Lesson video

Hi there, my name is Mr. Tilstone, and it's my favourite time of day, maths time.

You may have had some recent experience learning about square units.

In today's lesson, we're going to be giving those square units names.

It's gonna be quite a fun lesson today.

We're going to have a little bit of fun with some of the numbers.

So if you are ready, let's begin.

The outcome of today's lesson is I can measure the areas of shapes using square centimetres, Our keywords, which we're going to do now in a my turn, your turn style, are my turn rectilinear, your turn, my turn square centimetres, your turn.

Have you heard of any of those before? Maybe you know the definitions already, but it's worth a check.

These are important words today that we're going to be using quite a lot.

So a rector linear shape is a 2D shape with straight sides and right angles, so essentially it's made of rectangles.

Square centimetres are the area equal to a square that is one centimetre on each side, and we're going to be exploring that in quite a lot of detail today.

Our lesson outline, it's a two-cycle lesson.

Cycle one's going to be understanding square units.

There's lots of different kinds, we're going to explore that.

And cycle two is measuring shapes using square centimetres.

So we're going to focus specifically on one kind of square unit, square centimetres.

But we're going to start with understanding square units.

Let's go.

In this lesson, we've got a little gang to help us out.

You might have seen these before.

We've got Aisha, Alex, Jacob, and Andeep giving us a little bit of a helping hand.

So here's Jacob and Andeep.

Jacob and Andeep have been measuring the area of surfaces with square units and you might have had some recent experience yourself of doing that, but their squares are different sizes, can you see? So they've both got squares, but they're different sizes.

If you are to compare areas, you must use the same sized squares, so we need a standard measure.

Square units are used to measure area, and that's something you might already know, I hope you do.

A square has sides of equal length, and again, I'm quite confident that's something you already knew.

We describe the size of a square unit based on how long one side is.

So that's one unit squared or one unit squared.

That's how we show it, that's how we say it, the little two.

So we use that small two that sort of hovers above to represent squared.

So whenever you see that, I want you to read it as squared, okay? So there are lots of different kinds of square units, lots and lots, some imperial ones, some metric ones, there's all sorts, so let's look at a few now.

We've got a really, really, really teeny-tiny one.

What do you think this one could be? Have a look at the ruler.

Hmm.

That's a square millimetre.

It's extremely small, very, very small.

You can see square millimetres, but they're teeny-tiny.

The square has sides of one millimetre, so all the different sides on that square are one millimetre in length.

Now, that's really small to see, isn't it? I'm having to squint to see that.

So let's look at an enlarged version.

It won't be to scale or anything like that.

So look, one side is one millimetre, another side is one millimetre, it's a square.

So we read that as one millimetre squared.

So remember that little two, we read as squared.

Here we go.

So we can name that unit one millimetre squared.

Happy with that? Can you imagine a millimetre squared? Can you sort of see it in your mind? Could you cut one out, do you think? What might you measure in millimetre squared? I could imagine one, I think I'd struggle to cut one out, they're too tiny.

So the area of extremely small surfaces, such as a daisy petal or a very small coin, like a five pence, for example, could be estimated and measured in square millimetres and that's because they're very tiny surfaces.

So square centimetres, which we're going to explore later on, would be too big.

So anything that's really, really small, square millimetres are perfect for.

It's not a commonly used square unit, but it does exist.

So yeah, here we go.

Look, a small coin like a penny, daisy petal.

Another square unit, a much more commonly used one and you're going to be hearing about this quite a lot both in this lesson and for the rest of the unit, is square centimetres.

You might have heard of those.

Let's see that on the ruler.

So, can you see? Quite a lot bigger than that square millimetre.

It's a small unit of measure, though, we do still use it to measure quite small things.

The square has sides of one centimetre this time, not one millimetre.

Here we go.

And again, that's an enlarged version.

So the sides are larger in length this time.

So we read that as one centimetre squared.

Remember the little two means squared.

So we've named that unit one centimetre squared.

You might also hear it called one square centimetre.

So, can you imagine a centimetre squared? Try to picture that in your mind.

Could you cut one out? I think you could, that would be a little easier to cut out.

It'd be small still, but you could do that.

What kinds of things do you think you might measure in centimetres squared? And you might have had, again, some recent experience of measuring small things, like books, book covers, in square units.

