Lesson video

Hello there.

My name is Mr. Goldie and welcome to today's maths lesson.

And here is the learning outcome for today's lesson.

I can identify a rectangle as a four-sided polygon with four right angles.

Here are the keywords for today's lesson.

I'm going to say each keyword.

Can you repeat it back? The first word is polygon and the next keyword is rectangle.

Let's take a look at what those words mean.

So a polygon is a 2D shape made up of three or more straight sides.

So a triangle is an example of a polygon and so is a quadrilateral.

A rectangle is a 2D polygon with four straight sides and four right angles.

And here's the lesson outline.

So in the first part of the lesson, we're going to be investigating right angles in 2D shapes, and in the second part of the lesson, we're going to be marking right angles in shapes.

Let's get started.

In this lesson, you will meet Aisha and Laura.

Aisha and Laura really enjoy investigating shapes and really like solving puzzles to do with shape.

And they've got some interesting puzzles and problems for you to solve today.

Aisha and Laura are looking at these 2D shapes.

So here are six 2D shapes.

"What is the same about all of these shapes?" asks Laura.

Aisha says, "All the shapes have straight sides.

They also have sharp vertices." "Is there a name for all the shapes?" asks Laura.

"They are all polygons," says Aisha.

A polygon is a 2D shape with three or more straight sides.

How are the polygons different to each other? So these polygons have three sides and three vertices.

"These shapes are triangles," says Aisha.

"These polygons have four sides and four vertices," says Laura.

"These shapes are all quadrilaterals," says Aisha.

"This polygon has five sides and five vertices." "This shape is a pentagon," says Aisha.

"Which of the polygons have right angles?" So remember, a right angle is a square corner.

Laura is going to test some of these shapes to see whether they've got right angles or not.

She's going to start with this triangle.

This triangle here has a right angle.

"This triangle has one right angle," says Aisha.

Let's look at the shape.

So Laura's going to test it out, test each of the corners to see whether they are a right angle or not.

This quadrilateral does not have any right angles.

Let's take a look at that next polygon, which is the pentagon here.

This pentagon has two right angles.

Now it's your turn to have a look at the last three shapes.

Which of these polygons have right angles? Can you see any right angles in these polygons? So have a look at those last three shapes.

Can you see any right angles in them? Think carefully about how you're going to test the right angles.

Are you going to use a right angle measurer? Are you going to use the corner of a book or the corner of a piece of paper? Make sure whatever you are testing them with is a right angle as well.

Well, pause the video and see if you can identify any right angles in those polygons.

And welcome back.

Did you test all three shapes? Did you find any right angles? Let's see if you found them all.

So this triangle, the first triangle, has no right angles.

The second shape, this quadrilateral has four right angles.

So in fact, each of the corners on this shape is a right angle.

The quadrilateral has four right angles.

And finally, the last quadrilateral has two right angles.

So well done if you found all the right angles in those shapes.

Laura is very interested in one of the shapes.

So she's interested in this shape here.

Let's make the shape a little bit bigger.

"All the vertices in this polygon are right angles," says Laura.

"This is a special type of quadrilateral.

It's called a rectangle," says Aisha.

It's quadrilateral because it's got four straight sides and four vertices.

"A rectangle is the only simple 2D shape where all the vertices are right angles." You can't have a triangle with just right angles.

You can't have a pentagon with just rectangles.

A rectangle is the only simple 2D shape where all the corners are right angles.

Laura wants to find out more about rectangles.

"Two of the sides are the same length," says Laura.

So these two sides here are the same length on the rectangle.

"There's another pair of sides which are the same length too." So these two sides are also the same length and that's true for all rectangles.

All rectangles have two pairs of lines that are the same length as each other.

"The rectangle also has reflective symmetry." So it's got a line of symmetry running horizontally across the rectangle this way.

And there's another line of symmetry too.

All rectangles have at least two lines of symmetry.

There's a line of symmetry running this way.

So all rectangles have at least two lines of symmetry.

Some rectangles have more.

Laura tries to find the rectangles.

"I'm looking for shapes that have exactly four right angles." So which shapes have exactly four right angles? Let's have a look at those four shapes.

The first shape is not a rectangle.

Two of the lines do not meet to form a vertex.

So it hasn't got four right angles.

So it is not a rectangle.

In fact, it's not even a quadrilateral because it doesn't have four vertices.

Let's take a look at that second shape.

This is a rectangle.

It is a quadrilateral, a four-sided shape with four right angles.

So that is a rectangle.

Our next shape.

Is that a rectangle? This is not a rectangle, it is a quadrilateral, but it only has two right angles.

Remember, a rectangle has to have four right angles.

