Lesson video

Hi there.

My name is Mr. Tilstone and it's my great pleasure and delight to be working with you today on your maths lesson.

Today's lesson is going to be all about area and specifically it is going to be about square metres.

So if you are ready, let's begin.

The outcome of today's lesson is I can measure the area of large shapes using square metres.

Keywords, we've got just one today and that is my turn square metre, your turn.

You might be able to figure out what a square metre is.

You might already have a bit of an inkling what a square metre is.

Let's have a look though.

A square metre is a unit of measure equal to a square that is one metre on each side.

So there are different kinds of square units.

Today we're just going to focus specifically on square metres.

Our lesson is in two cycles.

The first is going to be estimate and measure surfaces in square metres and the second, different shapes with the same area.

But if you're ready, let's begin with estimate and measure surfaces in square metres, let's go.

In this lesson, you're going to meet two characters who are going to give us a little bit of a helping hand, and that is Jacob and Laura.

So welcome to those.

Jacob's class have been learning about area.

Jacob has been using a square centimetre to estimate and measure the area of small objects such as his bookmark.

And you might have had some very recent experience of doing exactly the same thing.

Jacob's teacher has set the class, the challenge of estimating and measuring the area of the classroom floor.

Hmm, do you think that square centimeter's going to be the right tool for that job? Jacob says, "This is gonna take forever! I can't even imagine how big this number will be.

There has to be a better way." I think he's right.

A square metre is a unit of measure suitable for measuring the area of larger surfaces.

It's a square with sides of one metre, just like this.

One square metre can be expressed as one metre squared.

And that's how we read that two, one metre squared, that's small two.

Jacob has created a square metre by combining metre sticks.

Here we go, that's something you might want to do in your classroom.

That's a square metre.

Laura draws around Jacob's square metre to make her own square metre out of paper.

And again, that's something you could do.

If you've got some really large paper and you've got four metre sticks, you can make a paper square metre just like this.

That's also one metre squared.

So two different representations of it.

Two forms of a square metre.

These can both be used to measure the area of larger flat surfaces, such as the classroom floor.

That seems a much better size, doesn't it to be measured in the classroom floor.

So Laura and her friends have cut out lots of square metres, so they've each got their own square metre or metre squared.

This is one square metre.

This can be expressed as one metre squared.

It can be expressed as one metre squared.

That's how we show that.

That's how we read that.

What do you think this is? This is two square metres.

That's two metres squared.

What's this? This is three square metres.

Three metres squared.

And we can say that with words or with the two.

Let's have a quick check.

Can you express that area in three different ways? Pause the video and have a go.

Okay, how did you get on? Did you get three different ways? Let's have a look.

You could say this is four square metres.

This can be expressed as four metres squared with the words and it can be also expressed as four metres squared using the symbol.

So well done, if you've got all three.

This is a representation of the classroom floor.

That's a bit like what it looks like, but obviously not to scale or anything like that.

And that's a representation not to scale of the metre, square metre.

Laura and Jacob look at their square metre papers and try to imagine how many times they were fit onto the carpet.

You might want to do that now look at that square metre.

How many times do you think that would fit on without any overlaps, without any gaps, anything like that, how many times? Have a think.

Have a number in your mind.

Jacob says, "I estimate it will fit 15 times.

So the area of the classroom floor will be 15 metres squared." Laura says, "I estimate it will fit 25 times.

So the area of the classroom floor will be 25 metres squared." You might want to write down your own estimate.

Jacob starts laying down the squares.

Okay, there we go.

Hmm, okay, something seems wrong about that.

"Wait Jacob!" Says Laura, "remember the squares can't overlap or it won't give the true area." No, it won't will it? It's going for two square metres there, but that's not quite too because of the overlap.

So let's do that again.

There we go, that's better.

Now we've got three square metres and so on.

So remember that it can't overlap.

So it laying down those squares to discover the area of the classroom and that's as many as it can fit in.

The classroom floor has an area of just over 16 metres squared or 16 square metres is 16 of those fitting in without any overlaps.

So Jacob and Laura could have carried out the task using just one square metre counting as they went along.

