Lesson video

Hello, there.

How are you today? My name is Ms. Coe.

I'm really, really excited to be working with you on this lesson as part of your geometry unit.

Now, you may not know the word geometry, but geometry is all about shapes and lines.

And so we're going to be doing lots of exploring with shapes and lines and the properties of shapes.

I'm really excited about this lesson, and I hope that you are too.

By the end of this lesson today, you will be able to say that you can make and draw quadrilaterals on circular geoboards and name different quadrilaterals according to their properties.

We have a few keywords in this lesson today.

I'm going to say them, and I'd like you to say them back to me.

Are you ready? My turn, quadrilateral.

Your turn.

My turn, vertex.

Your turn.

My turn, vertices.

Your turn.

My turn, parallel.

Your turn.

Fantastic job.

Let's see what those words mean.

A quadrilateral is a polygon with four straight sides and four vertices.

A vertex is a point where two lines meet, and the plural of that is vertices.

So with the picture of the triangle, we've indicated one vertex, and we know that a triangle has three vertices.

Parallel lines are straight lines that are always the same distance apart.

They never get closer together or further apart.

In this lesson today, we're going to be making and drawing quadrilaterals on circular geoboards, and our lesson today has two cycles.

We're going to start by constructing quadrilaterals, and then we're going to think about naming those quadrilaterals, thinking carefully about those properties.

So let's get started.

In this lesson today, you're going to meet Alex and Laura.

Alex and Laura are going to be providing some examples for us to think about, and also asking us some questions along the way.

So let's start here.

Take a close look at the polygons.

Which of these are quadrilaterals? How do you know? Think carefully about the properties of a quadrilateral.

Hmm.

Well, Alex is going to help us out.

Let's see what he thinks.

A quadrilateral has four straight sides and four vertices.

Take a good look.

Can you see any quadrilaterals immediately? So Alex says that these two indicated are rectangles, and they have four sides and four vertices.

A rectangle is a type of quadrilateral.

This one here does not count as a quadrilateral, though.

It does have four sides, but one of the sides is curved.

Remember that the quadrilateral has to have four straight sides.

This one doesn't count.

What about the other three? Well, this one actually has five sides.

One of the sides is really short, but it still has five sides, so it's not a quadrilateral.

It is in fact a pentagon, a five-sided shape.

This one has four sides and four vertices.

"I think it's a trapezium, which is a quadrilateral," says Alex.

I wonder if you agree.

And that leaves the last shape.

Hmm, I wonder, is that a quadrilateral? Alex says it is.

It has four straight sides and four vertices.

It might look a bit unusual, but it is definitely a quadrilateral.

Good sorting, Alex, well done.

Time to check your understanding.

Tick the quadrilaterals, and choose one of them that you know is not a quadrilateral and explain why.

Pause the video and have a go.

Welcome back.

So let's start by thinking which one of these are quadrilaterals.

A quadrilateral has four straight sides and four vertices.

So I can see that these four shapes all fit that criteria.

They have four sides, four vertices, so they're all quadrilaterals.

That means the other two are not quadrilaterals.

Did you choose one and reason why? You may have said that this shape here is a hexagon and not a quadrilateral.

It has six sides and six vertices, therefore it is a hexagon.

What about the last one? You may have identified that actually the sides here are not all straight.

Remember, a quadrilateral needs four straight sides.

So this shape does have four sides, but they're not straight, so it is not a quadrilateral.

Well done if you identified the quadrilaterals and reasoned why one of these shapes was not a quadrilateral.

So Alex and Laura are making quadrilaterals on circular geoboards.

You may have seen circular geoboards before.

They are circles with fixed points around them.

The points are the same distance apart.

Take a close look at the quadrilaterals that Laura and Alex have drawn.

What is the same about them, and what is different? Hmm.

Can you notice any special properties? Both of them have four straight sides and four vertices, so they are definitely both quadrilaterals.

Two of the vertices are in the same position.

So if we look at these two vertices in the shapes, we can see that they're in the same position on the circular geoboard.

They're at the same points.

Laura's shape has a pair of parallel sides.

Alex's shape does not.

