Lesson video

Hi, how are you today? I hope you're having a good day.

My name is Ms. Coe, and I'm really excited to be joining you for this maths lesson.

In this maths lesson, we're going to be looking at geometry.

Now you might wonder what geometry means.

Geometry is all about shape, so I'm really excited to say that this lesson is all about exploring different shapes.

I really hope you'll enjoy learning about this as much as I will enjoy teaching you.

By the end of this lesson today, you'll be able to say that you can draw polygons on isometric paper.

Now, you may not have heard of the word "isometric" before, but don't worry, it's one of our keywords, so we'll look at the definition in a moment.

There are three keywords in this lesson today.

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

Are you ready? My turn.

Isometric.

Your turn.

My turn.

Perpendicular.

Your turn.

My turn.

Parallel.

Your turn.

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

Isometric means distances between points stay the same.

So in this lesson we're just going to use something called isometric paper, which has equally spaced dots or points.

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.

So in this lesson today, we're going to be focusing on drawing polygons on isometric paper, and we have two cycles to our lesson.

We're going to start by drawing on isometric dotted paper, and then we're going to draw on isometric lined paper and you'll see the difference between those shortly.

Let's get started with our first cycle focusing on isometric dotted paper.

In this lesson today, you're going to meet Sofia and Izzy, and they're going to be helping us with our maths work along the way, and asking us some questions as well.

Let's get going.

Let's start here.

Sofia and Izzy are sorting out the paper tray in their classroom.

Now, I have lots of children in my class who absolutely love organising, and they really enjoy sorting out things like the pencil tray or the paper tray, so you might have done something like this yourself.

Izzy says, "Well, it's absolutely a mess in here." And to be fair, quite often the paper drawers do get messy.

"Let's sort by type," she says.

So, they sort out some different types of paper.

Sofia says that this paper is coloured paper and she uses it for art lessons.

You might do the same.

Izzy says that they use lined and squared paper in their maths lessons.

You might use lined paper in your English lessons as well.

But these two bits of paper have strange lines and dots on, and Sofia doesn't think she's seen this before.

She wonders what kind of paper it is.

Sofia and Izzy have found isometric paper, so this means that the dots or points are the same distance apart.

They're equally spaced.

So you can see that we have one with dots on and one with lines, but the points or the dots are the same distance apart, and this means that it's isometric paper.

That's all isometric paper is.

You might have seen some of this before.

Izzy and Sofia choose some of the dotted isometric paper and decide to try and draw some lines on it.

Izzy says, "We used a ruler to make sure our lines were straight." And I think that's a really good tip.

You might think that you can draw a straight line by connecting the dots, but it's much easier to do that if you line up your ruler along the dots and use a ruler to get that line super straight.

They've also started and ended at a dot, and that's one of the really good things to think about when using isometric paper.

Start and end at a point.

Sofia challenges Izzy to make a rectangle by adding sides to a line that she's already drawn.

Let's take a closer look.

We can see that Sofia has drawn a straight line, probably using a ruler, and she has started and ended at one of the dots on the isometric paper.

Hmm, how would you complete that to make a rectangle? That sounds like a tricky challenge, Sofia.

Watch what Izzy draws.

Has she completed the polygon to make a rectangle? Let's see.

What do you think? Izzy says that, "A rectangle has four right angles, which means that it has four pairs of perpendicular sides.

Remember, pairs of perpendicular sides are just two sides that meet at a right angle.

This is one pair.

Here is one example.

So remember there are four pairs in this rectangle.

It also has two pairs of parallel sides, and those parallel sides to make a rectangle have to be of equal length.

So I think that Izzy has drawn a rectangle.

She's happy that she's drawn a rectangle.

Do you agree? Time to check your understanding.

Sofia completes the polygon in a different way.

What polygon has she drawn, and how do you know? Take a moment to have a think.

Welcome back.

What kind of polygon has Sofia drawn? This shape is a quadrilateral called a trapezium, and I hope you said both of those words in your description.

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

Lots of different polygons can be drawn on this dotted isometric paper.

Sofia and Izzy take turns to draw sides to make a polygon.

Let's see what they do.

There is their polygon.

