Lesson video

Hi there, I'm Mr. Tilstone, and it's a real pleasure to be working with you today on your math lesson.

Today's lesson is all about area.

Now that's not an uncommon word, and it's a word you might have heard before.

But today, we're going to explore that in a mathematical context in some detail.

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

The outcome of today's lesson is, "I can explain what area is." And our keywords, we've got two today, which we'll explore now in a, my turn, your turn style.

So, my turn, polygon.

Your turn.

And my turn, tessellate.

Your turn.

Let's explore what those words mean.

Have you heard them before? You might have done.

A polygon is a two-dimensional shape with straight sides, such as a triangle or a pentagon.

So straight away, I'm thinking of another example, a rectangle, and I'm gonna think of a non-example, a circle, because it hasn't got straight sides.

And a shape tessellates if copies of it can fully cover a space without overlapping.

Our lesson today is a two-cycle lesson.

The first will be, what is area? And the second will be, exploring different shapes to determine area.

But let's begin with, what is area.

Ready? In this lesson, you're going to meet these two.

You're going to meet Andeep and Jacob.

You might have met them before.

They're here today to lend a helping hand.

Find an object with a flat surface.

This could be something like a book, maybe a maths book, or a table, the desk that you sat on, or a ruler.

And this image shows the back of a ruler.

I'm going to use some sticky notes for my flat surface.

Now, imagine that your finger has got paint in.

It's a magic finger that can paint.

Run your finger over the entire flat surface ensuring that you don't miss any parts.

So I'll do that with my Post-it notes.

So I'm going to pretend that I can paint, and I'm covering the entirety of my flat surface.

I'm not missing anything out.

There's going to be no gaps.

I'm going edge to edge.

I'm going all the way from the top to the bottom.

And there we have it.

I've painted the entire surface.

You've just explored the area of your object.

So if you'd like to do that now, please do.

And we've got a generalisation here.

"Area is the measurement of a flat surface.

It measures a 2D space." This is really important.

So I'm going to say that again, and I'd like you to say it with me.

Are you ready? Let's go.

"Area is a measurement of a flat surface.

It measures a 2D space." And I'd like you now just to say it on your own.

Are you ready? Go.

Very good.

So the ruler face is a two-dimensional shape, and that shape is rectangle.

So that's a polygon.

The area of this box face is a two-dimensional shape, and in this case, it's a square, which is a kind of rectangle.

The box has got lots of different flat faces, and each of them has an area, a flat surface, a 2D space, whose area can be measured, whose shape can be measured.

Lucas drew around the bottom of three objects, a sand timer on the left, a cup in the middle, and a pencil pot on the right.

All three of the shapes he had drawn were circles.

Lucas can paint the circles with his finger.

They each have an area.

So remember, circle is not a polygon, but it is a 2D shape, so it's got an area.

And Lucas, just like I did with my Post-it notes and just like you've just done with your flat object, you could paint the entirety of that surface.

Let's do a check for understanding.

Find an object in your surroundings.

Find a flat face and paint the area.

When you do it, I want you to complete this stem sentence.

"Area is a measurement of a mm surface.

It measures a mm." So if you've got a partner to talk to, do that, see if you can agree.

Pause the video.

I'll see you shortly with some feedback.

So how do you get on with that? Did you manage to find a object with a flat surface? Did you manage to paint it with your finger? So here's Jacob.

He chose a book.

The top of the book is a flat face, which is a rectangle.

So that front cover of the book has got an area, it's a rectangle, it's a 2D shape's, got an area.

So, once again, area is a measurement of a flat surface, and it measures a 2D space.

So here are some examples of polygons.

So I can see some different shapes here.

I can see a square.

I can see a triangle next to it.

I can see an eight-sided shape, so that's got to be an octagon.

And I can see a different quadrilateral there that's got a a different thickness, but it's still a a polygon.

So, can you sketch maybe some other examples of polygons? What other shapes can you think of that are polygons? So, remember, they've got to have some straight lines.

All straight lines, in fact.

So polygons are 2D shapes.

Polygons have a perimeter shown by straight sides, and the space enclosed by the perimeter.

