Lesson video

Ah, hello there.

My name is Mr. Goldie and welcome to today's math lesson.

And here is the learning outcome for today's lesson.

I can investigate right angles in shapes with more than four sides.

And here are the keywords.

I'm going to say both keywords.

Can you repeat them back? So the first keyword is pentagon.

And the next keyword is hexagon.

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

A pentagon is a 2D shape made up of five straight sides and vertices.

A hexagon is a 2D shape made up of six straight sides and vertices.

Here is our lesson outline.

So in the first part of the lesson, we're going to be exploring right angles in pentagons.

And in the second part of the lesson we're going to be exploring right angles in hexagons.

Let's get started.

In this lesson, you will meet Aisha and Laura and Aisha and Laura have been doing lots of investigating using pentagons and hexagons and they're going to be helping you with your work today.

So let's start off with what is a pentagon? The prefix penta means five.

Prefix just means the first part of the word.

A pentagon is a 2D shape with exactly five straight sides.

So this is a pentagon.

It has exactly five straight sides and five vertices.

And the vertices, remember, just the corners of the shape.

They're where two of the sides meet each other.

You can think of vertices as the places that sides go to hang out to meet each other and chat and get to know each other.

It's where they meet each other.

This is a regular pentagon.

All five sides are the same length and all five vertices are exactly the same size.

So in a regular pentagon, all the meeting places are exactly the same, all the vertices look exactly the same as each other.

I hope the signs don't get bored meeting each other there.

Aisha draws a pentagon on this grid.

"I need to use five straight lines," says Aisha.

A pentagon has five straight sides so Aisha has to draw five straight lines to draw a pentagon.

Aisha also needs to make sure that each vertex meets at one of the points.

So Aisha starts drawing the pentagon and she draws five straight lines.

"Does this pentagon have any right angles?" says Aisha.

Can you spot any right angles in that pentagon? Well, there's one here and there's also one here, and there's also one here.

This pentagon has three right angles.

Two of the angles are greater than right angles.

So this pentagon has three right angles and then two of the angles are greater than a right angle, those angles there are larger than right angles.

Aisha draws some other shapes.

Which shapes are pentagons? Aisha's drawn this shape here.

Is it a pentagon? Aisha has drawn five lines but she has made the lines meet.

She has actually drawn two triangles.

Now, of course the lines have to meet at the vertices of the shape but Aisha here has drawn a shape where she's actually got two of the lines meeting at a place that isn't a vertex.

So Aisha, sorry, that isn't a pentagon, it's actually two triangles.

Let's look at a different shape.

So Aisha draws again five lines.

Has she drawn a pentagon this time? Aisha has drawn five lines, however, one of the lines does not make a side of the shape.

It's kind of a quadrilateral with a tail that shape, isn't it? Definitely not a pentagon.

So Aisha draws another shape.

Has she drawn a pentagon this time? Aisha has drawn a pentagon.

It has one right angle.

So this vertex here is a right angle so Aisha has drawn a shape with five straight sides and five vertices, one of which is a right angle.

Well done, Aisha.

Aisha draws a pentagon with a right angle.

"I'm going to make sure I draw the right angle first," says Aisha.

So Aisha's going to start off by drawing a right angle and then she's going to see if she can complete the shape.

So she's got two sides of the pentagon already.

Here's side number three, side number four, side number five.

"Ah, this pentagon actually has two right angles.

I'm going to mark them with the correct symbol," says Laura.

Laura marks this right angle here using the right angle symbol.

And she also marks this right angle here using the right angle symbol.

So Aisha tried to draw a pentagon with just one right angle, she actually drew one with two right angles.

Aisha draws a different pentagon on this grid.

"I need to use five straight lines," says Aisha.

One, two, three, four, five.

Does this pentagon have any right angles? What do you think? Have a good look at that pentagon.

Can you spot any right angles? Pause the video and see if you can find any right angles in that pentagon.

And welcome back.

Did you find any right angles? Let's take a look to see whether you got all of them because there's more than one.

This pentagon has two right angles.

There's a right angle here, there's also a right angle here.

Very well done if you spotted both of those right angles.

Now, this vertex here is not a right angle.

This right angle is actually outside the pentagon.

Remember to measure the angles inside the shape.

Now there is a right angle here but it's outside the shape, it's an exterior angle of the shape and we're looking at the angles within the shape.

So, well done if you spotted the right angle there.

It's actually not within the pentagon.

Aisha uses five card strips.

"I'm going to attach them using split pins." Now all five strips are the same length as each other and they've already got two holes near the ends of the strips already.

So Aisha attaches them together using split pins and the split pins are there so that she can manipulate the shape and move it around.

"The five card strips fit together to create a pentagon," says Laura.

