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 math lesson.

In this math 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 shapes with given properties on a range of geometric grids.

We have a couple of keywords in our lesson today.

I'm going to say them.

I'd like you to say them back to me.

My turn, property.

Your turn.

My turn, properties.

Your turn.

Let's take a look at what this word means.

A property is a character or a quality something has.

So if we look at the triangle, we can say that a triangle has three vertices, and this is a property of the triangle.

The plural of property is properties.

In this lesson today, you're going to be drawing shapes with given properties on a range of geometric grids.

And we have two cycles in our learning today.

The first cycle, we're going to be focusing on drawing on different grids, and then we're going to move on to completing different shapes.

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

In this lesson today, you're going to meet Izzy, Jun, and Sam.

They're going to be sharing examples of their work and asking us questions along the way.

So let's start here.

Jun, Izzy, and Sam all have different types of grids to draw on.

Now, you may be familiar with square grids.

You might have these in your maths books, but you may be less familiar with the isometric grids, which are the dotty grids.

Isometric grids are points that are the same distance apart.

You might see squares or you might see triangles.

So the three children draw the same polygon onto their grid.

Let's see what they do.

This is what Jun draws.

This is what Izzy draws.

And this is what Sam draws.

What do you notice about these three polygons? Hmm.

Well, they're all pentagons, so they've all drawn the same polygon.

They've all drawn a pentagon, which has five sides and five vertices, but I'm not sure there's much else that's similar about them.

All of them have at least one pair of perpendicular sides.

Remember, a pair of perpendicular sides meets at a right angle.

So we can see in Jun's shape that he has one right angle, so he has one pair of perpendicular sides.

I wonder if you can spot them in Izzy and Sam's work.

There's Jun's.

Izzy has two right angles, so therefore, she has two pairs of perpendicular sides.

And Sam also has two right angles, so she has two pairs of perpendicular sides.

All of the pentagon's have one pair of parallel sides.

Remember, parallel sides stay the same distance apart.

We can show them by using arrows pointing in the same direction.

There's Jun, there's Izzy's, there's Sam's.

So actually, they looked different, but they had more in common than I thought.

Each child moves one vertex to create a new pentagon, so they've taken one of the vertices of the shape and moved it to create a different pentagon.

Take a close look at them.

Do they have the same properties as before? So do they all have perpendicular and parallel sides? Hmm.

Jun thinks carefully about the properties of his shape.

He still has a pentagon.

Remember, he just moved one of his vertices.

He didn't add one or take one away.

But what's different? It still has one pair of parallel sides, he says, and we can show that, remember, using our arrows.

But this time, it has no right angles.

So that means there are no perpendicular sides.

It's changed from his first example.

Izzy now thinks about the properties of her shape.

She still has a pentagon as well.

Remember, she just moved one vertex.

It still has one pair of parallel sides.

What else do we notice about it? It also still has two pairs of perpendicular sides.

And you can see there we have two right angles, so we still have two pairs of perpendicular sides.

Sam thinks about the properties of her shape, and she still has a pentagon as well.

But now, she doesn't think that any of her sides of her pentagon are parallel or perpendicular.

Hmm, she had one pair of each before.

Now she thinks she doesn't have any.

Time for a check of your understanding.

How could Sam check? So Sam doesn't think that she has any parallel or perpendicular sides in her shape.

What advice would you give her to check? Pause the video here.

Welcome back.

I wonder what Sam was going to do in this situation, and I wonder if you said similar.

Sam says she can use a right angle checker to see if any of her sides are perpendicular.

So we might check this pair of sides, but we can see here that this is not a right angle.

It is greater than a right angle.

So those two sides aren't perpendicular.

This one? Hmm, this time, it's slightly smaller than a right angle.

It's not a right angle, so no perpendicular sides there either.

We can also think about parallel lines by extending the lines of any sides that she thinks might be parallel to see if they stay the same distance apart.

So she thought that these two sides might be parallel, but if we extend the lines, we can see that they get closer together or further apart.

They don't stay the same distance apart.

So Sam was right, and we can use some strategies to check for perpendicular sides and parallel sides.

Hopefully, you gave her some similar advice.

Time for your first practise task.

For question one, I would like you to draw a triangle with a pair of perpendicular sides on each of these different grids.

