Lesson video

Hello there, my name is Mr. Tilstone.

I hope you're ready for today's maths lesson, which is going to be all about area.

Now, some parts of the lesson, you might find relatively straightforward, and there might be some questions that you can answer quite quickly.

Other questions, you might need to take a bit of time, and it might need a bit of perseverance and resilience, but with a positive attitude, you'll get there.

And you've got me to help you every step of the way.

So if you're ready, let's begin.

The outcome of today's lesson is I can calculate the missing dimensions in rectangles and compound rectilinear shapes.

Keywords, we've got two.

My turn, compound, your turn.

My turn, dimension, your turn.

Are either of those words or both of those words familiar to you? Let's have a look.

Let's have a check.

So a compound shape is made up of two or more shapes, and they can be any shapes.

But at the minute, we're focusing on rectangles.

And a dimension is a measurement of length in one direction.

So width and height are examples of the dimensions of 2D shapes.

So we could say in this example that the height is one of the dimensions and that the width is a different dimension.

Our lesson is split into two cycles.

The first is going to be missing dimensions in rectangles, so just rectangles, and the second, missing dimensions in compound rectal linear shapes.

So shapes made up of more than one rectangle.

So if you're ready, let's begin with missing dimensions in rectangles.

Let's go.

In this lesson, you'll meet Jun and Laura.

You may well have met those two before.

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

And here they are.

So Jun and Laura are playing a game.

Laura has a rectangle with one of the dimensions and area already given.

So you can see the area, look, is 40 centimetres squared, and one of those dimensions is given, five centimetres.

She's covered up one of the dimensions with a sticky note.

You know those little kinda sticky yellow post-it notes? She's challenged Jun to work out the missing dimension.

So have a look at that, see if you think you could work it out.

Jun says, "Hmm, I know "that if you multiply one dimension by the other, "you get the area.

"So five times something equals 40." This is a times tables fact, isn't it? Do you think you know the missing number? Five times something equals 40.

Well, Jun also knows his times tables off by heart, didn't need to do any calculating.

He knows that five times eight equals 40, so therefore the missing dimension has to be eight centimetres.

And here we go.

So she's taken away the post-it note and revealed the right answer.

It's eight.

"Well done, Jun," she says, "I'm going to have to make it a bit harder next time." I think she's right.

He's good, isn't he? Let's have a quick check for understanding.

So use your times tables knowledge, it's a times tables fact, to work out the missing dimension.

So you've got the area, it's 44 centimetres squared, you've got one of the dimensions, it's 11 centimetres squared.

What's the missing dimension? Pause the video.

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

Let's take away that yellow post-it note, and it's four centimetres, four times 11 equals 44.

"Okay, Jun, try this one," says Laura.

"You won't be able "to use your known times tables facts this time." So it's not in the times tables, this one.

So we've got the area again, look, 60 centimetres squared.

And we've got one of the dimensions, 15 centimetres.

We've got to work out the missing dimension.

And you might notice it's a different dimension this time.

"Hmm," says Jun, "15 times something equals 60." Now, you might notice that's gone beyond the 12 by 12 times table.

So it's not a times tables fact, it's not a fact that he might know off by heart.

"I could," he says, "Count in 15s until I reach 60." And that won't take too long, will it? "15, 30, 45, 60." And when I was counting those, I was using my finger.

So 15, 30, 45, 60, that's four lots of 15.

"The missing dimension, says Jun, "must be four centimetres." Four times 15 equals 60.

That sounds right, doesn't it? And it is.

Let's do a check.

Explain how counting can be used to work out the missing dimension this time.

So once again, you've got the area, that's 75 centimetres squared.

You've got one of the dimensions, either the length or the width, that's 25 centimetres.

So what is the other one? Can you count in the same way that we did before? Maybe use your fingers or whatever you need to do, okay? Pause the video, have a go.

How did you get on? What did you come up with there? Counted in 25s.

Well, that's fairly easy, to count in 25s I think, 25, 50, 75.

That was three.

So that's how you could use counting.

There are three 25s in 75.

So the missing dimension must be three centimetres.

And it is.

Well done if you got that, you're on track in the lesson.

Okay, Laura says, "What's the missing dimension this time, Jun?" Hmm, so we've got the area again.

It's 51 centimetres squared of this rectangle.

We've got one of the dimensions, three centimetres.

We don't know the other one.

Can you see already how this one's a little bit harder? For starters, it's definitely not a times tables fact, is it? So Jun says, "Hmm, three times something equals 51." So he knows what he's doing here, doesn't he? "Three times something equals 51.