If it doesn't have four right angles, it's not a rectangle.

So this is not a rectangle.

And our last shape, is that a rectangle? This is a rectangle.

It is a quadrilateral with four right angles.

Every vertex on that shape is a right angle.

So it is a rectangle.

Sometimes it's helpful to rotate a shape to see if it looks more familiar.

So sometimes rectangles are a little bit difficult to spot because they might be in a funny orientation, like that rectangle there.

But if we turn it around, we can see quite clearly that it's a rectangle.

It's much easier to recognise the right angles now.

Which of these shapes are rectangles? So three shapes there, A, B and C.

Are they all rectangles? Are none of them rectangles? Or is one or two of them a rectangle? So remember, a rectangle is a quadrilateral with exactly four right angles.

So pause the video and see if you can work out which of those shapes are rectangles.

And welcome back.

Did you identify the rectangles? Let's take a look, see whether you've got them right.

Hopefully you thought about how you're going to identify the right angles on the shapes.

Sometimes you can see quite clearly they're right angles.

Sometimes you have to use a right angle measurer.

So let's take a look at shape A.

So shape A is a pentagon, not a quadrilateral.

So straightaway, it can't be a rectangle because it's not a quadrilateral.

A rectangle has to be a quadrilateral with four right angles.

And also, it only has three rectangles.

So it's definitely not a rectangle.

That is not a rectangle.

Shape B, is that a rectangle? Looks like it could be.

Shape B is a quadrilateral but it has no right angles.

And finally, our last shape is this one here.

C, shape C is a rectangle.

It is a quadrilateral with exactly four right angles.

And remember, any shape that is a quadrilateral, that has four straight sides of all vertices, and it also has four right angles, any shape like that is a rectangle.

So shape C is a rectangle.

Let's move on to task A.

So in task A, you're going to sort the shapes into the table.

Here's Laura and Aisha to offer you some advice as well.

So remember, a rectangle is a quadrilateral with four right angles, has to have four right angles.

And Aisha's saying, "Check each of the angles carefully." So think carefully about checking every angle, especially if the shape is a bit of a different orientation, it's been turned around, rotated slightly so it's more difficult to recognise the right angles.

So if the shape is a rectangle, you are going to put it on the side of the table where it says "is a rectangle." If it is not a rectangle, you're gonna put it on the side of the table where it says "is not a rectangle." Can you sort the shapes correctly? And here are the 12 shapes that you are going to be sorting.

So count the number of sides in each of the shapes.

Does it have four sides? Is it a quadrilateral? Are each of the vertices right angles? If it does not have four right angles, it is not a rectangle.

So pause the video and see if you can sort those 12 shapes onto the table into the correct places.

And welcome back.

How did you get on? Did you manage to sort all 12 shapes? Have you definitely got them in the right places? Let's take a look to see whether you got them right.

So here are the answers.

So shapes B, F, G, J, and L were all rectangles.

Some of them, of course, were turned around slightly, rotated slightly so it's been more difficult to spot them.

But all of those are quadrilaterals with four right angles.

These shapes are all quadrilaterals with exactly four right angles.

So very well done if you sorted those into the correct place on the table.

The other shapes are not rectangles.

So shape C is not a rectangle because it only has two right angles.

Shape I is not a rectangle.

It looks a little bit like a rectangle, but in fact, none of the vertices on the shape are right angles.

So it is not a rectangle.

But very well done if you managed to sort all those shapes into the correct place on the table.

Excellent work.

And let's move on to part two of the lesson.

So part two of the lesson is marking right angles on shapes.

Aisha wants to show that shapes have a right angle.

"Is there a way of showing that shapes have a right angle?" asks Aisha.

"Yes, there is," says Laura.

A right angle is a square corner so a special symbol is used where the vertex forms a right angle.

So here is a right angle.

The special symbol looks like this.

So it actually looks like a little right angle stuck in the corner.

So how would you show the right angles on this rectangle? We can mark each vertex to show it is a right angle.

So each of the vertices we can draw a symbol to show it is a right angle.

Now, if you see a shape looking like that, it means it is a rectangle.

Each of those corners, each of those vertices has been tested, they're all right angles and you can only use that symbol when the angle is exactly a right angle.

Aisha marks the right angles in this shape.

"First, I'm going to check each angle." So Aisha checks the first vertex.

This is not a right angle, so Aisha cannot draw the symbol in that place there because it is not a right angle.

This is not a right angle either.

So Aisha cannot put the right angle symbol in that vertex either.

This is a right angle, so I'll mark it with the right angle symbol.

So Aisha draws that symbol in the corner to show she has checked it, to show it is a right angle.

And finally, this corner here, this is also a right angle.

