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 use different properties to identify and sort quadrilaterals.

Here are the keywords for today's lesson.

I'm going to sage keyword.

Can you repeat it back? The first keyword is quadrilateral.

The next keyword is vertex.

Next keyword is vertices, and the next keyword is properties.

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

A quadrilateral is a polygon with four straight sides.

A vertex is the point where two lines meet to form an angle.

Vertices are more than one vertex, and properties are a character or quality that something has.

Here's our lesson outline.

First part of the lesson is what is a quadrilateral? And the second part is sorting quadrilaterals by their properties.

Let's get started.

In this lesson, you will meet Aisha and Laura.

Now, shape is one of the parts of maths I find really interesting and really enjoy doing, and I think Aisha and Laura quite enjoy it too.

So Aisha and Laura are going to be asking you some tricky questions today.

They're gonna be helping you with your maths and they're also going to be doing lots of fun sorting problems with shapes.

Let's start off by thinking about what does quad mean? The word quadrilateral starts with the prefix quad.

But what does quad mean? The prefix quad means four and prefix is just the beginning part of the word quadrilateral.

Hmm.

Let's look at some words.

Where do you think the quad part is? So we're going to look at some other words that begin with quad.

We've got quad bike.

Can you see where the four is? A quad bike is a kind of motorbike with four wheels.

So it's called a quad bike 'cause it's got four wheels.

Here is a quadruped Now a quadruped isn't just another name for a cat, but a cat is an example of a quadruped.

A quadruped is a creature with four legs.

So a dog is also a quadruped.

Here are some quadruplets.

Can you work out what quadruplet is? A quadruplet is one of four babies born all at once.

And finally, quadruple or quadruple means to multiply a number by four.

So there's lots of examples of words starting with quad.

And quad means four.

So what are the properties of a quadrilateral? A quadrilateral is a 2D shape.

A quadrilateral has exactly four straight sides.

So a quadrilateral is any shape that has four straight sides.

This is a quadrilateral.

This is not a quadrilateral.

It does not have exactly four sides.

That shape's actually a triangle, isn't it? It has three sides.

Is this a quadrilateral? This is not a quadrilateral.

The sides are curved rather than straight to be a quadrilateral, it has to have four straight sides.

Is this a quadrilateral? What do you think? This is a quadrilateral.

It has exactly four straight sides.

What are the other properties of a quadrilateral? Well, a quadrilateral has four sharp vertices.

And a vertex is the point where two lines meet.

And a vertex is just one of them one point where two lines meet.

When we talk about more than one of them, more than one vertex, we call them vertices.

So this is a quadrilateral.

This is not a quadrilateral.

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

Is this a quadrilateral? This is not a quadrilateral.

The vertices, the corners are rounded rather than sharp.

Is this a quadrilateral? This is a quadrilateral.

It has exactly four vertices.

It's got four straight sides and four vertices.

Now have a good look at those six shapes.

Which of those are quadrilaterals? Which of them are not quadrilaterals? And can you explain why they are not quadrilaterals? So pause the video, see if you can work out which shapes are quadrilaterals and which are not.

And welcome back.

Did you manage to work out which ones are quadrilaterals and which ones were not? Did you think about why they are not quadrilaterals? Let's take a look.

So the first shape is a quadrilateral.

It's got four vertices, it's got four straight sides.

The second shape is not a quadrilateral and it is not a quadrilateral because two of the lines do not meet.

One of the vertices is actually missing on that shape.

This is also a quadrilateral.

It's called four straight sides and four vertices.

This is also a quadrilateral.

This is also a quadrilateral.

And finally, this shape here is not a quadrilateral.

This is not a quadrilateral because it has five sides rather than four.

To be a quadrilateral it must have four straight sides.

Aisha draws a quadrilateral on this grid.

I need to use four straight sides.

Aisha also needs to make sure the lines meet to make vertices.

Each vertex must meet at one of the points on the grid.

So there are nine points on the grid.

So every vertex must meet at one of the points on the grid.

Aisha starts here, draws one side of the quadrilateral, another side, another side, and another side.

So Aisha has drawn a shape with four straight sides.

She's also drawn a shape with four sharp vertices, not rounded vertices.

And they all meet the points on the grid.

So for this activity that's really important, Laura draws a quadrilateral next.

Aisha says, "It must be a different quadrilateral to mine." So there's Aisha's quadrilateral to remind us what that looks like.

And Laura's just reminding herself that it needs to have four straight sides and four vertices as well.

So here is Laura's quadrilateral.

It's got four straight sides and got four vertices.

Well done Laura.

Sorry Laura, but they're the same shape.

"Look what happens if I rotate mine, " says Aisha So Aisha rotates her shape and they are identical.