"It would take me a very long time to count in threes." Wouldn't it just, three, six, nine, 12, 15, 18.

I'm nowhere near, I'm nowhere near.

So I don't think that's the right strategy.

"I could," he says, "Use division to work out how many threes there are in 51." Because that's essentially what you're doing when you're counting in threes.

You're seeing how many make 51, that's division.

So it's the same as 51 divided by three.

So I can use my short division skills.

You may have had some recent experience of doing short division.

Here we go.

So 51 divided by three equals 17.

The missing dimension must be 17 centimetres, three times 17 equals 51.

That sounds right, doesn't it? And it is right.

Let's have a check.

Use your division skills to work out the missing dimension.

So the area is given, it's 96 centimetres squared.

One of the dimensions is given, that's six centimetres.

What is a missing dimension? Pause the video and off you go.

Did you get the answer? And if you got the answer, did you get the chance to compare with the person next to you, and compare methods? Let's have a look.

So the answer is if we use our division skills, 16.

So six goes into 96 16 times.

I don't have 16 fingers, so that wasn't the right strategy for that.

But usually something like short division or maybe even partitioning the 96 into 60 and 36 would work.

But either way you get 16.

So 16 centimetres.

Right, Laura has given him a tricky one this time.

Two post-it notes.

Hmm, what is she doing? "I'm not going to give you "either of the dimensions this time," she says, "All I'll say is it's a square." Hmm, what do I know about squares? Jun says, "Hmm, something times something equals 25." So this time, he's got two missing dimensions.

But do you know something about a square? "Because it's a square," Jun knows, "The dimensions must be the same," yes.

So a square's a special kinda rectangle where the length and the width are the same.

"Using my times tables knowledge, "I know that five times five equals 25." So therefore, the missing dimensions this time have got to be five centimetres and five centimetres.

Let's do a check.

We've got another square, we've got the area of the square, 64 centimetres squared.

Can you give the missing dimensions and think about the process that Jun just went through to calculate the missing dimensions of the previous square.

Pause the video and off you go.

Okay, how did you get on? Did you manage to get an answer? Did you manage to agree with the person next to you if you're working with somebody else? Let's have a look.

So something times something equals 64.

It's got to be the same number each time, hasn't it? So you might know your times tables facts, you might know which ones fit this one, and it's eight times eight.

Eight centimetres times eight centimetres equals 64 centimetres squared.

So brilliant if you've got that.

They're still playing the game.

Laura says, this time, "I'm not going to give you either of the dimensions.

"All I'll say is its area is 36 centimetres squared." So she's got a rectangle, and it's got an area of 36 centimetres squared.

And she's not giving either dimensions.

So there's some real thinking needed to happen here, isn't it, from Jun? Let's have a look.

"Hmm," he says, "Something times something equals 36." Now, I know more than one calculation that will give that answer, more than one times table where something times something equals 36.

Can you think of one? Can you think of more than one? "So using my times tables knowledge," he says, "It could be three centimetres times 12 centimetres." And I think Jun's used a little bit of a system there.

He started with the kind of lowest factor that he could think of for the first one.

So three centimetres times 12 centimetres equals 36 centimetres.

"But I can think of other possibilities.

"It could be four centimetres times nine centimetres." Did you get that one? "It could even be "a six centimetre by six centimetres square." Yes, it could.

Six times six equals 36.

So three times tables possibilities there.

Okay, time for some practise.

So number one, calculate the missing dimension.

So six times something equals 42 centimetres squared.

Think about your times tables knowledge.

And then for B, there's no (indistinct), but you've gotta figure out what's the missing dimension.

Same for C.

We've got one of the dimensions, not the other.

We've got the area.

Again with D, we've got the area and one dimension, work out the missing one.

And then for E, it's a square and both dimensions are missing.

But it's got an area of 144 centimetres squared.

And for number two, a rectangle has an area of 24 centimetres squared.

What could the dimensions be? Give as many answers as possible.

Okay, very best of luck with that and I'll see you soon for some feedback.

Number one, the missing dimension.

So for A, is seven centimetres, six times seven is 42.

And for B, it's 12.

12 times nine equals 108.

Both of those are times tables facts.

So maybe, just maybe you knew that automatically and you got there quite quickly.

And for C, we've got four times 18 equals 72 centimetres squared.

Now, that wasn't a times tables fact, so you may not have got that one instantly.

You might have needed to use your division skills to get there.

