Lesson video

Hello there, my name is Mr. Tilstone.

I'm a teacher and I really, really love maths, so I'm ever so excited to be with you today, teaching you a lesson all about perimeter.

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

The outcome of today's lesson is, I know that perimeter can be calculated by adding together the side lengths of a 2D shape.

You might have had some recent experience of counting to determine the perimeter of a shape, now we're going to use adding.

We just got one keyword, my turn, perimeter, your turn.

Can you explain what that means, do you think? If you can't, here's a little reminder.

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

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

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

The first will be using adding to find the perimeter of polygons, and the second, still using adding, but finding the perimeter when information is missing.

Let's start by using adding to find the perimeter of polygons.

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.

What's the perimeter of this shape? Hmm, what do you think? Well, we can go one, two, three, four.

We can count, but four what? It's not to scale, so it could be the shape has a perimeter of four millimetres.

Even bigger, the shape has a perimeter of four centimetres.

Even bigger, the shape has a perimeter of four metres.

And even bigger still, the shape has a perimeter of four kilometres.

And there are many other units of length, for example, miles.

Because the unit's unknown, it's best just to say, the shape has a perimeter of four units.

So that general term, units.

So that was counting.

Let's have a look at this one.

The shape has a perimeter of mm units.

You could count to determine that, but there's something we could do that's even quicker.

Let's start with counting though.

One, two, three, four, five, six.

The shape has a perimeter of six units.

Is there a quicker way though to work out the perimeter of this block without counting in ones? Hmm is this something that we could do with adding, for example? Lucas says, "Well, I know the side lengths." Two, one, two, one.

Couldn't I just add them together? Yeah.

Two plus one plus two plus one equals six.

So we can say, say it with me, the shape has a perimeter of six units, but we didn't count, we added.

And Lucas says, and he's right, "That was definitely quicker and more efficient than counting." And that's what good mathematicians do, they find the most efficient ways to do things.

Lucas tries the adding strategy to find the perimeter of this number block.

And if you've got some number blocks, you might want to explore this too.

So we've got that same stem sentence, the shape as a perimeter of mm units.

Different side lengths time though, the side lengths are given.

So we've got two and three and two and three.

What could we do? We could add them.

So two plus three equals five, and then five plus two equals seven.

The shape has a perimeter of seven units.

Hmm, I'm not sure about that, what do you think? Is he right? Hmm.

If he's not right, can you see where he's gone wrong? No, he's not added up all of the sides yet.

He did two add three add two, but he forgot to add that final three.

She hasn't remembered all of the sides.

It hasn't got a perimeter of seven units, that's not true.

Laura tries the adding strategy to find the perimeter of that number block, let's see how she gets on.

She says two plus three equals five, just like before.

Five plus two equals seven, just like before.

Seven plus three equals 10, that's what Lucas forgot.

And 10 plus two equals 12.

She says the shape has a perimeter of 12 units.

Hmm, is Laura right? What do you think? If she's not right, what's happened? She's added one of the sides twice.

Ah, okay.

So just like you can count more than once and be mistaken, you can add one of the sides more than once and be mistaken.

So it hasn't got a perimeter of 12 units.

Have you got a tip for them, I wonder? Hmm, what could they have done to avoid this happening? Well, they could circle the numbers as they add them.

So the numbers are written down, so they could do this.

Two plus three equals five, five plus two equals seven, seven plus three equals 10.

That way, they're all circled.

We know we've used them all, and we know we've not used any of them twice.

The shape has a perimeter of 10 units.

Is she right this time? Yes.

Well done, Laura.

Or they could put a little mark on the vertex of their starting line and we've chosen this vertex, but it could have been any of the vertices.

This time, the side lengths have been written on counters.

And you might have some counters in your class and some whiteboard pens, and your teacher might let you write on them.

You'll have to check, you'll have to ask.

So this time, they've been written on counters, two, three, two, three.

