product will be 10 times the size.

So if we know that 8 x 4 is 32, then 80 x 4 is 320.

Let's have a check.

To find the perimeter of a square, multiply the side length by four.

So that's our rule.

Now which of these shapes have a perimeter that can be worked out using that rule? Have a look at A, B, and C.

Which ones work? Pause the video and have a go.

Well they're not all squares, are they? Did you notice that? You can use that rule for this one.

So if you know that one of the sides is 9, you can do 9 x 4.

B, is B a square? Yes it is.

It's in a different orientation but it's still a square.

So we can see 60 four times.

60 x 4 is not a known times table fact but 6 x 4 is, could you use that as a starting point? It's a square.

You can multiply the 60 centimetres by 4, and that will give you 240 centimetres for the perimeter.

What about C? Is that a square? No, it's got long sides and short sides.

It's a rectangle but not a square.

It is time to put what you've learned into practise.

Number one, what's the perimeter of these squares? So you can see some more road signs.

They're all squares.

Different pieces of information have been given.

Can you work it out? Think about that 4 times table or multiplying by 4.

And then we've got another road sign, a square pizza, and then just a square.

Number two, class 4 Oak Academy have been asked to use a trundle wheel, which you may have used before to measure the perimeter of the school field, which is square shaped.

How could they measure this most efficiently? Have you got a good tip before they start? Pause the video, have a good think about that, and I'll see you soon for some feedback.

Welcome back.

Did you do well on that? Let us have a look.

The perimeter of the square.

So this is 7 x 4, that's the times table fact.

That's 28 units.

Here we've got 9 x 4.

It didn't show you that 9 was there four times, but you know it is, it's a square.

So 9 x 4, so times table fact.

Hopefully, you knew that automatically.

If not, you would hopefully worked out.

It's 36 units.

And this one is a square just in a different orientation.

We've been given one of the side lengths which is 100 centimetres, and we can see that four times, and 100 x 4 is 400 centimetres.

Not a times table fact but hopefully quite straightforward to calculate.

And then for D, we've got 3 metres.

How many times? Four.

So 4 x 3 metres = 12 metres, a times table fact.

What about this pizza? Got a side length of 30 centimetres, and we can see four of those, so 4 x 30 centimetres.

Could you use 4 x 3 as a starting point? It's 120 centimetres.

And you can use D to help answer E because 30 is 10 times the size of 3.

Did you spot that? Those two are linked.

And did you maybe spot a link between E and F? Hmm, we've got four lots of 60 metres so we are times in by four.

You can use E to help answer F because 60 is double 30.

You might not have spotted that but still got the right answer so well done either way.

And then class 4 Oak Academy have been asked to use a trundle wheel to measure the perimeter of the score field, which is square shaped.

What's the most efficient way? Have you've got a good idea? Well because it's square shaped, all of the sides are exactly the same length.

So do they actually need to walk around all of the school field to measure its perimeter? No they don't.

They only need to measure one side of it and then multiply by four.

They can save their legs that way.

You're doing ever so well? Are you ready for the second cycle? That's perimeter of other polygons.

We've thought about squares.

Let's think about other polygons that have got different numbers of sides.

And here's one to start off.

I bet you've seen this road sign before, haven't you? What do you notice about this road sign? Maybe a bit different to the shapes we've been looking at those squares.

All the sides are the same length.

They all look 5 and 5 and 5.

It's another regular polygon, just like the square is a regular polygon.

So is this one.

So we've got (hums) units x 3 = (hums) units.

So we've got something three times.

It's a three-sided regular shape.

5 units multiplied by 3.

That's a times table fact, equals 15 units.

The triangle has a perimeter of 15 units.

So it was quite similar to what we were doing with the squares, wasn't it? Except a different number of sides.

So we're multiplying it by a different number.

What about this polygon? Is it regular? Yes.

All of the side lengths are the same as each other.

All of the interior angles are the same.

It's regular.

What kind of shape is it? Have you counted the sides? It's a regular 8-sided polygon, and that is called an octagon.

It's a regular octagon.

An 8 times table fact, can be used to work out the perimeter of that road sign, the octagon.

Hmm, so you'd know it's got 8 sides, and you know each of them is 7 units in length.

What can we do with those numbers? Something units multiplied by 8 this time 'cause it's got 8 sides equals something units.

7 units, that's each side length times by 8.

That's a number of sides, 7 x 8.

Hopefully that's an automatic fact for you.

But if not, see if you can reason your way to it.

That is 56 units so that is the perimeter of that sign.

The octagon has a perimeter of 56 units.

Let's have a check.

Look at this sign, a stop sign.

What's the perimeter of this road sign? So look at the number of sides, and then you've got a piece of information, you've got a side length, what can you do with those numbers? Pause the video and give that a go.

Let's have a look.

Well it's something centimetres x 8.

This one's got 8 sides.

50 centimetres is the length of each side so 50 centimetres x 8.

Not a times table fact, but 5 x 8 is.

Could you use that as a starting point? That's 400 centimetres.

