Lesson video

Hello, there.

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

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

I know a square is a rectangle in which all four sides are of equal length.

And here are the keywords.

I'm going to say each keyword.

Can you repeat it back? So the first keyword is rectangle.

The next keyword is square.

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

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

A square is a 2D shape with four equal straight sides.

And here is our lesson outline.

So the first part of the lesson is called, "What is a square?" and the second part of the lesson is called, "Identify squares and their properties." Let's get started.

In this lesson, you will meet Aisha and Laura who will be helping you with your maths today and asking you some difficult questions as well.

Aisha makes some rectangles on this grid.

Here's one rectangle.

Here's another, here's another, and here's another.

"I've made four different rectangles," says Aisha.

Laura says, "I think that 3 of them are definitely rectangles." So this is a rectangle, this is a rectangle, and this is a rectangle.

"But I think one of them is a square." So Laura says this shape here is a square.

Aisha thinks about the properties of a rectangle.

A rectangle is a quadrilateral with 4 right angles.

Now remember, a quadrilateral is a 4-sided shape.

So any 4-sided shape with 4 right angles is a rectangle.

Laura says, "A square is a quadrilateral and it also has 4 right angles." So a square is a 4-sided shape with 4 right angles.

There are the 4 right angles.

Is a square also a rectangle? What do you think? Is a square a rectangle? A square is a rectangle.

Every square is also a rectangle.

But not every rectangle is a square.

A rectangle has two sides the same length.

So these two sides are the same length as each other.

It also has another two sides the same length.

So these two sides are also the same length as each other.

A square has 4 sides of equal length, so every side on a square is the same length as each other.

"A square is a regular shape," says Aisha.

Now regular just means that all angles are the same size and all sides are the same length.

So a square is a special type of rectangle where all the sides are the same length.

All rectangles have reflective symmetry.

Every rectangle has at least two lines of symmetry.

Here's one line of symmetry, and here's another.

How many lines of symmetry does a square have? Now it's a rectangle, so it must have at least two.

How many do you think it has? Let's take a look.

Let's use a mirror to check.

So here is one line of symmetry.

This is a way of putting the mirror on the line so you can still see the square as being the whole shape.

Here's another line of symmetry.

So you could also put the mirror in that place on the square and you can also see the whole square still.

Are there any more lines of symmetry? There's also a line of symmetry which goes diagonally through the square as well.

There's one line of symmetry here as well.

And there's a 4th line of symmetry, another diagonal line of symmetry through the shape as well.

So altogether, a square has 4 lines of symmetry.

Laura tries to find the squares.

So Laura's going to identify the squares.

Which shapes have exactly four right angles and have four equal sides? So the first shape here is a rectangle, but it is not a square.

The sides are not all equal length.

Two sides are longer than the other two.

So the shape here is a rectangle but it's not a square.

The second shape is a square.

It has 4 right angles and 4 sides of equal length.

This third shape here is called a rhombus.

Now it has 4 equal sides, but it does not have any right angles.

So, in fact, that shape there is not a rectangle.

And because it's not a rectangle, it cannot be a square.

And finally our last shape, this is a square! It has 4 right angles and 4 sides of equal length.

There are the 4 right angles.

Now Laura says, "Sometimes it's helpful to rotate a shape to check whether it's a square." Sometimes you look at a shape and think, that's not a square 'cause it doesn't look like it's got right angles.

But actually if you rotate the shape, it's much more obvious whether it is a square or not.

So we can rotate the shape and we can see quite clearly that is a square.

Now it's your turn to have a think about which shapes are squares and which ones are not.

Which of these shapes are squares? Remember, a square is a rectangle with 4 sides of equal length.

Pause the video and see if you can work out which of those shapes are squares and which are not squares.

And welcome back.

Did you manage to work out which shapes are squares? Let's take a look to see whether you've got it right.

So Aisha says, "Shape a is a square.

It is a quadrilateral with 4 right angles and 4 sides of equal length." This shape here, definitely a square.

Take a look at shape b next.

Shape b is a rectangle, but it does not have 4 sides of equal length.

So it has 4 right angles but it does not have 4 sides of equal length.

