Lesson video

Hello there, my name is Mr. Tilstone.

There are two things I'd like you to know about me.

Number one, I'm a teacher and number two, I love maths.

So you can imagine how excited I am to be teaching you a lesson today all about area.

So if you are ready, let's begin.

The outcome of today's lesson is I can calculate the areas of rectangles using multiplication.

We've got two keywords today.

So my turn length, your turn, my turn width, your turn.

Let's see what those words mean.

You might know them already.

So length and width are two quite interchangeable words that are used to describe the sides or dimensions of polygons.

So here we've got an example up, length and width.

Equally, we could have swapped those two words over and had width and length.

Our lesson today is split into two cycles.

The first is going to be calculate area of rectangles using multiplication and the second calculate area in different contexts.

But if you're ready, let's start with calculate area of rectangles using multiplication.

In this lesson you're going to meet Lucas, Sam, and Alex.

So the length and width of a rectangle can be labelled.

You might remember this.

So we could say that's the length, that's the width.

The two sides are connected at the vertex like so, and one side is adjacent to the other.

Any two of the sides connected at the vertex on a rectangle can be labelled as its length and width.

Here we go.

So it's a different part of the rectangle, but they're still connected in the same way, so we can call that the length and the width, or the width and the length.

The length and width can have, and do have, numerical values, so numbers are attached to them.

So here we could say that length is maybe 4 centimetres.

It's not to scale.

And the width we could say is maybe 8 centimetres.

So that's the length and the width, we're giving them values.

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

So in this case 4 centimetres multiplied by 8 centimetres gives us an area of 32 centimetres squared, and we can use that capital A for area.

Let's do a check for understanding.

What does the 4 represent? The 4 centimetres represents what? The 8 centimetres represents what? And the 32 centimetres squared represents what? Pause the video.

Okay, well the 4 centimetres represents the length.

You might have said width.

The 8 centimetres represents the width.

You might have said length.

And the 32 centimetres squared represents the area.

So yes, you might have had those the other way around.

So width and length.

But either way the 32 centimetre squared is the area.

So we've got our generalisation.

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

Let's say that together, shall we, because it's very important.

Are you ready? Let's go.

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

Now I'd just like just you to say it please.

Ready? Go.

This applies to lengths and widths beyond the 12 by 12 times tables.

So here look, 7 times 14 is not a known multiplication factor.

It's not a times tables fact that you might know off by heart.

It's gone beyond that.

So we need some strategies.

Not known facts will require a mental or written method.

In this case, the 14 centimetres can be partitioned, so split into parts, into 10 centimetres and 4 centimetres, turning the area into two different times tables facts.

Let's have a look at that.

So we partition that as so.

So instead of being 14 centimetres, now it becomes 10 centimetres and 4 centimetres, which is the same.

But now we have got two times tables facts.

So let's work out the area of each of those rectangles within the rectangle.

So 7 centimetres times 10 centimetres gives us an area of 70 centimetres squared, and 7 centimetres times 4 centimetres gives us an area of 28 centimetres squared.

What do you think we need to do with those two areas now? We need to combine them together by adding, so 70 centimetres squared plus 28 centimetres squared equals 98 centimetres squared.

And that's the total area.

The total area of the rectangle is 98 centimetres squared.

Lucas really likes that method, but he's not quite got it.

He wants you to explain it one more time.

How can partitioning be used to calculate the area of this rectangle? Have a think about that.

Pause the video and see if you can come up with a really good explanation for Lucas.

Okay, here's what you could do.

You could partition that 13, right? So split it into two different rectangles.

So it won't be 9 times 13 anymore.

It's going to be 9 times something and 9 times something.

So the 13 could be partitioned into 10 and 3.

This would turn it into two known facts.

10 times 9 and 3 times 9, which are then combined.

So 10 times 9 is 90, so that big rectangle is 90 centimetres squared, and 3 times 9 is 27.

So the small rectangle, smaller rectangle is 27 centimetres squared.

Combine those, add those together and you've got 117 centimetre squared.

The area is 117 centimetre squared.

Sam things she can show this calculation using expanded multiplication.

So she's got it all set out.

You might have had some recent experience doing this.

You might be quite good at this, hopefully you are.

So there's a 14 and there's a 7, so we're multiplying those two together.

She's worked out the 7 by 4 rectangle, so that's what that represents.

7 times 4 is 28, and then the 7 times 10 rectangle, 7 times 10 is 70, and then add them together and you've got 98.

So 98 centimetres squared.

That's the area.

Alex likes that, but he thinks he can save some time by doing it as a short multiplication.

And again, maybe you are getting quite good at doing this.

Maybe you've had lots of practise doing this, hopefully.