Remember, a pair of parallel sides means the sides stay the same distance apart.

We can see that there are two lines that stay the same distance apart on Laura's shape, and we can't see any of those on Alex's shape.

Remember that we can show parallel sides using arrows pointing in the same direction.

Laura changes the position of one of her vertices.

Look closely at what she does.

Here is her first shape.

And here is how she's changed her shape.

Does her shape have the same properties as her previous shape? Hmm.

What do you think? Laura says that both of her shapes are quadrilaterals because they have four sides and four vertices.

And I agree with that.

She's moved one of the vertices.

She hasn't added them or taken them away.

So it still has four sides and four vertices.

Her new shape though does not have any pairs of parallel sides.

If you look closely at the sides, there aren't any sides that stay the same distance apart.

Alex changes the position of one of his vertices.

So this is his starting shape.

And watch closely at how he changes the shape.

This is his new shape.

Does his shape have the same properties as his previous shape? Hmm.

What do you think? Alex says that both of his shapes are still quadrilaterals, because they have four sides and four vertices.

He again only moved one of his vertices.

He didn't add one or take one away.

But his new shape does have a pair of parallel sides.

Can you spot them? Can you see the pair of sides that stay the same distance apart? Well done, Alex.

He's remembered to mark them using arrows pointing in the same direction.

So his previous shape didn't have any pairs of parallel sides, whereas his new shape has one pair of parallel sides.

Time to check your understanding.

Alex makes a new shape.

Change the position of one vertex so that his quadrilateral has a pair of parallel lines.

So if you look closely at Alex's current shape, you can see that it does not have any pairs of parallel lines.

What I would like you to do is think about how you could move one vertex, just one, so that his shape would have a pair of parallel sides.

If you have some circular geoboards, you might want to sketch Alex's shape and see how you could move it to solve the problem.

Pause the video here and have a go.

Welcome back.

Did you think really carefully about what you could do? For example, you may have moved this vertex one place around.

So you can see where it was originally, and we've moved it one space to the right around the circle.

Can you see now how his shape does have a pair of parallel sides? The horizontal sides are now parallel to one another.

You may have found a different way.

For example, you may have moved this vertex.

So again, you can see the original position of the vertex, and we've moved it one space around the circular geoboard.

And now this time, we have two slightly different parallel sides.

Well done if you identified either of those changes that would result in a shape with one pair of parallel sides.

Time for your first practise task.

I would like you to construct different quadrilaterals, four-sided shapes, using this geoboard.

So for question one, I'd like you to think about the largest quadrilateral that you can make.

Think about what would take up the most space in that geoboard.

For question two, I'd like to think about, can you make the same quadrilateral but from different starting points? And question three, can you make different quadrilaterals that have one vertex in the same position? So remember, the positions are the points around the circular geoboard.

Good luck with those three tasks.

Enjoy drawing lots of quadrilaterals.

I'll see you shortly for some feedback.

Pause the video here.

Welcome back.

How did you get on? Did you find some interesting quadrilaterals to make using the circular geoboard? There are lots of different quadrilaterals that you can make on this circular geoboard, so we've just shown a few of them here.

Look closely at the two we've got here.

What do you notice? Can you identify any properties of these two quadrilaterals? I can see that both of them have one pair of parallel sides.

And I can see that the one on the right is larger than the one on the left.

It takes up more space.

I wonder if that was the biggest quadrilateral that I could make.

Here are a couple of other examples.

I noticed that both of these are trapeziums. They look slightly different, but they have the same properties.

They have exactly one pair of parallel sides.

Maybe you made some other trapeziums. Or maybe you made the same trapezium but in a different position on the circular geoboard.

Here are a couple of examples of very large quadrilaterals.

They take up a lot of space inside the circular geoboard.

Hopefully you made a couple of examples like this too that take up a large amount of space in the geoboard, therefore they're the largest shapes that you can make.

But which one of these two is larger? Well, if we overlay the second shape onto the first, we can see that it takes up more space than the first one.

That means the second shape you can see here is the largest quadrilateral that you can make on this circular geoboard.

Well done if you spotted that.

