Lesson video

Hello there, I'm Mr. Tilstone and I'm absolutely delighted to be joining you today for your maths lesson.

The theme of the lesson is area.

So if you are ready to begin, let us go.

The outcome of today's lesson is I can compare the area of different shapes.

We've got some keywords that we're going to explore now in a my turn, your turn style.

Are you ready? My turn area, your turn.

My turn ascending, your turn.

My turn descending your turn.

Are those familiar words to you? Hopefully area is.

Let's have a little recap on those words and their definition.

So area is a measurement of a flat surface.

It measures a 2D space and the whole of this unit is all about area.

When numbers are in ascending order, they are arranged from smallest to largest.

When numbers are in descending order, they are arranged from largest to smallest.

And I always think of D for down, D for descending.

They're going down the numbers are, we've got a two cycle lesson here.

The first is comparing shapes according to their areas and the second ordering shapes according to their areas.

But if you are ready to begin, let's start by comparing shapes according to their areas.

In this lesson, you're going to meet these two, Andeep and Jacob, have you met those before? They're gonna be here to give us a little helping hand.

So Andeep and Jacob are discussing area it's something they've been learning about in their class.

They are considering the area of the front cover of this book.

They find items with a greater area than the front cover of the book.

So Andeep says, "My tabletop has a greater area than the book cover it takes up more space." And Jacob says, "The window pane has a greater area than the book cover.

If we covered both objects with squares, the window pane would need more." Who's right? They're both right.

Now they are discussing items that they can see which have a smaller area than the front cover of the book.

See if you can think of any before they say theirs.

So Andeep says, "The top face of my pencil case has a smaller area than the book cover.

It takes up less space." And Jacob says, "This plastic coins face has a smaller area than the book cover.

If we covered both objects with squares, the coin would need fewer." And again, they're both right.

Just two different ways of saying the same thing.

So the boys clearly understand a little bit about area.

Let's do a quick check.

So look at the front cover of your maths book or if you don't have your maths book with you something similar.

Number one, find and discuss some objects with a surface area with a greater area than your maths book.

And then number two, find and discuss some objects with a surface with a smaller area than your maths book pause the video and have a go.

How did you get on with that? What kinds of objects did you come up with? Well there are thousands really of things you could have said.

But some possible responses are the interactive whiteboard.

If you've got one of those in your classroom, which you're quite likely to have the classroom door and the ceiling, they're all flat surfaces and in those cases they're all rectangular as well, although they don't have to be.

But they all have a greater surface area than your maths book.

And then the top of a glue lid, an eraser, a sticky note, they all have a surface with a smaller area than your maths book.

So the boys are back and they're comparing the area of these two shapes.

Have a look at those two shapes Andeep says, "Shape A has a greater area because it takes up more space." And Jacob says, "Shape B has a greater area 'cause it has more square units." Hmm.

Who do you agree with there? Who's correct? The boys aren't seeing this one on the same way.

But who's right do you think? Andeep is correct, these shapes cannot be compared according to their square units because the units are not the same size.

They must have the same size squares to be comparable.

Let's have another check, true or false? It is possible to compare the areas of these shapes by counting the square units.

Is that true or is that false? And your options are A, the size of the square units is the same.

And B, they are different types of shapes.

Pause a video and have a go.

What did you come up with? If you are working with somebody, did they manage to say the same thing as you? Did you come up with an agreement on this one? Well it's true.

You can compare those two shapes the reason behind that is that the size of the square units is the same.

So that makes them comparable.

So what do you notice about the area of these two shapes? And so let's a look at that, two different looking shapes.

We've got a stem sentence here.

This shape has an area of square units.

What do you notice? Have a look, have a count.

Well with shape A we can say this shape has an area of six square units.

And with B we can also say this shape has an area of six square units they've got the same area as each other.

So it is possible for two shapes to look different but have the same area? This can be checked using equal size square units.

And the equality symbol can be used.

The equal sign you've probably used that many, many times.

So six square units equals six square units.

Two different shapes to each other.

What do you notice about the area of these two shapes? Maybe give them a little count.

What do you notice? This shape, shape A has an area of six square units.

Shape B, this shape has an area of seven square units.