So very, very well done if you got that.

Let's have a look at this shape.

What do we have here? Explain how you could work out the perimeter of this regular hexagon.

What would you do? Well, a hexagon is a 6-sided polygon, so that's important.

Six, we can use that.

This one is regular.

So find the length of one side and multiply it by 6.

We don't know the length of one side, but when we do, we can multiply it by 6 to get the perimeter of the whole hexagon.

Let's have a check.

Which of these shapes have a perimeter that can be determined using the rule for a regular polygon? Multiply the side length by the number of sides.

Which ones would that work for? Pause the video, have a think, have a discussion, and then we'll share some answers.

Let's see.

Did you come up with an agreement? Well, the only regular shape there is C, the Pentagon.

So that's the only shape that follows that rule.

So in that case, if we knew one of the side lengths, it didn't matter which one, they're all the same.

If so if we knew one, we can multiply it by five.

Well done if you found C to be the right answer.

Time for some more practise.

"Complete the table to show some different possible perimeters for this regular triangle." So you've been given some information, the number of sides each time is 3.

It's a regular triangle.

You've been given some possible side lengths, 2, 4, 5, 8, 10, 50 and 80, and a little bit of a clue.

What do you notice about those numbers? Some of those numbers are related to each other.

Can you work out the perimeter? What would you do? "Number two.

Always, sometimes, or never.

The perimeter of a triangle is three times the length of one of its sides." Is that always true, sometimes true or never true? Can you explain your thinking please.

Prove it.

And then number three, "Complete the table about regular polygons." So all different polygons, we've got the number of sides is time, 3, 4, 5, 6, 7, 8, and 12, and the first one's been done for you.

So if it's got three sides, the perimeter is the length of one side times three.

And then if the side length is 5 centimetres, that would be 5 centimetres x 3 = 15 centimetres.

So can you do that for all the other shapes? And they've all got a side length of 5 centimetres, remember? And number four, this hexagon has been made from the regular triangle that we can see, and that regular triangle's got a side length of 8 centimetres.

Who's correct? Laura or Lucas, and why? Let's see what they've got to say.

Laura says, "The perimeter of the triangle is 24 centimetres, so you have to multiply 24 by 6 because it's six triangles." Okay, Lucas says, "No, you have to multiply the side length of the triangle by 6 because there are six sides." Okay, one of those is right.

See if you can find who.

Pause the video.

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

Welcome back.

How did you get on? Let's have a look.

So number one then, so it's going to be three sides each time, so if the length of the side is 2 centimetres, that means the perimeter's 6.

If it's 4, it's 12 'cause we multiply 'em by 3.

3 x 5 is 15, 3 x 8 is 24, 3 x 10 is 30.

They're all times table fact so maybe you know that automatically, that would be great.

And then 3 x 50 is not a times table fact, but you've already worked out 3 x 5 so we can use that.

3 x 50 is 150, and again 3 x 80 is not a times table fact, but 3 x 8 is.

So we could use that for a starting point, 3 x 80 is 240.

And always, sometimes or never.

The perimeter of a triangle is three times the length of one of its sides.

Sometimes the triangle has to be regular for that to be true.

Not all triangles have equal side length.

You could draw a three-sided shape with the sides aren't equal so it wouldn't follow that rule.

So that only works if the side lengths are the same.

So well done if you said sometimes.

And then here if it's got four sides, 5 x 4 is 20.

If it's got five sides, 5 x 5 is 25, 5 x 6 is 30, 5 x 7 is 35, 5 x 8 is 40 and 5 x 12 is 60.

And every single one of those was a times table fact so if you're good with your tables, I bet you rattled through that.

And then the hexagon has been made from the regular triangle.

Who's right? So Laura is thinking because we know the perimeter of the triangle's 24 centimetres, which she's right about, by the way, is 24.

She says you have to multiply 24 by 6 because there's six of them.

But not all of the sides of that triangle are on the outside of the big shape, are they, of the hexagon? So not quite right.

Lucas says, "You have to multiply the side length of the triangle by 6," and I think that might be right, don't you? Because if one of those sides is 8 centimetres, that means each of those six sides of that hexagon is also 8 centimetres so we're looking at 8 x 6, and 8 x 6 is a times table fact.

Again, it's 48.

So in fact it's 48 centimetres.

So Lucas, your method was correct.

We've come to the end of the lesson.

Today's lesson has been understanding that the perimeter of a regular polygon, it has to be regular, can be calculated by multiplication because the sides of a regular polygon are all the same.

There's no need for any addition when finding the perimeter.

We can make it really quick and simple, particularly if it's a known times table fact.

Can be done in just one step using multiplication.

What we have to do is this.

Multiply the length of a side by the number of sides.

Often this can be done using a times table fact such as 6 centimetres x 4, or a fact related to a times table such as 60 centimetres x 4.

And we can use 6 centimetres x 4 to help us with that.

You've been amazing today, I'm so impressed with you.

Well done.

I cannot wait to work with you again.

Until then though, enjoy the rest of your day.

Take care and goodbye.