Lesson video

Hello there, my name is Mr. Tilston.

If I've met you before, it's nice to see you again, and if I haven't met you before, it's nice to meet you.

Today we're going to be talking about one of my favourite subjects, which is maths.

So if you are ready, I'm ready, let's begin.

The outcome of today's lesson is I know that a regular polygon has sides that are the same length and angles that are the same size.

We're going to explore lots of examples of that, and by the end of the lesson, I'm sure you'll be very confident.

Our keywords are, my turn, regular polygon, your turn, my turn, irregular polygon, your turn, my turn, interior angles, your turn.

There might be some quite unfamiliar vocabulary there for you.

Let's have a look at what those words mean.

A regular polygon has sides that are all equal and interior angles that are all equal.

An irregular polygon has sides that are not equal or interior angles that are not equal.

And interior angles are the angles formed inside, so interior, inside a polygon by two of its sides.

Here we go, that's one interior angle, that's another, that's another, and that's another.

So there's two sides of each making an angle.

Our lesson today is split into two cycles.

The first will be polygons with the same length sides, and the second will be the angles in regular polygons.

So if you're ready, let's start by looking at polygons with the same length sides.

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

Have you met Laura before? She's here today to give us a helping hand with our maths work.

A polygon is a two dimensional or 2D shape with closed, straight sides.

Sometimes you'll see 2D written down like that, and it's short for two dimensional.

Help Laura to decide if the following shapes are polygons.

Let's have a look at that.

Is there a two dimensional shape? Has it got closed, straight sides, what do you think? Well, it hasn't got straight sides.

No straight sides.

So no, it doesn't meet the criteria of a polygon.

What about now, it's got some straight sides, hasn't it now? Has it got all straight sides? Well, no, not all of them are straight.

Two of them are, but one isn't, so no.

Let's have a look at this one.

So remember, polygons are a two dimensional shape with closed, straight sides.

I think I can see an issue straight away there.

What do you think? It's not 2D, is it? That's a 3D or three dimensional shape.

And Laura knows that, so no, that doesn't qualify.

What about this one? Hmm, is it two dimensional, has it got closed, straight sides? It's certainly got some of those things, hasn't it? What has it got? Well, it's got straight sides definitely, but it's not closed.

Those two sides aren't joined together, can you see? "The shape isn't closed," says Laura, "The lines need to join together." They do, we could turn it into a polygon, couldn't we? But at the minute it's not, so no.

What about this one, is it 2D? Has it got closed, straight sides? Well, what do you think? It is two dimensional, it is closed and it has got straight sides.

So it fits all of the criteria of a polygon.

"It's a 2D shape with closed, straight lines.

It is a polygon." What about this one, is it two dimensional? Has it got closed, straight sides, what do you think? Maybe thumbs up if it is, thumbs down if it isn't.

Yeah, it is 2D, it has got closed sides and they are straight, it's a polygon.

Laura is creating polygons with number rods.

You might have some of these in your classroom.

If you have, join in.

Give us some feedback.

Has she created a polygon? Let's have a look, ready for her shape.

Here we go, so that's one of these sides.

And that's another, and that is another.

So look at the shape inside that.

Is it a polygon there? The sides are all straight, so it ticks one of the boxes.

So it has one feature of a polygon, but they're not closed, so it's not a polygon.

It's gotta meet all of those criteria.

Laura has another go at making a polygon.

So that's the number rods.

And when she takes that away, it leaves that shape.

Would you say she'd made a polygon this time? Hmm, well, it's a 2D shape and it's got closed, straight size.

Yes, it is a polygon.

Let's do a quick check for understanding.

Select the correct option in this description of polygons.

A polygon is a 2D or 3D shape with open or closed sides? And the sides, are they all straight, sometimes straight or all curved? Pause the video and have a think.

Let's see, a polygon is a 2D shape, if it's 3D, it's not a polygon with closed sides.

Even if they're nearly closed, doesn't count.

If they're closed, yes, polygon, and the sides are all straight.

So if you've got a shape and all of the sides are straight apart from one tidy little curved line, then it's not a polygon.

Laura has listened to your feedback and created another triangle.

What do you notice? Here we go, so that's one side, another side and another side.

And that's the shape that's created.

This time, all of the sides have the same length.

Did you spot that? There we go.

This is one of the features of a regular polygon.

And you could see by the fact that the number rods were the same colour, that they were the same.

Laura is making another polygon where all of the sides are the same length.

Let's have a look, what is she making this time, what do you think? Okay, same colour again, that.

And again and again, it's a four-sided shape.

What do we call those? They're quadrilaterals, what kind of quadrilaterals there? Specifically, the shape she's made is a rhombus.

All the sides of the same length.