And we know the perimeter, it's got a perimeter of 10 units, that's fine.

Lucas and Laura both decided to start with what you can see there is the top counter when adding the numbers, and they worked clockwise, so they did this.

Two plus three plus two plus three, that's how they added.

However, you could start with any side, as long as all of the sides are added.

So how else could we have done that, instead of starting with that one? Is there a different one we could have started with? What about that one, starting with a three? Three plus two plus three plus two, we still used them all.

We still haven't used any of them more than once, we've done it correctly.

You could even add the long sides first and the short sides second, hmm.

So instead of going round clockwise, you can do this.

Three add three, and two add two.

If you wanted to, you could even do the short sides first, longer sides second, it doesn't matter, you'll still add all of them.

When finding the perimeter of a 2D shape, the sides can be added in any order.

This is an important fact.

Let's say that together, are you ready? We're gonna read that together, let's go.

When finding the perimeter of a 2D shape, the sides can be added in any order.

So remember that, because there are more efficient ways to add some of these perimeters together.

Lucas says, "I like this order more." He likes three plus two plus three plus two.

I wonder why he likes that more.

Hmm, what do you think? He says, "I find it easy to add fives." Yes, I could see that, a couple of fives there.

"I knew that three plus two equals five, so all I did was five plus five." Oh, that was efficient, Lucas.

Yeah, he saved a step or two there, didn't he? Well done.

Laura likes this method more, I wonder why, hmm? "Because I'm good at doubling by adding twice." Ah, yes, I can see the doubles there.

So she knew double three, she knew double two, and she added them together, and that gave her six plus four.

Let's do a check.

Can you give the perimeter of this shape in more than one way using adding? Explore using a real number shape if you have one.

If you haven't, you can use the image on the screen, but can you use please that stem sentence? The shape has a perimeter of mm units.

Pause the video and have a go.

Let's see, how many different ways did you do this? You might have had some real counters to explore it with as well, so that you can move them about.

Well, here are the side lengths, two, four, two, four.

Could have gone like this.

Two plus four plus two plus four, that's one way to do it.

So clockwise starting from the top, that's one way.

Or anticlockwise, starting from the top as well.

Or maybe you started with the longer side.

So four plus two plus four plus two, went around clockwise or anticlockwise.

Is there another way? Yeah, there's a couple more ways.

This is one of them, just maybe start with a long side first, four plus four plus two plus two.

Well done if you've got any of those, and especially well done if you've got all of those.

Whatever way we do it, the shape has a perimeter of 12 units.

Which order did you prefer? Okay, let's have a look at another shape.

What's the same and what's different about these shapes? Have a good look at them, have a good think.

See what you can notice.

That's what good mathematicians do, they notice things.

What's the same and what's different? Well, they are the same rectangle with the same side lengths given, so they've got the same perimeter, but what's different? You cannot see the squares inside the second shape, but we don't need to, we know the side lengths.

Still got a perimeter of 12 units.

So as long as we know the side lengths, we can still add them, even if we can't see these squares inside.

Pairing counters and using known number facts can make finding the perimeter more efficient.

Hopefully you're quite good at adding two one digit numbers together and you can do it automatically.

You don't need to do any calculation, you don't need fingers, you don't need bridging or anything like that, you just know them off by heart.

If so, that's really useful.

So let's have a look at this one.

We've got that same stem sentence, the shape has a perimeter of mm units.

I wonder how we can pair them to be more efficient.

Well, eight add four.

That is a known pair of numbers for me.

Hopefully it is for you, and I know what they total when they're added together.

They're 12, I just knew that off by heart.

And so, that eight plus four, that's a number fact, that's 12 as well.

So this time, all we're doing then is 12 plus 12.

The shape has a perimeter of 24 units.

Can you see how we cut out a few steps there? We made it even quicker and even more efficient by using our number facts, our known number facts that we've got off by heart.

Let's do another one, let's pair those counters in a different way so that they're doubles.