You could also measure them in square centimetres or centimetres squared.

So the area of smaller surfaces, such as a brick face, for example, or a clock face, so they don't have to be rectangular, there can be all sorts of 2D shapes, could be estimated and measured in square centimetres.

So here we go.

Just a couple of examples of things that are just about the right kind of size for square centimetres.

Too big for square millimetres, it would be far too many, it would take too long, but square centimetres seem reasonable for that.

All right, let's have a little bit of fun now with those numbers.

We're gonna play a little guessing game.

You can do this with your partner if you like.

If you're in a classroom, you might all like to have a little guess.

Maybe write on your whiteboard, something like that.

How many square millimetres do you think make one square centimetre? So we can see them together, look, on two rulers that are the same as each other.

Square millimetre on the top, square centimetre on the bottom.

How many of those square millimetres make one square centimetre? Have a little think.

Have a little guess.

You might be surprised.

Let's have a look.

100, 100 of those little square millimetres make one square centimetre.

Maybe a little bit more than you thought.

Some of you might have said 10, I think, but no, it's 100, so quite a lot.

That's why it wouldn't really do to measure things like a book cover in square millimetres, there will be far too many, 100 just for one square centimetre.

Let's look at a different unit now.

So we've looked at square millimetres, we've looked at square centimetres.

There are other units.

Another unit is square metres.

So it's a square this time with sides of one metre.

So not one millimetre, not one centimetre, one metre, so bigger.

So Jacob's using a metre stick.

You might have one of these in your classroom.

You might have seen one of these recently.

That's a metre stick, that gives you a little bit of an idea of the length of one metre.

So again, look, it's a square.

Again, this isn't to scale, but just to show you that if we've got a square with sides of one metre each, we've got one square metre or one metre squared, and that's what we can name that.

It would be possible for Jacob and Andeep to cut out and hold a square metre.

Very possible.

The area of larger surfaces, such as a football pitch or a kitchen floor, could be measured and estimated in square metres.

So again, if we're thinking about something like a book or a television screen, square metres wouldn't be the right unit.

We're looking at bigger surfaces.

So yeah, here we go.

Look, a football pitch and kitchen, big, flat surfaces.

So Jacob has created a square metre by combining metre sticks.

And if you are in a classroom, you might be able to do this yourself, create a square metre.

If you've got four different metre sticks, you could do exactly what Jacob has done just here.

Let's have a little more fun, let's have a little guessing game again, or you might be able to work it out even, I don't know.

How many square centimetres do you think make one square metre? So think about those square centimetres that we just looked at.

How many do you think would fit into one square metre? Maybe have a little chat, maybe talk to your partner, maybe share it with a class, maybe write on your whiteboards.

Have a guess.

What do you think? 10,000.

Did you say 10,000? 'Cause I imagine not many people have said that one.

That's much higher than I would've thought, but no, it's 10,000 square centimetres going to one square metre.

It's a big number, isn't it? Here we go.

So that's why it wouldn't really do to measure large surfaces in square centimetres, it would take forever.

Can you imagine measuring a football pitch, for example, using square centimetres? Oh my goodness.

So surfaces greater than a square metre would take far too long to measure in square centimetres.

Now, I didn't stop there, there are even larger standard square units, for example, square kilometres.

So this square has sides of one kilometre.

I'm gonna show you that in a second.

That is roughly the distance between Jacob's house and school.

So if you walk to school, maybe you walk about a kilometre, I don't know.

It's a walkable distance, put it that way.

So here we go, look.

Again, of course, this isn't to scale, but this is a square with sides of one kilometre in length, and we read that as one kilometre squared.

So that's what we can call that, one kilometre squared.

So a farmer's field, for example, might have an area of approximately one kilometre squared or one square kilometre, so we're talking very big surfaces now.

It would not be possible for Jacob and Andeep to cut out and hold a square kilometre, it is far too big for that.

The area of very large surfaces, such as villagers, towns, and cities, could be estimated and/or measured in square kilometres.

So wherever it is that you live, I live in a town, that could be measured in square kilometres.

Here we go.

So it's a really big unit, massive unit, in fact.

So here's Jacob again with his square metre.