What polygon has been drawn? What do you know about it? Can you identify any properties in the polygon? Well, Lizzie has noticed that their shape is a hexagon, and she says that's because, "it has six sides and six vertices," and that is a special name for a polygon with six sides and six vertices.

It also has two pairs of parallel lines.

Can you spot them? We have one pair going horizontally and one pair going vertically.

Even though one of those lines is very short, it still is parallel to the other.

It doesn't get closer together or further apart.

She continues.

"The shape has three right angles, so it has three pairs of perpendicular sides." She has shown you there an example of the perpendicular sides.

I wonder if you can spot the others? Izzy and Sofia continue to draw different polygons.

Take a look at the ones that they've drawn.

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

I wonder what you can notice? Well, in this case, both of the polygons are pentagons, because they have five sides and five vertices.

One is bigger than the other.

It takes up more space on the paper.

So we can see that the one on the right is larger in size than the one on the left.

One of them has a pair of perpendicular lines and one does not.

And we can check to see if there is a right angle.

So remember, you might use a right angle checker, like this one, to see.

And in the right hand pentagon, it looks like it could have been a right angle, but it's not a right angle.

It's a little bit bigger than a right angle.

Whereas, the left hand polygon definitely has a right angle, so it has a pair of perpendicular sides.

Time for your first practise task.

I would like you to draw two interesting polygons with fewer than 10 sides on the isometric paper.

Then, I'd like you to draw some different quadrilaterals.

I'd like you to tell a friend about the quadrilaterals that you've drawn.

If you don't have anyone to talk to, you might like to write them down.

I hope you have fun drawing lots of different polygons, and I'll see you shortly for some feedback.

Welcome back.

How did you get on? Did you enjoy drawing those different polygons? I wonder which ones you drew? Let's take a look at some of the examples of quadrilaterals.

We've drawn a few different ones here.

Now remember, you might have drawn different quadrilaterals.

They might have been bigger or smaller in size than the ones we have here.

Let's take a look at some of the properties of these quadrilaterals.

Polygons A and B are rectangles.

They have four right angles and they have two pairs of parallel sides.

So we can also say that they have four pairs of perpendicular sides.

Polygon C is a trapezium.

Well done if you spotted that, or well done if you drew any trapeziums yourself.

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

This particular trapezium doesn't have any right angles, so it doesn't have any pairs of perpendicular sides.

Polygon D is a parallelogram.

Parallelograms have two pairs of parallel sides, and this one doesn't have any right angles, so this one doesn't have any perpendicular sides either.

Finally, polygon E has no parallel sides or any perpendicular sides.

It is still a quadrilateral though, because it has four sides and four vertices.

Well done if you drew some interesting quadrilaterals.

Let's move on to the second cycle of our learning, where we're going to think about drawing on isometric lined paper.

Remember, at the start of the day, Sofia and Izzy were sorting through the paper and they found two different types of isometric paper.

What do you notice about this isometric paper? Izzy notices that the points are joined by lines and the lines are all the same length.

They make small triangles that have three sides of the same length, and you can see one of them highlighted there.

We can use this paper to draw different triangles.

Let's see what Izzy does.

Here are some different triangles that we've drawn using this lined isometric paper.

Sofia and Izzy practise drawing lines on the paper, and Sofia is reminding us that we still need to use a ruler to make sure that we draw straight lines.

Even though there are straight lines on the paper, it's really helpful to make sure they're super straight by using a ruler each time.

I notice that Sofia and Izzy are starting and ending at the vertex or corner of a small triangle each time, so they're making sure that they start and end at the points of the triangles.

And they're following the lines of the isometric paper, so you'll notice that the lines they've drawn follow the sides of the triangles.

They're not cutting through any triangles.

And those are really good rules to follow when working with this isometric paper.

So they're not going to use lines like that one, for example, because it cuts through the different triangles.

Even if we stick to those rules, lots of polygons can be drawn on this isometric paper as well.

Sofia and Izzy take turns to draw sides to make a polygon.

Let's watch what they do.

Ooh, that's an interesting polygon.

I wonder what you notice about it? Can you say any properties of the polygon? Can you say what type of polygon it is? What shape has been drawn? What do you know about it? Sofia says that they "drawn a hexagon.