Aisha can create different pentagons.

So by moving the strips she can create different pentagons.

Now this pentagon here has no right angles.

"Can you make another pentagon with no right angles, Aisha?" asks Laura.

So Aisha changes the shape which creates this shape here.

Has that got any right angles? This pentagon also has no right angles.

There are no right angles in the pentagon, Aisha creates another pentagon.

So again, she manipulates that shape, moves it around to create a different pentagon.

Still the pentagon still got five straight sides, still got five vertices.

Can you find any right angles in this pentagon? Pause the video, see if you can spot any right angles.

And welcome back.

How did you get on? Did you find any right angles? Let's take a look.

So this vertex here is a right angle.

So I don't know if you spotted that one.

This vertex at the top here looks similar to a right angle but it's actually smaller than a right angle so this one here is not a right angle.

So it's always worth checking all the angles that you think could be a right angle.

Quite often you can just look at an angle and think that's definitely not a right angle.

Sometimes you have to check.

So well done if you spotted that this pentagon has one right angle.

Very well done.

And here is task A.

So in the first part of task A, you're going to draw some different pentagons with right angles.

Each vertex must meet at one of the points.

So each of those grids has got nine points in it so each vertex must meet one of those points.

And then mark the right angles on each pentagon.

Aisha's given you a very useful piece of advice here.

She says, "You might want to draw the right angle first." Can you come up with eight different pentagons, each of them with at least one rectangle.

That's the first part of task A.

And here is the second part of task A.

We're going to use five card strips of equal length and five split pins.

Gonna fit them together to make a pentagon.

Now find out whether it is possible to make a pentagon with zero right angles.

A pentagon with one right angle, a pentagon with two right angles, and a pentagon with three right angles.

Now you've seen some of those are possible already but can you make them for yourself? So pause the video and have a go at task A.

And welcome back.

Let's take a look at task A and see how you got on.

So here are some possible answers for the first part of task A.

So here are eight different pentagons and each of them has at least one right angle.

So well done if you found some of those shapes or you found different shapes that also have right angles as well.

Excellent work.

And here are some possible answers for part two of task A.

Now of course the pentagons you've made might have looked quite different to these 'cause there are so many different ways of making pentagons using those five card strips.

A was make a pentagon with zero right angles.

That was a fairly easy one to make.

It's quite easy to make a pentagon with no right angles.

It could have been a regular pentagon of course.

B was make a pentagon with one right angle.

Bit trickier but you should have been able to make one with one right angle, and of course it's really important to check any angles that could be right angles because you only wanted to have one right angle.

C, make a pentagon with two right angles.

Bit trickier this one but it is possible.

Looks a bit like the outline of a house, doesn't it? We've got there two right angles.

And D, make a pentagon with three right angles.

Now, this is actually impossible if all the angle strips are the same length of each other, but it is possible if the length of some strips are changed.

So we're gonna start off with a very similar shape to shape C.

It's got two right angles and you can shorten the length of the two strips at the top to give you a third right angle.

But it's impossible to make a pentagon with three right angles if all the sides are the same length as each other.

So very well done for working hard at task A and very well done indeed if you got onto part two of task A and you had a look at D, and you realised that you could not make a pentagon with three right angles.

That's excellent.

And let's move on to part two of our lesson.

So our part two of our lesson we're going to be exploring right angles in hexagons.

So what is a hexagon? Now the prefix hexa means six.

Remember that's just the beginning part of the word.

Hexa means six, so a hexagon is a six-sided shape.

A hexagon is a 2D shape with exactly six straight sides.

So the shape here is a hexagon.

It has exactly six straight sides and six vertices.

And this is a regular hexagon.

All six sides are the same length and all six vertices are exactly the same size to each other.

Laura draws some 2D shapes.

"Which shapes are pentagons, which are hexagons, and which are neither?" says Laura.

So have a good look at those four shapes there.

Can you work out which of those shapes are pentagons, which are hexagons, and which neither are hexagon nor a pentagon? Pause the video, see if you can work out the names of those shapes.

And welcome back.

How did you get on? Did you manage to name all four shapes? Let's take a look to see whether you labelled them correctly.

This first shape here is a pentagon.

It's got five straight sides and five vertices.

Second shape, bit tricky to see this one but this is a hexagon.

It's actually got six sides.

Any shape that has exactly six straight sides and exactly six vertices is a hexagon.

The shape here is a pentagon.

It's got exactly five straight sides and exactly five vertices.

And this large shape here is neither a pentagon nor a hexagon.

It is in fact a quadrilateral, which is of course the name of a four-sided shape.

So very well done if you labelled those shapes correctly.

Laura draws a hexagon on this grid.

"I need to use six straight lines," says Laura.

