Lesson video

Hello there.

I'm Mr. Tilston, I'm a teacher, and I really love maths, so you could imagine how excited I am to spend this maths lesson with you.

It's going to be a very fun maths lesson, very practical and very hands-on, all about perimeter.

If you are ready, I'm ready.

Let's begin.

The outcome of today's lesson is, I understand that different 2D shapes can have the same perimeter.

And you might have had some recent experience with perimeter, so think about everything you know so far.

Our keywords, we've got two.

My turn, polygon, your turn.

My turn, perimeter, your turn.

As I say, you might have had some recent experience with perimeter, you might remember what that word means, I'm going to give you a reminder.

What about polygon? Let's have a look.

A polygon is a 2D shape made up of three or more straight sides.

We've got some examples there, so they've got to be straight sides and closed.

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

So here we go, here's an example of perimeter.

You might have explored that recently by running your fingers around the outside of an object, maybe you used string.

Our lesson today is split into two cycles, the first will be shapes with the same perimeter and the second polygons with the same perimeter.

So if you're ready, let's explore shapes in general with the same perimeter.

In this lesson you go to meet Laura and Lucas.

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

Lucas is exploring the perimeter of this leaf by drawing round it's outline to create a 2D shape.

Have you done that recently? You might have done.

Here we go, so he's drawn round that same leaf, and then he's taken the leaf away and you can still see the outline.

Now he's recreated that perimeter with string, so he is gone around the outline that he's drawn with a piece of string.

And again, maybe you've done that recently.

He opens the string into a straight line.

Is it still showing the perimeter of the leaf? Yes, it is.

It still shows the perimeter of the leaf.

Lucas takes the string and forms a new leaf shape with it.

Can you see? He's turned into a different leaf shape.

And then a different one.

What could you say about those leaf shapes? What do you think? Have a look at all three of them.

What's the same about them and what's different? Well, they are different shapes, you can see that very clearly, but they have the same perimeter as each other.

If you open them out, they've all got the same length of string, they're all made from the same length of string, in fact.

This time Lucas uses string to investigate the perimeter of a circular object.

He's got a little record there, a man after my own heart.

He makes different shapes with the string.

So he is wrapped it around that circular object, that's showing the perimeter, and then he's opened it back out to create a different shape with the same perimeter.

And again.

So, all three of those shapes are different shapes, but what about the perimeter? The same, same perimeter.

Let's have a quick check for understanding.

How can you tell if two different 2D shapes have the same perimeter? Here's some choices.

Wrap string around their outline.

If they use exactly the same amount of string, they have the same perimeter.

Wrap string around their outline.

If they use a different amount of string, they have the same perimeter.

Or two different shapes cannot have the same perimeter.

What do you think? Have a think, discuss it if you can, and pause the video.

What did you think is this one? So if you wrap string around their outline and they use exactly the same amount of string, they have the same perimeter as each other.

It is time for some practise.

Number one, draw around the perimeter of a leaf to create a 2D shape, so hopefully you've got some leaves there, you might need to go on a hunt for some if not.

Go around the outline with string.

What other leaf shapes can you make with the same perimeter? So just like we've seen before.

If you don't have a leaf, go around this picture of a leaf on your worksheet with string and then make some different leaves from that string.

Number two, find the perimeter of the face of an object such as a paper plate using string.

And you might have used some objects quite recently to explore perimeter, you can use the same ones again, no problem.

How many other 2D shapes can you make that have the same perimeter? So use that same amount of strength.

So, be creative.

Pause the video.

Have fun with that, I think you will, and I'll see you soon for some feedback.

Welcome back.

Did you have fun there? Hopefully you had some leaves or different objects to explore and some string.

Let's have a look.

So let's have a look at this example.

This leaf here, or the one that was on your sheet, can be reshaped into another leaf using the same length of string.

So that's the perimeter of that leaf.

You could straighten that up and then reshape it into a different leaf shape, and they've got the same perimeter.

So they're clearly different shapes, but they have the same perimeter, the exact same.

And then number two, you might found the outline of say a triangular object and reshaped it into a quadrilateral using the same length of string.

And those two shapes, although different, have the same perimeter.

I think you're ready for cycle two.

That's polygons with the same perimeter.

So, so far we've just looked at shapes in general like leaf shapes, now we're going to look at polygons, so those shapes with straight sides.

This time, Lucas has found the perimeter of his whiteboard, which creates a rectangle, and that rectangle is a polygon.

There we go.

That's the perimeter of his whiteboard, might have done that by drawing around it or using string.

He uses the same string to make a different rectangle with the same perimeter.

What do you notice about those rectangles? Have a look, what do you think? He says, "I can see the width of my rectangle has increased." Did you notice that as well? Look at the width, it's increased on the second one.

"For the perimeter to be the same, the length must have decreased." Yeah, they can't both increase or the perimeter would be increasing altogether, wouldn't it? So, the width has increased and the length has decreased.

What about that one? What do you think? It's been made from the same string as the original one that went around the whiteboard, he's made a new rectangle.

The three rectangles have different dimensions, but all of them have the same perimeter.

All three of those are the same type of shape, rectangles.

They've all got the same perimeter even though they're different dimensions.

Laura creates an irregular polygon with number rods.

