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.

So by the end of this lesson today, you will be able to say that you can make compound shapes by joining two polygons in different ways.

We have two key words 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, polygon.

Your turn.

My turn, quadrilateral.

Your turn.

Now, you may have heard these words before, but you might not be very familiar with them.

But by the end of this lesson, you'll be able to use them with confidence.

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

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

And we'll see lots of examples of those today.

A quadrilateral is a special type of polygon that has four straight sides and four vertices.

In this lesson today, we're looking at making compound shapes by joining two polygons in different ways.

And our learning is split up into two cycles.

In the first cycle, we're going to be exploring joining shapes.

So we're going to be doing lots of practical things, looking at how we can connect shapes together.

And in the second cycle, we'll be focusing on parallel lines.

Now, you may not know what parallel lines are, but don't worry, by the end of this lesson you will.

In this lesson today, we're going to meet two friends, Lucas and Aisha, and they're going to be helping us with our learning and doing some thinking along the way.

So let's start here.

At homework club, Lucas noticed something about triangles.

Let's see what he got up to.

Well, first he noticed that he was playing with these two triangles, and he noticed that they were identical.

So that means they were exactly the same.

He decided to rotate or turn one of those triangles, so it looks like this.

And then he put them together.

And when he put them together, he made a new polygon, and he said, "I don't think my shape is a triangle anymore.

It's a polygon.

But what is it?" What are the properties of this polygon? What do you know about Lucas' new shape? Can you define any of the properties? Lucas is absolutely right.

He put those two triangles together and he now has a square.

It has four equal sides and four vertices, and we can see that those vertices or corners are right angles so they form a right angle, which remember, is a square corner.

So we can see that he joined those two identical triangles together and he formed a square.

Lucas decides to think about this a little bit more, and he sets Aisha a challenge.

He says, "I wonder how many different polygons that you can make with these two identical triangles?" So remember, he put them together to make a square, which is a different polygon, and he's challenging Aisha to find other polygons that she can make with these two triangles.

Hmm, I wonder if you can visualise or imagine what these might look like.

And he reminds Aisha that the triangles must be joined up along a side.

The sides must line up exactly.

He also reminds her that you can rotate the triangles so you can turn them around, but you can't flip the triangles over.

So we can't just flip the triangles.

We have to rotate them or move them around, but we can't flip them.

And he reminds Aisha that this is his first one, and it fits those rules.

Remember, he rotated, he turned one of those triangles to make the square.

He didn't flip it over.

And we can see that two sides of the triangles line up exactly.

To help Aisha out, he shows her a non-example.

He says, "This one is not an example because the vertex is touching the side." So remember, the two sides needs to join up to meet Lucas' challenge.

Time to check your understanding.

Which of these layouts would be allowed in Lucas' game? So take a close look at A, B, and C, and decide which of them would be allowed according to his rules.

Take a moment to have a think.

Welcome back.

Now, remember, Lucas' rules said that we can rotate the triangles but we can't flip them.

And it also said that when we connect the two triangles together, we need to have sides lining up exactly.

So, A, fits that perfectly.

We have joined the two triangles together along one side.

Those sides connect exactly together.

B and C, however, are not correct.

So the sides in B don't line up, so they don't form a polygon that is part of Lucas' challenge.

And in C, we've overlapped those two triangles and that doesn't work either.

Well done if you spotted that.

So now Aisha has a go at Lucas' challenge.

I wonder what she does.

I wonder what you would do.

She says she's going to rotate one triangle, like so, and then she's going to join two sides up so they line up exactly.

So she has created a new polygon from those two triangles.

Has she followed Lucas' rules though? And what is her new shape? Hmm, I wonder.

Well, her new shape is still a triangle.

It has three sides and three vertices.

However, it is bigger in size because we've joined the two smaller triangles together.

So, this time Lucas is thinking about four-sided shapes.

And remember, these are called quadrilaterals, and he's using a different pair of identical triangles.

Lucas notices that these triangles don't have a right angle.

So we look really closely at those two triangles, there isn't a right angle or a square corner like there was with his previous pair of triangles.

But he still thinks he can make different quadrilaterals.

What do you think? Can you visualise rotating and moving these triangles to make different quadrilaterals? Can you see how he has created this quadrilateral? Lucas says that he's rotated one and put 'em together, and his new shape has four sides, so it is a quadrilateral.

He thinks though that he can continue to make some different quadrilaterals.

What do you think? Can you imagine rotating them a different way so that you make a different quadrilateral? That brings us onto our first task.

I would like you to use two identical triangles, and I'd like you to make and record as many different quadrilaterals as you can.