So the space inside the perimeter is a shapes area.

So, once again, back to my example, so we've got a rectangle here, and the rectangle's got a perimeter, it's closed, and inside that perimeter is the area of the shape.

So we've got the triangle again.

It's a polygon.

It sides are closed.

It's not got any open sides, therefore it has a perimeter.

And because it's got the perimeter, it's got an area inside it which can be measured.

So that's our keyword, area.

And let's have a look at a different shape.

Is that a polygon? What do you think? If so, why? And if not, why not? Hmm.

It's not a polygon.

Not this time.

Can you see why? Something different about it, isn't there? It sides are not closed.

And because the sides are not closed, it doesn't have a perimeter.

It does not, therefore, have an area which can be measured.

These are 2D shapes but are not polygons.

Do they still have an area? What do you think? So they're not polygons.

And the reason they're not polygons is because they don't have all straight sides.

A couple of them have got some straight sides, but they've got curved sides too.

So they're not all polygons.

But have they got an area? Yes.

Yes, they do.

Because they've got a perimeter.

And because they've got a perimeter, they've got an area inside that perimeter.

And once again, area is a measurement of a flat surface.

It measures a 2D space.

Okay, let's have a look at this shape.

Is it a polygon? No.

No, it's got curved sides.

It is a 2D shape though.

It sides are closed, therefore it's got a perimeter.

So that's important.

So it passes that test.

And because of all that, it has an area which can be measured.

So the inside, what's inside of the perimeter, is the area and that can be measured.

Have a look at this shape.

What do you think about that shape? Is it a 2D shape? Does it have a perimeter? Does it have an area? Hmm, I don't think so, do you? Let's investigate why.

No, it's not a 2D shape.

It sides are not closed, therefore it does not have a perimeter.

And because it doesn't have a perimeter, it doesn't have an area which can be measured.

So, another generalisation.

All two-dimensional shapes have an area which can be measured.

Again, this is really important.

So I'm going to ask you to say it with me.

Are you ready? Let's go.

"All two dimensional shapes have an area which can be measured." And because it's so important, now I'd like you to say it all by yourself.

After three, one, two, three.

Fabulous.

Let's have a check.

Which of the following examples have an area, and see if you can think about explaining why or why not.

Pause a video and give that a go.

Did you manage to agree with the people around you, if you've got people around you? Which of the following shapes have an area? Let's see.

A does, because it's got a perimeter, so it's got an area inside it.

And C does as well for the same reasons.

Neither of them are polygons, but they are 2D shapes.

B doesn't, because it's not got a perimeter, it's not closed.

And the same for D.

So they don't have an area, but A and C do.

Time for some practise.

Are you ready? I think you are.

Right.

So number one is going to be A, fill in the blanks.

So, "Area is a measurement of a flat mm.

It measures a mm space." So that important generalisation there we explored before.

Can you remember it still? And then B, find three small objects around you such as a pencil pot, pencil sharpener, a bookmark.

Don't make it too big.

Draw around the bottom of the object and show the area by shading in the shape that you've drawn, and the bit that you shade will be the area.

And number two, work with a partner.

Find as many different objects as you can around the classroom, which have a flat surface.

And paint the surface with your finger.

So not literally paint.

Remember, just pretend you've got a magic finger that can paint.

And some little challenges here.

See if you can find some different surfaces.

Can you find a surface of a 2D shape, which is a square? What about a rectangle but not a square? What about a circle? Can you find one of them? What about a regular polygon but not a square? So maybe pentagon, maybe equilateral triangle, something like that.

And can you find a regular polygon? One with sides that are different lengths? Pause the video.

Have fun.

See you soon.

Welcome back.

Hope you enjoyed exploring the different surfaces and their area, and painting them with your finger.

Let's do a little bit of feedback.

So area is a measurement of a flat "surface", is the word we're looking for.

It measures a "2D" space.

You might have put some slightly different words in.

For example, you might said two dimensional, something like that.

But they're the kinds of answers that we are after.

And then the three small objects could be any 2D shape that you've shaded in, but the shape must be closed.

That is important.