Laura's come up with the same shape, she needs to come up with a different shape.

Oh no, it's exactly the same shapes as Laura.

So Laura, I think you need to have another go at drawing a quadrilateral.

So Laura tries to make other quadrilaterals, "Which shapes are correct?", says Aisha.

So here's one here.

Has Laura drawn that correctly? There's another one.

Has Laura drawn that correctly? And here's the third shape.

Is that correct? Have a good look at those three shapes and see if you can work out whether Laura has drawn them correctly.

Are they quadrilaterals? Do all the vertices meet on one of the points on the grid? Pause the video, see if you can work it out.

And welcome back.

How did you get on? Did you manage to find any shapes that Laura has drawn correctly? Did you spot any mistakes she's made? Let's take a look, see whether you got it right.

So the first quadrilateral is correct.

Laura has drawn a quadrilateral.

It's got four straight sides, it's got four vertices and all the vertices meet at one point on the grid.

In the second shape, one vertex does not meet at one point of the grid.

The shape is a quadrilateral.

But for this problem the lines have to meet at a point.

So Laura has drawn a quadrilateral, but for this activity the vertices have to meet at one of the points on the grid.

So Laura has not drawn that one correctly.

This vertex here is not at one of the points on the grid.

So good try Laura, it's not quite right.

And finally this third shape is also a quadrilateral.

Well done Laura.

And here is task A.

So in task A, you're going to draw some different quadrilaterals.

So each vertex must meet one of the points on the grid.

Now there are 16 different grids there, because there are 16 possible different answers.

But don't expect to find them all 'cause they're quite tricky to find.

And be really, really careful when you are drawing your shapes.

Make sure they're different to all the other shapes you've drawn so far.

So pause the video, see how many of those 16 shapes you can find, good luck.

And welcome back.

How did you get on? How many shapes did you manage to find? You may have found lots.

Did you manage to find 16? Are you sure that they are all different? Let's take a look at those answers.

So here are the 16 possible different answers and all those shapes are different to each other.

Well done if you found some of them.

And if you've got anywhere near 16, that is fantastic.

If you actually found 16, you have done an absolutely brilliant job.

You need to give yourself a pat on the back.

That is brilliant.

But very well done for working hard at that activity.

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

So we've looked at what quadrilaterals are.

We're now going to be sorting quadrilaterals by their properties.

All quadrilaterals share some properties.

So every quadrilateral has four straight sides and four vertices.

If it doesn't have four straight sides and four vertices, it is not a quadrilateral.

Some quadrilaterals have other properties too.

What do you notice about this quadrilateral? It's definitely a quadrilateral, isn't it? It's got four straight sides.

It's got four sharp vertices.

Do you notice anything else about this quadrilateral? Here's a bit of a clue.

Can you work out what it is? Well this quadrilateral has a right angle.

Some quadrilaterals have one or more right angles.

So there are some properties which are the same for all quadrilaterals, but some quadrilaterals have other properties too.

And right angles is one of those properties.

Laura searches for right angles in these shapes.

I'm going to check if these quadrilaterals have any right angles.

So Laura checks this first shape here and yes it does have right angles.

This quadrilateral has two right angles.

Now sometimes you can look at an angle and go, that definitely is not a right angle.

It's definitely bigger than a right angle, smaller than a right angle.

Sometimes you have to check really carefully as well.

She goes onto the second shape.

Does it have any right angles? It does not.

So this quadrilateral has no right angles.

And finally the last quadrilateral, does it have any right angles.

Yes it does.

This quadrilateral has one right angle.

Does this quadrilateral have any right angles? So have a good look at that shape.

Can you see any right angles? Now think carefully about how you could check the right angles.

You might have a right angle measurer, but you could use a corner of a book or the corner of a piece of paper or anything else that is a right angle to help you check, pause the video and see if you can work out if there are any rectangles in that shape.

And welcome back.

Did you find any right angles? Let's see whether you got it right.

There is a right angle in that shape and there is another right angle in that shape.

This quadrilateral has two right angles.

Excellent work if you identified both of those right angles.

Some quadrilaterals have sides the same length.

"Let's use the quadrilaterals we made earlier," says Aisha.

Here's one quadrilateral.

This quadrilateral has two sides the same length.

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

Laura says this quadrilateral has two sides the same length.

So these two sides here are the same length and it also has another pair of sides at the same length as well.

So in fact this shape has two pairs of sides that are the same length as each other.

And here is one more shape.

Does it have any sides of the same length? This quadrilateral has sides which are all different lengths.

So as well as right angles.

Another property of quadrilaterals is do they have sides that are the same length as each other? Here's a couple of shapes for you to look at on your own.

