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 shapes with and without parallel and perpendicular sides.

Here are the keywords for 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, compound.

Your turn.

My turn, vertex, your turn.

My turn, vertices, your turn.

Excellent work.

Let's see what those words mean.

A compound shape is one created using two or more basic shapes.

And we're going to see some examples of those in the lesson today.

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

So we can see that we have identified one vertex in the triangle, and we can say that a triangle has three vertices.

You might have used the word corner to describe this, but we're going to really try hard today to use the word vertex and vertices.

In our lesson today, we are going to be making and drawing shapes with and without parallel and perpendicular sides.

And we have two lesson cycles today.

The first lesson cycle, we're going to be composing compound shapes, and we're going to be thinking about what that means.

You may have heard the word decompose recently, so think about what it might mean to compose a shape.

And then in the second cycle we're going to be drawing shapes.

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

In this lesson today we're going to be meeting Sam, Jacob, and Sofia, and they are going to be sharing some examples and helping us with our learning.

Let's get going.

So Jacob and Sam use some 2D shapes to make new shapes, and when you do that, their new shapes are called compound shapes.

So you can see here, for example, that the first shape is made up of a square and a triangle, and we've combined those shapes to make a new shape.

That shape is called a compound shape.

In the second example, we have a compound shape that is composed or made up of two rectangles.

Sam carefully draws around the two shapes using a ruler.

Let's watch what she does.

There we go.

What are the properties of Sam's new shape? What can you say about Sam's new shape? Well, that's right, Sam.

First, she had two different rectangles, so she started off with two different rectangles.

Does she have a rectangle now? Is that shape still a rectangle? Hmm.

Well actually, she's made a new compound shape, and that shape has different properties to the rectangles that she started with.

Her new shape has six sides and six vertices.

That means that it is a hexagon.

A hexagon is the name for a six-sided shape.

So rectangles are quadrilaterals, they have four sides, but when we put them together to make this new compound shape, our new shape has six sides.

It's a hexagon.

I wonder what else is similar or different about it.

I wonder if you notice any other properties that the rectangle has, that this shape still has, or anything that might be slightly different.

Jacob chooses two different 2D shapes, and he makes a compound shape and he carefully draws it around it as well.

Let's see what Jacob does.

There's his compound shape, and then he's carefully drawn around it.

What are the properties of Jacob's new shape? Hmm.

Well, Jacob says he started with two different polygons, a rectangle and a triangle.

So think about the properties of those two shapes.

His new shape is also a hexagon, because it has six sides and six vertices.

So we can see that Jacob started with two different shapes to Sam, but they still ended up both making hexagons.

Jacob looks more closely at the compound shape he has made.

I wonder if you can spot anything special about his compound shape.

"My compound shape has at least one pair of parallel lines," he says.

"This is one pair." And you can see there that the two horizontal sides in Jacob's hexagon are parallel.

Remember, parallel lines stay the same distance apart.

"I can also see at least one pair of perpendicular lines," he says.

Did you spot those as well? And he's shown one pair there.

Remember, we can show perpendicular lines by showing a right angle, using the right angle symbol, and the lines that connect together to make that right angle are perpendicular.

You might have spotted other pairs of perpendicular lines in Jacob's shape.

Time for a check of your understanding.

Describe Jacob's shape to a friend.

Can you spot any properties that he has not seen? Take a moment to have a chat with a friend, pause the video here.

Welcome back.

Well, we know that Jacob identified one pair of parallel sides, and one pair of perpendicular sides.

I wonder if you spotted any other properties.

Well, Jacob noticed that there is another pair of parallel lines here, so that means there are two pairs of parallel sides in his shape altogether.

Well done if you spotted that, and identified that there were two pairs altogether.

There's another pair of perpendicular sides there, so in the opposite corner to the first one.

So we can see lots of different properties in this one hexagon.

This time, Sam chooses two triangles, and she combines them to make a compound shape.

She draws around her new shape.

Let's see what Sam does.

There's her new compound shape, and she's now drawn around it to make a new shape.

Jacob has used the same two triangles as Sam to make a compound shape as well.

So he also draws around his compound shape to make a different shape.

Sofia has also used those same two triangles, and she has made a compound shape.

So she's put the two triangles together, and she's also going to draw around her shape.

So the children have made three compound shapes, and remember, they started with the same two triangles to compose their new compound shape.

Take a close look at them.

What is the same about them? What is different? Is there anything that you notice? Well, well done if you spotted that all of the shapes are pentagons.

All of the shapes have five sides and five vertices, and pentagon is the special name that we give to a five-sided shape.

What else did you notice? Some shape has a pair of perpendicular sides.

I can see one right angle in some shape, which means there is a pair of perpendicular sides.

I cannot see any right angles in Jacob's shape or Sofia's shape.

So that means that there are no perpendicular sides in those shapes.

There are no pairs of parallel sides in any of the shapes.

So if we look really closely at all of them, there are no pairs of sides that stay the same distance apart.

Time for your first practise task, and there are a few different questions I'd like you to have a go at.

We are going to ask you to work with these five shapes, so make sure you have these at the ready, because you're going to be moving them around to compose different compound shapes.