So we've given you three different pairs of triangles.

You can see them on the screen, A, B, and C, and you'll notice that the triangles are identical in each pair, but each pair is slightly different.

So the first pair, for example, has a right angle, and the second pair does not have a right angle.

Your challenge is to see how many different quadrilaterals you can make using each pair of triangles.

Can you always make a square or a rectangle with those triangles? And can you make any polygons with more than four sides? Take some time to really investigate with these three pairs of triangles.

Remember, the sides of the triangles must line up exactly and you can rotate or move the triangles, but you can't flip the triangles over.

Good luck with that task, and I will see you shortly for some feedback.

Welcome back.

How did you get on with that task? Did you enjoy moving those triangles around, and did you create lots of different quadrilaterals four-sided shapes? Let's see some of the things you might have created.

So for the first example, you may have noticed that these were the triangles that Lucas began with in his homework club and he made a square.

So, hopefully, you managed to make that square too.

But there were also some quadrilaterals you could make.

These are examples of the same quadrilateral and the whole thing has just been rotated.

So, well done if you made either of those.

There are two unique or different quadrilaterals that can be made by joining those two triangles.

So, hopefully, you found the square and one of the quadrilaterals on the other side of the screen.

So, for the second set of triangles, you may have again noticed that these were the triangles that Lucas set Aisha a challenge with.

This is the quadrilateral that Lucas made, so hopefully you managed to make that too.

And there are two more quadrilaterals that can be made by joining these two triangles.

So, hopefully, when you're exploring, you found two other quadrilaterals that look like these.

A square or a rectangle though, cannot be made using these two triangles.

I wonder if they have something different to the other two pairs of triangles.

For C, you may have made some of these shapes.

Do they all fit the rules? Let's have a closer look.

Well, actually, some of the examples here are not quadrilaterals and are in fact triangles.

So it is absolutely fine if you manage to make some other polygons.

But remember, we're really carefully thinking about quadrilaterals, which are four-sided shapes.

The rest of the examples here are four-sided shapes that could be made with this pair of triangles.

Well done if you found all of those.

This time there are four unique or different quadrilaterals that can be made with this pair of triangles.

And you may have noticed that you can make a rectangle with this particular pair of triangles.

So far, in this lesson, we've been exploring joining shapes together to make different shapes, and we've been thinking particularly about quadrilaterals or four-sided shapes.

For the rest of the lesson, we're going to be thinking about parallel lines, which is a special property that some shapes might have.

Let's get started.

Lucas looks more closely at the quadrilaterals that he has created, and you might have created some of these quadrilaterals yourself.

Lucas says that he knows that they are all quadrilaterals because they all have four sides and four vertices.

And if we look very closely at them, we can see that they look different but they all have four sides, and they all have four corners or vertices.

That shape is a rectangle because it has four vertices like all the others do, but all of the vertices are right angles.

Remember, right angles are a square corner.

This rectangle has another special property, because it also has pairs of parallel lines.

Aisha decided to draw around the joint triangles that make the rectangle, so you can see that we now have the rectangle shape to make it easier to look at.

Lines are parallel when they are always the same distance apart, they never get closer together or further apart, and that is the definition for parallel.

Can we say that together? Are you ready? Lines are parallel when they are always the same distance apart.

They never get closer together or further apart.

Great job.

Can you already see some sides that might be parallel in the rectangle? Hmm, let's take a closer look.

This pair of sides, shown in green, are parallel.

They stay the same distance apart.

So if we look at the two horizontal sides of the rectangle, we can see that they stay the same distance apart.

And remember the word for that is parallel.

And if we look at the vertical side of the rectangle, we can see that that pair of sides are also parallel, because they stay the same distance apart from one another.

This means that the rectangle has two pairs of parallel sides.

And Aisha wonders, "Are there other quadrilaterals that have parallel lines?" Maybe you've seen some in this lesson so far.

Lucas looks for parallel lines in this quadrilateral and he says he knows this quadrilateral is still a quadrilateral because it has four sides and four vertices, but he knows it's not a rectangle, because it doesn't have four right angles.

If you look closely at the vertices, you will see that they are not right angles, they're not square corners.

He still thinks there's parallel lines though.

The two sides are the same distance apart.

How could Jacob check to see if he's correct? Hmm, good thinking, Jacob.

Jacob's used some lollipop sticks and he's put them along the sides.

He can see that those lollipop sticks stay the same distance apart.

The lollipop sticks don't get closer together or further apart.

They stay the same distance apart from one another.

So we can say that that pair of sides, the vertical pair that you can see in this quadrilateral, are parallel.