Let's do a quick check for understanding, which of these shapes are polygons with equal length sides, equal? Pause the video and have a go.

Well again, because we've used number rods here, the same colours are a clue.

So if we look at A, that is a square and all of the sides are the same length.

So it's a polygon with equal length sides.

B isn't, it's a polygon, but the sides aren't the same length.

Two are longer and two are shorter.

And C has got all sides that are the same length, it's got six sides, it's a hexagon.

How about another quick check? Laura says, "I have created a polygon with equal length sides." Have a look, do you agree or disagree? Pause the video.

Hmm, this was a bit trickier, wasn't it? Because she has used the same colour rods.

But do those sides look the same length? They don't, do they? That doesn't look like a square to me.

It's a quadrilateral but not a square.

Hmm, looks like it's got two longer sides and two shorter sides.

She used the same blocks, but a polygon has two long sides and two short sides, it's a rectangle but not a square.

They haven't got the same length sides.

Can be fixed, what could we do, what do you think? Could we turn that into a shape that has got the same length sides? A quick bit of movement and there we go.

Now we've got a square.

It's a polygon with equal length sides.

It's time for some practise.

Number one, tick all of the polygons.

Think about those three things that a polygon needs to have.

Number two, use number rods if you've got them, or an alternative such as straws or something like that to create a polygon with equal length sides.

How many different examples can you create? And little bit of a bonus challenge.

Can you name the polygons that you've created? Pause the video, and good luck.

I'll see you soon for some feedback.

Welcome back, how did you get on learning about polygons? Let's have a look.

So these are the polygons.

They've got to be two dimensional and have closed, straight sides.

Let's have a look, that does, that does, that does and that does.

The others, some are 3D, some have got curved sides, some aren't closed, all sorts of things are stopping them being polygons.

And number two, if you've got number rods, you would've used them to make some polygons with equal side lengths.

And perhaps you created one polygon but in different sizes.

Or perhaps you had a system starting with a triangle and increasing the number of sides each time.

So a triangle and quadrilateral, then pentagon, and so on and so on.

Perhaps you created a shape with a very large number of sides, perhaps you were very ambitious.

Here's an example that creates this polygon, all equal length sides, that's a hexagon.

Here's another polygon with equal length sides.

It's a square.

Are you ready for cycle two? That's the angles in regular polygons.

We've looked at the fact they've got the same length sides.

Now we're looking at the angles in regular polygons.

Well, let's go.

What's the same and what's different about these two polygons? Have a look, hmm, what do you think, what's the same? Something's jumping out at me straight away about what's the same.

Have a little think about the colour that you can see.

Well, both are quadrilaterals.

They've both got four sides and the sides are equal length.

They're made with the same number rods, in fact.

But they're not the same shape, are they, not quite? They are quadrilaterals but not the same kind.

Look at those interior angles.

What do you notice, those angles inside the shape, what do you notice, are they the same or different? In the first polygon, the interior angles are not all the same as each other.

We've got two that are smaller than a right angle.

They're the same as each other but not as the other ones.

And we've got another two that are greater in size than a right angle.

So you cannot say that all four of those angles are the same size.

But what about the square? Are the angles the same size, the interior angles, the inside angles? Yes they are, and they're a special kind of angle in this case, they're right angles.

For a shape to be a regular polygon, two things must be true.

And we've explored both of them now.

The first thing is the sides must have the same length as each other.

So for it to be a regular polygon, the sides must be the same length, and the interior angles must also be equal to each other.

So two things.

Here we go, here's an example.

The side lengths are the same in this square, and the interior angles are the same.

Here's another one.

Side lengths the same, interior angles the same.

And here's another one.

Side lengths the same, interior angles the same.

We can rotate a regular polygon to show the angles are always the same size.

And watch the vertex marked by the dot.

So let's have a look.

So there's one of the vertices and we're gonna rotate it so that dot's gonna move about because we're rotating the shape, here we go.

What do you notice about those two angles? They're the same, and we've rotated again.

And it looks the same because the angles are all the same.

Let's do it with a different shape.

Let's do it with a pentagon.

There we go, we are going to rotate that shape.

And again and again and again.

And that angle is not changing.

What is the name of the regular polygon with the smallest number of sides? Have a think, what do you think, the smallest number of sides, the smallest regular polygon? Well, that's it, well, can you name it? It's an equilateral triangle.

It's not called a regular triangle.

It's got a special name, an equilateral triangle, so equilateral.

What's the name of the regular polygon with four sides? It's got a special name, it's a common name, you've heard it a lot, you've used it a lot.

We've talked about it today, in fact.

There it is, what's that? That's a square, it's not called a regular quadrilateral, that's not its name.

That would describe it, but it's called a square.