And then you were working with a partner, finding some different objects around the classroom and painting the different surfaces of them.

So you could do any object with at least one flat surface.

And examples might be a reading book, a laptop, paper, a table, a clock, a bookmark, an eraser.

These are all things that you might find in the classroom if that's where you are right now.

Let's move on to cycle two, which is exploring different shapes to determine area.

So imagine that you could paint the surface of your object using a flat shape as a printing block.

So imagine you could actually put paint on it and sort of press down with that shape onto your surface.

So, again, I've still got my sticky notes here.

So, Andeep has chosen to use a circle for his printing block.

And the image shows the back of the ruler again as it did before.

Would the circle be a useful shape to cover that surface in paint? Hmm, try and picture it before we explore.

Do you think that will be a good shape? Let's have a look.

Hmm, straight away I can see a little bit of an issue here.

Can you see it? And the issue is that circles do not tessellate.

So that's one of our keywords today.

They don't fit together without gaps.

So, therefore, they wouldn't cover the whole area.

There's going to be gaps.

So you can see, you know, up above, and down below, and in between the circles we could see gaps.

So maybe circles wouldn't be the best shape.

I wonder if there's a better one.

Okay, Jacob needs to cover this rectangle in sparkly paper, but he needs to know the area, and he starts by covering it with circles.

Here we go.

Hmm, same issue as before.

Same as Andeep.

Circles don't tessellate.

They leave gaps.

So maybe there's a better shape.

What about this one? So we've got a five-sided shape here, a pentagon.

Imagine we could use that as a printing block.

It's a regular pentagon.

Would that be better at covering the whole area? Again, have a little thing, see if you can picture it, see if you can visualise it before we explore.

That'd be a good choice.

Hmm, we've started covering the shape, and can you see another issue? A bit like the circles, they don't actually tesselate.

They leave gaps, just like the circles did.

So you can see them above and in between gaps.

So not ideal.

There must be a better shape, I think.

There's those gaps.

So he decides to try a square.

Do you think a square will be better at covering the whole area of his book? Hmm.

Let's have a look.

Ah, can you see something different this time? I certainly can.

That's covering that surface very nicely indeed, isn't it? Squares do tesselate.

So they tesselate perfectly on all four sides.

They leave no gaps in between them.

So it's a great shape to use to cover an area.

And they've covered most of the shape.

You can see there's a little bit left just on the right-hand side.

But they've done a pretty good job, would you agree, at covering that surface? 30 of Jacob's squares cover this shape with a bit of the shape left over.

And you can see that by, first of all, counting the first row, there's five on there, so I could count to fives.

Five, 10, 15, 20, 25, 30, 30 of those shapes.

I could do it another way as well.

I can see the columns are going in sixes, and I can count in sixes.

Can you? So 6, 12, 18, 24, 30.

Either way we look at it, there's 30 of Jacob's shapes, which is squares, 30 squares.

So the area of that rectangle is just over, just a little bit over, 30 of Jacob's squares.

Squares can be used to cover large parts of other 2D shapes.

So let's have a look at another shape.

So here we've got a pentagon, five-sided shape, and we're going to start to cover it with squares.

And yes, we've got a couple little gaps to the left and right of the squares, but they actually tessellates very well.

So they're covering quite a lot of that surface.

There we go.

We couldn't fit any more complete squares in there.

So this time, we can say 24 whole squares have been used to cover most of this 2D shape.

And if you like, you can count those to prove it.

But there's 24 whole squares there.

Again, with a few little gaps.

But no more whole squares would fit inside that perimeter.

So the area of this 2D shape is 24 whole squares with some space leftover.

Okay, time for a check for understanding.

Have a look at the image, have a look at the circle.

What kinds of things can you say about that circle? Think about area.

Okay? Pause the video.

Have a chat.

What sorts of things did you say? Let's see what sorts of things you might have said.

You might say something like, "It's got an area of 26 whole squares with some space left over." So it's got an area of just a little bit more than 26 whole squares.

Jacob has cut out a square, and he's using it to measure the area of the back of his ruler.

Count with him.

