Lesson video

Hi there, I'm Mr. Tilstone.

I'm delighted to be with you for this maths lesson which is going to be all about area.

So if you are ready, let's begin.

The outcome of today's lesson is I can use understanding of area and counting strategies to solve problems involving area.

So lots of problem solving today.

Our keywords, which we're going to explore in a my turn, your turn style are my turn area, your turn.

My turn rectilinear, your turn.

I think these words might be familiar to you already.

Hopefully they are, but if not, let's have a quick recap anyway.

So area is the measurement of a flat surface.

It measures a 2D space.

Rectilinear shapes are 2D polygons composed of one or more rectangles and they feature right angles and right angles only.

Our lesson is split into two cycles today.

The first will be area problems involving counting, and the second will be area problems involving drawing.

But we're going to begin with area problems involving counting.

Let's go.

In this lesson, you're going to meet two characters who might be familiar to you you might have seen these two before.

Aisha and Andeep, they're going to be here to lend a helping hand.

Andeep's teacher has spilt coffee on this rectangle.

And by the way, I'm not Andeep's teacher.

It wasn't me.

Is it still possible to work out the area by counting the squares? Then we've got the stem sentence here.

This shape has an area of mm square units, but you can see because of the coffee spillage that some of those squares are now covered up.

Is it still possible to work it up? 'Cause we certainly can't count them all individually.

Have you got a strategy? Have you got a solution? Have you got an idea for us? Well have a look at this, we can see a complete row there and the complete row's got six square units in it.

You can see rows of six and there's another row of six there.

Again, that one is completely uncovered as well.

And another one that's just got a little tiny bit of coffee on, but I can see another row of six.

Now that one's got some coffee on, but it would've been a row of six, would you agree? And the same for that one.

Got lots of coffee on it, but it would've been a row of six.

So we can count 6, 12, 18, 24, 30.

This shape has an area of 30 square units.

So we can still count even though there's some coffee on the squares.

Let's have a check.

More coffee, more coffee's been spilt on this shape.

What is the area of this rectangle, which has had coffee spilled on it? Use this stem sentence, this shape as an area of mm square units.

Pause the video and have a go.

Did you manage to figure it out? This shape has an area of 21 square units.

So I could see we were counting in rows of three.

You might have done it a different way as well, you might have seen that we were counting in columns of seven.

So we could go 3, 6, 9, 12, 15, 18, 21 or we could go 7, 14, 21.

Mm-hmm, what's the area in square units of this shaded shape? Can you see something that's different about this? Very different about this to the shapes that we've been looking at before in this lesson and other lessons too? Hmm, have you spotted it? Well, the thing is we can't see the squares inside this shape, but it has still got an area.

I can see shapes outside.

I can see squares outside the shape however, so we can use that.

So Aisha says "One way is to extend the grid lines that are already there, using a ruler." Hmm.

Not a bad idea, you could do that.

And now we can count them.

It take a while though, wouldn't it? So she says, "The squares are now easier to count.

The area is 50 square units." So she's counted them.

"It Took a long time though.

There has to be a better way!" She thinks.

I think she's right, don't you? Have you got a better idea.

Hmm.

I think Andeep, has you know.

Goes, "Hmm, it's tricky.

I can't count the squares inside the shape." No you can't.

"But I can see three rectangles." So in his mind, Andeep split that into three different rectangles.

"And I think I can work out the area of each." Now there's lots of ways to split this into rectangles, but this is the way that Andeep's done it.

So can you now see it's got three rectangles and he thinks it's possible to use the squares around it to help him determine the area of each one.

So, "I'm looking at the squares around the first one.

I can see that there are two squares in each row and six rows." So 2, 4, 6, 8, 10, 12.

Yeah.

So that part of this rectilinear shape has got an area of 12 square units.

And he says, "I can count in sixes to work out the area in square units of the next rectangle." Because, look, he's seen above the or below the rectangle are six squares.

So that's what we're counting in.

So that it goes 6, 12, 18.

18 square units.

And I can count in fours, again, you can look on top of the rectangle or underneath the rectangle you can see a row of four squares.

So we're counting in fours and we go 4, 8, 12, 16, 20.

So that rectangle, that part of this rectilinear shape has got an area of 20 square units.

And then all we've got to do is add them together.

So 12 + 18 + 20, those numbers go together quite well, don't they? I can see that eight and the two are going to make a number bonded 10.

So that's helpful.