There is one pair of parallel sides.

Time to check your understanding.

We know that Jacob said that the vertical sides that you can see in this quadrilateral are parallel.

They stay the same distance apart.

But has Jacob found all the pairs of parallel lines in this quadrilateral? Pause the video and have a think.

Welcome back.

What did you think? Well, actually, the pair of lines that we can see here are also parallel.

They stay the same distance apart.

Well done if you spotted that.

This means that this quadrilateral has two pairs of parallel lines just like the rectangle.

And this quadrilateral has a special name.

It's called a parallelogram.

I'm going to say that name once more and I'd like you to say it back to me.

My turn, parallelogram.

Your turn.

Great job.

And can you see the word parallel in that name? Good spot.

A parallelogram is a quadrilateral, a four-sided shape, with two pairs of parallel sides.

This shape is a quadrilateral, but its special name is a parallelogram.

So both of these shapes are parallelograms. However, only the top one is a rectangle.

Remember, a rectangle also has to have four right angles to be a rectangle.

Time to check your understanding.

If a parallelogram is a quadrilateral with two pairs of parallel sides, then which of these shapes are parallelograms? Take a close look at the five shapes that you can see, and pause the video to have a think about which of them are parallelograms. Welcome back.

How did you get on? Let's take a closer look.

We've ticked the three parallelograms. Let's take a closer look at why they are parallelograms. If we look at the first shape on the left-hand side, it is a rectangle.

We know it's a rectangle because this is a quadrilateral with four right angles.

And we can also see that the horizontal sides in that rectangle, and the vertical sides in that rectangle, are parallel.

Remember, parallel lines don't get closer together or further apart, they stay the same distance apart.

If we move to the middle top shape, we can see that this shape is a parallelogram.

We can see that although it doesn't have four right angles, it does have two pairs of parallel sides.

The shape on the right is a square, and we know that a square is a special type of rectangle.

And we can also see that it has two pairs of parallel sides.

The sides stay the same distance apart.

So all of these polygons are quadrilaterals with two pairs of parallel sides so they count as parallelograms. The other quadrilateral on this screen is a quadrilateral, but it only has one pair of parallel sides.

Only the horizontal sides are parallel.

It is therefore not a parallelogram.

And what's about that last shape then? Well, that one does have parallel lines, but it's not a quadrilateral.

Remember, a quadrilateral has four sides, and that shape has six.

It's a hexagon, so it's not a parallelogram.

Well done if you identified all of those.

Time for your second practise task.

In this task, I would like you to revisit and remake some of the shapes that you made in Task 1 with your triangles, and I would like you to carefully draw around them.

So you might need to use a pencil and a ruler to really carefully draw around them.

Then for each of the shapes that you've drawn around, I would like you to draw along two sides that you think are parallel.

You might want to use a different colour to show those.

For question 2, I'd like you to have a think about what Lucas is saying.

Lucas has made some shapes and he says, "I think one of these shapes has more differences than similarities to the others." Hmm, what do you think Lucas means by this statement? I would take a really close look at the four shapes that he's made.

One of them has more differences than similarities.

What do you think? Good luck with those two tasks, and I'll see you shortly for some feedback.

Welcome back.

How did you get on? So for the first one, remember that this will depend on the shapes that you made, but here are some of the ones we looked at.

We have taken two different shapes that we made in Task 1, and we've carefully drawn around them.

And then you can see that we've marked a pair of lines on each.

Do you think that the lines we've marked are parallel? Well, yes.

In both examples, the lines drawn stay the same distance apart.

They do not get closer together or further apart.

Therefore, they are a pair of parallel sides.

Well done if you drew around your shapes and identified some parallel sides.

For question 2, there were lots of different things to think about, but you might have said that all of these shapes are polygons and quadrilaterals.

Three of these shapes though are parallelograms. This polygon here is the only one that doesn't have any parallel sides.

It is a quadrilateral, but it is not a parallelogram.

So it has more differences than similarities.

Well done if you spotted that one.

We've come to the end of our lesson, and hopefully you've really enjoyed joining shapes together to make different shapes.

And we've made compound shapes by joining two polygons in different ways.

Let's summarise what we've learned.

Using the same parts can create a different whole.

Two polygons can be joined together to make different shapes.

Lines are parallel when they are always the same distance apart.

Remember, they don't get closer together or further apart.

And a quadrilateral with two pairs of parallel lines is called a parallelogram.

Thank you so much for all your hard work today.

I hope you've enjoyed making different shapes, and I look forward to seeing you again in another math lesson soon.