How many times does his square fit inside the ruler? So he's going to take one square, he is gonna put it down, lift it up, move it along, put it down, lift it up, move it along.

He's gonna count every time.

So are you ready to count with him? I'll do it with you too.

Ready? So, one, two, three, four, five, six, seven, eight, nine, 10, 11, and I think that's it.

Because if we lifted it up again, it will go over the edge of it.

So the shape has an area of just over 11 square units, and we could see them if they were all together, if he did have lots of different shapes, that's how they would look.

But he only needed one to measure.

So, just over 11 square units is what we're going to start calling them for the area of that ruler.

Andeep has caught wind of the fact that squares are pretty good for area, and he's cut out a different square.

So it's not going to be exactly the same.

And in fact, it's slightly smaller than Jacob's square.

And again, just like before, we're going to count with him.

How many times does his square fit inside the surface of the back of the ruler? Are you ready? Let's count together again.

So here's your square look.

So, you can't really see on there, but it is a little smaller than Jacob's square.

So ready? So one, two, three, four, five, six, seven, eight, nine, 10, 11, 12, 13, 14.

So that fitted in a few more times, didn't it? It wouldn't fit in again though, would it? That space is too small.

So here, they are all together.

So this shape has an area of just over 14 square units.

14 of Andeep's square units, that is.

So, now we can see the two squares together with the two boys, as Jacob's slightly larger square, and there's Andeep's slightly smaller square.

Jacob can measure the area of different flat surfaces using his square, saying which ones have a bigger or smaller area.

So he could then go on to measure a different flat surface such as his book, or his table, something like that, with that same square.

But he just needs to ensure that he uses the same square to do that.

And Andeep can do exactly the same thing as long as he keeps using his own square.

And we're going to call these square units.

So Andeep has got a square unit, and Jacob's got a different square unit.

Let's have a check.

So let's us use Andeep's square.

Count with him and say the completed stem sentence.

Okay, you ready? So the stem sentence is going to be, "The shape has an area of just over mm square units." So, this time, I won't count with you.

I want you to do it.

Are you ready? Okay, let's go.

Okay, did you get that? Right.

Say it with the stem sentence.

And that stem sentence was, The shape has an area of just over "nine" square units.

Well done if you got that.

Final task.

Task B, number one, draw and cut out a square, just like the boys did.

Use your square shape to cover the area of the different flat surfaces that you explored in Task A.

So, if for example, you use a bookmark, use that same thing again.

Use a bookmark again, but this time use a square to cover it, not your finger.

Use a stem sentence every time.

"The shape has an area of just over mm square unit." So each object you explore, use that stem sentence at the end, please.

So work with a partner.

Now, they're going to use one square, and you are going to use a different square.

And I want you to compare the answers that you get.

So one square is going to be slightly bigger than the other square, and one square is going to be slightly smaller.

And number two, in your own words, can you explain what area is? So write that down, what is area.

That's our big question for today.

And B, why squares are a useful shape when finding the area of a 2D shape? Pause the video.

Have fun.

I'll see you soon.

Welcome back.

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

So, for number one, responses will vary according to the size of the surface.

But hopefully, each time you said that stem sentence, "The shape has an area of just over mm square units." And then what is area? Your responses may very well differ slightly, but that generalisation that we explored earlier on was exactly this.

"Area is a measurement of a flat surface.

It measures 2D space." We're going to be using that generalisation a lot in this unit, so make sure you've got that one locked and loaded.

And then B, why is squares useful when finding the area of a 2D shape? Well, squares tesselate, that is to say they fit together well on all four sides because the sides are straight and equal, so they don't leave those gaps.

So well done if you said anything like that.

And that is the end of the lesson.

So today, we've been explaining what area is.

So area is the measurement of a flat surface.

It measures 2D space.

Squares are a useful way to cover the area of a surface.

And again, we're going to be exploring that in greater detail in the upcoming lessons.

And then finally, area can be measured in square units.

And again, that is terminology that's going to be coming up again and again.

I've had great fun today exploring the concept of area with you, and I hope you've enjoyed it too.

It would be lovely to see you again soon.

In the meantime, take care and goodbye.