Lesson video

Hello there, my name is Mr. Tilstone.

I'm a teacher and it's a great pleasure to be here with you today, because I get to talk about my favourite thing, which is maths.

Today, we're going to be learning about perimeter.

If you're ready, I'm ready.

Let's begin.

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

You might have had some recent experience with counting to determine the perimeter and you might have had some more recent experience of adding to find the perimeter.

Well, we're gonna be doing some more adding, but this time multiplying as well.

Our keywords, my turn, perimeter, your turn.

My turn, double, your turn.

Let's have a reminder of those words.

You might know what they mean already, but it's worth a check.

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

That's a rectangle and that's its perimeter.

And to double is to have two of something, and I'm sure that's something you've done a lot of in the past and it's something that we're going to be doing a lot of today.

Our lesson is split into two parts, two cycles.

The first will be add then double and the second double then add.

So if you're ready, let's start by adding and then doubling.

In this lesson, you're going to meet Aisha, Laura and Lucas.

You might have met them before.

They're here today to give us a helping hand with our maths.

Lucas has learned to add the sides of a 2D shape to give its perimeter.

Maybe that's something you learned recently as well.

Here look, we've got a two and a three and a two and a three.

If we add them together, it will give us the perimeter, but Lucas says, "I think there could be an even quicker way of doing this.

I can see two groups of two plus three." Can you see that? Can you see one group of two plus three then a different group of two plus three? Let's have a look.

That's one two plus three, so those two sides there, a long side and a short side and then a long side and a short side again to make a different group of two plus three.

So two plus three appears twice or five appears twice.

So he says, "Rather than adding, couldn't I just use doubling?" Could we not just double the five? I think he might be onto something here.

So using doubling, so adding first and then doubling.

And when we do that, we could see the shape as a perimeter of 10 units.

So we didn't just add this time, we added first and then doubled.

Let's have a quick check for understanding.

So we've got what does the three represent here? So can you see a three, what's the three? Can you see a two, what does the two represent? What does the five represent and why is the perimeter five times two? Can you explain all of that? So the perimeter has been given, why is it five times two? Pause the video and have a think about that.

What do you think? Well the three represents the long side.

The two represents the short side and the five represents the sum of the long side and the short side, so those two added together.

So why is the perimeter five times two then? Because there are two groups of long sides and short sides and that's why the perimeter is 10 units and that's how we can get there by adding first and then doubling second.

Let's do another quick check.

Can you give the perimeter of this shape by adding the short side and the long side and then doubling? So can you use the add then double strategy? Pause the video and give that a go.

Don't forget to use the stem sentence.

Well, let's think, so what are we adding here? Four plus two make six and then we're going to double.

Six times two or double six gives us 12.

This shape has a perimeter of 12 units.

That was very quick and very efficient, much quicker and more efficient than adding up all the sides separately.

Because a rectangle has pairs of equal length sides, it is not necessary to be given all four side lengths, and you might have explored that quite recently.

Knowing the lengths of the long and short side is enough, because the long side comes up twice in a rectangle and the short side comes up twice as well.

So let's have a look.

Eight and four make 12 and that might be a known fact for you, hopefully it is.

And then we're doubling 12, that comes up twice.

Double 12.

Well, 12 times two is a times tables fact, so hopefully you know that off by heart.

That's 24, this shape has a perimeter of 24 units.

And the sentence can be shortened using P for perimeter.

We don't need to write the word.

We can save some time there as well.

P equals 24 units.

That same method of adding then doubling can be used even when the perimeter cannot be derived from times tables facts.

So here we've got a long side of 18 units and a short side of nine units.

What are we going to do with those? Add them together and then double them.

So that gives us double 27 or 27 times two.

Now, that's not the times tables fact.

Now, partitioning two digit numbers can make doubling even more efficient.

So instead of 27, what else could we have? How could we split that number? We can make the 27 into 20 and seven and then double each part.

That seems a bit easier, doesn't it? So double the tens.

Double 20 is 40 and then double the ones.

Double seven's 14.

What do you think we do now with those two numbers? Recombine.

You might call this a double diamond, and that gives us 54.

So it took a little bit more work, but we could still use the adding and doubling strategy there.

The perimeter equals 54 units.

Let's have a check.

Calculate the perimeter of this rectangle by adding the short side to the long side and then doubling.

And I'll warn you, it's not a times tables fact, you might need to do some written work to get there.

Maybe one of those doubles diamonds.

Pause the video and give that a go.

Let's have a look.

So we've got 28.