So that shape there, shape b, is not a square.

Shape c is a square! It is a rectangle with 4 sides of equal length.

So it has 4 right angles and it also has 4 sides that are equal length.

So very well done if you identified that shape a and c were squares, shape b was a rectangle but it was not a square.

Aisha sorts these shapes onto the Venn Diagram.

So there's a circle that says "rectangle" in it.

So all the shapes that are rectangles would have to go into that circle there.

And then there's a circle within that circle which says "square." So any shape that is a square would go inside that circle.

Aisha says, "Shape a is a rectangle, but it is not a square." So shape a would go in here.

Shape b is a square, which is a type of rectangle.

So it has to go inside the rectangle circle, but it also goes inside the square circle as well.

So shape b will go in here.

What about shape c, wonder where that would go? Well shape c is not a rectangle, so it cannot go in the rectangle circle.

So shape c would actually go on the outside of the Venn Diagram here.

Now it's your turn to sort two shapes, the shape d and the shape e.

So where would they go on the Venn Diagram? Pause the video and see if you can work out where shape d and shape e should be sorted onto the Venn Diagram.

And welcome back.

How did you get on? Did you manage to sort both shapes? Did you definitely get them in the right place? Let's take a look, to see whether you got them right.

So Aisha says, "Shape d is a square, which of course is a type of rectangle." Shape d has 4 right angles and 4 sides of equal length.

So shape d will go inside this circle here.

It is a type of square, which, of course, is a type of rectangle.

Shape e is not a rectangle.

So shape e would actually go on the outside of the circle here.

Very well done if you managed to get both of those shapes in the correct places on the Venn Diagram.

And here is Task A! So Task A, you're going to be sorting the shapes onto the Venn Diagram.

Remember, a rectangle is a quadrilateral with 4 right angles, and a square is a regular rectangle.

It has 4 sides of equal length.

So if it's got 4 right angles, it's a rectangle.

If it's got 4 right angles and 4 sides of equal length, it is a square.

So here are the 12 shapes that you are going to be sorting.

So see if you can work out where they would go on that Venn Diagram.

Good luck! Pause the video and have a go at Task A.

And welcome back.

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

So here are the answers.

So shape c, g, l, a, k and d were not rectangles, so they all went on the outside of the Venn Diagram.

But all the shapes in this circle are rectangles.

So e, f, i, b, h, j are all rectangles, they go inside the rectangle circle.

And all of the shapes in this circle are squares.

So b, h, and j, not only are they rectangles, they are also squares, so they go inside that circle there.

Very well done if you sorted some or all of the shapes into the correct place on the Venn Diagram.

Excellent work.

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

So the second part of the lesson is, identify squares and their properties.

Aisha and Laura think about how to recognise a square.

Sometimes it's easy to tell whether a shape is a square or not.

There's three shapes here.

Which of those are squares? Well, this is a rectangle, but it is not a square.

It's quite easy to see that, isn't it? The 4 sides are definitely not of equal length.

This second shape here is a square, the sides are all of equal length.

And this shape here is not a square.

The sides are equal length but it has no right angles.

Can you remember the special name for that shape? It's called a rhombus.

Laura says, "Sometimes it's much harder to tell.

This shape is a rectangle, but is it also a square?" Hmm, what do you think? It looks like it could be a square, doesn't it? Well this is a rectangle.

Are all the sides of equal length? Aisha and Laura want to classify this shape.

"First, I'm going to check each vertex to see whether they are all right angle." So Aisha goes through and checks each vertex of the shape.

"This quadrilateral has 4 right angles, so it's a rectangle." So it's definitely a rectangle.

Question is, is it a square? "I'm going to mark each vertex with the right angle symbol," says Aisha.

"Is the shape a square?" says Aisha.

"We have to measure every side to find out if they are equal length," says Laura.

So Laura measures this side here of the shape, "We have to start each measurement from 0 centimetres." So it's really important when you're using a ruler, to line up the ruler so that one of the ends of the line is on that 0, that 0 centimetres.

That first line there that Laura has measured is 4 centimetres long.

Laura moves the ruler around this shape, around this rectangle, to measure the second line.

