Lesson video

Hello everybody, my name is Mr. Kelsall.

and welcome to today's lesson about calculating the area and perimeter of rectangles.

Now, before we start, you will need a pen, piece of paper, and a ruler.

Also, please try and find a quiet place, somewhere you won't be disturbed, and don't forget to remove any sorts of distractions.

For example, put your mobile phone on silent or put it away completely.

Pause the video, and then when we're ready, let's begin.

Today's lesson is looking at comparing the area and the perimeter of rectangles.

We'll start by looking at the area and the perimeter and the difference between those two.

We'll then look at how to use a formula to calculate both.

After that we'll take our independent task.

And finally, our quiz.

I mentioned earlier, the pen, piece of paper, and a ruler.

Let's start with our task is: How many different ways can you find to make a rectilinear shape with a perimeter of 12 units? Just remind yourself, the perimeter is the distance around the outside of the shape.

Pause the video.

And then when you're ready, press play to continue.

You can approach this question logically.

If we start with a one unit line, I measure five units along, I'll have one, one, five, five.

So my perimeter for this shape is 12 units.

If I carry on working logically, and I do two down, think how many long I need to go? Well, the other side must be two units down.

So I've used up my 12 units.

I've used four of them.

So I've got eight units remaining.

And that means if I split it into two parts, I've got four parts.

So if I look at this, I've got two, four, two, four, add them together, gives me a perimeter of 12 units.

I'm then going to do three down.

So I've got three down on one side, three down on the other side, that's a total of six.

I've used six for my 12, which means I've got six remaining.

That means this side must be three by three.

And it's a square rather than a rectangle, but these are all the shapes that I can draw with a perimeter of 12 units.

Because if the carry on my next rectangle would be a four down and I know that's going to be two along.

now, this is the same shape, a shape number two.

So, I'm not going to draw that.

There are however different shapes.

And we can look at a different and irregular shape.

So if I go one, two, three, four, five, six, seven, eight, nine, 10, 11, 12, I could have a shape like this.

Have an X explore.

See if there's any other shapes that you can find, which have a perimeter of 12 units.

Again, pause the video.

And when you're ready, press plays, continue.

Then heading to our second question.

Why have I used the word units and not centimetres? Well, centimetre is measurement of one centimetre.

If you look at your ruler, you can say one centimetre.

However, we don't know how big these squares are.

A lot of the time people use centimetres as the default number, but actually if we're not told how big these are, then we don't want measurement to use.

There might be one centimetre, one millimetre, one metre, one kilometre, we don't know.

Sometimes the questions will tell you how big it is.

And if it tells you how big something is, you need to use those units.

Okay, On the screen we have a statement.

What do you think of the statement? The value of the perimeter of a shape will always be greater than the value of the area.

Let's just remind ourselves what we mean about area.

So when it comes to area, it's all to do with the space inside the shape.

And here I can see that area of this shape is eight centimetres squared.

I can count the inside, or I can measure two centimetres by four centimetres which is eight centimetres square.

So, pause the video, sketch some shapes, calculate the area, calculate the perimeter.

And then try to think of this statement is true all of the time, some of the time or never.

And then when you're ready, press play to continue.

So I sketched a few shapes on the screen and every single shape I sketched, I realised that the perimeter was greater than the area that wasn't until I came to one more shape and I realised this was a square.

I don't realise with the square, the perimeter was 20 centimetres and the area is 25 centimetres squared.

So I found an example where the area is bigger than the perimeter.

That means that the statement is not true.

The value of the perimeter of the shape will always be greater than the area.

Sometimes it will be true sometimes it's not true.

It brings us to our next statement, the area of a square, will always have a greater value than the perimeter.

Can you explore this statement? Can you work out whether it's true all of the time, sometimes or never.

Try drawing some squares of different sizes, calculate the area of the square and calculate the perimeter of the square.

Pause the video, and then when you're ready, press play to continue.

