Lesson video

Hello there.

My name's Mr. Tilstone.

I'm a teacher, and I'm delighted to be working with you today on your maths lesson, which is all about area.

You might have done quite a few lessons about area recently, and you might be getting to be quite the area expert.

So let's see how you get on today.

If you are ready, let's begin.

The outcome of today's lesson is, "I can calculate the area of shapes made from two rectangles by decomposing the shape in different ways." Our keywords today, we've got two.

My turn, "rectilinear." Your turn.

My turn, "compound." Your turn.

Have you heard of either of those words before, or maybe even both? So, a rectilinear shape is a 2D shape with straight sides and right angles.

So, essentially, it's made of rectangles.

And a compound shape is made up of two or more shapes.

Our lesson today is going to be split into two cycles.

The first will be splitting rectangles into smaller rectangles, and the second will be splitting rectilinear shapes into two rectangles.

So if you are ready, let's begin by splitting rectangles into smaller rectangles.

So we've got a generalisation here, which I'm going to say and then we'll say together, and then I want you to say on your own.

So, to find the area of a rectangle, multiply the length by the width.

Let's say that together.

Ready? "To find the area of a rectangle, multiply the length by the width." And now just you.

Ready? Go.

And that's a really important piece of information, probably the most important piece of information from this whole unit.

Now, this can be done using partitioning.

So in this case, that 14-meter dimension can be partitioned into 10 metres and 4 metres, turning the area into two different times tables facts.

Because in the minute, 7 times 14 is not a times tables fact.

However, if we split it like so, so now it's two rectangles, so two different areas, and instead of 14 metres, it's 10 metres and 4 metres.

So we can work out now the areas of the two different rectangles.

So, the one on the left, that's 7 metres by 10 metres, that's 70 metres squared.

And the one on the right, that's 7 metres by 4 metres, and the area of that is 28 metres squared.

Both of those were times tables fact.

So hopefully, were instant recall for you.

Now, we need to do something with those two areas.

What do you think we need to do? Add them together.

So 70 metres squared plus 28 metres squared, equals 98 metres squared.

And that's the area of the rectangle.

However, this is not the only way for this rectangle to be split into two parts.

There are many, many ways.

For example, we could split it like this.

What do you think we've done here? So instead of 14 metres, what will this be, do you think? They look about the same, don't they? 7 metres and 7 metres.

So what are the dimensions going to be now of the two rectangle? Well, here we've got 7 metres by 7 metres equals 49 metres squared.

And of course it's going to be the same with the other one.

So the area is 49 metres squared.

So 7 times 7 was a times tables fact.

And that's an instant recall fact, making that quicker to calculate.

Add them together, and we've got 98 metres squared once again.

Now, it could be split into two parts horizontally.

So before we split it vertically, we could do it horizontally too.

So we could partition at that 7 metres.

We could do it like this.

What do you think I've done here? So instead of 7 metres, it's going to be 5 metres and 2 metres.

Now, that gives us 5 metres times 14 metres, which is not an instant recall fact, it's not a times tables fact, but it's relatively straightforward to work out.

Maybe you could do 10 times 14 in the half of it, or 5 times 10 and 5 times 4 and put them together.

Not too difficult to work that one out.

So that's 70 metres squared for the area.

And then the other one, again, not a times tables fact, but quite straightforward to work out 'cause it's doubling, 2 metres by 14 metres, gives us an area of 28 metres squared.

And then what do we need to do with those two areas? We combine them.

70 metres squared plus 28 metres squared, equals 98 metres squared.

So that was a different way to partition that rectangle into two rectangles.

Let's do a check.

So you're going to sketch some other ways to split the rectangle into two rectangular parts, either horizontally or vertically.

So that's the examples we've done so far.

Can you think of any other ways? So by sketch, we don't mean be accurate, just be really kinda do a nice quick one, and don't worry too much about the exact kind of proportions when you partition it.

So just do a sketch please, but add the values to it.

Okay, pause the video.

Off you go.

Lots of answers for this.

Lots of possibilities.

You might have done something like this.

So, maybe you split that 7 into 3 and 4, so that would give you 3 times 14 and 4 times 14.

Maybe you split the 14 into 9 and 5, and that would give us two different times tables facts, 7 by 9, 7 by 5, combine them together.

Lots of different ways to do it.

Time for some practise.

Number one, partition each rectangle into two different rectangles using a horizontal line.

It's a horizontal line.

Write the areas of each rectangle and the area of the whole rectangle.

And number two, repeat that using a vertical line.

So, a vertical line.

Pause the vide.

Best of luck.

Welcome back.

How did you get on with that? For number one, there are lots and lots of possibilities, and here's just a couple of them.

So, for A, you might have done 7 times 14 and 2 times 14, so that's 98 plus 28, which is 126 metres squared.

And then for B, you might have split it so that it's 5 by 14 and 4 by 14, and it gives you 70 metres squared plus 56 metres squared, and altogether, that's 126 metres squared.

But again, there might be other ways to do it, as long as it's a horizontal split for the first one.

And for number two, this time using a vertical line.

Again, many possibilities.

You might have done a 9 by 10 and a 9 by 4.

That's 90 and 36, that's 126 metres squared.

Or you might have done 9 by 7 and 9 by 7, which is 63 and 63, that's 126 metres squared.

I quite like that one.

That took away one of the steps.

Let's do cycle two.

That's splitting rectilinear shapes into two rectangles.