Now, is that 4 centimetres? It's not, is it? So again, we're starting the ruler on 0 centimetres.

And if you actually look really carefully, we get to 3 centimetres and then there are 5 millimetres more.

So the measurement there is 3 centimetres, 5 millimetres.

I think we've already answered Aisha's question there.

Aisha has asked, "Is the shape a square?" Is it a square? Hmm, don't think it is, is it? Let's measure this next line.

So that's also 4 centimetres long.

So remember, of course, when you are looking at a rectangle, two sides of equal length and the other two sides are equal length.

So this side here is 4 centimetres long.

And finally, this last side here should be 3 centimetres, 5 millimetres long.

So the shape is not a square because not all the sides are equal.

The shape is a rectangle but it is not a square.

Aisha and Laura want to classify this shape.

"First I'm going to check each vertex to see whether they are all right angles," says Aisha.

So Aisha goes through, uses a right angle checker, and they are all right angles.

"This quadrilateral has 4 right angles, so it's a rectangle," says Laura.

"I'm going to mark each vertex with the right angle symbol," says Aisha.

So she goes through and marks each vertex with the correct symbol.

"Is this shape a square?" says Aisha.

Well it's definitely a rectangle.

Is it a square? "We have to measure every side to find out if they are equal length," says Laura.

So Laura starts off with this side here, again starting with 0 centimetres.

How long is that side there? It is 5 centimetres long.

Next side here is, have a look at that, it's also 5 centimetres long.

And the next side is 5 centimetres long.

And the next side is 5 centimetres long.

So is the shape a square? The shape is a square because all the sides are equal length.

This shape is a rectangle, it is also a square.

So remember, all squares are rectangles, not all rectangles are squares.

Laura has marked the right angles and measured the length of the sides in these shapes.

So there are shapes there, shape a, shape b, shape c.

Which shapes are squares? So look carefully at Laura's measurements.

She's done most of the work for you already.

You've just got to identify whether the shape is a square or not.

Pause the video and see if you can work out whether those three shapes are squares or whether they are not squares.

And welcome back.

Let's take a look, see how you got on.

So shape a is not a square.

The sides are not all equal length.

It's got two sides that are 6 centimetres long and two sides that are 5 centimetres long.

It does have 4 right angles, so it is a rectangle, but it is not a square.

Let's look at shape b next.

Shape b is a square! The sides are all equal length.

It's got 4 right angles and it's also got 4 sides of equal length.

So shape b is a square.

What about shape c? Shape c is not a square.

The vertices are not right angles.

Yes, it has 4 sides that are of equal length, so it's a rhombus, but it is not a square.

Laura creates a square on this grid.

"The square needs to have 4 right angles and 4 sides of equal length," says Laura.

So here's one side of Laura's square.

Here's another, here's another, and here's another.

"I'll mark each right angle with the correct symbol," says Laura.

Now a really good way if you're drawing shapes on a grid to work out whether the sides are equal length or not, is by counting the number of points that each line goes through.

So you can see there, that all together, each line goes through five points all together.

It starts off one point, it goes through three more, and it ends on another.

So each line is five points long.

Because they're all going through five different points and all the points are the same distance apart, that shape there must be a square.

Aisha creates a square on this grid.

This one's a bit trickier because, of course, the line is diagonal.

It's not a horizontal line.

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

"I need to make sure all the sides are of equal length." So Aisha can look carefully to see how many points each line goes through.

"I'm going to use an angle checker to help me draw the square accurately." And she makes sure that the vertex of the shape is a right angle and then she draws the line.

Then she uses the right angle checker again to make another line.

And uses it once more to create the last line.

And she double-checks that last vertex just to make sure it's a right angle as well.

"All the vertexes are right angles.

I'll mark each of them with the correct symbol." So Laura uses the right angle symbol in each of the vertices to show that each corner is a right angle.

So Aisha has drawn a square, it's got 4 right angles and all 4 sides are of equal length.

Laura uses a line to complete a shape.

"Have I made a square?" says Laura.

Have a good look at those three shapes.

Has Laura made a square? Pause the video and see if you can work out the answer.