I did this myself and I started off drawing a five by five square and I calculated the perimeter by saying five add five add five add five.

And it works out at 20 centimetres.

And then the area I did five times five, which was 25 centimetres squared.

So I found an example where the area of the square is bigger than the perimeter of the square, great.

And then do the six by six square.

And the perimeter was 24 centimetres.

This time I found a quick way to do it instead of adding six add six add six add six, I knew that square had four equal sides.

So I just did six multiplied by four to give me a perimeter of 24 centimetres.

The area then did six multiply by six, which gave me an area of 36 centimetres squared.

Again had an area of 36 centimetres squared, which is bigger than the perimeter.

Great, so I think there's true.

This statement is true all of the time at the moment I carried onto the 10 by 10 square, the perimeter was 40 centimetres and the area was 100 centimetres squared, great.

I found a newer example where the statement is true and I thought it was a really big number and see if that made a difference.

So I drew, or I calculated a square with an area with a side of 24 centimetres.

So the perimeter was 96 centimetres four walls of 24.

And the area I have 176 centimetres squared.

I found four examples where the statement is true.

Did you find that any examples with where the statement was not true? Then thought I draw one more example.

So I did a square with sides three centimetres and the perimeter, the square was 3612 centimetres squared.

And the area was three by three, which is nine centimetres squared.

And then I realised that actually the area was less than the perimeter.

So I realised, I thought, although I found four examples where the statement was true, I kept searching and eventually I found an example where it was not true.

So, I've got examples where it's true and examples where it's not true.

That means the statement must be true some of the time we're going to bring some to generalise in a formula for area and for perimeter.

Now, if we've got a rectangle and we've got a length, a or length b, where a and b we don't know what size these are.

Can we find a general way of finding these rules? Well, I know that to find the perimeter, I did add a+a+b+b or I can write it as two lots of a and two lots of b.

I could do two lots of b first and then add two lots of a.

So I've got three ways of working out the perimeter for a rectangle.

Now, you might have your own way and you might find that one of these is quite easy and you might stick with that way.

Find the area of the shape, i multiply a by b.

So let me give you some examples here.

If a is two centimetres and b is five centimetres.

Using method one, so method one, I've got two and two and five and five.

The premise is 14 centimetres.

Using method two, two, lots of two is four, two lots of five is 10, add them together get 14 centimetres.

using method three to add five is seven, two lots of seven is 14 centimetres.

So all three of these methods for the perimeter will work with a rectangular shape.

The area will be the length multiplied by the width, eight times b.

And this will work for all rectangles.

That brings us on to the area and the perimeter of a shape of a square.

So I know that the perimeter of a square is d+d+d+d, or I could say it's for lots of d.

Again, both of these work.

This time, if your perimeter is, let's say six centimetres six add six add six add six is 24 centimetres.

Four lots of six is also 24 centimetres.

And finally the area previously we did eight times three, where a and b were different lengths.

This time we know where the square that actually, this the length is the same side.

So we just do d or a or b or whatever the length of the side is multiply by itself.

So it's d by d or we can write it to d squared.

You might have seen this little to symbol before.

This is the word, represents the word squared.

And it means d multiplied by itself.

That brings us to our independent task.

You have two tasks.

It's all to do with investigating the area and the perimeter of rectilinear shapes.

Question number one, how many different rectilinear shapes can you find with a perimeter of 12 centimetres? Question number two, how many rectilinear shapes can you find with an area of 12 centimetres squared? Pause the video, and then when you're ready, press play to continue.

Congratulations on completing your task.

If you'd like to, please ask your parent or carer to share you work on Twitter, tagging @OakNational and also #learnwithOak.

So that brings us to the end of today's lesson on calculating the area and perimeter of rectangles.

a really big for all the fantastic learning that you've achieved.

Now, before you finish, perhaps quickly review your notes and try to identify the most important parts of your learning from today, all that's left is for me to say thank you, take care and enjoy the rest of your learning for today.