Lesson video

Hello there.

My name is Mr. Tilstone.

I'm a teacher.

I teach all of the different subjects, but the one that I enjoy most just has to be maths.

If I haven't met you before, it's nice to meet you, and if I haven't met you before, it's nice to see you again.

Today we're not going to be thinking too much about the number side of maths, we're going to be thinking about shapes and sketching shapes.

So if you're ready, I'm ready.

Let's begin.

The outcome of today's lesson is, I can use my knowledge of shape properties to sketch and identify shapes, and I'll bet you already know quite a bit about shapes.

Let's see if we can build on that.

We've got some keywords.

My turn, regular.

Your turn.

My turn, irregular.

Your turn.

So what do those words mean in the context of shape? Well, a regular polygon has all sides equal and all angles equal.

In an irregular polygon, that is not the case.

So we've got some examples here of a regular polygon, all the sides are the same length, all the interior angles are equal, but that's not true about the other one, so that's irregular.

Our lesson is split into two cycles, the first will be sketching polygons and the second, sketching polygons with different properties.

So if you're ready, let's start by looking at sketching polygons.

In this lesson you're going to meet, among many others, Alex and Sam.

Have you met them before? They're here today to give us a helping hand with our maths.

(mouse clicking) The class six teacher at Oak Academy sets the pupils a challenge, and this is a challenge that you might like to take part in too.

(mouse clicking) They have to sketch a quadrilateral.

Hmm, do you think you could do that as well? Maybe do one that you think nobody else in the class will have done, something like that, an unusual one.

She's asked them to work in a group and each sketch a different kind of quadrilateral.

Are you ready? (mouse clicking) Here are what some of the Oak pupils drew, what do you notice? Have a little look at them.

First of all, are they all quadrilaterals? Hmm.

Secondly, are they all different kinds of quadrilaterals? Hmm.

(mouse clicking) Well, let's start with Alex.

Alex did not draw a quadrilateral because his shape has five sides and five vertices.

A quadrilateral is a four-sided shape.

So, hard luck, Alex, it almost looks like one, doesn't it, but that corner cut off on the bottom left stops it being.

Sam and Aisha both drew a square.

Did you spot that they were both squares? I bet you definitely saw that Sam's was.

How do we know that they're both square, though? (mouse clicking) Both shapes have equal side lengths and four right angles.

They're both regular.

Aisha's just happens to be in a different orientation, that's all.

(mouse clicking) Andeep and Izzy's quadrilaterals both have two pairs of parallel size.

Did you notice that? So they're sort of different, but sort of similar too.

(mouse clicking) Andeep's quadrilateral has four pairs of perpendicular sides.

Do you see that? So it's got four right angles, what kind of shape is that? Here are what some of the Oak pupils drew.

What do you notice? Again, are they all quadrilaterals? What kinds are they? Some of these are quite unusual ones, aren't they.

Maybe you drew one a bit like this.

(mouse clicking) Jun's quadrilateral does not have any parallel sides, it's got two pairs of adjacent sides which are equal in length.

(mouse clicking) Jacob and Lucas have both drawn shapes with parallel sides, but are they the same as each other? So those final two shapes have both got some parallel sides.

Hmm, have a look at Lucas', that's the one in the middle, how many pairs of parallel sides has that got? Just the one.

And what about Jacob's on the right, how many has that got? Two pairs.

So they are different shapes, even though they've both got parallel sides.

Jacob's shape has two pairs of parallel sides, the sides are also equal in length, and you couldn't say that about Lucas' shape.

(mouse clicking) So the question is, how many of these quadrilaterals can you name? So think back, it might be a long time since you've thought about these names.

Now, I've got a little tip for you today.

If you've got something that you can make notes on, make some notes because there's going to be a lot of things to remember, a lot of shape names to remember, a lot of terminology.

So if you are ready to get naming, work together, pause the video.

All right, how many could you name? Let's have a look.

Got a square in a slightly different orientation to what you might expect, but still a square, still got four right angles and four equal length sides.

A square is a regular rectangle.

We don't tend to use that term, but that's what it is.

It's also a parallelogram, because it's got parallel sides, pairs of parallel sides.

This is a kite, that's a mathematical term.

This is a trapezium, with one pair of parallel sides.

This is a rectangle.

Now something to know, a rectangle is also a parallelogram because it's got two pairs of parallel sides.

And that's a parallelogram as well, for the same reason.

What about the last one? Hmm.

Tricky one to remember, perhaps, this one.

What's it called? Two pairs of parallel sides, all the sides equal in length.

It's not square though, is it? It's a rhombus.

And a rhombus is a kind of parallelogram, because it's got two pairs of parallel sides.

