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 use equipment to construct and compare quadrilaterals with and without parallel and perpendicular sides.

This lesson today, we have three keywords.

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

Are you ready? My turn, polygon, your turn.

My turn, perpendicular, your turn.

My turn, parallel, your turn.

Great work.

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

A polygon is a 2D shape made up of three or more straight lines.

Two lines, which meet at a right angle are perpendicular and 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 constructing quadrilaterals with and without parallel and perpendicular sides.

We have two cycles in this lesson.

In the first cycle, we're going to be constructing polygons, and then in the second cycle we're going to focus our attention specifically on quadrilaterals.

If you're ready, let's get started with the first cycle.

In this lesson today, we are going to meet Aisha and Alex and they are going to be helping us with our maths as always, and posing some questions and challenges for us to think about.

So, let's start here.

Aisha and Alex find some construction sticks in their classroom.

You might have seen something like this before.

You might have played with them before or made things with them before.

They realise that they can join them together through the holes like this.

And once they've done that, the sticks can rotate, but they still stay joined together.

So, you can make different angles like this one.

They think that they can use these sticks to make different polygons.

Now, if you have sticks like this in your classroom, you might want to explore with these as well and you might want to see if you can make different polygons with them too.

Let's see what they get up to.

Aisha goes first.

"I have made an excellent polygon," she says.

"It has four sides and loads of cool properties like parallel and perpendicular sides." And that's the polygon that she's made.

Hmm? Alex says he's not so sure.

Oh dear, I wonder what's happened.

He says, "I'm not so sure about that, Aisha.

I can definitely see some right angles, so those sides are definitely perpendicular, but your sides don't join up, so it's not actually a polygon." Can you see that? Remember a polygon has closed sides.

So actually, Aisha's had a really good go, hasn't she? But she's not made a polygon, because there is a gap in her construction sticks.

"Oh yes," she says, "of course, I agree.

What if I do this?" And she tweaks her model ever so slightly.

Do we think now that she has a polygon? What do you think? So, she thinks she's got a polygon now, but some of the properties are different.

It still has four sides.

"I agree, Aisha, I think now you have a polygon.

Definitely has four straight sides." Her polygon is a quadrilateral, because she used four construction sticks to make four sides, and we can see those four sides there.

Alex has also noticed that there is a right angle and they're going to use a right angle tool like this one to check that it is a right angle.

You might want to use a right angle checker yourself in this lesson today to make sure that you've definitely got a right angle, which remember is a square corner.

We can definitely see a right angle in Aisha's quadrilateral.

So, that means her quadrilateral has one pair of perpendicular sides, because they form a right angle.

Absolutely right, Aisha.

So, we can say that Aisha has made a quadrilateral with one pair of perpendicular sides.

Now, Alex has a go at making his own polygon.

Take a close look at Alex's polygon.

What do you notice? Do you notice any special properties? Alex says his polygon has five sides, because he used five construction sticks.

So, Alex has a pentagon, which is the name we give to five-sided shapes.

"Oh," says Aisha, "your polygon has more right angles than mine did.

I can see three and check using the checker." Can you see which three angles Aisha might think are right angles? There's one, there's another, and there's a third.

We have three right angles.

So, that means that Alex's polygon has three pairs of perpendicular sides.

Remember we have a pair of perpendicular sides where they meet at a right angle.

So, Alex's shape has three pairs of perpendicular sides, because it has three right angles.

Good work both of you.

"It also has some parallel sides," says Alex.

These two sides here, the vertical sides, stay the same distance apart, and we can see that can't we? We can see that those two sides stay the same distance apart all the way up and down, therefore they are parallel.

"Hmm.

So, do these two," says Aisha.

Can you see the sides that she's marked? Those two horizontal sides are also parallel.

They stay the same distance apart.

So, Alex's shape is really interesting, because it has perpendicular sides and it has parallel sides.

So, he can say that his polygon has two pairs of parallel sides as well.

He says he really likes this shape, and I do too.

It has lots of interesting properties.

Times check your understanding.

Take a close look at Alex's polygon and Aisha's polygon.

What is the same and what is different about the polygons? Take time to discuss with a friend, if you have one nearby.

Pause the video here.

Welcome back.

Did you take a close look at both polygons and think about what was the same and what was different? Well, Aisha's polygon is a quadrilateral with four sides and Alex's shape is a pentagon with five sides.