How many square metres do you think make one square kilometre? Go on, let's have a little bit of fun.

Have a guess.

Talk to your partner, talk to your class.

Write on a whiteboard if you can.

How many square metres do you think make one square kilometre? What we think, we've been surprised before, haven't we? And we're gonna be surprised again on this one.

Should we find out? 1 million! 1 million.

I'll bet you didn't say 1 million.

If you did, congratulations, that's fantastic.

But no, 1 million square metres equals one square kilometre.

That's a big number, isn't it? So that's why it just would not do, it would not be possible or feasible to measure something like a town in square metres.

We need a different unit, bigger unit.

So yeah, one square kilometre.

Surfaces greater than a square kilometre would take 40 long measuring square metres, far too long.

So we need the right square unit according to the size of the surface.

Okay, let's do a little check for understanding.

So for each image, decide which square unit would be best to use when measuring the surface area.

So remember we've looked at square millimetres, square centimetres, we've looked at square metres, we've looked at square kilometres.

So you decide.

So A is a school playground, which one would be best for that? B is a blade of grass, which one would be best for that? And C is the page of a book, which one would be best for that? Okay? Pause the video.

I'll see you soon.

Welcome back, how did you get on? Let's find out.

So school playground, the sensible unit would be metre squared for that.

A blade of grass, millimetre squared.

And the page of a book, centimetre squared.

So well done if you got those.

Okay, let's do some independent practise.

So task one, list some examples where the area of one surface could be measured in square metres for a, square millimetres for b, square kilometres for c, and square centimetres for d.

Pause the video, have a go at that.

Be creative and I'll see you soon for some feedback.

Welcome back.

Let's have a look at some possible answers.

There's all sorts of things that you could have said for this, sir.

So for square metres, your examples might have been a park, you might have said something like that, and the ground floor of a house.

For square millimetres, you might have said something like a lady bird wing and a grain of rice.

It's quite hard to think of square millimetre ones, I think, they're not as common.

Square kilometres, you might say something like a farm or the city of Manchester, something like that.

And square centimetres, you might have said a picture frame or a birthday card.

And there are examples of things that could be measured in square centimetres.

Okay, let's move on to cycle two.

We're going to focus now specifically on one of those square units, which is square centimetres.

Are you ready? Let's focus on those square centimetres.

Just a little reminder, look.

Here's what they look like.

The sides have a length of one centimetre.

We read it as one square centimetre or one centimetre squared.

Okay, we're gonna be looking at measuring shapes using square centimetres.

So Alex knows that if you paint, you're not really going to paint, but you might remember doing this before you might have done something similar.

If you paint a flat surface with your finger, you are covering the area of that surface.

This has given him an idea.

He cuts out a one centimetre square from a sticky note.

Remember it is possible, they're quite small, but you could cut out a one centimetre square.

So he uses one of those sticky notes, you might call them Post-it notes.

And can you see there that little yellow square centimetre? And he sticks it on his fingertip.

You might want to do this yourself.

Here we go, look.

So he is got that little, tiny square centimetre stuck to his finger.

He lifts his finger up and down and touches every part of the cover of his notepad, counting as he goes.

And he's gonna make sure he leaves no gaps and he is gonna make sure that it doesn't overlap either.

And then that will take him to the end.

So now he's touched every part of that.

So 30 square centimetres covered the front of his little notebook, so the area of the front cover is 30 centimetres squared.

Let's look at that again in a little bit more detail.

So here's your centimetre squared, so that's what you would've touched at the top left-hand corner.

And then five of those would give him a row, and that would take him to five centimetre squared for that part.

There are five centimetre squared in a row, so counting in fives will be a quicker way to establish area rather than counting ones.

So you don't need to touch every part of it.

If you've established that one row is five centimetres squared, you could use that.

Here we go, look.

That's 10 centimetres squared.

What do you think this is going to be? 15 centimetre squared, have you got the pattern? What's this going to be? 20 centimetre squared.

Let's keep going, have you seen the pattern yet? Yeah, we're counting in fives, aren't we? That's 25 centimetres squared.

So if you can guess what's gonna come up now.

That's 30 centimetres squared.

So the notebook cover has an area of 30 centimetres squared.

You read that as 30 centimetres squared, so remember that's how we read that two.