So we've got eight add eight and hopefully, again, that's a known fact for you.

A known double, that's 16, and four add four.

Again, hopefully that's a known fact, that's eight.

So again, all we're doing now is adding those two together.

That's 16 plus eight, pretty efficient.

And again, the shape has a perimeter of 24 units however we do it.

That was quicker though, don't you think? I liked that.

I liked using those known number facts.

Now, the letter P can be used to represent perimeter.

So we don't need to keep writing the word perimeter, we can say P and we can write P.

So we can say P equals 24 units.

The perimeter of other shapes can be found using adding when the side lengths are given.

So this time, it's not a rectangle, it's a triangle, but we can still use that same method of adding these side lengths together.

So we've got a six, a seven, and a four.

The side lengths can be added in any order, but what do you notice? Is this something that jumps out at you about those numbers? Hmm, something that might make it a bit easier.

There's a number bond to 10, did you spot that? Well done if you did, making the calculation even easier.

So we've got six and four make 10, a number bond, a known fact.

So all we're doing is 10 plus seven.

And 10 plus seven equals 17.

So that's 17 units.

P, or perimeter, equals 17 units.

So if you can spot a number bond to 10 with your side lengths, I would start with them.

Let's have a quick check for understanding.

Use addition to find the perimeter of this pentagon.

So we've not explored pentagon's before, but you know what to do with those side lengths.

And take a little time before you start, do you notice anything about the numbers? All right, pause the video and have a go.

Did you spot it? Did you spot the number bond? The sides can be added in any order, but you may have spotted the number bond to 10 and started with that, that's my top tip.

That was it, seven and three make 10.

So starting with tens, even easier and even quicker.

So we've got 10.

Now, I've got a little tip for you here.

We've got to turn the counts over when we've used 'em so that we don't use them more than once.

You might have two coloured counters, and we can turn them over like that.

So now, I'm definitely not going to use those again.

And then we can go in any order at all.

But we could add five, that's the next biggest, you could do it that way, that makes 15.

Turn it over, add two if you like.

That would make 17, turn it over.

Then all we've got to do now is add that four, and that gives us 21.

Turn it over because we've used it.

So the perimeter is 21 units.

So there were so many different ways we could have added those counters together.

But that one was pretty efficient, I think starting with that number bond.

It's time for some practise.

Number one, can you work out the perimeter of this rectangle in four different ways? Number two, work out the perimeter of these shapes, and think about how to calculate efficiently.

What could you do? Can you see any number bonds, for example, or any known number facts, anything like that that would make it even easier and even quicker? I would recommend taking a little bit of time before you dive in, look before you leap.

Good luck with that, pause the video, and I will see you soon for some feedback.

Welcome back.

How did you get on with adding? Did you find some efficient ways to do it? Number one then, here's four ways to do it.

You could do four plus five plus four plus five, sort of clockwise starting from the top.

You could do five plus four plus five plus four, so starting from a different side.

You can maybe start with the longer sides, the two longer sides, five plus five plus four plus four.

You might have even had four plus four plus five plus five, that's a different way to do it.

All of them will give you the same answer and that is, perimeter equals 18 centimetres.

When you add those together, it gives you 18 centimetres.

Number two, work out the perimeter of these shapes.

You may wish to explore that with counters, you may have done that.

So what do you think? Let's have a look at the first one.

That's 14 units.

Now, I don't how you did it, but I did the doubles first.

So I did double four, that's eight, double three, that's six, eight and six make 14.

That was my method.

And for B, what did you do? I looked at the number bond.

I saw six and four make 10, and added the six on.

You might have started with your double though, that would've worked too, and then added the four on.

But either way, 16 units.

And then what about C? What could we do there? Well, I like counting in fives and adding fives together.

So I could see that three and two made five, so I had five and five and then one.

And that gave me 11 units.

Again, you might have had a different way, and that's absolutely fine.

That was efficient for me.

You're doing well, you're doing really well.