So this time they don't have the same area as each other.

They look different and they've got a different area.

So when two shapes are unequal equality symbols can be used to show this.

So shape A has a smaller area than shape B six square units is less than seven square units.

So therefore we can use this symbol the inequality symbol six square units is less than seven square units.

That's how we write is less than.

And we can look at it the other way round as well.

Shape B has a larger area than shape A.

Seven square units is greater than six square units.

Can you remember how to write greater than the inequality symbol should we see.

Seven square units is greater than six square units.

So that's how we say it and that's how we write it.

Sometimes it's easy to see just by looking that two shapes have unequal areas.

You can see that with these two.

Shape B is clearly bigger, it's got a bigger area than shape A I can see that I don't need to count that.

So counting the squares becomes unnecessary.

It's clearly got a greater area than shape A.

And to use those inequality symbols we can say the area of shape B is greater than the area of shape A.

We can look at it the other way round as well.

The area of shape A is less than the area of shape B.

When two shapes have clearly unequal areas as hopefully you can see shape A and shape B do, they can be compared even without squares to guide the comparison.

So hopefully you can see that shape B's got a greater area than shape A even without the squares.

So we can say the area of shape A is less than the area of shape B.

And likewise we can say the area of shape B is greater than the area of shape A.

And in this case we we didn't need squares to help us to guide that comparison.

Let's have a check for understanding.

So without counting, so I don't think we need to in this case, use inequality symbols to compare the shapes based on their areas and explain your answer.

Pause a video and give that a go.

Okay, how did you find that? Did you need to count? I don't think you did, I can see that one's got a greater area than the other one.

So let's have a look.

So the area of shape A is greater than the area of shape A and that is the correct inequality symbol.

Or you might say the area of shape B is less than the area of shape A.

And if you said both of those things brilliant even better.

And explaining that and justifying it, you might say something like, shape B would fit inside shape A with space left over that would be a good explanation.

You might say A and B have got the same height yes they have, but A has a greater width so it takes up more space.

But either way you can clearly see that A's got a greater area.

Sometimes we do need to count the square units to check whether areas are equal or unequal.

And remember to check for half squares.

So I can see plenty of half squares here.

So triangles that would combine together to make a whole square unit.

We're going to use a stem sentence this shape has an area of square units.

So let's start by thinking about shape A, give that to count, hopefully find an efficient way.

This shape has an area of 16 square units.

Now try B.

Remember to count the two triangles as one complete square unit.

I'll give you a little chance to do some counting there.

For shape B this here, this shape has an area of 18 square units.

Therefore the area of shape A is less than the area of shape B.

And the area of shape B is greater than the area of shape A.

So do be careful when writing those inequality symbols that you've got the right ones.

Let's do a check.

So work out the areas of these shapes and compare them using inequality symbols.

So our stem sentences, this shape has an area of square units.

And then when you've done that, the area of shape A, the area of shape B, think about the inequality symbol and the area of shape B, the area of shape A.

Have a go at that and pause the video please.

Okay, let's see.

Shape A, this shape has an area of 15 square units and shape B this shape has an area of 13 square units.

So therefore the area of shape A is greater than the area of shape B.

And the area of shape B is less than the area of shape A.

So I did need to count those to be able to be sure, sure there but well done if you've got those correct, you're on track.

I think you are ready for some independent work.

What do you think feeling confident? For each pair of shape circle the shape of the greatest area.

You might notice there's no squares inside those you don't need them.

You can see hopefully that one has got a greater area than the other.

Number two, compare each pair of shapes by writing less than or greater than or equals in the blank box.

So you've got A, and B, and C.

Pause the video.

Good luck with that and I'll see you very soon with some answers to the tasks.

Welcome back, how'd you find that? Did you get an okay with that? Let's have a look.

So for number one, the shape of the greatest areas are bit circled in each example.

Let's see if you've got the same ones.

For number two, those two shapes are equal.

So we need the equal sign for the for A and then for B it's greater than and C is less than.

That's cycle one complete, let's move on to cycle two ordering shapes according to their areas.

In the same way that some pairs of shapes can be compared without the need for counting square units.

Some groups of shapes can be ordered and without counting.

So have a look at these shapes.