These are regular polygons.

These shapes are irregular polygons, the sides are not the same length and or the angles are different.

So they are polygons, but they're not regular polygons.

The top ones are.

Other polygons can be regular polygons.

Here's some regular polygons.

That's a regular pentagon.

All the sides are the same length, all the interior angles are the same.

What's this then, what's that called do you think? Regular hexagon, same length sides, same interior angles.

What's that one called, do you think? This is a bit more unusual, not quite as common a word, but do notice these side lengths and the angles, they're the same.

And that's called a septagon, a regular septagon.

And what about this one? A little bit more common, how many sides has that got? They're all the same, look, the angles are all the same as well inside the shape.

That's a regular octagon.

And we can have a irregular polygons with the same number of sides.

But these are irregular because the side lengths and or the interior angles are not the same.

Does the orientation of the shape, the position of it affect whether or not it's a regular polygon? Let's have a look at this, there's a square.

Is that still a square? Yes, is that still a square? Yes, the sides are still the same length and the interior angles are still all equal.

So they are still regular polygons, they're just in different orientations.

They're still regular.

Does the size of the shape affect whether or not it's a regular polygon? What do you think about that, the size of the shape? Hmm, shall we investigate? Let's have a look.

Well, that's a square again, but much bigger this time.

And here's a smaller square and an even smaller square.

Are they all still regular? As long as the sides are the same length as each other and the interior angles are all still equal, they are still regular polygons.

So what you can see there are three regular polygons.

Let's have a look at this shape, what do you think? Are the sides all the same length? And are the interior angles all the same? Where would you put that? Would you put that in some of the interior angles are the same, it's not a regular polygon or would you put it in all of the interior angles are the same, it's a regular polygon? There, not all of those interior angles are the same.

Some are reflex angles and some are acute angles.

What about that one? Are the interior angles all the same? Yes, it's a regular polygon.

What about this one? Side lengths all the same? Yes, what about those interior angles? The angles inside, are they all the same as each other? Have a look, what do you think? Yes, they are, it's a regular polygon.

What about this one? Side lengths the same? Looks like it.

Interior angles, are they the same, what do you think? I can see that some are less than a right angle and some are more than a right angle.

So it's not a regular polygon because those angles are different.

Let's do a quick check.

What are the criteria for a regular polygon? All the sides are same length, all straight sides, must contain a right angle, all interior angles the same.

There's more than one option here, pause the video.

Well, let's have a look.

For it to be a regular polygon, all the sides must be the same length, all straight sides, that's a criteria of any polygon, and all interior angles must be the same as each other.

They don't have to contain a right angle, but sometimes they do.

But the important thing is the interior angles, those angles inside must be the same for it to be a regular polygon.

Time for some more practise.

First of all, tick all the regular polygons.

Think about those two things that need to be true.

For each of the polygons, say whether it's a regular polygon or an irregular polygon, and explain why.

See if you can be as clear and concise as you can.

And lastly, go on a hunt of your classroom or school environment with your teacher's permission.

How many examples of regular polygons can you find? You're looking for regular polygons.

Have fun with that, pause the video.

Welcome back, let's see how you got on.

So the regular polygons were these.

That's regular, all the same side lengths, all the same interior angles.

And this shape too, and this one, and this one and this one.

One of them was not even a polygon, did you spot it, which one? The circle and the others.

The side lengths may be different or the interior angles may be different.

Something is stopping them being regular polygons.

Number two, is it a regular polygon or irregular, and why? Well, the first one, A, is a regular polygon, 'cause all of the sides are the same length and all of the interior angles are equal.

So an explanation that recognises those two things please.

And B, that's an irregular polygon.

It looks regular, doesn't it? But it's not quite, the interior angles are equal.

So it ticks one of the boxes, but it has some shorter sides and some longer sides.

So it's not a regular polygon.

So hopefully you said something a bit like that.

And you have found examples in your environment such as bunting on a display that was in the shape of an equilateral triangle or sticky notes that were square shaped? What else did you find? Well done if you found a regular polygon with a large amount of sides, such as a regular hexagon, something a little bit more rare.

We've come to the end of the lesson.

Today's lesson has been knowing that a regular polygon has sides that are the same length and angles that are the same size.

Regular polygons are 2D shapes with equal side lengths and equal sized interior angles.

And we've got some examples there.

And irregular polygons are 2D shapes with unequal side lengths and or unequal sized interior angles.

So once again, regular polygons have got to have sides the same length and angles the same as each other.

I've had great fun today exploring regular polygons with you.

Hope you've enjoyed it too, hope you've learned lots.

Hopefully I'll get the chance to spend another math lesson with you in the near future.

But until then, enjoy the rest of your day.

Take care and goodbye.