So he's gone straight for 14 times 7, so 7 times 4, so that will be the smaller rectangle is 28.

7 times 10, the bigger rectangle, that's 70.

add the 2, 98.

Area, 98 centimetres squared.

That was quicker, wasn't it? Well done, Alex.

But whichever method is chosen, the following stem sentences can be used.

The length is (vocalises) centimetres, the width is (vocalises) centimetres, (vocalises) times (vocalises) equals (vocalises).

The area of the rectangle is (vocalises) centimetres squared.

And they're colour coded just to give you a little bit of a help.

So here look we've got the length is 7 centimetres, so what's the width going to be? The width is 14 centimetres.

And remember we could've had those the other way round as well, 14 and 7.

7 times 14 equals 98.

So the area of the rectangle is 98 centimetres squared.

Let's do a check.

Calculate the area of the rectangle by partitioning it into two rectangles.

Complete the stem sentence.

So think about how you could split that into two rectangles.

Okay, pause the video, off you go.

Okay, while I'm looking at that, I'm thinking that 13 looks like it needs partitioning.

That's going beyond the times table.

So let's have a look at that.

What could we turn that into? Well, the length is 6, we know that for a fact.

The width is 13.

6 times 13 is going to give us 78.

The area of the rectangle is 78 centimetre squared.

And what I did, I turned the 13 into 10 and 3.

So I did 6 times 10 and 6 times 3 and added them together.

It's time for some independent practise.

Number one, fill in the blanks to calculate the area of this rectangle.

So a lot of the work's been done already for you there.

The partitioning has been done already for you, you've gotta fill in the blanks.

Number two, use expand multiplication to calculate the area of the rectangle that's been set up for you already.

You've gotta complete that.

Number 3, use short multiplication, and again, that's being set out for you to calculate the area of that rectangle.

Number 4, calculate the area of the rectangle and complete the stem sentences.

Use the colours I would recommend to help you out there.

There's something a bit unusual about B, isn't there? Can you spot it? And finally, C, we've got a really unusual example there.

Really long thin one.

So which multiplication strategy will be the most efficient to calculate the area of the rectangle? Okay, pause the video and off you go.

Welcome back, let's give you some feedback.

So number one, 80 centimetres squared plus 40 centimetres squared equals 120 centimetres squared.

Use expander multiplication, here we go.

So that's 14 times 6.

6 times 4 is 24, 6 times 10 is 60.

Add them together and we've got 84.

So it's 84 centimetres squared.

And for number 3, that's a short multiplication, that's 256 centimetre squared.

Number 4, the length is 17 centimetres, the width is 7 centimetres, 17 times 7 equals 119.

The area of the rectangle is 119 centimetres squared.

You might have swapped the width and the length over there.

That's absolutely fine.

And the same for B.

The length is 8 centimetres, the width is 19 centimetres, 8 times 19 equals 152.

The area of that rectangle is 152 centimetres squared.

And for C, that really unusual one.

So the length is 3 centimetres, the width is 216 centimetres or swap them over, that's fine.

3 times 216 equals 648.

The area of the rectangle is 648 centimetres squared.

Are you ready for cycle two? Let's have a look.

This is calculate area in different contexts.

Okay, we've got a map.

What's the area of the green square? The green square, that's important on the map.

So let's have a look.

This time the unit is kilometres, a much, much, much bigger measurement.

Much bigger than centimetres.

So we need to make a little bit of an adjustment to that stem sentence, I think.

It will need to be amended, he's quite right.

So instead of saying centimetres, it's going to say kilometres.

So now our stem sentence has become, The length is (vocalises) kilometres, the width is (vocalises) kilometres.

(vocalises) times (vocalises) equals (vocalises).

The area of the rectangle is (vocalises) kilometres squared.

Same principle as before, same calculation, just different unit.

So this business about square then? Hmm.

Because it looks like there's not enough information on there, but in fact there is.

It's a square, so therefore the other length must be 7 kilometres as well.

'Cause the sides are the same length on a square.

Hopefully you knew that.

So the length is 7 kilometres, the width is 7 kilometres, so that gives us a calculation of 7 times 7 which equals, hopefully this is a no multiplication fact for you.

49.

The area of the rectangle is 49 kilometres squared or 49 squared kilometres.

Time for a check.

We've got a similar question here.

What is the area of the green square on this map? And you've gotta complete this stem sentence.

The length is (vocalises) kilometres, the width is (vocalises) kilometres.

(vocalises) times (vocalises) equals (vocalises).

The area of the rectangle is (vocalises) kilometres squared.

Pause the video and off you go.

How did you get on? Let's have a look.

So the length is 6 kilometres, and because it's a square, the width is also 6 kilometres.

6 times 6 equals 36.