"Laura also needs to make sure that each vertex meets at one of the points," says Aisha.

So Laura starts by drawing her shape.

So one, two, three, four, five, six.

Laura has drawn a shape with exactly six straight sides.

"Does this hexagon have any right angles?" asked Laura.

What do you think? Can you spot any right angles in that shape? Let's count says one here, two, three, four, five.

So shape here actually has five right angles.

"This hexagon has five right angles.

One of the angles is greater than a right angle." So that last angle here is greater than a right angle.

And again, you may have spotted there, it's got a right angle on the outside of the shape but inside the shape is much greater than a right angle.

Laura draws a different hexagon on this grid.

"I need to use six straight lines," says Laura.

One, two, three, four, five, six.

"Does this hexagon have any right angles?" Pause the video, see if you can spot any right angles in that hexagon.

And welcome back.

Did you spot any right angles? Let's see whether you spotted them all.

So this hexagon has two right angles.

There's a right angle here and a right angle here.

All the other angles are either larger than a right angle or smaller than a right angle.

So very well done if you found those two right angles.

Laura uses six card strips.

"I'm going to attach them together using split pins," says Laura.

So Laura attaches them together using split pins to make a shape.

The six card strips fit together to create a hexagon.

Laura can create different hexagons.

So this hexagon has no right angles.

There are no right angles at all in a hexagon.

And Laura has changed the shape to make a different hexagon.

"This hexagon also has no right angles." Laura creates another hexagon.

This time she's created this shape here.

Can you find any right angles in this hexagon? What do you think? Now you should be able to look at that shape and think some of those angles are definitely not right angles but some of them could be.

So any that could be, have a good look and check to see whether they are right angles or not.

Pause the video and see if you can work out how many right angles that hexagon actually has.

And welcome back.

Did you manage to find all the right angles? Let's find out.

So Laura says, "I'm going to check the vertices that could be right angles." So this vertex here.

Now it's not a right angle, is it? This vertex is greater than a right angle.

This vertex here, oh, it looks quite similar to a right angle but it's actually greater than a right angle as well.

It's actually slightly bigger than a right angle.

Ah, this vertex here is a right angle.

So this hexagon has one right angle.

And let's move on to task B.

So in task B you're going to draw some different hexagons with right angles.

Each vertex must meet up one of the points on the grid.

Mark the right angles on each hexagon.

And Aisha again says, "You might want to draw the right angle first." So you might wanna start off by drawing a right angle and then drawing the rest of the hexagon.

And remember to be a hexagon, it needs six vertices and exactly six straight sides.

And then part two of task B, use six card strips of equal length and six split pins.

Fit them together to create a hexagon.

Find out whether it is possible to make a hexagon with zero right angles, a hexagon with one right angle, a hexagon with two right angles, a hexagon with three right angles.

You have seen some of those already but see if you can make them for yourself.

Pause the video and have a go at task B.

And welcome back.

How did you get on? Did you manage to complete all of task B? Very well done if you did 'cause there's quite a lot to do there.

Let's take a look at some of those answers.

So here are some possible answers for the first part of task B.

So there are eight different hexagons, all of which have at least one right angle and some of them have more than one right angle.

So very well done if you made some different hexagons.

You may have made the same shapes as those or you may have made some different shapes.

Let's take a look at part two of task B.

So here are some possible answers and again, your hexagons may look quite different to these.

So for a, make a hexagon with zero right angles, that's fairly easy to make.

Laura's already shown you a couple of ways of doing that already.

So this hexagon here has no right angle at all.

B, make a hexagon with one right angle.

And again, not too challenging that one.

This hexagon here has got exactly one right angle.

All the other angles are greater than a right angle.

Make a hexagon with two right angles.

It's getting a bit trickier now but it's still possible to do this.

This hexagon here has two right angles, there's a right angle here and a right angle here.

So it's possible to make one with two right angles.

D, make a hexagon with three right angles.

Is that possible? Actually, it is very tricky to find this and very, very well done if you managed to get the correct answer to this one.

But you can create a hexagon with three right angles.

Very tricky to do.

You can't have two right angles next to each other.

There's always gotta be an angle that's larger than a right angle between each of the right angles.

But this vertex here is a right angle, this vertex here is a right angle, and this vertex here is also a right angle.

Very well done if you manage to find a hexagon with three right angles, that's absolutely brilliant and I hope you enjoyed today's lesson.

I hope you're feeling much more confident about recognising pentagons and hexagons with right angles in them.

Excellent work today.

Very well done.

And let's move on to our lesson summary.

So polygons with more than four sides can contain a right angle.

Polygons with more than four sides can contain more than one right angle.

And shapes can be drawn to match a description including angles and number of sides.