When you add those two together, that's 28.

That's the easier part of this calculation, adding the two side lengths together, doubling it is a little bit trickier in this case.

It's not a times tables fact, it's not a double you really would know off by heart, I don't think.

So 28, we need to partition it just like before into 20 and eight.

Double 20 is 40.

Double eight is 16.

Recombine them and we've got 56.

The perimeter equals 56 units.

Very well done if you got that.

It is time to put all of that into practise.

So using this strategy of adding then doubling, work out the perimeter of these number blocks.

Now, if you've got some real number blocks in front of you, you could use those as well.

That would be nice and helpful.

So perimeter equals how many units.

Use that same strategy of adding then doubling to work out the perimeter of these shapes.

The side lengths are given this time.

Can you add the side lengths and double? And we've got some more here.

And number three, the dimensions of this rectangle of grass around the tennis court are given.

What's the perimeter of the grass? That's A.

You've got enough information there, you're going to have to do a little bit of calculating, but you'll get there, and B, the long side of the tennis court itself is 21 metres and the short side is 13 metres, what's the perimeter of the tennis court? Hmm.

Give that a go, good luck.

If you've got somebody to work with, it's always good to work together in maths.

Pause the video and I will see you soon with some answers and some feedback.

Welcome back, how did you get on? How did you find that? Let's have a look.

So number one, using adding and doubling, that's a strategy for all of this cycle.

Here we've got two plus one is three and then double three is six.

A nice easy one to start with hopefully.

The perimeter equals six units.

And for this one, the side lengths, the long side's five, the short side's two.

Five and two makes seven.

Double seven is 14.

And hopefully that was a known fact, not too much thinking to do there or calculating.

Perimeter equals 14 units.

And then what about this one? So this time we've got short side four, long side five, together they make nine, nine units or nine centimetres in this case and then double that makes 18.

That's got a perimeter of 18 centimetres and the next one, long side seven units, short side five units, combine those, that's hopefully a known fact that's 12 units and double it.

You've got 24 units.

Well done if you got that.

For C, the numbers are a bit bigger now, but 17 and 30, there's a relationship between seven and three and 17 and 30 and I wonder if you used that.

70 plus 30 equals 100, so that's those sides combining and then double it, it is 200.

So that's got a perimeter of 200 metres and of course, that's not to scale, that's a big perimeter.

And for the next one, add those two sides together, they are 35 plus 21 equals 56, but then doubling that's quite tricky, you might have needed a written method.

Double 56 is 112.

So that's got a perimeter of 112 centimetres.

Well done if you got that.

Number three, the dimensions of the rectangle of grass around this tennis court are given.

Can you see 25 metres and 16 metres? So first of all, what's the perimeter of the grass? Well, if we add 25 and 16, it gives us 41 and then double that, double 41, hopefully fairly straightforward for you, that was 82.

So that's 82 metres is the answer to the first one.

What about the second one? The long side of the tennis court itself is 21 metres, the short side is 13.

So what can we do with that? Same thing again, adding then doubling.

So add them together.

21 plus 13 equals 34 and then double 34 is 68, so that's got a perimeter of 68 metres.

You are doing really well, really, really well.

I think you're ready for the next cycle.

Now, we're going to reverse it this time.

We're going to do doubling first and then adding.

So Laura says, "I can think of a different way to use doubling.

Double the long side." Ah-ha.

So double three is six.

Then double the short side.

Double two is four.

And add the totals together.

Six and four.

So this time we started with doubling.

We double the long side, we double the short side and then we added them together.

Hmm, that's different and it achieves the same result.

Six plus four equals 10.

So that's got a perimeter of 10 units.

Let's have a check.

So what does the three represent this time? What does the two represent? How many long sides are there? How many short sides are there? And why is the perimeter six plus four? So a little bit to discuss there.

Pause the video.

Let's see.

The three is the long side.

The two is the short side.

How many long sides are there, it's a rectangle.

So there's two.

How many short sides are there? Again, it's a rectangle, two.

So why is the perimeter six plus four? Where do those numbers come from? It's the total of the long sides plus the total of the short sides.

We've doubled the long sides, doubled the short sides and combine them, added them together.

That's 10 units.

Well, let's have another check.

Can you give the perimeter of this shape by doubling the long side, doubling the short side and adding the totals together? Pause the video and off you go.

Let's have a look at that.

We're doubling the long side first.

Double four is eight.

Then we double the short side.

Double two is four.

Eight plus four is 12.

That's got the perimeter of 12 units and there you double first, added second.