So you have the three grids that the children were using.

Can you draw a triangle this time with a pair of perpendicular sides? For question two, I'd like you to draw a quadrilateral with one or more pairs of parallel sides on each of these different grids.

Remember to use a ruler.

I know that the grids appear to have straight lines, and they do, but it's useful to be super sure that your lines are straight by using a ruler.

For question three, I'd like you to choose one of the grids this time so you can choose between the three grids that we've been using.

I'd like you to draw a hexagon and identify its properties.

Then I would like you to change one vertex to make a new hexagon.

So like the children did earlier, move one of the vertices so that you make a new hexagon.

And then think about compare the two.

Have the properties changed? What's the same and what's different? Good luck with those three tasks.

Enjoy drawing all those different shapes, and I'll see you shortly for some feedback.

Pause the video here.

Welcome back.

How did you get on? Let's start by thinking about question one, which was about triangles.

Here are some examples of triangles with a pair of perpendicular sides.

Now, your triangles may have looked different to these ones and that's fine, but check carefully.

Do you have a right angle in each of your triangles? You might have marked that with a little square, which is the symbol for a right angle, like we have done here.

Remember, the triangles can look different.

The one in the middle is bigger than the other two, but they do have to have that pair of perpendicular sides.

So look carefully, check your triangles, make sure they fit that description.

For question two, there are lots of different quadrilaterals that you could have drawn, so here are some examples.

You may have drawn a trapezium.

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

You may have drawn different parallelograms. So remember, a rectangle is a special type of parallelogram because it has four right angles.

So that's the third example we have here.

But all of these shapes have at least one pair of parallel sides.

You may have chosen to mark the sides using arrows pointing in the same direction.

Have a really good look at your quadrilaterals.

Do they have four sides and four vertices? And do they have at least one pair of parallel sides? Well done if you've managed to do that.

For question three, there are lots of different ways you could have tackled this.

We chose to use the dotted isometric grid, and here is one example.

The properties of this polygon is that it is a hexagon, which means it has six sides and six vertices, and it also has one pair of parallel sides.

If we were to move the vertex that I've circled down into a different position, like so, I have a new hexagon.

What are the properties this time? Well, it's still a hexagon, so it still has six sides and six vertices.

This time, it has one pair of perpendicular sides, and I've marked that using a small square to show there is a right angle.

It doesn't have any parallel sides this time.

The properties have changed just by moving one vertex.

I wonder what properties you changed.

Hopefully, you still had a hexagon, but I wonder if you started off with parallel sides and then didn't have parallel sides or vice versa.

Well done if you thought really carefully about how the properties changed when you moved one of your vertices.

Let's move on to the second cycle of our learning today, where we're thinking about completing shapes.

Jun, Izzy, and Sam all tackle the same problem.

Let's look at that problem together.

The grid shows four vertices of a hexagon, and you can see them there marked by black dots.

The challenge is to complete the hexagon.

Izzy is reminding us, thanks Izzy, that hexagons have six vertices, so they all need to draw on two more vertices to complete the challenge.

We can see four vertices of the hexagon drawn.

We need to draw two more to make six altogether.

Good thinking, Izzy.

We can then use a ruler to make the side straight.

That's a really important point as well.

Remember that even though we have the straight lines of the grid, it's super useful to use a ruler to make sure those signs are really straight.

This is how Jun, Izzy, and Sam all responded to the question.

So remember, they had four vertices, and they had to add two to make a hexagon to complete the shape.

What do you notice? Have they all completed the task properly? They all look different.

Does that matter? Hmm.

Jun and Izzy's hexagons have at least one pair of parallel sides, so they mark some of them.

Sam's doesn't, so she doesn't need to mark anything.

All of the examples are hexagons, but they have different properties so the children have completed the task properly, but the hexagons just look different because they have different properties.

Time to check your understanding.

Create a different hexagon by adding two additional vertices.

So if the same problem as the children, what are the properties of your hexagon? Pause the video here and have a go.

Welcome back.

How did you get on? Now remember, there are lots of different ways you could have completed this problem.

This is how Izzy chose to do it, and Izzy said the properties of the hexagon that she drew is that it has six sides and six vertices and one pair of parallel sides.