It has six sides and six vertices." And remember, hexagon is the special name for a polygon with six sides.

I wonder what else she notices about it? She can't see any right angles, so that means there are no pairs of perpendicular sides.

And if we look really carefully at each vertex, none of them are a right angle, so no perpendicular sides there.

She does notice though, that the two lines that she's shown on the isometric paper are parallel, so they never get closer or further apart.

So that means that the two sides that are shown are also parallel.

We can say that their hexagon has one pair of parallel sides.

Time to check your understanding.

Find a different way to complete this to make a polygon with no more than eight vertices.

Pause the video and have a go.

Welcome back.

How did you get on? Now remember, there are lots and lots of possibilities that you could do, because we have no more than eight vertices, so you could have had three, four, five and so on.

We could have drawn something like this.

Or we could have drawn something like this.

What do you notice about this one? I can see that there are three sides in this particular polygon, that are parallel.

The horizontal sides, there might be three of them, but they are still all parallel to one another.

They remain the same distance apart.

Well done if you drew an interesting polygon.

Time for your second practise task.

I would like you to draw three different shapes on this isometric paper, and make sure that each of those shapes has no more than 10 sides.

So think really carefully.

Can you draw a shape that you think no one else will have drawn? Can you be really unusual and interesting in your shape? Now remember, when you're drawing these shapes, you need to stick to a couple of rules.

Firstly, you need to make sure that you begin and end at points, so the vertices of the triangle.

And secondly, we're following the lines of the isometric paper, so we shouldn't be drawing lines through any triangles.

For question two, I would like you to use the isometric paper to draw a few different things.

So first of all, I'd like you to draw two different hexagons.

Think about how many sides you need for a hexagon? Then I'd like you to draw a hexagon with exactly two angles that are smaller than a right angle.

So think about what a right angle looks like? We need two angles that are smaller.

A hexagon with exactly three angles that are smaller than a right angle.

And then a hexagon with more than one pair of parallel sides.

Take your time with those ones.

Check really carefully that you follow the rules for the hexagons, and I look forward to giving you some feedback shortly.

Pause the video here to have a go at these tasks.

Welcome back.

How did you get on? Let's take a look at some possibilities.

For question one, you could have drawn a huge range of different polygons.

Here are some more unusual ones that we thought to draw.

Take a close look at them.

What is the same? What is different? For example, I can see that polygons B and C are both septagons.

They have seven sides and seven vertices.

A has fewer than that, so it is not a septagon.

But if we look at B and C, even though they are both the same type of shape, they have different properties.

I can see that both of them though, have at least one pair of parallel sides.

Well done if you drew a really interesting polygon in your exploration.

And let's think about question two.

Here are some of the hexagons that you may have drawn.

Now remember, your hexagons might have looked different to ours.

Let's take a closer look.

If we think about shape A, they are two different hexagons.

Hexagons have six sides and six vertices, so hopefully you drew some shapes with six sides and six vertices.

Shapes B have exactly two angles that are smaller than a right angle, and we've circled them there.

So if we look at the top shape B, we can see that the two angles circled are definitely smaller than a right angle, which is a square corner.

And I can see that the other four vertices are bigger than a right angle.

You may have used a right angle checker to make sure that you are making smaller ones.

Shape C has exactly three angles that are smaller than a right angle.

It's still a hexagon, it still has six sides and six vertices, but we can see that exactly three of them are smaller than a right angle, and the other three are greater than a right angle.

And then finally, for D, shapes D have more than one pair of parallel sides.

Some of them are shown.

So we can see in both of them that the horizontal lines that you can see, are parallel.

They never get closer together or further apart.

Remember, your shapes might have looked different to this, but make sure they were all hexagons, count the sides carefully.

Did you have six sides and six vertices? Well done for having a really good go at that tricky challenge.

We've come to the end of our lesson where we've been drawing polygons on different isometric paper.

Let's summarise our learning.

We know that isometric paper allows us to draw polygons which have straight sides.

Different patterns allow us to draw polygons with different properties.

Shapes with the same number of sides can have different properties, and we've drawn different hexagons today.

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