Same for D, seven times 21 equals 147.

And again, that's not a times tables fact, but you can get there using division.

And then for E, for me, this one was one I could do quite quickly because I know my times tables and I was given the area, we were given the area, 144 centimetres squared.

So something times something equals 144.

That's 12 by 12.

So 12 centimetres and 12 centimetres.

Very well done if you got that.

And for number two, a rectangle's got an area of 24 centimetres squared.

What could the dimension be? Give as many answers as possible.

So the times tables facts which fit this criteria are two by 12 or 12 by two, three by eight or eight by three and four by six or six by four.

Now, they're the times tables facts, but you might have got some that are outside the times tables.

So for example, you might have got one by 24, and that's correct too.

Are we ready for cycle two? That's missing dimensions in compound rectilinear shapes.

Let's begin.

The area of this compound shape is 87 centimetre squared.

What's the missing dimension? Hmm, okay, we're going to need to do a little bit more thinking about this one, aren't we? It's going to take a little bit more time.

I think we've got some information though that we can use to help us.

So the area of that larger rectangle can be calculated by multiplying the two dimensions.

So it's got dimensions of nine and seven.

Again, it's a times tables fact.

That will give us 63 centimetres squared.

So we've got one of them.

Hmm, we're getting there.

Right, now the total area of the compound shape is 87 centimetres squared, and we've got one of the rectangles in there.

So I wonder what we could do with the numbers we've got, the information that we've got to work out that missing side length.

Hmm, do you think you can maybe work out what the area of the smaller rectangle is now that we know that the bigger one's 63 centimetres squared? So the difference between the larger rectangle's area and the total area of the shape will give the area of the smaller rectangle.

So we're using subtraction, and you could count on from 63 to 87 or you could do 87 takeaway 63.

But either way, that will give us the area of the smaller rectangle.

So 87 centimetres squared subtract 63 centimetres squared equals 24 centimetres squared.

We're not quite there yet though, are we? So that's the area of that smaller rectangle, and we've got one of the dimensions of the smaller rectangle.

What can we do with that information to work out the missing dimension, hmm? Think about how Jun was thinking earlier on.

Something times something equals something.

So here, we could say something times six equals 24.

What would that information be, the missing information? So six times something equals 24 or 24 divided by six equals something.

Think you've got it? It's a times tables fact.

It's four centimetres.

the missing dimension is four centimetres.

So that took a few steps, and it took a little bit more time, but we got there.

It took a bit of thinking too, but we got there in the end.

Let's do a different one that uses similar skills.

So the area of this compound shape is 62 centimetres squared.

What is the missing dimension? So just exactly like before.

Now, you might notice a couple of differences here.

For instance, the shape with the dimensions that are given is now on the right hand side, not the left hand side, but I think we can use similar skills.

So the area of the rectangle on the right can be calculated by multiplying its two dimensions.

So that's nine and three.

A times tables fact, hopefully you've got this instantly.

Nine times three equals 27.

So that rectangle is 27 centimetres squared.

That's the area.

And the difference between the area that's just been calculated and the total area of the shape will give the area of the rectangle on the left.

So remember, we know that the total area of the compound shape is 62 centimetres squared, and we've got the area of one of the rectangles, that's 27 centimetres squared.

We can use our subtraction skills, 62 centimetres squared take away 27 centimetres squared, and that will give us 35 centimetres squared.

Now, final step, we know the area and we know one of the dimensions.

So five centimetres times something equals 35 centimetres squared.

Think you know it, it's a times tables fact.

Five times something equals 35.

35 divided by five equals something, and that something is seven.

So seven centimetres, the missing dimension is seven centimetres.

Again, it took a few steps but we got there.

Let's have a check.

Talk your partner through the steps to solving this problem, which is very similar to the last two that we've just looked at.

Now, this time, the area of this compound shape is 66 centimetres squared.

What is the missing dimension? Pause the video, have a go.

Okay, how did you get on? Did you manage to explain the steps to your partner? Did they manage to do the same to you? Let's have a look.

You might have said something like this.

Work out the area of the large rectangle, that's the six by eight one, subtract it from the total area to give the area of the smaller rectangle, and then divide the area of the smaller rectangle by the known dimension of the smaller rectangle, which is two centimetres, and that will give you the missing dimension.

So well done if you managed to go through those steps, and you might even have worked it out as well.

So that one's 48 centimetres squared, smaller one's 18 centimetres squared, and two times nine equals 18.

So the missing dimension is nine centimetres.