It's a rhombus.

Have you got some number rods in front of you? Because this is a great way to explore perimeter.

She turns her rods back into a straight line, you might have done something very similar recently.

The straight line shows the perimeter of the rhombus.

It can be turned into a different irregular polygon with different interior angles but the same perimeter.

So if we use those rods again to make a different shape and change the angles and things, the perimeter won't have changed, will it? But the shape will.

Let's have a look.

There we go, that's a different one this time, different quadrilateral.

It can be turned into a regular polygon with the same perimeter.

There we go.

So, we've seen three shapes so far made from the same rods, so they've got the same perimeter but different shapes.

Let's have a quick check.

Look at these shapes that have been made from number rods.

True or false? These polygons have the same perimeter? And don't just say true or false, see if you can explain why.

All right, pause the video.

It's true, one is an irregular pentagon and one is a trapezium, but the rods show that the perimeter is the same.

So, it's not that new rods were used or different length rods or anything like that, they're exactly the same rods.

You may wish to see if you can create a different shape with the same blocks that has the same perimeter.

Time for some more practise.

Number one, create a triangle with string.

How many other triangles can you create with the same perimeter? Hmm.

So, think about what you know about triangles.

Number two, use number rods or straws to create a polygon.

It can be regular or it can be irregular.

How many other polygons can you make with the same perimeter? So remember what we mean about polygons, straight sides.

And number three, you might have some number blocks in your classroom just like this, and great if you do, you can use the physical ones, and if you don't, you can use the picture on your worksheet.

The question is this, do any of these number shapes have the same perimeter as each other? You may wish to investigate this with actual number shapes if you have them.

So have a look at them.

They're all different shapes, would you agree? But is it possible for them to have the same perimeter? And if so, which ones do? How could you find out? Number four, combine those number shapes if you have them together to make a single shape.

Then combine different shapes to make a shape with the same perimeter.

And it doesn't have to be just two blocks, but it can be, it can be more than two, but you are combining them together to make a brand new shape.

The two shapes must have the same perimeter as each other.

How many different ways can you do that? And there are absolutely loads, so don't stop if you've got just one, keep going.

Good luck with that.

Have fun again, I think you will.

Pause the video.

Welcome back, let's have a look then.

So number one, create a triangle with string.

How many other triangles can you create with the same perimeter? There's all sorts of different triangles and they've all got different kinds of names.

So we've got the same side lengths and we've got different ones.

This is a regular one, all sides are the same length and all angles are the same size.

So that's a regular triangle, and a regular polygon as well.

You might have had some recent experience learning about those.

Then let's have a look at this one.

This is an irregular triangle, because the side lengths are not all the same and the angles are not all the same, it's irregular.

Some sides are the same length and some angles are the same size, but not all.

It's got the same perimeter though as the other triangle, it's made from the same amount of string.

And this is another irregular triangle, this time no sides are the same length and no angles are the same size.

It's different, you can see all three are different, but crucially, it's got the same perimeter.

So look at those three triangles, they're all different, but they've got the same perimeter, so that is possible.

And then you're using number rods or straws to create a polygon, could be regular or irregular.

How many other polygons can you make with the same perimeter? There were absolutely 100s of ways you could have approached this, here's just an example.

So, these are quadrilaterals with the same perimeter.

So, we've got one quadrilateral, do you know what it is? It's a rectangle.

And here is another one, it's a parallelogram.

They've got the same number rods in them, same length, same amount, all that kind of stuff.

They've got the same perimeter, but they are different shapes.

And another one, a different quadrilateral, again, they're using the same rods, same length rods, the same amount, so the perimeter is exactly the same.

It's a different shape, same perimeter.

And then for number three, you were investigating the number blocks and seeing if any of them had the same perimeter as each other.

Yes, they do, even though they're different shapes, here's an example.

Look at three and four.

Look at those two sides of the three block that point inwards, like so, you can make them point outwards, like so, and nothing has changed, it then forms the four block.

That's one example, there were others, did you find any others? And they're all next to each other, by the way.

Let's have a look.

These blocks have the same perimeter as each other.

Three and four do, six and seven do for that same reason that you can make these sides that point inwards go outwards and form a square, seven and eight do, and nine and 10 do.

So, well done if you've got those pairs.

And number four, you were combining those number blocks together to make a single shape and then do the same with a different shape, with the same perimeter.

There's lots and lots of ways you could have done that, and here is just one.

So if you were to wrap string around that first shape, the same amount of string could be used around the second shape, they've got the same perimeter.

We've come to the end of the lesson.

I've had so much fun today, I hope you have too.

I've really enjoyed exploring perimeter with string and number blocks and leaves, and things.

Today's lesson has been understanding that different shapes can have the same perimeter.

Do you think you get that now? Do you understand that? Great! Different two-dimensional shapes can have the same perimeter as each other.

The shapes may or may not be polygons and may or may not be regular polygons.

If the distance around them is the same, they have the same perimeter and you can explore that, for example, with string, to prove it.

You've been brilliant today.

Give yourself a little pat on the back, it's very well deserved.

Thank you for spending this maths lesson with me.

I hope I get the chance to spend another maths lesson with you in the future.

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

Take care, and goodbye.