Let's move onto the second cycle, that's finding the perimeter when information is missing.

We are still going to be adding.

What information is needed to find out the perimeter of this tablet.

Hmm, what do you think? What kind of things do we need to know? The side lengths, we need to know the side lengths.

So there's a side length.

Have we got enough information now to work out the perimeter of that tablet? No, we know the long side, we don't know the short side, so it's not enough yet.

We need to know more than one side length in this case.

Okay, well if that's seven, then the other one's seven as well because they're the same.

Is that enough information, do you think? No, we still don't the short side length, do we? You need to know different side lengths.

What about now, we've got the long side and the short side.

Have we got enough information? I can't see all four of the sides, have we got enough information though to work out the perimeter? What do you think? Yeah, we have.

Because it's a rectangle, the opposite sides are the same.

So we know that one side's seven, the long side's seven.

And the long side comes up twice, so the other one's seven too.

And we know the short side is five units, so that makes the other short side five units because it's a rectangle.

So we didn't need to see those counters, we knew what they were, we could figure it out very easily.

Just like before, there is more than one way to find the perimeter, what would you do? How would you find the perimeter, now you know the information that you need? Hmm, well, what about doubles? You could double the seven, that's 14.

Double the five, that's 10.

Known facts these are, and then add them together.

So there we go, look.

Double seven, double five, add.

That's 14 plus 10, and that's 24 units.

Perimeter equals 24 units.

Is there another way? You could add seven and five twice.

So seven and five, that's a known fact for me, that's 12.

Hopefully it was for you as well.

So we're just doing 12 plus 12.

There you go, and then we can't see it, but we know it's there, we know that's also seven and five.

Just add them together, that's 24.

So the perimeter equals 24 units however we do it.

There is a square-shaped pond at Oak Academy.

I'll say that word again, a square-shaped pond.

Think about what you know about squares.

The arrow and that counter tell you that one side has a length of five metres.

Hmm, is there enough information to work out the perimeter of that pond? Remember, it's a square.

What do you think? We can only see one side this time.

One side wasn't enough before, was it? Is it enough this time? Yes it is, it's a square.

So all of the sides are the same length, they're all five metres.

There you go.

And then we can add them together, five plus five plus five plus five.

You might have done it as 10 plus 10 as well.

And either way, that gives us 20 metres, it's got a perimeter of 20 metres.

Let's have a check.

We've got a triangle, and it's a regular triangle, the side lengths are all equal.

What is its perimeter? Have you got enough information there, do you think? If you have, how can you use adding? Pause the video and give that a go.

Was there enough information? It was a regular triangle, all the sides are same length.

That means they're all seven.

So, yes, there was enough information.

What can we do with those numbers? We can add them.

You could do seven add seven is 14, and hopefully that's a known fact.

Hopefully you did that straight away off by heart.

And then add the other seven on, and that gives you 21.

So it's only really two steps.

So the perimeter was 21 centimetres.

If you got that, you are doing really well, and you are on target it.

It's time for some more practise.

Work out the perimeter of these shapes.

You may wish to explore it with counters if you've got them.

And if your teacher gives you permission to write on them, that will be good.

If not, you don't need to do that.

Either way, work out the perimeter.

Not all of the information is given, but hopefully you can work it out.

And number two, work out the perimeter of this square.

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

You've got one piece of information, is that enough? Can you work out the perimeter from that? Number three, what's the perimeter of this regular pentagon? That's A, and then two of the pentagons have been combined, what's the new perimeter? Number four, complete the table, which is about rectangles.

So we've got the length of one of the sides, 10, 20, 30, 40, and 50 centimetres.

And could it have a perimeter of 80 centimetres each time? Just write Y or N, yes or no.

And then can you explain why? And then B, what's the longest whole number that one side length could be? Hmm, something to think about there, a bit trickier.

All right, pause the video, good luck with that, and I will see you soon for some feedback.