So we're going to look at compound rectilinear shapes.

So what would happen if one of the rectangles from that previous question changed position? So you might recognise this.

What would happen if we took one of the rectangles and changed its position? So we've rotated it.

They'd still join together, but it's no longer a rectangle.

It's rectilinear.

It's a compound rectilinear shape.

So rectilinear shape's been formed, it's not a rectangle, but the area of the shape is still the same.

We haven't added anything to it, we haven't taken anything away from it.

We've just repositioned part of the shape.

We've rotated it, specifically.

So the area is still exactly the same.

It's still 126 metres squared.

There's a different way we could do that as well.

How about we keep the 36 metres squared in the same position, but we've rotate the 90 metres squared.

So, again, a different rectilinear shape's been formed, but the area hasn't changed, it's still 126 metres squared.

As well as being rectilinear, these shapes are also compound shapes.

A shape made up of two or more shapes.

So they're compound rectilinear shapes.

We've got a generalisation here.

I'll say it, we'll say it, and you say it.

The area of a compound shape made of two rectangles can be calculated by adding the area of each rectangle.

It's a bit of a mouthful, isn't it? But it's an important piece of information.

Let's say it again.

Ready? Let's go.

"The area of a compound shape made of two rectangles can be calculated by adding the area of each rectangle." Now, just you say it.

Ready? Go.

Fantastic.

So let's have a look.

What's the area of this compound shape? And we'll use that generalisation.

Work out the area of each of those rectangles and add them together.

We've got enough information there.

Got the length and the width of both rectangles.

Doesn't matter which one you calculate first.

We can do the small one first.

We can do the big one first.

It doesn't matter.

It'll give us the same total in the end.

So multiply the length and width of one of the rectangles.

We could start with the small one.

4 times 2, that's pretty straightforward, isn't it? It's 8 metres squared.

And then multiply the length and width of the other rectangle.

These are all times tables facts, 7 by 7.

7 times 7 is 49 metres squared.

Now, what do we need to do? Can you remember? We're not quite there yet.

We're almost there.

We've done most of the hard work.

One last step, which is to add the two areas together.

So 49 plus 8, and that gives us 57 metres squared.

And that is the area of the compound shape.

Let's do a check.

What's the area of this compound shape? So the values have changed slightly.

See if you can work this one out, okay? Pause the video.

Off you go.

Okay, did you do it? Did you manage to compare answers, swap answers with the person next to you? Did you come up with an agreement? Let's have a look.

Well, if we multiply 2 times 3, it's 6.

So 6 metres square for the small rectangle.

And if we multiply 7 times 8 is 56, 56 metres square for the big one.

Add the two together and we've got 62 metres squared.

And if you've got that, you are on tracking today's lesson and you are doing really well.

So well done.

Okay, let's do some independent practise.

So calculate the area of this compound rectilinear shape.

There's enough information there.

Think about what you need to do.

We've got the length and width of one rectangle, the length and width through the other, and then add them together.

And for number two, calculate the area of this compound rectilinear shape.

And what do you notice? And number three, the front playground at Oak Academy has an area of 80 metres squared.

It's a compound rectilinear shape which can be split into two rectangles.

Draw some possible shapes that the playground could be.

Lots of possibilities there.

Time to get a bit creative there, I think.

Okay, pause the video and I'll see you soon.

Welcome back.

How did you get on? Let's check.

Let's give you some answers.

So this is compound rectilinear shape.

So you can see it's made up two rectangles, and the length and width of each one is given.

So 3 times 8 is 24, 7 times 6 is 42.

Add those two together, and you've got 66 centimetres squared.

Number two, calculate the area of this compound shape.

What do you notice? So we've got 3 times 2, 6, 6 times 10 is 60, and then 60 plus 6 is 66 centimetres squared.

So the area of that compound shape is 66 centimetres squared.

And you might have noticed the shape can be split into rectangles in different ways, but the area is still the same.

Number three, the front playground Oak Academy has an area of 18 metres squared.

Now, there's so many different ways that we could have a compound rectilinear shape with an area of 80 metres squared, but draw some possible shapes that the playground could be.

So this is just one of many, many possible examples.

So it's gonna be two rectangles, and maybe one of them is 4 by 5, 4 metres by 5.

So that would give the area of 20 metres squared for that part of the playground.

So if that's 20 metres squared and the whole area is 80 metres squared, we need to look at the difference between 20 and 80, which is 60.

And then I'm thinking what would be the dimensions or possible dimensions of a rectangle with an area of 60 metres squared, or 5 times 12 equals 60, or the possibilities too, it could be 10 by 6, anything like that.

And that's 60 metres square.

So that's one possibility.

Hopefully you've got the opportunity to compare answers with your classmates.

And we've come to the end of the lesson.

Today's lesson has been calculating the area of shapes made from two rectangles by decomposing.

So taking apart the shape in different ways.

So a rectilinear shape, and by that it could be rectangles, they're rectilinear, or compound rectilinear shapes, they're made up of two or more rectangles, can be split into rectangles in different ways.

So you can split a rectangle into rectangles, and you can split a compound rectilinear shape into rectangles.

The area will be the same however it is partitioned.

Calculate the area of each rectangle by multiplying the length by the width, and then recombine the two areas to find the total area of the compound rectilinear shape.

I've had great fun working with you on today's lesson.

Hopefully you've enjoyed it.

Hopefully you've learned lots.

Have a great day.

Take care and I'll see you soon.

Buh-bye.