Let's take a look at the shapes I'm going to ask you to make.

First of all, I would like you to combine two shapes to make different pentagons.

What is the same about the pentagons you've made and what is different? You might like to draw around the pentagons that you make, so you can compare the properties of them, and think about what's the same and what's different.

Then I would like you to combine two shapes to make compound shapes that are not pentagons, but have parallel and perpendicular sides.

Can you make an unusual shape? So for this question, we need not pentagons, so think about how many sides you will not need.

We'd like you to think about parallel sides, sides that stay the same distance apart, and perpendicular sides.

So remember, you're looking out for right angles.

Can you make an unusual shape, perhaps one that no one else will think of? And then for question three, we'd like you to combine two shapes to make a compound shape that doesn't have parallel or perpendicular sides.

Can you make one that isn't a pentagon? Good luck with those three tricky challenges, and I'll see you shortly for some feedback.

Welcome back.

How did you get on with those three tasks? I hope you had lots of fun composing compound shapes from these five 2D shapes that we started with.

Let's take a look at some of the shapes you may have created.

For question one, Sam came up with these four different pentagons which have five sides and five vertices.

What do you notice about them? What is the same and what is different? B, C and D all have parallel and perpendicular sides, but A does not.

If we look at shape A, I can see that there are no right angles in shape A, so that means there are no pairs of perpendicular sides.

I can also see that none of the sides are parallel.

They would all get closer together.

B, C and D do have parallel and perpendicular sides.

So if we look at D for example, I can see that there are one, two, three right angles, which means that there are three pairs of perpendicular sides.

And I can also see that there are two horizontal sides which are parallel to one another, and there are also two vertical sides that are parallel to one another.

Well done if you spotted those, and well done, if you made some of your own interesting pentagons and discussed the properties.

Sam noticed that they all used one of the triangles and either a square or a rectangle to make the compound shape.

I wonder if that's what you did too.

For question two, here are some of the examples that you could have made, that had parallel and perpendicular lines.

Can you spot the right angles that we've included? So if we look at shape B for example, I can see that there are one, two right angles, which means that there are two pairs of perpendicular sides, and I can see that there is one pair of parallel sides.

Shape C is an unusual shape because it has seven sides and seven vertices.

This shape is called a septagon.

I wonder if you made any septagons in your example.

For question three, we asked you to think about shapes with no parallel or perpendicular sides that were not pentagons.

Shape A is a pentagon, but it doesn't have any parallel or perpendicular sides.

So you may have made an example like that.

Shape B is a hexagon and it doesn't have any perpendicular sides, but I can see that it does have parallel sides.

So it's really tricky to draw a shape that didn't have any parallel or perpendicular sides.

I wonder if you managed to do it.

I really hope you enjoyed making lots of different compound shapes and talking about the properties.

And I hope you now feel a little bit more confident in identifying parallel and perpendicular sides.

Let's move on to the second cycle of our learning, where we're focusing on drawing shapes.

Let's start here.

The children at Oak Academy have so far been drawing shapes by drawing around other shapes and using a ruler.

Sam wonders whether we can actually draw shapes without using other shapes as a guide.

So far, compound shapes have been drawn by drawing around two 2D shapes, and that's absolutely fine.

There's nothing wrong with using other shapes to draw another shape, but Sam wonders whether we can do it without that.

I wonder if we can.

They decide to use isometric paper, a pencil, and a ruler.

Now you may have come across isometric paper before.

Isometric paper uses dots or points that stay the same distance apart.

So you can see in this isometric paper, the dots form squares, and the spaces between the dots are all the same distance apart.

This is an example of isometric paper.

They're going to use this and a pencil and a ruler.

A ruler is very important here.

Even though the dots form straight lines, it's really important to still use a ruler so that you have super straight lines.

Sam's strategy is to mark the vertices of the shape first.

So Sam says, "I want to draw a pentagon, which I know has five vertices.

I'll start by making the dots on the paper where I want them." So she has drawn five points where she would like the five vertices of her pentagon to go.

You can see them here.

Remember that when we are using isometric paper, we use the dots.

So all the vertices are on the dots, they're not in between the dots.

Now she says, "I'll use a straight line to join the dots up, making a polygon." So she's gonna start here and work all the way around, using a ruler and a pencil, to complete her polygon.

Remember, it's only a polygon when this is all connected up together.

So now she says, "I've made a pentagon.

It has five sides and five vertices." And that is a brilliant strategy for making a pentagon.

Well done, Sam.

Jacob decides to think about the properties of his polygon.

So he says, "I want to draw a pentagon too." So he also needs five sides and five vertices.

But he says, "I want to make sure my pentagon has a pair of perpendicular sides." Remember, perpendicular sides meet at a right angle.

"So I'm going to draw that pair of sides first," he says.

There we go.

We can see that he has drawn a pair of sides using the dots on the isometric paper that form a right angle.

So we know that those two sides will be perpendicular.

"I can now add two more vertices," he says, "And join them up to form the sides." It doesn't matter where those two vertices are going to go.