So 12 + 18 + 20 = 50, So that's 50 square units.

Let's do a check for understanding.

What is the area in square units of this shaded shape? So you might want to split it into rectangles, and see if that helps.

Notice what's above and below the rectangles.

Pause the video and give it a go.

Okay, how did you get on? Let's have a look.

So if we split it into rectangles, that's one way to do it.

It's not the only way, but that's one way to do it.

We could say this part, this rectangle's got 12 square units.

That one's got six square units and that one's got seven square units.

And we can word that out even though the squares aren't inside, we don't really need to use Aisha's method, Andeep's is even better and it's quicker.

So 12 + 6 + 7 = 25 square units, that is the area of that shaded shape.

Let's have a look at this one.

What's the area in square units of this shaded shape? That's different, isn't it? That's not rectilinear.

Hmm.

Going to need to use some different skills I think for this.

But we can still split it into different shapes.

So Andeep can see a rectangle and a triangle.

So can I.

"I can count in sixes to work out the area of the rectangle." He says.

Yes, I can see six squares underneath that rectangle.

So I can count in sixes.

So 6, 12, 18, 24.

And I can split the triangle into two triangles like so.

And each one is half of three square units.

So if you combine them you get three square units.

So 24 square units + 3 square units = 27 square units.

What's the area in square units of this shaded shape? So pause the video and have a go at that.

Quite tricky.

We did need to do some splitting up.

And we needed to do some thinking and noticing and counting.

Let's have a look.

You could split them this way.

The rectangle will be 24 square units.

The two triangles are each half of an eight unit rectangle, making eight units altogether when you combine the two triangles.

So 24 + 8 = 32.

So it's got an area of 32 square units.

If you've got that, congratulations, you are on track in today's lesson.

You are doing well.

So let's put that to the test.

Let's see if you can do some independent practise.

So task A, write and complete the stem sentence for each of the shapes which have had paint spilled on them.

And for number two, what is the area in square units of these shaded shapes? Pause the video, give that a go and I'll see you soon for some feedback.

Let's see how we got on then.

So for number one, this shape has an area of 56 square units and you can count in eight or sevens.

That is a rectangle.

B is rectilinear but not a rectangle.

But we could split it into two rectangles and this shape as an area of 25 square units.

For number two, we can't see the squares inside but we can count.

We could split it as so.

And then we've got 27, 15 and 14.

And when we combine those, that equals 56.

So 56 square units.

And for this one we can split it into a square and a triangle and the square is 16, which is a square number and the triangle is two square units altogether.

Making 18 square units.

Well done if you've got that.

There are other ways of splitting the shapes.

Cycle one is complete.

Let's move on to cycle two.

That is, area problems involving drawing.

Andeep and Aisha have been learning about using square units to measure area and they are setting each other some challenges.

Andeep says, "I challenge you to draw a rectangle with an area of 15 square units." Aisha says, "No problem, I'm going to draw three rows, each with five square units." Oh, okay, can you notice something about that? He says, "Nice try Aisha, but you haven't been accurate." She had a good idea but she wasn't accurate.

"This shape would have an area greater than 15 square units." It's probably more like 16 or maybe 17.

"Have another go but this time try and stay on the lines." Good advice Andeep.

Good advice.

Ah, that's better isn't it? Aisha's completed the challenge, accuracy is essential when drawing shapes.

Use a ruler and the grid lines to help.

So stay on that line.

So a little check using your square paper, accurately draw a rectangle with an area of 12 square units.

Pause the video.

Okay, well there's some possibilities there.

That is an example, that's a different example and that's a different example.

All different rectangles within an area of 12 square units.

Well done if you've got any of those, well done if you've got more than one of those and very well done, if you got all of those.

They might have been in a different orientation as well.

Andeep has set Aisha a new challenge.

He says, "I've drawn a triangle, I challenge you to draw a rectangle with the same area." Okay, that's harder, isn't it? Okay, let's see.

Aisha begins by seeing what she notices about the area of the triangle.

Do you notice anything? She says, "I could count all of the square units first and then add the triangles together.

So two of them make one square unit." Yes, could do that.

That's right, like so.

"And I've also noticed," she's good at noticing is Aisha, she's noticed that it's half of a square with rows of six.

So it goes 6, 12, 18, 24, 30, 36.

But either way the triangle's got an area of 18 square units.

So my rectangle also has to have an area of 18 square units.