Those are the properties of that hexagon.

You might have approached this in a different way, but you might want to check with a friend if you have one nearby that your properties are what you think they are.

Well done for having a good go and drawing a different hexagon.

Izzy takes a look at those four vertices and wonders what other shapes we could use using those points as vertices.

Hmm, I wonder if you can visualise any shapes.

Well, she starts by just connecting the vertices up.

What shape has she made? Thanks, Izzy.

This is a trapezium, so she hasn't added any extra vertices.

So it is a four-sided shape.

And remember, a trapezium has exactly one pair of parallel sides.

That is one of its properties, so that's what makes it a trapezium.

She could also use one extra vertex and make a pentagon.

Remember, a pentagon has five sides and five vertices.

That's part of its properties.

Does this one have any other properties? Absolutely, Izzy.

This Pentagon also has a pair of parallel sides and she thought those sides might be perpendicular, but they're not.

They're not a right angle, and I can see why she thought that.

If you at those, if you look at that vertex, it looks really close to a right angle, but she's used a right angle checker, which is a great strategy and checked and found that it's actually slightly bigger than a right angle.

That means there are no perpendicular sides in her shape.

She then thinks a little bit more if she moves that additional vertex, the properties of the pentagon change.

I wonder if you can identify the properties.

Time to check your understanding.

Describe the properties of Izzy's pentagon.

Pause the video here and have a go.

Welcome back.

How did you describe Izzy's pentagon? Hopefully, you said something like Izzy.

"The properties of the pentagon I drew are that it has five sides and five vertices.

It has no parallel or perpendicular sides." Well done if you identified that about Izzy's pentagon.

Time for your second practise task.

For question one, two sides of a square have been drawn.

I would like you to complete the square.

Think carefully about what you need to do to make a square and use a ruler when you're drawing any sides.

For question two, I would like you to complete the shape to make a regular hexagon.

Remember, regular shapes have all the sides the same length and all the angles the same size as well.

For question three, I'd like you to use the same dots there to complete the shape to make an irregular hexagon.

And then for question four, I would like you to complete the shape in different ways to make (a) a quadrilateral with at least one pair of parallel sides, and (b) a hexagon with at least one pair of parallel sides.

So you can see there you have only two vertices, so think about how many more you need to add to make a quadrilateral and then a hexagon.

Good luck with those tasks.

I'll see you shortly for some feedback.

Pause the video here.

Welcome back.

How did you get on with those tasks? I hope you enjoyed drawing lines and vertices to complete the shapes.

Let's take a look at some answers.

For question one, in order to make a square, we had to make sure that we had four sides the same and we had to make sure that we had four right angles.

So this is the only way that you could have completed that square.

For question two, you had to complete the shape to make a regular hexagon.

So remember that regular polygons have sides of the same length.

This is the only way that you could have completed that to make a regular hexagon.

However, for question three, you had to make an irregular hexagon, and you could have done lots of different things here.

Here are some examples.

So remember, we only had to put in one more vertex because we had five vertices already.

So there are lots of different ways you could have placed that vertex to make a hexagon.

Have a check.

Does your shape have six sides and six vertices? If it does, it is an irregular hexagon.

Very well done.

And for question four, you had a couple of vertices in place, so you had to complete them to first make a quadrilateral with at least one pair of parallel sides.

Here are a couple of examples.

You could have made something like a rhombus.

A rhombus has two pairs of parallel sides, or you could have made a trapezium and that one has exactly one pair of parallel sides.

Well done if you made a shape with four sides and four vertices that had one or more pairs of parallel sides.

I also asked you to make a hexagon that also had at least one pair of parallel sides.

There are lots of different ways you could have used those two vertices to make a hexagon.

Here are just a couple of examples.

These both have six sides and six vertices, and the first one, as you can see, has two pairs of parallel sides, and the second one has one pair of parallel sides.

Well done if you manage to complete that tricky challenge.

We have come to the end of the lesson, and I really hope you've enjoyed drawing shapes with different properties on different geometric grids.

Let's summarise our learning.

If you know the properties of a shape, then you can draw it.

Using a grid and a ruler is helpful in order to be more accurate.

The same shape type can have different properties.

For example, some pentagons can have parallel sides and some do not.

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