Well done if you got any of those, well done if you've got most of those, and a big special weld done if you've got all of those.

This time the class six teacher has asked the pupils to sketch some different triangles in their group.

Do you want to have a go at that too? That'd be great, see if you can get some unusual ones, see if you can name them as well.

Here's what they came up with.

What do you notice? Again, first of all, are they all actually triangles? Are they the same kinds of triangles, different kinds of triangles? Have they got names? Well let's start with Aisha.

She's not drawn a triangle, it's not a polygon.

It's almost a triangle, isn't it, I can see why she might think it was.

Do you know what stopping it being a polygon or a triangle? It's the fact that it hasn't got three straight sides, one of those is curvy.

Alex's triangle has three equal sides, and three angles that look equal.

And I'll bet, if you were to think of a triangle, that's probably the kind of triangle you think about straightaway.

There we go, there's the equal sides, three of them.

And Sam has a triangle, but only two of her sides are equal.

Can you see which two are equal? And one side is longer.

So those two are equal to each other, but one's longer so it's a different kind of triangle.

Andeep and Jacob are debating whether they're triangles are the same or different.

What do you think? Same type of triangle or different? Why might they think they're the same? Hmm.

(mouse clicking) Andeep has sketched a triangle where none of the side lengths or the angles are equal.

Do you notice that? Look at those sides.

Got a short one, a medium one and a long one.

(mouse clicking) But you could say that of Jacob's as well, couldn't you, that's got a short one, a medium one and a long one.

(mouse clicking) But Jacob's triangle is also a right-angled triangle.

Did you spot that? Those two perpendicular sides in the right angle that they form.

(mouse clicking) There we go.

So they sort of the same and they're sort of different too.

(mouse clicking) Now Jacob and Izzy are debating whether their triangles are the same type or different types.

What do you think? Have a look at them.

Same or different? Let's have a look.

(mouse clicking) Well, they're both right-angled triangles so they've got something in common with each other.

However, two of Izzy's side lengths are the same.

Can you spot which two? Whereas Jacob has three different side lengths.

So they've got something in common, but something different about them as well.

(mouse clicking) Here we go, so there's these is two sides that are the same, but you can't say that of Jacob's.

(mouse clicking) Okay, let's bring back some knowledge, hopefully, about triangle names.

How many of these can you name? Pause the video.

Let's have a look.

Okay, they've all got special names.

This one's an equilateral triangle.

All of the sides are the same length and all of the interior angles are the same as well, it's equilateral.

It's in a slightly different orientation to what you might expect, but that doesn't stop it being an equilateral triangle.

(mouse clicking) And what about this one then? So this time we've got two side lengths that are the same, making that an isosceles triangle.

So if your triangle's got two equal side lengths and two equal interior angles, it's isosceles.

And how about this one? A couple of things we could call this, a couple of names.

There's a little clue there.

(mouse clicking) It's a right-angled triangle, you could call it, or you could call it a scalene triangle.

And that's what we call triangles that have got three different side lengths and three different interior angles.

So we could say right-angled triangle, we could say scalene triangle, or we could combine them and say right-angled scalene triangle.

Well done if you got those.

(mouse clicking) It can be difficult to sketch some regular polygons because all of the angles have to be exactly the same, and all of the side lengths have to be exactly the same.

So that's quite difficult.

Alex is attempting, he's having a go at drawing a regular Pentagon.

Let's have a look.

So he's got a side.

Okay, so far so good, he's got it straight.

Two sides.

He says, "Are those sides the same length? Maybe not." I don't know, it's hard to see, isn't it.

You have a look, what do you think? Sometimes I look and they look the same, sometimes different, it's very hard to tell.

Hmm, so we can't really say for sure that it's regular.

He's done another one.

And he says, "I think those angles are different to each other." What do you think? So, so far he's formed two angles.

Hmm, yeah, I think he's right, I don't think they're the same either.

He's carrying on, though, he's done another side length, and another one.

Okay, well let's give him some feedback.

What do you think? It's not regular, is it? It's a Pentagon, and it's a polygon because all the sides are straight and closed, and all of that, but it's not regular.

I can see it's not, I can see it's got some slightly shorter sides than others, so it's a ing but not a regular one.

It's tricky, isn't it, to draw or sketch regular polygons.

It is much easier to sketch and irregular polygon because you're not quite as tied to equal side lengths and things, and the same with the angles.

As long as it's got the right number of sides.

So to classify as a Pentagon, the shape needs to have five join straight sides.

It doesn't matter about the length, as long as they're joined in straight.

Alex says, now I've got a bit more freedom, he's a bit more confident now.