So Aisha draws the symbol in that corner as well.

Aisha marks the right angles in this pentagon.

"First, I'm going to check each angle." So this is not a right angle, in fact, it's quite a lot larger than the right angle.

So Aisha can't use the symbol there.

At the top of the pentagon, there is a right angle.

So Aisha marks it with the symbol in the correct place here.

"This is not a right angle," says Aisha.

This is a right angle.

So Aisha draws the symbol in that corner as well to show that she's checked it, show it is a right angle.

And finally, that last vertex here, "This is also a right angle.

The pentagon has three right angles." Very good checking there, Aisha, well done.

Aisha marks the right angles on these shapes.

So there's three shapes there.

She's marked the right angles on the shapes already.

"Have I missed any right angles?" asks Aisha.

What do you think? Can you spot any missing right angles? Pause the video and see if you can work out if there are any missing right angles and where on the shapes they might be.

And welcome back.

Did you manage to find any missing right angles? Did Aisha miss any out? Let's take a look to see whether you found 'em all.

Let's start off with shape A.

So Aisha has missed a right angle in this triangle.

So this vertex here on the triangle is actually a right angle.

Let's look at shape B next.

Aisha has missed a right angle in this rectangle.

This vertex here is also a right angle.

And finally, shape C, Aisha is correct.

This quadrilateral has no right angle so you can't mark any of them with the right angle symbol.

So well done, Aisha, only missed two out.

Very well done if you spotted the two that Aisha had missed out.

That's excellent work.

Aisha and Laura draw rectangles.

"Each vertex has to meet at one of the points on the grid," says Aisha.

Each vertex must be a right angle.

Remember to be a rectangle, shape's got to have four right angles.

"I'm going to draw a rectangle on this grid," says Aisha.

Aisha starts by drawing one side and another side and another side and another side.

So Aisha's drawn a shape with four straight sides and four right angles.

And then she marks each vertex using the correct symbol.

"I'm going to draw a different rectangle," says Laura.

Laura draws one, two, three, four straight sides and each of the vertices is a right angle.

And again, she marks each of the vertices with the correct right angle symbol.

Aisha completes this rectangle.

"I already have one side of the rectangle." So how could Aisha complete that shape to make it into a rectangle? "Remember to use rectangles for very vertex," says Laura.

So Aisha draws three more lines, three more sides to complete her rectangle.

"I have completed the rectangle.

I'll mark the right angles." So in each of the vertices, Aisha uses the right angle symbol to show that each one is a rectangle.

"Can you find a different way to make a rectangle?" asks Laura.

So Aisha makes a different rectangle.

So she's still starting from the same starting place.

She's still got the same side to start off with, but she's going to create a different rectangle this time.

"I already have one side of the rectangle," says Aisha.

"Remember to use right angles for every vertex," says Laura.

So this time, Aisha completes her rectangle like this.

"I have completed a different rectangle and again I'll mark the right angles." So in each vertex, Laura uses the correct symbol to show that each corner, each vertex is a right angle.

Excellent work, Aisha.

"I wonder if there are other ways to make a rectangle," says Laura, Can you find a different way to make a rectangle? So this has got to be one side of the rectangle.

Can you find a different way of completing a rectangle? Now, Aisha's already done it two different ways.

Can you find a third way? "Use this line as one side of your rectangle." "Remember to use right angles for every vertex," says Laura.

Pause the video and have a go at that problem.

And welcome back.

Did you manage to complete the shape? Did you manage to draw a rectangle? Did it definitely have four right angles? Let's take a look to see how you could have completed that shape.

So here is one possible answer.

You may have solved that problem in a different way.

So you could have drawn your rectangle like this.

So very well done if you completed that problem.

And of course, Aisha and Laura can go through and put in the right angle symbols to show that each vertex is a right angle as well.

But well done if you solved that problem.

Excellent work.

Aisha uses a different line to make rectangles.

This is gonna be more tricky to solve because this time, the line is no longer horizontal.

"This is much trickier.

How am I going to make a rectangle?" asks Aisha.

"Use an angle checker to help create the shape," says Laura.

"I'll use the points to draw the rectangle accurately," says Aisha.

So Aisha uses an angle checker, using it to make a right angle so she knows where to draw the line and she can use that to help her work out which point she should be drawing to.

So Aisha draws a side of the rectangle to that point there.

She moves her angle checker around to here.

So again, she's creating another right angle and again, she can work out which points she should be drawing to.

And then she moves it one more time and then takes it back to the beginning and then just checks that last angle to make sure it's a right angle as well.

So Aisha has drawn a rectangle.

Well done Aisha.

Let's mark the right angles.