So, that's one difference.

Both of them have at least one right angle, which means both of them have at least one pair of perpendicular sides.

So, that's something that's the same about both of them.

Aisha's polygon though has no parallel sides, but Alex's polygon has two pairs of parallel sides.

So, that is a different property between the two polygons.

Well done, if you identified all of those similarities and differences.

So, this time Aisha and Alex work together to make a different polygon.

Take a close look at this polygon.

What properties does this shape have? "So, this is a pentagon like Alex's shape," says Aisha, "because it has five sides." they used five construction sticks to make the shape.

So, this is also a pentagon.

Aisha says, this vertex here is nearly a right angle, but she can use her right angle checker to see that it's actually a bit smaller than a right angle, and that's a really good thing to do.

If you're not sure, use a right angle checker.

Is it smaller than a right angle, bigger than a right angle or exactly a right angle? Because the sides are not perpendicular unless it is exactly a right angle.

So, these pair of sides are not perpendicular.

This means that the polygon doesn't have any perpendicular sides, because there aren't any right angles in the polygon.

Hmm, she thinks though that there is a pair of parallel sides here.

She thinks that they're the same distance apart, but she's not really sure and actually, sometimes it can be hard to tell if lines are parallel just by looking.

So, it's okay to say that you're not sure about these lines.

Aisha thinks they might be parallel, but she's not sure.

So, she's not going to say for definite that this shape has that property.

Time for your first practise task.

Make different polygons using construction sticks.

Your polygons must have a maximum of eight sides, so no more than eight sides.

First, I would like you to make a polygon with no parallel or perpendicular sides.

Then can you make a polygon with more than one pair of perpendicular sides? Remember, you're thinking about right angles there.

And then can you make a polygon with at least one pair of parallel sides? Pause the video here and have a go at those tasks.

Welcome back.

How did you get on? I hope you had lots of fun creating lots of different polygons to try and fit the categories here.

So, here are some examples that we came up with of polygons that have no parallel or perpendicular sides.

Remember, you might have come up with different ones.

You can see here that we've made a triangle using three of the same construction sticks.

That shape I cannot see any right angles and I can't see any of the sides that stay the same distance apart.

So, we can absolutely say that, that triangle has no parallel sides or perpendicular sides.

Well done, if you made some exciting shapes and justified why they didn't have any parallel or perpendicular sides.

We also made some examples of shapes that had more than one pair of perpendicular sides.

Again, you may have made different shapes to these ones.

These shapes also have at least one pair of parallel sides.

Can you spot how many pairs of parallel and perpendicular sides the square has? Maybe you made a square yourself.

I can see that there are four right angles in the square.

So, that means that the square has four pairs of perpendicular sides.

I can also see that the vertical sides are parallel.

So, that's one pair.

And then I can see that the horizontal sides are also parallel to one another.

So, it has two pairs of parallel sides and four pairs of perpendicular sides.

Well done, if you created some shapes with at least one pair of perpendicular sides.

And well done, if you managed to create some different shapes that had parallel sides as well.

Let's move on to the second part of our learning today where we're going to be constructing quadrilaterals specifically.

So now, Aisha and Alex are going to create quadrilaterals using only four construction sticks.

So remember, a quadrilateral has four sides, so we only need four construction sticks.

And Alex wonders whether his polygons will still have different properties even though they're using the same number of sticks.

I wonder, will all quadrilaterals have the same properties? Let's see.

Alex and Aisha both made quadrilaterals and you can see them here.

First, Aisha's, then Alex's.

They compare their quadrilaterals.

What do you notice about the quadrilaterals? What is the same and what is different about them? Hmm.

Well, Aisha notices that they both have quadrilaterals and they do look a little bit similar and she's going to rotate hers.

She's going to turn hers around so that she can compare them a little bit more easily.

There we go.

What do you think now? What do you notice about the quadrilaterals? Alex's quadrilateral has one pair of perpendicular sides.

So, you can see there that Alex's quadrilateral has a right angle, and so, therefore it has one pair of perpendicular sides, but Aisha's, and we could check if we needed to with a right angle checker, Aisha doesn't have any right angle.

So, therefore it has no pairs of perpendicular sides.

Neither of them have any parallel sides, so none of the pairs of sides stay the same distance apart.

So actually, while Alex's does have a pair of perpendicular sides, the shapes are very similar.