Aisha has seen a different way to count the square centimetres efficiently, and I like that word efficiently.

She's got to sort a quicker, better way to do it.

That's what good mathematicians do.

Okay, can you see what she's done? She's not counted from left to right, she's counted up to down, top to bottom.

And there's six, six square centimetres in a column, so she's counting the columns.

So, what's two going to be, do you think? 12, yeah, you got it.

What's next? 18, that's right.

And another column would be, 24, yes.

And one more would be, 30.

So she had a different approach to Alex, but they both got to 30 centimetres squared.

The notebook cover, once again, has an area of 30 centimetre squared.

Now, sometimes the 2D shape is shaded and the square centimetres inside it cannot be seen.

So if you can imagine cutting out a rectangle from a piece of paper and placing it onto square paper, let's say, you wouldn't see the squares inside the shape, would you? We'll cover them up as well.

Okay.

But we could still work it out.

The area can still be worked out by looking at the squares around the shape.

So look around the shape, not inside it.

So above the shape there are three squares.

So it goes three, six, nine, 12, 15.

So, can you see that? We're counting in three like Alex did.

To the left of the shape are five squares, so that goes 5, 10, 15, like Aisha did.

So the area of that shape, even though we can't see the squares inside it, we can work out is 15 centimetres squared.

And you could almost visualise or imagine the squares underneath, couldn't you? You could sort of imagine extending the squares that we can see there.

But there would be 15, 15 centimetres squared.

Here we go, now that's what it would look like if it was transparent or translucent.

Let's do a check for understanding, shall we? Complete and read out the stem sentence? Okay, so that's the area of the shape is, mm, mm.

So we're looking for the number and we're looking for the unit that we've using there, okay? And we've got a little bit of a clue down there.

Look, we can see that we're dealing with centimetres.

So pause the video, talk to your partner, have a go.

See you soon.

Did you find that easy? Did you manage to get an answer? Let's have a look.

25 centimetre squared.

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

Okay, the area of all 2D shapes can be measured using square units.

So we looked at rectangles there, but any shape whatsoever can be measured using square units.

We can split this shape into smaller rectangles to measure its area.

Can you see that? Can you see that shape is made of three rectangles? Okay, so we're going to use this stem sentence again.

This shape has an area of, mm, centimetres squared.

Let's have a look, let's investigate, let's explore.

16 centimetres squared.

So you could count them all individually, that would work and that would take you to 16, but you might have a more efficient way to do it as well.

Maybe counting in columns or rows.

Right, let's do a check.

So use counting to determine the area of this shape.

And again, you might have an efficient way, you might not need to count all of the squares individually, but you're going to tell me what the area is of the shape.

And once again, you're going to use that stem sentence, this shape has an area of, mm, mm, okay? Pause the video, give it a go.

Let's have a look.

19, well done.

If you've got 19, and 19 what? 19 centimetres squared.

So congratulations if you got that.

And if you read that properly, a centimetre squared.

Well done.

A stem sentence can be used to help work out the total area of a non-rectilinear shape.

So everything we've looked at so far, including the last shape, was rectal linear, so made of rectangles.

This one has got some rectangles in, but it's got some other shapes too.

I can see some triangles in there.

But we can still measure its area using square units, and in this case, centimetre squared.

So this shape has an area of, mm, complete square centimetres, so you could count those first.

And then, mm, extra square centimetres are made from combining the partial squares.

And again, you might have done something very similar quite recently, not with centimetres squared, just with general square units, combining two half squares together to make one square unit.

So this shape has a total area of, mm, centimetres squared.

Well, let's have a look.

Well, it's got 11 complete square centimetres, so you might want to count that and check that, but it's got 11.

And then what about the extra square centimetre that we can get from combining? Let's have a look.

You get one extra square centimetre.

So this shape has a total area of, put 11 and one together and you get 12.

This shape has an total area of 12 centimetres squared.

Let's use that stem sentence again.

Got a different one.

Let's think about the complete square units, the complete square centimetres, and then the extra square centimetres too, and then combine them for the total.

You might want to have a look before I do it.

Okay, so this shape's got an area of 10 complete square centimetres.

Let's think about the extra ones made from combining those two half squares.

Three.

'Cause I've got two halves there, another two halves, another two halves, that makes three extra square centimetres made from combining the partial squares.