Let's have a look at that.

They didn't need all the different pieces of paper, just one would do.

Let's have a look.

Here we go.

So we lay it down, pick it up, and then put the next one.

Put the same one, sorry, down next to it.

And we keep doing that like so.

Counting as you go, counting how many times you're laying it down.

The classroom has an area of just over 16 metres squared or 16 square metres and here we go.

That's what that looks like.

Laura says, "I think you can make a couple more full square metres out of the gaps.

So it's probably more like 18 square metres or 18 metres square." I think she's right.

Let's have a look at that.

So yeah, I think you could probably make one more out of that gap and probably another one out of that gap.

I think she's right, probably more like 18 square metres.

A little bit more perhaps something like that though.

It's definitely more than 16 square metres though.

Jacob says, "We could use the paper metre square to estimate other larger areas too." "We could stick some paper together to make a metre square and use it to check the area of our classroom." Are you ready for a check for understanding? Let's have a look.

Which of these is the correct way to begin measuring the area of the rectangle in square metres? And then so find the right way, but what's wrong with the other ways? Pause the video.

See if you can explain that one.

Okay, did you find the right way? Let's have a look.

So that's the right way to do it.

What's wrong with A though? Can you explain? The square metres are overlapping on A, so that's not right.

What's wrong with C do you think? It is wrong, isn't it? The sides of the square metres are not tessellating.

There are gaps.

So that wouldn't give a true measurement.

Okay, task A, estimate and measure large areas in metres squared.

You could use a metre stick to help imagine the square metres on the surfaces.

If you're allowed to, you might draw some square metres in chalk or mark them out with tape.

So something you can measure could be the playground marking such as hopscotch grids, if you've got those on your playground.

Shapes drawn on the playground with chalk, maybe a teacher might want to draw some of those for you.

Areas created using cones or skipping ropes and the flat floor or wall surface of a corridor.

Now that's one version of this task, but if you've got the resources, you might want to do an alternative version.

If you've got square metres made from paper, you can use them to complete the activity, a bit like we saw earlier.

So again, find a flat surface in the environment around you estimating, then measure its areas in metres squared.

And again, we've got those same examples.

Things like playground marking, shapes drawing chalk, areas created using cones or skipping ropes and the flat floor or wall surface of a corridor.

Okay, so you're going to do one of those two activities.

Have fun.

I think you will.

Good luck and I'll see you soon.

Welcome back.

How did you get on with that? Did you have fun? So you were estimating and measuring large areas using square metres.

And the example that we've got here is a corridor.

Okay, so let's have a look at that.

We've got a corridor and it's been measured in square metres and we can lay them down like that.

Then we've got 1, 2, 3, 4, 5, 6, 7, 8, 9, 10.

Probably just a bit more than 10 though, isn't it? Because of the gaps around it.

So I think something like 12 square metres including the extra bits around the squares.

And again, you might have done that in a different way.

Okay, are we ready for cycle two? That's different shapes with the same area.

So Laura and Jacob are experimenting with different ways of making a 2D shape with an area of two metres squared using their paper square metres.

So look, they've got two metres squared.

It's a different two metres squared, isn't it? So Laura has the idea of changing the orientation of their shape.

So it looks different, but it still has an area crucially of two metres squared.

What about that one? Have a look at that.

What do you think? Is that two metres squared? Hmm, I'm not sure about that one.

Jacob has the idea of making the shapes meet at the vertices.

So look, they're touching each at the vertex of the bottom right of the first one and the top left of the second.

Does that made a shape though? No, that's a non-example.

Because it's two shapes they've got to touch at the sides, so no.

Hmm, what about this one? What do you think? Laura has the idea of having partially connected sides.

So they're not fully connected at this sides.

Do you think she's right? Is that a good idea? I think it is.

Yes, it still has an area of two metres squared.

It's a rectilinear shape.

That is not a rectangle.

Now this one.

What do you think? Hmm, Jacob uses Laura's idea but he rotates the shape.

So it's very similar to Laura but rotated.

Do you think it's still a shape with an area of two square metres? Yeah, it is.

It still has an area of two metres squared.

Oh, okay.