Welcome back, how did you get on? Do you want some answers? Let's have a look.

So the perimeter of these shapes, lots of ways you could have done it.

For example, five plus five plus six plus six.

So you could have used your doubles, and that gives you 22 centimetres.

Perimeter's 22 centimetres.

And for B, one way that you could have done this, I saw a number bond to 10, seven add three plus seven add three, so 10 plus 10, and that's 20 centimetres.

So even though some information is missing, we knew that information, we could see.

It's still a rectangle, so we don't need to know the missing side lengths, we know what they are.

And then 40 and 80 are bigger numbers, but I think I could use my knowledge of four plus eight, that's a known number fact.

We could use doubles, so if I know double eight is 16, I know double 80 is 160.

And then double four's eight, so double 40 is 80.

And when you add all of those together, it gives you 240 millimetres.

You might have done it differently, you might have done 80 plus 40 and then doubled it.

Lots of ways to do it.

And then work out the perimeter of this square.

Because it's a square, all the sides are the same length, and we know what this side length is, it's seven centimetres.

And, again, lots of ways you could do that using adding.

We could maybe use doubles.

Seven add seven is 14, so 14 add 14, lots of ways to do it, but the answer is perimeter equals 28 centimetres.

This regular pentagon, so a pentagon has got five sides, it's regular, each one's going to be three centimetres.

Add all of those threes together in whatever way you prefer, whatever way you found the most efficient, gives you 15 centimetres.

The pentagon has a perimeter of 15 centimetres.

And then two of those pentagons have been combined, what's the new perimeter? Well, for example, you may have added the perimeter of two of the pentagons and then subtracted the two sides inside that shape, that would've been efficient.

You would've done that really quickly and efficiently that way.

So that would be 15 plus 15, because we know that's a perimeter.

So 15 plus 15, which is 30, take away three take away three, or even take away six.

Whatever way you did it, that would give you a perimeter of 24 centimetres.

And then the table, so 10 centimetres, it could have a perimeter of 80 centimetres, yes.

10 plus 10 plus 30 plus 30, that could be the length of the sides on the rectangle.

Could it be 20 centimetres for one of the side lengths? Yes, it could.

20 plus 20 plus 20 plus 20 gives you 80.

That would be a square, it would've to be a square, and a square is a kind of rectangle.

Could it be 30? Yes, it could.

30 plus 30, which is 60, plus 10 plus 10 equals 80 centimetres.

So that's possible, the long side could be 30 centimetres.

Could it be 40 centimetres? No, it couldn't because 40 centimetres plus 40 centimetres is already 80 centimetres, even if they were the longest sides.

So no, it couldn't work.

And the same logic for 50 centimetres.

When you add those together, it's already more than 80 centimetres.

So no, that's not possible.

And the longest whole number that one side length could be, in this case, is 39 centimetres.

It will be a very long thin rectangle.

The sides will be 39 centimetres and 39 centimetres for the long sides.

And then one centimetre and one centimetre for the short sides, but it's possible.

We have come to the end of our lesson.

I've had really good fun today, and I hope you have too.

Today we've been looking at the fact that perimeter can be calculated by adding together the side lengths of a 2D shape.

So before, you were counting, today you were adding.

And would you agree, it's much more efficient to add? If all of the side lengths in a polygon are given, you can add them all up to work out the perimeter of the shape.

All of the sides must be added, but they can be added in any order.

So it's worth taking a little bit of time to think about that, and think about the most efficient way to do it, you could save time in the long run.

You can use things like known facts, including doubles, to make addition more efficient.

It is often still possible to work out the perimeter of a shape, even if one or more of the side lengths are missing if those side lengths are the same as other given sides.

So sometimes you need to do a little bit of thinking, but all the information is there.

Well done on your accomplishments and your achievements today, you have been amazing.

I think you deserve a little pat on the back.

I hope you have a great day whatever you've got in store.

Take care, see you soon I hope, and goodbye.