Laura says, "I know lots of doubles off by heart." That's great, so do I, do you? Are you good at knowing your doubles off by heart? Here we go, so we've got double eight, which is 16 and then double four, which is eight.

Add them together.

24.

The perimeter is 24 units, so you can do that relatively quickly and relatively easy if you know your doubles off by heart, which Laura does.

The same method can be used even when the perimeter cannot be derived from times tables facts.

So we could still use that method.

It just might not be off by heart this time.

"I know double nine off by heart," says Laura, so she knows one of them.

That's 18.

But I don't know double 17 off by heart.

No, that's a bit less common, isn't it? It's not in the times table, so I'm not surprised she doesn't know that.

Well, she could work it out.

Partition it into 10 and seven.

Double the tens.

Double the ones.

Recombine.

Double 17 is 34, so a few quick jottings and she got there, a little bit of partitioning and she got there.

So that gives us 34, which is the long side doubled and 18, which is the short side doubled.

Now we need to combine them.

34 plus 18 is 52.

The perimeter of that shape is 52 units.

That took a little bit more work and a little bit more time but we got there.

Let's have a check.

Calculate the perimeter of this rectangle by doubling each side and then adding the totals.

And again, you might need to use a few jottings here.

Pause the video and give that a go.

Well, I can spot a double that I do know off by heart there and that's double six and then a double that I don't know off by heart that I'm going to have to work out.

If you do know it off by heart though, that's great.

So we're going to double six.

That's 12.

And then double 19, we might need to use our partitioning and our double diamonds.

We can partition that into 10 and nine.

Double the tens, double the ones.

That gives us 20 and 18.

Recombine.

That gives us 38.

So double 19 is 38.

What do we do now with those two numbers, 38 and 12? Add them together.

The perimeter equals 50 units.

Well done if you got that.

It's time for some practise.

Number one, a rectangle has a long side of eight metres and a short side of seven metres.

Who's correct here? And explain what mistakes the other children have made.

Number two, what is the perimeter of the football pitch? Use that double then add strategy.

So we know the long side is 25 metres.

We know the short side is 10 metres.

Can you do some doubling and then add? Number three, what's the perimeter of this rectangle? Use doubling and then adding.

The numbers look a little bigger here, but think about what they remind you of and if they've got relationship with other simpler numbers.

Right then, I think you are ready to give that a go and I think you're going to do really well on it.

So good luck and I will see you soon for some feedback.

Welcome back, it's time for some feedback.

So number one, a rectangle has a long side of eight metres and a short side of seven metres, who is correct? So eight plus seven equals 15, the perimeter is 15 metres.

What did you think, was that correct? No, Laura has forgotten to double the sides before adding.

Double eight is 16.

16 plus seven equals 23.

The perimeter is 23 metres.

Is that correct? No, Lucas has only doubled one of the sides, not the other.

And then we've got double eight is 16, double seven is 14, 16 plus 14 equals 30.

The perimeter is 30 metres, is that correct, do you think? Yes, Aisha's correct.

That is how to work out the perimeter.

And then the football pitch using that doubling then adding strategy.

Double 25, that's the long side, is 50.

Double 10, that's the short side, that's 20.

50 and 20, hopefully that's quite straightforward for you to do, that is 70 metres.

That's the perimeter of the football pitch.

And then the perimeter of this rectangle and the numbers were a bit bigger, but I thought of seven and four as a starting point.

If I know double seven, I know double 70.

So double 70 is 140.

Double 40 is 80.

Add those two numbers together, those two doubles, and you've got 220 millimetres.

Well done if you've got that.

We have come to the end of the lesson.

Today's lesson has been knowing that the perimeter of a rectangle can be calculated by addition and multiplication.

Whilst addition alone can be used to calculate the perimeter of a rectangle, and maybe that's something you've done recently, it's not usually the most efficient way to do so.

There are quicker ways, better ways.

Multiplication and specifically doubling alongside the addition is usually more efficient when we're thinking about rectangles.

This can be done in one of two ways, and you've explored both of these.

You could add the long side to the short side and double.

So for example, eight plus four in this case, is 12, double twelve is 24.

Or you could double the long side, double the short side and add those totals.

So in this case, we've got 16 plus eight.

Hopefully you agree it's much more efficient to do it this way than just by adding.

Very well done on your accomplishments and your achievements today.

I think a little pat on the back is in order.

I hope I see you again soon for another maths lesson, but until then, enjoy the rest of your day.

Take care and goodbye.