What about this one? That's not a rectilinear shape.

It's a non-rectilinear shape.

It's not composed just a rectangles anymore.

So Laura has the idea of folding two square metres in half to make a non-rectilinear shape.

I think that's clever, don't you? I like that.

Good thinking, Laura.

Thinking outta the box.

It still has an area of two metres square because if you combine them together, those two partial squares, it would create one square.

So it's still got two square metres.

Well done, Laura.

Brilliant.

How about this one? Hmm.

What do you think of this one? Jacob's got the idea of having partially connected sides to make a different non-rectilinear shape.

Do you think it's an example? It is.

It still has an area of two metres squared.

It's a really unusual one, isn't it? Well done Jacob.

It's non-rectilinear and it's an unusual version of that.

So yeah, well done.

Two metres squared.

Hmm.

Okay, back to rectilinear shapes.

Laura has the idea of folding two square metres in half a different way to make a rectilinear shape.

So before they folded them in half to make triangles.

This time they folded them in half to make rectangles, but they still half squares.

It still has an area of two metres squared.

Good stuff Laura.

Creative aren't they, these two.

I like it.

So Jacob knows that there are many different ways he could fold his square metre to give fractions of a square metre, not just halves.

Well that's true, isn't it? Not just halves.

Okay, can you think of a different fraction that we could fold into? What's this one? Quarters.

Yeah, a different way of folding into quarters.

Very nice and a different way again of folding that square metre into quarters, lovely stuff.

So these are different ways of folding that square metre into quarters.

Lisa realises there are lots of other fractions that can be explored when folding the square metres such as thirds.

So we've looked at halves, Jacob looked at quarters.

Laura's thinking about thirds.

Yeah.

Here we go.

A bit harder to fold into thirds, I must say.

But it works.

Yeah, not as easy to fold, but it does work.

Okay, let's have a check for understanding.

Which of the following show a single, a single 2D shape within an area of three metres squared or three square metres.

Select all that apply.

So have a look, which ones are showing three square metres? Pause the video.

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

Yes, A definitely.

That was probably the easiest one of the lot.

B isn't though they're touching at the vertices.

They're not connected by the side.

So no, not B.

C is though.

It's a different way.

It's a rectilinear shape, but it's three metres squared.

And D is as well.

It's a really clever one isn't it? Because we've got halves on it, but they've been folded into different ways.

So that's a really clever non-rectilinear shape that's got an area of three square metres.

So well done if you said A, C and D.

You're on track.

Time for some practise.

So using your paper square metres or drawing on square paper, make as many different shapes including non-rectilinear shapes like we've just seen as you can with an area this time of four square metres.

So think creative just like Jacob and Laura did.

And then number two, these shapes are the outlines of new rugs for the school.

Decide where the rugs will fit in different places around the school.

And if you've made the shapes with square metres, try them out in different places.

If you've drawn the shapes, take a metre stick to estimate where the rugs will fit around the school.

Have fun with that, that does sound like a lot of fun and I'll see you soon for some feedback.

Okay, let's have a look.

So just a few possibilities for four metres squared.

Some of these very creative, I think you'll agree.

I particularly like the one that's got the square quarters on.

I think that's very creative.

That's a very unusual rectilinear shape.

And we've got a nice non-rectilinear shape at the bottom where there's a half that's a rectangle and a half that's a triangle.

Very good.

You might have come up with something completely different.

And well done if you did, you might want to share your creations with the rest of the class.

So number two, these are the outlines of new rugs for the school.

Decide whether the rugs will fit in different places around the school.

Did all the rugs fit in the place that you tried? Hope you had good fun exploring that.

And then which rugs were the easiest to fit into different places? So we've come to the end of what I think has been a really good, fun lesson.

We've been measuring the area of flat shapes using square metres.

Some surfaces are too large in area to be measured in square centimetres and it's quicker and more appropriate to measure them in square metres or metres squared.

Different shapes can have the same area in square metres, including non-rectilinear ones.

And that's the end of the lesson.

It's been great fun working with you today, and I really do hope that we get the chance to work together in the near future.

But until then, take care and goodbye.