The area of the rectangle is 36 kilometres squared, or 36 squared kilometres.

Well then if you've got that, you are definitely on track in today's lesson.

So the school that Lucas, Sam and Alex attend is Oak Academy.

There are two year 5 classrooms, maybe that's the same in your school, I don't know, both of which have a rectangular floor.

Lucas and Sam are in one of them.

The floor has a length of 12 metres and a width of 8 metres.

We can do something to those numbers, can't we? To work out the area.

Alex is in the other one.

His floor has a length of 14 metres and a width of 7 metres.

We can do something to those numbers, can't we? Which classroom has the bigger area? So here we go.

So this is Lucas and Sam.

This is Alex.

The rectangles are representations of the classroom.

And Lucas rightly says, "It's hard to tell.

Our classroom's a bit longer, but your classroom's a bit wider".

"The length and width of our classrooms are the same as a times tables fact I know, 12 times 8.

Ours has an area of 96 metres squared".

and that was an instant recall fact for Lucas 'cause he knows his times tables.

So Alex says, "I'm calculating 14 times 7 tog the area.

I'm going to partition the 14.

So 10 times 7 is 70, 4 times 7 is 28.

My classroom has an area of 98 metres squared and yours was 96 metres squared".

So they were very close, weren't they? Very close, just two square metres apart.

Alex's classroom has a bigger area.

Let's do a check.

This time we've got some representations of lawns.

Which of these lawns has a bigger area and by how much? Pause the video and give it to go.

Okay, well we can do some multiplying here, can't we? 14 times 5 will give us the area of A and 8 times 11 will give us the area of B.

One of those is a multiplication fact, a no multiplication fact and the other one isn't.

So the one that isn't is this one, 14 times 5, but 14 times 5 is 90.

So 90 metres squared is the area of that one.

The next one is a known fact.

8 times 11 is 88.

Very close again.

So A has just slightly got the bigger area.

And if we use our subtraction skills, we can count on from 88 to 90, and that's two metres squared.

So A's got the bigger area by two metres squared.

Congratulations to you if you've got that.

Okay, time for some more independent practise.

So number one, A, Lucas has found a blade of grass and measured it.

It's 5 millimetres wide and two centimetres long.

Okay then, if you notice we've got some mixed units there, you're going to have to do something to convert those I think.

What's the area of the blade of grass? B, the hall at Oak Academy needs a new floor.

There's enough money in the budget for a 150 metres squared floor.

The current floor has a length of 9 metres and a width of 17 metres.

Will they be able to replace it? So you need to do a calculation there with those numbers.

At Oak Academy, the key stage one playground is a square shape and there has a length of 12 metres.

It's square, remember that.

Key stage two playground is a rectangle with a length of 15 metres and a width of 9 metres.

Which one has the greater area and by how much? So you're going to need to do a few different calculations for that one.

Pause the video and give that a go.

Okay, let's see how you got some with that.

So number one, the area of the blade of grass.

You needed to do a bit of conversion there.

So maybe turn the 2 centimetres into 20 millimetres.

So 5 millimetres times 20 millimetres.

It's 100 millimetres squared, which is the same as one centimetre squared.

You might have said that.

And the whole Oak Academy needs a new floor and there's enough money in the budget for a 150 metre square floor.

The current floor has a length of 9 metres and a width of 17 metres.

Will they be able to replace it? No they won't.

9 times 17 is 153, so unfortunately it's just a bit out of budget.

It's 3 metres too large an area.

They're going to need to find some more money I think.

And the key stage one playground square shape with a length of 12 metres, that means it's width is also 12 metres.

Key stage two playground's a rectangle with a length of 15 metres and a width of 9 metres.

We need to multiply those together.

Which one's got the greater area and by how much? So the key stage one playground, that's 12 by 12, which is 144 metres squared.

Key stage two playground is 15 metres by 9 metres, so that's 135 metres squared.

Then we need to use our subtraction skills.

144 metres squared, take away 135 metres squared gives us metres squared.

So the key stage one playground is 9 metres squared bigger in area.

Well done if you got that.

We've come to the end of our lesson.

Today's lesson's been calculating the areas of rectangles using multiplication.

The area of any rectangle can be worked out by multiplying its length by its width, regardless of the type of square you'd have been using.

iI could be centimetres squared, millimetres squared, metre squared, kilometres squared.

area can be sometimes calculated using known facts, especially when the length and the width are times tables facts up to 12 by 12.

Sometimes however other mental or written strategies will need to be used to multiply the length and the width, such as partitioning or short multiplication.

Hope you've enjoyed today's lesson, I definitely have, and hopefully I'm going to see you again soon for some more maths.

But in the meantime, take care and goodbye.