Do these quads have sides the same length? And can you identify those sides that are the same lengths as each other? Pause the video, see if you can work out whether those quadrilaterals have sides the same length or whether they do not have sides which are the same length.

And welcome back.

Let's check to see whether you've got these right.

So the first quadrilateral has two sides the same length, a little bit tricky to spot these two, but they are here.

They are the same length as each other.

And our second quadrilateral has two sides the same length as well.

These two sides here are the same length.

And it also has another two sides the same length as well.

So very well done if you spotted either of those two pairs being the same length or you spotted both of them, excellent work.

Some quadrilaterals have reflective symmetry.

A reflective symmetry is when one half of the shape is a reflection of the other.

If I fold the shape, the two halves would match if the shape had reflective symmetry.

"Let's look at three quadrilaterals," says Laura.

So here is our first quadrilateral.

Does it have reflective symmetry? Could you fold that shape into half? Some people can just look at a shape and go, I think that's got reflective symmetry.

Some people have to actually use a mirror or fold a shape to actually work out whether it has got reflective symmetry or not.

Let's look at that first shape.

So the first quadrilateral has one line of symmetry.

"I can show this using a mirror," says Aisha.

So Aisha puts a mirror on this shape and the reflection of the shape still gives the same shape that we started with, it is still the same shape So this shape here has reflective symmetry.

Let's take a look at the second shape.

Does it have reflective symmetry? The second quadrilateral has no lines of symmetry.

If I place the mirror on the shape in different places, the reflection changes the whole shape.

So in fact, Aisha places the mirror here, and the shape that she can now see is not the same shape.

It's changed from a quadrilateral.

Here is our quadrilateral into what looks like a triangle that's not the same shape.

And she puts it here, she ends up with a completely different shape.

And here is one more shape.

Does it have reflective symmetry? Could you put a mirror on that shape and divide it exactly into half? Could you fold the shape over so those two sides overlap each other exactly in the same place? Yes you could.

This last quadrilateral has one line of symmetry.

A bit tricky to spot, but you can actually place a mirror on that line here and you'd still see the same shape.

Do these quadrilaterals have reflective symmetry? What do you think? So pause the video, see if you can work out whether those two shapes have reflective symmetry or not.

And welcome back.

Did you manage to work out the answers? Let's take a look to see whether you got it right.

So the first quadrilateral has no line of symmetry.

Wherever you placed a mirror on that shape, wherever you folded that shape, you would not end up with the same shape.

The second quadrilateral has one line of symmetry.

As one line symmetry running diagonally across the shape here you could place a mirror on that shape there and you'd see exactly the same shape still.

So very well done if you spotted that first shape had no lines of symmetry and the second shape had one line of symmetry, excellent work.

Aisha sorted these quadrilaterals into two groups.

So she's got two circles there.

Wonder how she sorted the two groups? "I sorted these quadrilaterals into two groups," she says.

All the shapes in the first circle have at least two sides the same length.

So all their shapes there have at least two sides the same length.

Some of them have two pairs of sides the same length.

All the shapes in the second circle do not have two sides the same length.

So these shapes here do not have two sides of the same length.

Every shape has four sides, which are different lengths to each other.

Now how has Laura sorted these quadrilaterals? What property do the quadrilaterals in each circle have in common? So look at the four quadrilaterals in our first circle.

What do they all have in common? Look at the four quadrilaterals in our second circle.

What do they all have in common? Pause the video and see if you can work out the labels for each circle.

And welcome back as quite a tricky problem.

So very, very well done if you've got this correct.

Don't worry if you couldn't spot what they had in common 'cause it's quite tricky this.

So that first circle, what do they all have in common? All the quadrilaterals in the first circle have a right angle.

So every quadrilateral in that first circle has at least one right angle.

Some of them have more than one.

Look at that second circle.

So in the second circle, all the quadrilaterals do not have a right angle.

So every shape in there has no right angles whatsoever.

So very, very well done if you managed to spot those two missing labels.

Aisha describes a quadrilateral to Laura.

"Can you work out which quadrilateral I am describing?" she says.

"I'm going to do my best," says Laura.

Or we can ever ask Laura, well done.

So Aisha starts by saying my shape does not have any sides the same length.

So Laura says, "I'm looking for quadrilaterals without any signs the same length as each other." So it cannot be this shape because it has four signs the same length as each other.

It cannot be this shape, it cannot be this shape, it cannot be this shape either.

It cannot be this shape, it cannot be this shape.

So she's left with two shapes.

Those two shapes do not have any lines the same length as each other.

Aisha gives Laura another clue.

My shape has one right angle.

So one of those shapes has a right angle, one of them does not.

Which one does have a right angle? "This quadrilateral does not have a right angle," says Laura.

"Is this the quadrilateral you were describing Aisha?" asks Laura.

Spot on.