He wanted his pentagon to have one pair of perpendicular sides, so it doesn't matter where the other two have gone.

He already has three vertices from the lines that he has drawn, so he only needs to draw two more.

So he has put them up, and then he is going to join them up.

So remember, we haven't got a pentagon until all the sides are connected.

He also has a pentagon, but his has a pair of perpendicular sides.

So his strategy was to draw that property first.

I think that's a really useful strategy if you want to think carefully about the properties that your shape is going to have.

Sofia is going to think about a different property.

She says, "I want to draw a pentagon too." So she also needs five sides and five vertices, but she says, "I want to make sure my pentagon has a pair of parallel sides, so I'm going to draw that pair of sides first." Let's see what she does.

There we go.

Are we happy that those sides are parallel? Yes, they stay the same distance apart.

They don't get closer together or further apart.

This time, because of the way she's drawn the line, she has four out of her five vertices in place already.

So she's drawn four points, so she has four vertices.

That means she only needs one more.

It doesn't matter where she puts that last vertex, because she's put in the property, the parallel lines that she wants her pentagon to have.

What does she need to do now? Absolutely, well done.

She needs to join the vertices to make her pentagon.

Let's see.

Now it's a pentagon because all the sides are connected up together.

"Great!" She says.

"Another pentagon, but this time it has a pair of parallel sides." Well done, Sofia.

That's a really good strategy if you need your shape to have parallel sides.

Special marks can be added to parallel lines to show that they are parallel.

You can see here that the horizontal sides of this shape are parallel, and we have marked that by using a small arrow pointing in the same direction.

This shows that this pair of sides are parallel to one another.

The arrow marks show that the two sides of the shape are parallel.

It's important that they point in the same direction.

Time to check your understanding.

Add arrow marks to show the pair of parallel lines on the shape that Sofia has drawn.

Take a moment to have a think.

Think about what they need to look like.

Pause the video here.

Welcome back.

Let's see what the arrow should have looked like.

There we go.

So we've identified that the vertical sides in this shape are parallel, and therefore we have drawn arrows to show that.

This time the arrows point upwards because the sides are vertical.

They show that the two sides are parallel.

Well done if you drew those on this shape.

It's time for your second practise task.

I would like you to draw some shapes on the isometric paper to fit into each category, and then I would like you to draw arrows to show the parallel lines if you need to.

So first one, I would like you to draw a hexagon.

So simply draw a hexagon.

Then I would like you to draw an octagon, please.

Think about which strategy you'd like to use.

Would you like to draw the vertices first, like Sam did? Or would you like to think about the properties first? For C, I would like you to draw a shape with parallel lines and six or more vertices, so it needs to be a hexagon or larger.

And for D, I would like you to draw a shape with perpendicular sides and fewer than eight vertices.

So your shape needs to be a septagon, a seven sided shape, or smaller.

Good luck with those two tasks.

Think really carefully about the strategy that you want to use.

Sometimes it might be easier to draw in the properties of the shape first.

Good luck and I'll see you shortly for some feedback.

Welcome back.

How did you get on? Now for A and B, we asked you to draw a hexagon and an octagon.

A hexagon has six sides and six vertices, and an octagon has eight sides and eight vertices.

Here are a couple of examples that we've drawn.

Now remember, your hexagons and octagons might look completely different to mine, and that's fine.

As long as your hexagon has six vertices and your octagon has eight, you will have successfully drawn a hexagon and an octagon.

Do you notice any special properties about the two shapes we've drawn? Well, well done if you've spotted that B is an octagon, but it also has a pair of parallel sides.

So remember, we show the parallel sides by drawing an arrow pointing in the same direction.

You might have also spotted that there are some pairs of perpendicular sides in the octagon as well.

For C and D, again, there were lots of different polygons that you could have drawn, and I hope that you were super creative.

For C, we had parallel lines and six or more vertices, so you may have drawn a hexagon or a septagon or an octagon or even bigger.

I decided to draw a septagon, so it has seven sides and seven vertices, and you can see that my septagon has one pair of parallel sides, which I have marked with the arrows.

This time they're pointing down, because it is a vertical line.

For D, we needed fewer than eight vertices, so I decided to draw a pentagon, which has five sides and five vertices.

Can you spot my pair of perpendicular sides? That's right.

If we look in the bottom left hand corner, we can see that we have a right angle.

So that vertex is a right angle, which means the two sides make a pair of perpendicular sides.

Well done if you started by drawing the properties that you wanted your shape to have, and then filled in the vertices.

That was a really good strategy for these two questions.

We've come to the end of our lesson, and I hope you've really enjoyed making and drawing shapes that had and did not have parallel and perpendicular sides.

Let's summarise what we've learned.

Shapes can be composed or made up from other 2D shapes.

These shapes are called compound shapes.

Polygons are shapes with three or more vertices.

Shapes can have parallel sides or perpendicular sides.

Some shapes can have both parallel and perpendicular sides, and some shapes don't have any parallel or perpendicular sides.

Thank you so much for all of your hard work today.

I hope you've really enjoyed this lesson, and I hope to see you in another maths lesson soon.