And welcome back.

Did you spot a square? Is there a square? Let's take a look.

So shape a, Laura uses an angle checker to check the angles on the shape.

That's not a right angle, is it? So the vertices in shape a are not right angles and the sides are not of equal length.

So the shape is definitely not a square.

Let's take a look at shape b.

So again, Laura uses a right angle checker to check the angles on her shape.

Is that a square? It is not, no.

The angles in shape b are not right angles and the sides are not of equal length.

This shape is also not a square.

Bad luck, Laura.

Let's look at shape c.

Is it a square? Oh, Laura's used the right angle checker and that is a right angle.

The vertices in shape c are right angles and the sides are of equal length.

This shape is a square.

So Laura uses the right angle symbol in each vertex of that shape as well.

And because it's got 4 right angles and the sides are of equal length as well, it is a square.

So very well done, Laura.

You managed to draw a square.

Very well done if you've identified that shape c actually was a square.

Well done.

And let's move on to Task B.

In the first part of Task B, you're going to identify which shapes are squares.

So remember, to be a square, it has to have 4 right angles and it also has to have 4 sides of equal length.

So some of those shapes might be rectangles, but they might not be squares.

So think about what you got to use to work out the answer.

So right angle checkers will be very, very useful here.

And so would a ruler, to check that all 4 sides are of equal length.

And here is part 2 of Task B.

So complete the squares using these grids.

One side of the square is already given.

So you've got to make sure that each square has 4 equal straight sides and 4 right angles.

So again, you might need to use an angle checker on there.

And look really carefully to see how many points each line goes through on your square.

'Cause, of course, they have to be equal length lines, otherwise it is not a square.

And then finally, a bit more of a challenge this one.

Part 3 of Task B, complete the squares using these grids.

One side of the square is already given.

So this time, the lines are not horizontal.

So it's a bit more tricky to work out how long the lines are.

So you may need to use a ruler to measure the lines after you've drawn each shape to check that they are equal length.

And don't forget, of course, each corner, each vertex of the shape needs to be a right angle, otherwise it's not a rectangle and it definitely is not a square.

So pause the video and have a go at Task B! And welcome back.

And let's take a look at those answers.

So here are the answers for part 1 of Task B.

So shape a was a square and so was shape c.

And so was shape e.

All those shapes were squares.

Shape b is not a square because the sides are not of equal length.

Shape d is not a square because the sides are not of equal length.

So they are both rectangles, those shapes, but they are not squares.

Shape f is not a square because the vertices are not right angles.

All the sides are of equal length but the vertices were not right angles.

So that is not a square.

It is instead a rhombus.

And here are the answers for part 2 of Task B.

So Laura completes each square using a ruler and a right angle checker.

So Laura uses a right angle checker to make sure that each vertex of the shape is a right angle.

And she also uses a ruler to ensure that each side is equal length.

That is what your finished square should look like.

And let's take a look at shape b.

The completed shape for shape b should look like this.

And here is shape c completed.

Very sweet little square, that one, isn't it? So when you're drawing your shapes, you have to make sure that each square had 4 equal straight sides and 4 right angles.

If it doesn't have both those things, it is not a square.

And again, this is how Laura completes each square using a ruler and a right angle checker.

So again, use a right angle checker to make sure that each vertex of the shape is a right angle.

Use a ruler to ensure that each side is the same length.

So shape a, square a, should look like this.

So you've got to ensure that each square has 4 equal straight sides and 4 right angles.

If it does not have those things, it's not a square.

So shape b should look like this.

And finally, shape c, when you've used your right angle checker and your ruler, should look like this.

So they're quite tricky to make those.

But very, very well done if you got onto part 3 of Task B and you managed to draw those shapes accurately and carefully as well.

Very well done indeed.

And well done in today's lesson.

And hopefully, you're feeling much more confident about what a square is.

And hopefully, you can recognise when a shape is a square and when it is not.

Very well done.

Excellent work today.

And finally, let's take a look at that lesson summary.

So a square is a rectangle with four sides, all of equal length.

A square has four right angles at its vertices.

And a square can rest on a side or a vertex.