There are lots of examples of one quadrilateral that you can make from different starting points.

Here we've used a trapezium.

And you can see that the trapezium is exactly the same on each of them.

We've just started at a different starting point.

Well done If you found one quadrilateral that you could make from different places.

For the third task, we asked you to think about making different quadrilaterals using one vertex in common.

So you can see that Laura here started with a circled position on the circular geoboard, and she made two different quadrilaterals.

They have different properties, and they look different.

There are lots of different options here.

So well done if you found lots of different quadrilaterals that you could make using one vertex that was the same.

Let's move on to the second part of our learning where we are naming and constructing quadrilaterals.

Remember that a quadrilateral is any 2D shape with four straight sides and four vertices.

But some quadrilaterals have special names.

And you've probably come across some of these already.

What do we call these two shapes? Can you remember the names? These are both rectangles.

Rectangles have four right angles or four pairs of perpendicular sides.

So I can see in both of these polygons, they are quadrilaterals, because they have four sides and four vertices.

But they are rectangles, because additional to the four sides and four vertices, they have four right angles.

You may have also noticed that this first shape is a square.

A square is a rectangle with four equal sides.

The sides are the same length.

So a square is just a special type of rectangle, and both of them are quadrilaterals.

Time for a quick check of your understanding.

All of these shapes here are rectangles.

I would like you to tick the squares.

Pause the video here and have a think.

Welcome back.

Did you manage to identify the squares that were hidden amongst the rectangles? These two shapes here are both squares.

Remember, a square is a rectangle with four equal sides.

The sides are all the same length.

Well done if you identified those two as being squares.

Let's look at another example of a special quadrilateral.

This is a parallelogram.

I'm going to say that again, and I'd like you to say it back.

My turn, parallelogram.

Your turn.

It's a tricky word, isn't it? A parallelogram is a quadrilateral with two pairs of parallel size.

And remember, we can mark parallel sides using arrows like this.

The sides in a parallelogram can be longer or shorter, but they have to be parallel.

So you can see in both of these examples that we have a horizontal pair of parallel lines, and a nearly vertical pair of parallel lines.

But if we were to extend those lines, they would be the same distance apart from one another.

If all the sides are the same length, then this has an extra special name, and that is a rhombus.

I'm going to say it.

I want you to say it back to me.

My turn, rhombus.

Your turn.

Great job.

Look carefully at how I've shown the pairs of parallel sides.

You will notice that one pair of parallel sides has a single arrow, and the other pair has a double arrow.

And that's just to distinguish between them.

So you can see with the rhombus that we have one pair of parallel sides shown with a single arrow, and the second pair shown with the double arrow.

So all parallelograms are a special type of quadrilateral, and they have two pairs of parallel sides.

So if a parallelogram is a quadrilateral with two pairs of parallel sides, then that means that squares and rectangles are also parallelograms, because they have two pairs of parallel sides, as you can see here.

So this can feel quite complicated, because these shapes are quadrilaterals, they are also parallelograms, and they are also rectangles.

Try and use the most specific word that you can.

So the most specific word for the first example is a square, because it is a regular rectangle.

The second one is a rectangle.

Don't worry though if you do decide to call them parallelograms. You're not incorrect.

Rectangles always have four right angles though, and that's what makes them different from parallelograms, because other parallelograms do not always have to have four right angles.

Time to check your understanding.

All of these quadrilaterals are parallelograms. I would like you to tick the ones that are also rectangles.

Pause the video here.

Welcome back.

Did you remember that rectangles have right angles as well as two pairs of parallel sides? So they have four pairs of perpendicular sides.

So these are the three rectangles.

Well done if you spotted those.

Look carefully at the other three.

We can see that they do not have right angles.

Rectangles are parallelograms with four right angles.

Remember, you can always check right angles using a square corner or a right angle checker.

Laura and Alex look carefully at this circular geoboard, and they don't think that they can make any parallelograms using that geoboard.

I wonder, you might want to have a look at your task A.

Did you make any parallelograms with your circular geoboard? You might want to take a moment to have a little check.