Let's go.

There we go, one, two, three, four.

"That was my fourth side," and he says, "The fifth just needs to join back to the first," easy peasy.

There we go.

So he is drawn an irregular pentagon, that was much easier, wasn't it? Here are some irregular polygons.

You may wish to have a go at sketching your own example before it appears.

So if you've got a whiteboard at the ready, you might want to use it now.

Let's start with irregular hexagon, you want to have a go at sketching that? What might that look like? It's got six sides, what could it be like? Could be like that, yours might look completely different but still have six sides.

(mouse clicking) And about irregular septagon, that's got seven sides.

Sometimes called heptagon, we're gonna call it a septagon.

Could be like that.

It's got seven sides, they're all straight and joined.

What about irregular octagon, do you wanna have a go at that? This one's got eight sides, it's unusual, isn't it.

Yours probably look completely different to that.

What about an irregular nonagon? It's got nine sides, do you want to have a go at that? Make sure that final side joins to the start.

Could be something like that.

That's got nine sides, not equal in length.

What about decagon? 10 sides, have a go if you like.

How about that? It's very irregular, very different, very unusual, but it is a decagon.

Lots of terminology there and if there's any that you're a bit unsure about, why not write it down as a reminder.

It might be, for example, septagon, you weren't sure about that name.

I think maybe Hexagon you may be more secure with, but nonagon and decagon also might be ones you're insecure with, so write down anything that you might need to help with your memory.

Okay, time for a check.

Sketch an irregular hexagon.

I'm not gonna tell you how many sides that's got, either you know it or maybe you wrote it down.

Can you sketch one that no one else would've drawn, a really unusual one? Have a go, pause the video.

What did you come up with? Have you had a chance to share with the class or with the pupils on your table? Let's have a look at one.

Well, it's any closed six-sided shape with straight lines.

Here's just one example, It's not likely you've done the same one.

That is my irregular hexagon, it's got six straight joined sides.

It's time for some independent practise.

So number one, complete the quadrilaterals, quadrilaterals, four-sided shapes, by adding two more lines to each to make the following.

So A is going to be a kite, B is going to be a parallelogram, C's going to be rhombus, and D is going to be a trapezium.

So see if you can complete those shapes.

Number two, complete the triangles by adding two more lines to make the following.

A is going to be equilateral, B is going to be isosceles, C is going to be scalene and D is going to be right angled.

There's more than one way that you can do some of these, by the way.

And number three, sketch and name some irregular polygons that are not triangles or quadrilaterals.

Have fun with your sketching, and I'll see you soon for some feedback.

Welcome back, how did you get on with sketching those shapes? Hopefully getting more confident with those shape names too.

Well, let's have a look at some possibilities.

That's a kite, that's a possibility for a kite, or the possibility for this one.

This is a parallelogram, two pairs of parallel sides.

That's a rhombus, so four sides all equal in length.

And this is a trapezium, one pair of parallel sides.

You might have done that for a trapezium, there are different ways you could do that.

And number two, many, many possibilities for this one because there's only one line drawn, so here's just some examples then.

So A, that's what an equilateral triangle could look like, three side length, the same.

B, that's what an isosceles one could look like.

You might have done it the other way round as well.

That has got two equal side lengths, and one that's different.

And, C, a scalene triangle, so we're looking for all three sides different lengths.

For example, that, You've probably done something completely different, but we're looking for three different side lengths.

And then a right-angled triangle.

Well, that's one possibility.

And for number three, sketch and name some irregular polygons that are not triangles or quadrilaterals.

Well, you had a lot of freedom and flexibility here, but here's just one example.

This is irregular octagon.

Here we go.

It's got eight sides, they're all straight, they're all closed.

They're not the same length, it's an irregular octagon.

You're doing really well so far, I think it's time now to move on to sketching polygons with different properties.

The teacher sets a new challenge.

Sketch a quadrilateral with exactly two right angles.

Hmm, do you think you could do that? Why don't you have a go first? Let's have a look.

Andeep says, "I will sketch the right angles in first." That is a really good tip, hmm.

Each one will be a vertex.

So that's the first right angle and the first vertex.

So he's doing a quadrilateral, so how many vertices will it have? Four, that's one of them.

The next one will be opposite so that they can form one of the sides.

Yeah, he's got some choices here about where to put this.

I think he's got a few choices, but that's what is chosen.

Here we go, look, so that is another right angle.

So another one of the vertices, got two of them now.

He's got those two right angles so he can't draw any more right angles, that's his limit now.

But now he's joined them together to form a side.

Gotta sketch three other sides in, as long as they've not got right angles, he's fine.