You can see they've got different areas.

Can we put them into an order? Can we put them into ascending order to start with so going up.

The triangle has the smallest area and the circle has the greatest area.

Let's see that so smallest.

And then getting the areas getting bigger as we go along.

And the circle's got the greatest area.

So they've now been put into an order.

We can go the other way, descending order.

The circle's got the greatest area.

So that will come first and the triangle's got the smallest area.

So those shapes are now in descending order D for down.

Let's have a check.

Put these shapes into descending order according to their areas.

Pause the video.

Okay, how'd you get on with that? Find that straightforward, let's have a look.

This is the correct descending order, B, A, D, C.

And if you've got that well done, you're doing well.

Sometimes it's necessary to count the squares and part squares to determine a total area in square units of each shape.

So when I'm looking at these shapes, I'm not really sure which one's got the biggest area and which one's got the smallest.

It's not jumping out at me, I do need to count to start my comparison.

And we're going to look how many square units each one's got.

Remembering that two triangles in these cases combine to make one square unit.

So A, when we do that it's got 17 square units.

B has got 14 square units and C has got 18 square units.

So let's put them into order.

Let's do it in ascending order.

So that goes B, A, C, 14, 17, 18.

And the inequality symbols can be used here as well.

So we could say the area of B is less than the area of A, is less than the area of C.

Descending order the other way, it goes C with 18 square units, A with 17 square units and B with 14 square units.

And just like before, we can use those inequality symbols to compare them.

So we could say the area of C is greater than the area of A, which is greater than the area of B.

Let's have a check consider the areas of the following shapes.

Are they in ascending order, or descending order, or neither? So you're going to need to do a little bit of counting and then decide if they're in order or not.

Pause the video.

What did you think? They are in ascending order.

They are increasing in area as they go.

So well done, if you've got that.

I think you are ready for some more independent practise.

So number one, put the following shapes into ascending order according to their areas and use those inequality symbols so they're greater than and less than symbols.

Number two, same.

You're gonna need to do some counting.

Now these are a bit trickier though.

See if you can see why these ones are a little bit trickier.

And number three, put these shapes in ascending order according to their areas.

This time you're going to use inequality symbols.

And number four, draw a shape either side of shape B, so that the statement is correct.

So look at the inequality symbols.

I won't say which one it is 'cause I want you to word that one out.

And then draw a shape either side and it might be a rectilinear shape, it might be a non rectilinear shape you can be creative.

Okay, pause the video.

Good luck with that, enjoy and I'll see you soon.

Okay, how did you get on? So here A's got nine square units, B's got eight square units and C's got 10 square units.

So we can say the area of B is less than the area of shape A, which is less than the area of C and those are the correct inequality symbols to use.

Number two, A's got seven square units, B's got 10 square units and C's got eight square units.

So we could say the area of B is greater than the area of C and it's greater than the area of A.

So those are the correct inequality symbols to use for that one.

Number three.

So A's got 20 square units and B's got 12 square units, and C's got 15 square units.

So we needed need to do that counting before we were able to put them in order.

And you can see that they're quite unusual shapes for different reasons, but we could say the area of B, is less than the area of C, which is less than the area of A.

And those are the inequality symbols to use make sure you've got the right ones.

And maybe you got a bit creative here there's so many different possibilities.

Very unlikely that you got the same ones as me, but these are the ones I got.

So any response where A is less than 13 square units and B is greater than 13 square units will be a correct answer.

And I've shown you an example here with my non rectilinear shapes.

We've come to the end of the lesson.

Today's lesson has been explaining how to compare the area of different shapes.

Two or more shapes can be compared according to their area using equality, so that's the equal sign and inequality symbols.

So there's your inequality symbols.

So that is less than and greater than.

Shapes can be put into either ascending or descending order based on their area.

So ascending means they're going up, descending means they're going down.

Use efficient strategies to compare an order area, deciding when it is necessary to count squares.

So you don't always need to count the squares sometimes you can just see.

I've thoroughly enjoyed exploring, comparing the area of different shapes with you.

I hope you've enjoyed the lesson too.

Hope you've got lots out of it and I hope I see you again soon for another maths lesson.

But until then, take care of yourself and goodbye.