Laura and Alex did make some quadrilaterals with exactly one pair of parallel sides though.

And you can see that here.

Alex says, "I know this one.

This is a trapezium.

It is a quadrilateral with exactly one pair of parallel sides.

Did you make any different trapeziums in task A? Maybe you want to have a little look back at your work.

Were any of your shapes trapeziums? Were they quadrilaterals with exactly one pair of parallel sides? Time for a check of your understanding.

Sort these shapes into parallelograms or trapeziums. Pause the video and have a go.

Welcome back.

How did you get on? Here they are sorted.

Remember that parallelograms have two pairs of parallel sides.

Trapeziums only have exactly one pair.

Parallelograms have two pairs of parallel sides.

Remember they can have four equal right angles, like the second example, but they don't have to.

Trapeziums have exactly one pair of parallel sides.

Remember, all of the shapes that we've looked at so far are still quadrilaterals.

They have four sides and four vertices.

Sometimes a quadrilateral doesn't have a special name, and so we can just call it a quadrilateral.

This example here doesn't have any perpendicular or parallel sides.

So we can just say this is a quadrilateral.

Time for a check of your understanding.

Label these shapes.

If the shape doesn't have a special name that you know, label it as a quadrilateral.

But try if you can remember to label the shapes with their proper names.

Pause the video and have a go.

Welcome back.

How did you get on labelling these shapes? This one is a parallelogram.

It has two pairs of parallel sides.

This one here is a rhombus.

Remember, a rhombus is a parallelogram.

It has two pairs of parallel sides, but it also has equal sides.

So this makes it a rhombus.

Next one is a trapezium.

It has exactly one pair of parallel sides.

This one here is a quadrilateral.

It doesn't have any particular special properties to notice, so we can call it a quadrilateral.

And hopefully you recognise the last one is a square.

It has four equal sides and four equal angles, which are all right angles.

Well done if you identified all of those shapes.

Time for your second practise task.

In this task, I'd like you to use a 12 pin geoboard.

So remember this is a geoboard with just 12 points around it.

I would like you to try and construct each of these shapes.

So the first one, a rectangle that is not a square.

Then a square.

For C, I'd like you to create a trapezium.

And D, I'd like you to create a different quadrilateral that is not a rectangle, a square, or a trapezium.

I'd like you to as well mark any parallel sides that you see and label your shapes.

Remember, we can mark parallel sides using arrows pointing in the same direction.

And if there's more than one pair, we can use a double arrow to do that.

For question two, I'd like to see if you can create more than one square, but on a single geoboard.

Good luck with those two tasks, and I will see you shortly for some feedback.

Pause the video here.

Welcome back.

How did you get on? I hope you had fun during lots of different quadrilaterals.

So for question one, your rectangle may have looked like this.

There are a couple of examples.

You might notice that this is the same rectangle just rotated around.

Here are the squares that can be made with this geoboard.

Remember, a square has equal sides, and it has four right angles.

So these are all exactly the same square.

They've just been rotated around depending on where you started on the geoboard.

Hopefully you drew one of those.

For part C, did you make one of these trapeziums? Now, these trapeziums may look different, and the one in the middle is certainly bigger than the other two, but they have the same properties.

They all have exactly one pair of parallel sides.

And for D, there are a few different quadrilaterals that you could draw.

But these quadrilaterals do not have any parallel or perpendicular sides.

So they don't fit with any of the definitions that we have so far, so we can call them quadrilaterals.

For question two, hopefully you drew a beautiful pattern like this one.

Three different squares can be made on this geoboard.

They have the same properties, but the vertices are in different places.

And you can overlay them like this.

We've made it to the end of the lesson, and I'm really impressed at all the hard work you've put in today.

Let's summarise our learning.

Quadrilateral is the name for any 2D shape with four straight sides and four vertices.

Some quadrilaterals have special names, and some can have more than one name.

So today we have looked at squares, rectangles, a rhombus, a parallelogram, and a trapezium.

And we know that square, rectangle, rhombus, and parallelogram can all be thought of as parallelograms. Thank you so much for all your hard work today, and I look forward to seeing you in another math lesson soon.