Okay, here's a shape made from three identical rectangles.

So they're all three the same.

One of them is in a different orientation but they are the same.

The area of the shape, so altogether, those three rectangles give an area of 72 centimetres squared.

What are the missing dimensions? Okay, that's a little trickier.

We're going to need to do some thinking about this one.

We're going to need some resilience and perseverance I think.

But let's have a look.

Let's explore this together.

So we're going to start by calculating the area of each rectangle.

It doesn't look like we've got a lot of information there, but I think we've got enough.

We just need to do something with it.

So 72, that's the area of the total shape, divided by three, that's how many rectangles there are, can use our division skills there, but that gives us 24.

So the area of each rectangle is 24 centimetres squared.

That's not what the question was, but that's going to help us out.

What do you think we need to do next? Have a look.

The area of one of the missing dimensions can be worked out by halving 12.

So that's hopefully quite straightforward for you.

1/2 of 12 is six.

So 1/2 of that length on the left is six.

So that means that the length, the dimension of that rectangle there is six centimetres.

Now, I think we've now got enough information there to work out the missing dimension because we've got 24 centimetres squared for the area of the rectangle on the right and six centimetres for one of the dimensions.

So six times something equals 24, or 24 divided by six equals something.

So times tables fact, it's four.

So the missing dimensions are six centimetres and four centimetres.

Let's have a check.

A similar kind of problem, different orientation this time for our compound rectilinear shape.

Here's a shape made from three identical rectangles, just like before.

The area of the shape has changed though.

This time, it's 120 centimetres squared.

I think it might be a little bit easier to work out this time.

What are the missing dimensions? Pause the video, work with a partner if you can, and off you go.

Okay, how did you get on with that one? Did you manage to work out those two missing dimensions? So when we divide 120 by three, we get 40 centimetres squared.

That's the area of each rectangle.

If we 1/2 that 20, it's going to give us 10.

So we know that that's one of the dimensions of the rectangle, 10.

And we know the area is 40, so we've got 10 times something equals 40.

10 times four equals 40.

So that's the missing dimensions.

Very well done if you got that.

That was tricky.

If you got that, you are definitely on track.

Time for some independent practise, I think.

So task B, number one, the area of this compound shape is 103 centimetres squared.

What is the missing dimension? It's going to take a few steps.

Number two, this compound shape is made from two rectangles, the larger of which is a square.

Its total area is 73 centimetres squared.

What are the dimensions of the missing sides? Number three, here's a shape made from three identical rectangles.

The area of the shape is 96 centimetres squared.

What are the missing dimensions? So a little bit similar to the problem that we did quite recently.

Good luck with that.

Pause the video, and I'll see you soon for some feedback.

Welcome back, how did you get on? Are you ready for some answers? Let's have a look.

So if the area of the compound shape is 103 centimetres squared, the missing dimension, well, working out the area of that shape, that's eight by five, that's 40 centimetres squared.

Subtract that from 103 centimetres squared and it gives us 63 centimetres squared.

So seven times something equals 63.

Seven times nine equals 63.

That is a missing dimension, nine centimetres.

And this compound shape's made from two rectangles, the larger of which is a square.

It's a square, remember? So two of the dimensions must be the same.

Its total area is 73 centimetres squared.

What are the dimensions of the missing sides? Okay, well, I think we can work out that larger one first.

So seven times seven, because it's the same, equals 49 centimetres squared.

And the total area is 73 centimetres squared.

So 73 take away 49 gives us 24 centimetres squared.

And then four times something equals 24, or 24 divided by four equals something.

And that is six.

So that is the missing dimension, six centimetres.

And here's a shape made from three identical rectangles.

The area is 96 centimetres squared.

What are the missing dimensions? 96 divided by three gives us 32 centimetres squared.

That's the area of each.

1/2 of 16 is eight, so that's one of the dimensions.

And eight times something equals 32, eight times four equals 32.

So they're the missing dimensions.

Congratulations if you got that.

That was tricky.

We've come to the end of the lesson.

Today's lesson has been calculating missing dimensions in rectangles and compound rectilinear shapes.

If the area of a rectangle is known and one of its dimensions is known, the missing dimension can be calculated by dividing the area by the known dimension.

And you can use subtraction to work out the area of one rectangle in a compound rectilinear shape.

So you've used lots of different skills today.

Hope you've enjoyed the lesson, hope found it challenging.

Hopefully I'll get to see you again soon and we can do another maths lesson together.

But until then, take care.

Enjoy your day, and goodbye.