So Laura and Aisha use the right angle symbol to mark all the vertices of the rectangle to show that they are right angles.

Excellent work, Aisha.

That's really good.

Laura makes shapes using the same line.

"Have I made three rectangles?" asks Laura.

So are those shapes all rectangles? They're all quadrilaterals.

She's drawn four-sided shapes each time.

But is each of them a rectangle? Have a good look at each of the shapes.

Again, you might want to use an angle checker or a square corner to help you check the right angles.

But pause the video, see if you can work out which of those shapes is a rectangle and which of those shapes is not.

And welcome back.

Did you manage to find out which shapes are rectangles and which ones weren't? Let's take a look to see whether you got it right.

Let's start with shape A.

So we can use angle checkers to check the angles on that shape.

Well, if one of the angles is not a right angle, it can't be a rectangle.

So the angles in shape A are not all right angles.

The shape is not a rectangle.

Okay, so shape A definitely is not right.

Shape B, oh, that's a right angle.

The angles in shape B are all right angles.

This shape is a rectangle.

So it's got four right angles so we can mark each of the vertices with the correct symbol.

So that one is correct.

Very well done, Laura.

And lastly, shape C.

Is that a rectangle? Well, that angle there is quite a lot larger than a right angle, so it cannot be.

Remember, if one of the angles is not a right angle, the shape cannot be a rectangle.

The angles in shape C are not all right angles.

This shape is not a rectangle.

Okay, so good try, Laura, but only shape B was correct.

So very well done if you spotted that shape B was a rectangle, but that shape A and C were not rectangles.

Excellent work.

Let's move on to task B.

So in task B, you're going to use the right angle symbol to show all of the right angles in these polygons.

And then you're going to write the number of right angles each shape has got.

Check each vertex really carefully.

Check to see whether it is a right angle and if it is a right angle, use the correct symbol to show it is a right angle.

And then you're going to complete the number of right angles that each shape has got.

And if it has zero, write zero.

Those shapes A, B, C, and D there and there are more shapes, E, F, G, and H.

Which of those have right angles? Look really carefully.

And here's part two of task B, bit of a challenge this one.

Use each grid to create a rectangle.

Use the line given as one side and make each vertex meet at a point.

So the line you're given already is gonna be one side of the rectangle.

Can you complete a rectangle? "Use an angle checker to help create each shape." Very, very good advice, Laura.

So as you're drawing that shape, really take your time and use an angle checker to make sure that each vertex of the shape is a right angle.

So pause the video and have a go at task B.

And welcome back.

How did you get on with task B? Did you manage to get to part D? Did you manage to complete some of those tricky rectangles? Let's take a look to see how you got on.

So here are the answers for part one of task B.

So here's Shape A.

Shape A is a pentagon and it has three right angles.

Well done if you spotted that extra right angle.

So all together, there are three right angles on that pentagon.

You should have marked three vertices with the right angle symbol.

Let's take a look at shape B.

Shape B has zero right angles.

It is a quadrilateral but it is not a rectangle.

So well done if you spotted that.

Shape C has four right angles.

All rectangles have four right angles.

That is a rectangle, it's a quadrilateral and it has four right angles.

Well done if you spotted all four rectangles in that shape.

Shape D, the number of right angles is one.

This is a right-angled triangle.

So well done if you looked at those four shapes, and got those four correct.

Let's move on to the next four.

So shape E also has four right angles because all rectangles have four right angles and that is a rectangle.

Shape F has two right angles, it's a quadrilateral but it is not a rectangle.

Shape G also has two right angles.

So well done if you spotted those.

Now, shape H is quite tricky 'cause there are five right angles all together.

So well done if you spotted H actually has got five right angles inside the shape.

Let's move on to part two of task B.

Now, here are some possible answers.

You may have come up with rectangles that look different.

Now, all three shapes are rectangles because they are quadrilaterals with four right angles.

And you may have used the right angle symbol to show that each vertex is a right angle as well.

So very well done if you've got on to part two and you managed to make three complete rectangles.

That's brilliant work today.

Very well done.

And hopefully you can now recognise when a shape is a rectangle and when a shape is not a rectangle.

And you can use different language to describe a rectangle.

Thinking about the number of sides a rectangle has, thinking about the number of right angles that a rectangle has.

Think about the lines of symmetry in a rectangle and thinking about whether the sides are equal length or not.

Excellent work today.

Very well done indeed.

And finally, here is our lesson summary.

So our polygon is a 2D shape made up of three or more sides.

A rectangle is a four-sided polygon with four right angles.

A four-sided shape with fewer than four right angles is not a rectangle.

A right angle is marked with a symbol inside the angle.