Aisha thinks about her different possibilities and there's one.

That's another one, she'll count in twos this time 2, 4, 6, 8, 10, 12, 14, 16, 18.

She'll count in threes.

Look.

3, 6, 9, 12, 15, 18.

"My rectangles could be rotated as well.

So there's lots of possibilities there." Lots of ways to complete that challenge.

So they're both the same rectangle but one's rotated.

Check.

A check for understanding.

How many different rectangles can you describe which would have the same area as Aisha's triangle.

And this time though the triangles are not half of a square.

But can you remember another method? Pause the video and have a go.

Let us have a look.

So here are three different rectangles.

They each have the same area as Aisha's triangle.

This time Aisha has set Andeep a challenge.

She says, "I have drawn and shaded a trapezium.

I challenge you to draw a different quadrilateral with the same area." And Andeep says "That's hard because I can't see the squares inside the shape! But I think I can still figure out the area." So do I, Andeep.

So do I.

"I will start by splitting it into a rectangle and a triangle, like so.

I can see four squares beneath this shape.

So each row has four square units." So he's thinking about what's underneath the shape.

Good idea.

"And there must be three of those rows.

So 4, 8, 12.

there are 12 full square units.

and the triangle's half of a row of four squares.

So it must be two square units.

So 12 square units plus two square units equals 14 square units." And there are different ways you can complete that challenge.

And that's two of those ways, different rectangles with an area of 14 square units.

"I could even draw a non-rectilinear four-sided shape with an area of 14 square units." That's brave, isn't it? That's challenging.

I like that.

He's gone a bit deeper.

Yes, that would work wouldn't it? That would have an area of 14 square units.

Well done, Andeep for going a bit further with that challenge.

So, "well done, Andeep.

You completed my challenge in different ways.

My top tip is you could have drawn the lines onto my shape with a ruler to find the area." So do that if you need to, but if you don't need to do that, it's quicker and easier I think.

So that's one possibility if you're stuck.

So a check, use your squared paper to draw one or more quadrilaterals with the same area as the shaded trapezium.

Pause the video and give that a go.

Okay, let's have a look.

So any four-sided shape with an area of 12 square units, including non-rectilinear shapes.

You might have been a bit ambitious and adventurous and done a non-rectilinear one.

So we've got some examples.

That's a rectangle there, rectilinear.

That's a non-rectilinear example that's got 12 square units.

Let's have a go at some independent practise.

So task B one, on square paper, draw two different shapes each with an area of 12 square units.

One must be rectilinear and one must be non-rectilinear.

And then number two, Andeep draws a rectangle which consists of two rows of 12 square units.

On square paper, draw two different rectangles with the same area.

Number three, draw two different rectangles onto the grid with half the area of the hexagon, half the area.

So work out the hexagon's area and then halve it and draw two different rectangles with that same area.

Number four, draw triangles with the same area as the rectangle.

As many as you can possibly think of.

Pause the video, have a go at that.

Good luck and I'll see you soon for some feedback.

How did you get on then? So for number one, here are some rectilinear possibilities for that.

These are rectangles and that's not a rectangle, but it is rectilinear and they've all got areas of 12 square units.

And the non-rectilinear ones, many, many possibilities.

And here's just three of them.

They've all got an area of 12 square units.

That was a bit trickier, wasn't it? That one.

So well done if you got them.

And then number two, any rectangle in any orientation with an area of 24 square units.

So that would be one, that would be a different one.

And number three, two different rectangles with half the area of the hexagon.

So work out the area of the hexagon and halve it.

And any rectangle in any orientation with an area of eight square units would do it.

That would be a nice simple example.

And there's a different one.

Number four, draw triangles with the same area as the rectangle.

Any triangle in any orientation with an area of 12 square units.

Some examples are as follows.

That is one.

That is another one.

That's tricky.

So very well done if you got that.

That's really challenging All right we've come to the end of our lesson.

So today's lesson's been about solving problems involving counting and drawing the areas of different shapes.

It is possible to work out the area of shapes even without squares inside them by considering the squares surrounding the shape.

And when drawing shapes for the same area as other shapes, ensure accuracy by using a ruler and the grid lines, accuracy is essential.

I've thoroughly enjoyed working with you on today's lesson about counting and drawing the areas of different shapes and solving problems to do with that.

Hope you've enjoyed it too.

Hope you've learned something and I hope to see you again soon.

But in the meantime, take care and goodbye.