Let's see what he does.

That's one, two, and then the little one there on the right makes three.

So let's just count, one, two, three, four.

Yeah, he's got four sides.

Let's check, he's got four vertices.

One, two, three, four, yes, he has.

Let's check if he's got two rectangles and no more than two.

Yes, he has.

Well done Andeep, brilliant work.

Andeep's shape is a trapezium, it's got exactly one pair of parallel sides so any shapes that you draw today that have got one pair, and one pair only, of parallel sides are called a trapezium.

You might have drawn one already.

The teacher sets a new challenge.

Sketch a triangle this time with exactly two acute angles.

Acute angles, okay.

Think about that, what kind of angles are acute angles? Let's have a look, let's see what Izzy does.

She says, "I need two angles less than 90 degrees." Yes you do.

"They will join to make a side." Okay, so that's a bit like Andeep.

So we've got one of the vertices.

Is it acute? Yes it is.

(mouse clicking) The next one will be opposite so that they can form one of the sides.

That's like what Andeep did, isn't I.

Well, let's have a look.

(mouse clicking) Yeah, fantastic.

Two acute angles.

"Now we just have to sketch the other sides in," so she's joined those together and she's drawing a line there, and another line.

It's gone a little bit over, hasn't it.

Doesn't matter, we can sort that out.

Get rid of that.

There we go.

So has Izzy succeeded? Hmm, it said two angles less than 90 degrees.

How many can you see, less than 90 degrees? I can see three.

Hmm, she tries again.

Well done, Izzy, that's what good mathematicians do.

If they don't succeed, they have another think and they try again.

Let's have a look.

"If I make these angles smaller, the other angle will have to be bigger." Yes, I like that.

They've got to equal 180 degrees altogether, so if you make those two acute angles smaller, that forces the other one to be bigger.

Let's have a look.

So that's smaller, it's a smaller acute angle.

And another smaller acute angle.

Join together to make a side length.

Let's see if she's succeeds this time.

Just like before, she's drawn a line, and another one.

Gone a bit over, so it needs to just sort that out.

Easily done.

(mouse clicking) Right, what do you think now? Has she succeeded this time? Has she got exactly two acute angles? Yes.

The third angle is obtuse.

Well done, Izzy.

Izzy has made an isosceles triangle.

Two of the sides are the same length.

(mouse clicking) Let's do a check.

Sketch a triangle with an obtuse angle.

What type of triangle have you created and can you make a different type? If you've got square of paper, that's great.

If not, just a whiteboard is fine.

Pause the video and have a go.

Let's have a look.

Lots of examples.

This is one of them.

(mouse clicking) That's a triangle with an obtuse angle.

What type is it? That's scalene triangle, got no equal side lengths.

What about this one? (mouse clicking) It's got an obtuse angle and two acute ones.

What kind is it this time? It's not scalene, (mouse clicking) because two of the sides are the same length.

It's a isosceles triangle.

(mouse clicking) It is time for some more practise.

If you've got some dice, roll two dice.

If not just randomly pick two numbers, one to six, to give you a shape name and an angle description.

Explore whether it is possible to sketch a shape that matches that criteria.

Some of the combinations will be possible and some of the combinations will not be possible.

And then when you've done that, do it again.

And when you've done that, do it again, and just keep going and going until your teacher says stop.

Good luck with that.

Have fun, and I'll see you soon.

How did you get on, did you find some that were possible? Did you find some that were impossible? Well, let's have a look at some examples.

So if you rolled a four, that will give you a hexagon with two obtuse angles.

Let's see if that's possible.

Yeah, that has got two obtuse angles, and no more.

It's got some acute ones, it's got a reflex angle, it's got a right angle, but it's got exactly two obtuse angles.

(mouse clicking) Now some combinations are not possible, so here's an example.

A triangle with two right angles isn't possible because the three angles in a triangle sum to 180 degrees, and the two right angles already total 180 degrees so it's not possible to have another angle in there.

(mouse clicking) We've come to the end of the lesson.

I hope you've had fun sketching shapes and revising all those shape names.

Today we've been using knowledge of shaped properties to sketch and identify shapes.

Irregular polygons are easier to sketch than regular ones because there's no need for size to be exactly the same, or for the angles to be exactly the same.

It is possible to sketch polygons with specific properties, such as a certain number of acute or obtuse, or right angles, by plotting them in first; so that is a top tip.

Keep all of that knowledge handy from today, all of those shape names, you're very likely to need them again in the near future for upcoming lessons.

It's been a real pleasure working with you today, hope to see you again soon for another maths lesson.

But until then, enjoy the rest of your day, take care and goodbye.