Well done Laura.

Yeah, very well done Laura for working that out.

It's quite difficult problem that one.

Aisha sorts shapes onto the Venn diagram.

So this time the circles are overlapping.

There are two groups in one group go the quadrilaterals and the other group go shapes that have at least one right angle.

Now there's an overlapping part in those two circles because you can have quadrilaterals of course, that have at least one right angle.

So Aisha starts by sorting the shapes.

So Aisha says, "Shape A is a quadrilateral without a right angle." So it needs to go in the quadrilateral circle in the quadrilaterals group.

But it must not go in the has at least one right angle circle.

So shape A would go here.

Shape B is a quadrilateral with at least one right angle.

It's actually got two right angles this shape.

So shape B would go in here.

"Shape B is inside both circles, because it belongs in both groups," says Aisha.

And finally she's got one more shape to sort, shape C.

Shape C is not a quadrilateral, it's a triangle, but it does have at least one right angle.

So it's a right angle triangle.

So that would go in this group here.

Well done Aisha.

Now it's your turn.

There are two more shapes to sort, where they go in the Venn diagram? So shape D and shape E, see if you can work out where there we go.

Pause the video and try and sort those shapes into the Venn diagram.

And welcome back.

Let's take a look to see whether you sorted those two shapes correctly.

So shape D is a quadrilateral with a right angle.

So it belongs in both groups.

Shape E is not a quadrilateral and it has no right angle.

So shape E does not belong in either of the groups.

Very well done if you sorted those two shapes correctly.

Excellent work.

And let's move on to task B.

So part one of task B, you're going to choose one of the shapes.

You're going to describe it to a partner and see if they can get what shape you are thinking of.

Now here are some ideas to help you.

So you could say this shape has four vertices.

If it is a quadrilateral of course, if it's not a quadrilateral, you couldn't say that.

This shape has at least one line of symmetry.

So you've gotta check very carefully has it got a line of symmetry? You can use that as a clue to describe the shape if you wanted to.

Or of course if it's got no lines of symmetry, you can say instead this shape has no lines of symmetry.

You could say this shape has two sides of the same length, or this shape does not have two sides of the same length If it does not.

And you might say this shape has at least one right angle, that could be a clue you could give as well.

So that's part one of task B.

Describe a shape to a partner.

And then of course afterwards they can describe a shape to you and see if you can work out what shape they are describing.

And here's part two of task B.

So you're gonna sort the shapes onto the Venn diagram.

So in this Venn diagram there's one group where all the quadrilaterals would go, and there's a group where all the shapes that have at least one right angle would go.

And of course there's an overlapping part where quadrilaterals with at least one right angle would go.

And here are the eight shapes you are going to be sorting.

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

And welcome back.

How did you get on the task B? Did you manage to get to the second part of task B? Did you manage to sort those shapes onto the Venn diagram? Very well done.

Let's take a look at part one of task B.

So your learning may have looked like this, so of course you are choosing a shape and you're going to describe it to a partner.

But this is how Laura decided to do it.

So Laura, choose the shape.

So we've gotta try and work out what shape is describing.

So Laura says this shape has a right angle, so we've gotta get rid of all the shapes that do not have a right angle.

So it can't be any of these shapes here.

Laura says, "This shape has at least two sides the same length." So we've gotta get rid of any shapes that do not have sides the same length.

This shape here does not have any signs of the same length.

I think it's just that one, isn't it? And finally, this shape has four vertices.

So one of those shapes has four vertices, the other two do not.

So shape D has five vertices.

Shape H has three vertices, so it can't be that one.

So the answer would be shape B.

So this is Laura's quadrilateral.

This is Laura's shape that she chose to describe.

So hopefully your partner managed to guess what shape you were describing and maybe you had to go trying to guess her partner's shape as well and managed to work out what shape they were describing to you.

So very well done if you've got that correct.

And here are the answers for part two of task B.

So A and B were both quadrilaterals with at least one right angle.

Shape C, G and F were all quadrilaterals, but they had no right angles.

Shape D and H were not quadrilaterals, but they had a right angle.

And then shape E belonged in neither group.

It was neither a quadrilateral and it did not have any right angles.

So very well done.

If you got onto to part two of task B and you managed to sort those shapes into the correct place as well.

And excellent work today and hopefully you're feeling much more confident about what a quadrilateral is.

And you can discuss and describe some of the properties of quadrilaterals as well, including right angles, maybe lines of symmetry, maybe sides that are the same length as well.

Excellent work today.

Very well done.

And finally, let's move on to our lesson summary.

So quadrilaterals always have four sides, four vertices, and four angles.

Quadrilaterals always have straight sides and sharp vertices.

Quadrilaterals can have right angles.

And vertices are the corners of a shape.