Put them together and we've got 13.

This shape has a total area of 13 centimetre squared.

Okay, complete the stem sentence.

There's an extra gap this time, this is a little check.

So this shape has an area of, mm, complete square centimetres.

When the partial squares are combined, there is or there are, mm, extra square centimetres.

This shape has a total area of, mm, mm.

So we want the units as well at the end, please.

Pause the video.

Let's have a look.

So this shape has an area of eight complete square centimetres.

When the partial squares are combined, there are four extra square centimetres.

This shape has a total area of 12 centimetres squared.

Very well done if you got that.

So Jacob and Izzy are drawing different rectilinear shapes each with an area of six centimetres squared.

They start by plotting dots in the squares they wish to be part of their designs.

How many dots do you think they're going to do? Six.

Here we go, look.

So that's what Jacob wants his design to look like, he's done six dots, and Izzy's done six different dots on hers, like that, but they're all joined, look.

Then they draw around the outline of their shapes using a ruler, have some look.

And they're going to be very particular about drawing on the lines, not between.

So there we go, look.

You're using a ruler to join up this side like so.

And now Jacob's got a shape, a rectilinear shape, that's got an area of six centimetres squared.

And Izzy's going to do exactly the same.

She's got a different shape, different rectilinear shape, in fact, that's got an area of six centimetres squared.

So let's use that stem sentence.

These shapes each have an area of, mm, centimetres squared.

Do you think you can do it? You can have a go.

These shapes each have an area of six centimetres squared.

Let's do a quick check for understanding.

Using centimetre squared paper, draw two different rectilinear shapes each with an area of six centimetres squared.

Pause the video.

Well, here's one of many possible examples of two different shapes with an area of six centimetres squared.

You might well have got something very different to this.

That's one and that is a different one.

Time for some practise.

So number one, complete the stem sentence for each of the shapes.

This shape has an area of, mm, centimetres squared.

For b, I've not told you the unit, let's see if you can work it out.

This shape has an area of, mm, mm.

And you might notice that the squares inside have disappeared on b as well, so that's a little harder.

For number two, write and complete that stem sentence for each of the shapes.

If you can't remember it, just have a look at the previous one.

And again, one's a little easier because you can count the squares inside it and one has not got the squares inside it, so more of a challenge, but use the squares around it to help.

C, this shape has an area of, mm, complete square centimetres.

When the partial squares are combined, there are, mm, extra square centimetres.

This shape has a total area of, mm, mm.

So complete the stem sentence.

It's a non rectilinear shape.

And finally, number three, a bit of an open-ended one for you.

Draw as many different rectilinear shapes as you can with an area of eight centimetres square.

Be creative.

Okay, pause the video, have fun exploring that, and I'll see you soon for some feedback.

Welcome back, let's have a look.

So number one, this shape has an area of 12 centimetres squared.

That's a.

B, this shape has an area of 10 centimetres squared.

And we can work that out by looking at the squares around it.

Five on top of it, two to the right of it.

For number two, a, this shape has an area of 18 centimetres squared.

You could count 'em individually or you might have had a more efficient strategy such as I would maybe counting fours initially.

And then for b, this shape has an area of 15 centimetres squared.

A little bit trickier that one.

But again, maybe you had a good efficient way that you'd like to share with the class.

C, this shape has an area of 14 complete square centimetres.

When the partial squares are combined, there are three extra square centimetres.

This shape has a total area of 17 centimetres squared.

And as many different rectilinear shapes as you can with an area of eight centimetres squared.

Well, here's just some of the many possibilities.

Maybe you've got something completely different and well done if you did.

We've come to the end of the lesson.

I've had so much fun with this.

There are lots of different standard square units that can be used to estimate and measure area, and one of these, the one that we've really focused on, is square centimetres.

So let's have a look at this example.

The area of this shape is 12 square centimetres or 12 centimetres squared.

Two ways of saying the same thing.

This can be calculated by counting the individual square units, but it's more efficient in this example to think of the rows or columns and either counting fours or counting threes, so we didn't need to count them individually.

And that's the end of the lesson.

It's been a great pleasure working with you on your math lesson today, and I do hope to see you again in the future.

But until then, take care and goodbye.