They're both quadrilaterals, they both look very similar in shape, but Alex's just has one right angle, whereas Aisha's doesn't.

This time Alex and Aisha rearrange the four construction sticks that they used to make their first shape to make different quadrilaterals.

So, you can see that Aisha had two yellow, one pink, and one green construction stick in her previous shape and she's rearranged them to make a different shape.

What do you notice about the quadrilaterals now? Can you notice any special properties? Aisha says she's rearranged her construction sticks.

She still has a quadrilateral, but it looks different to the one she had before.

What makes it different? Alex's quadrilateral looks different too, but he still has a pair of perpendicular sides and you can see there that Alex's shape still has a right angle, which means it has a pair of perpendicular sides.

Aisha's still doesn't have any right angles, so still no pairs of perpendicular sides.

Sorry, Aisha.

And still, neither of the shapes have any parallel sides.

So, we can look really closely at those pairs of sides and notice that none of them are parallel.

They'd all get closer together.

So, Aisha wonders, "I wonder if I could make other shapes using the same four sticks." And will she ever get a pair of perpendicular sides? What do you think? Could she make a shape using those four sticks that did have a pair of perpendicular sides? I wonder what they do next.

Time for your second practise task.

I would like you to take two longer and two shorter construction sticks.

You might, for example, use two yellow ones, which are shorter ones, and two green ones, which are your longer ones.

Use them to create different quadrilaterals.

What is the same about the quadrilaterals you can create, and what is different? It might help you here to make one quadrilateral and carefully draw it before you make a second one so you can really see the similarities and differences between them.

For question two, I would like you to think about trapeziums. Remember, a trapezium is a quadrilateral, which has exactly one pair of parallel sides.

Using any of the construction sticks this time, how many different trapeziums can you make using the construction sticks? So, have a really good think.

I wonder if you can work systematically thinking about the different sticks that you could use.

Pause the video here and have a go at those two tasks.

Welcome back.

How did you get on? Did you enjoy making lots of different quadrilaterals and thinking really carefully about those properties? I hope you got the chance to use the words parallel and perpendicular a lot in your descriptions.

For question one, remember you may have used two different, shorter and longer sticks, but we used two yellow and two green sticks.

I wonder if you made parallelograms like the ones we've got.

One of these parallelograms, the rectangle, has four pairs of perpendicular sides, because it has four right angles.

The other one does not have any perpendicular sides, but it does have two pairs of parallel sides.

So, both of these shapes are parallelograms. But remember a rectangle is a special type of parallelogram.

Both of them have two pairs of parallel sides, but only one has any perpendicular sides.

You may have also made different quadrilaterals.

So, these three quadrilaterals here look similar.

Shape A has one pair of perpendicular sides.

I can see that the two yellow construction sticks have been joined together to make a right angle, but B and C do not.

I can't see any right angles in B or C.

I also notice that these quadrilaterals don't have any pairs of parallel sides.

So, these are interesting quadrilaterals that look similar.

One of them has a pair of perpendicular sides and none of them have any parallel sides.

Well done, if you made shapes like this while you were exploring.

Let's think about trapeziums. Now remember, you could use any of the construction sticks to make your trapeziums, and here are a couple that we made.

Remember, a trapezium has to have exactly one pair of parallel sides.

So, shape A and B both have exactly or only one pair of parallel sides.

In shape A, you can see that it is the horizontal sides, and in shape B, it is the vertical sides there that are parallel.

Did you notice as well that shape B is still a trapezium, but that one has two pairs of perpendicular sides? I can see two right angles at the bottom of the shape, which means there are two pairs of perpendicular sides.

Shape A however, does not have any right angles, so it has no pairs of perpendicular sides.

We've come to the end of our lesson and I really hope you've enjoyed playing around with construction sticks and making lots of different quadrilaterals and other polygons.

Hopefully, you've constructed lots of polygons with and without perpendicular and parallel sides.

Let us summarise our learning.

Equipment like construction sticks, means that you can create different polygons with different properties.

When a polygon has a right angle, it means the sides are perpendicular.

A polygon can have more than one pair of perpendicular sides.

Quadrilaterals can have perpendicular sides and parallel sides.

Some quadrilaterals have both of them and some have neither of them.

Thank you so much for all of your hard work today, and I look forward to seeing you in another maths lesson soon.