Lesson video

Hi, welcome to today's lesson.

My name is Mr. Peters and this is the first lesson in our unit thinking all about angles.

I don't know about you, but once I began to find out and understand a bit more about angles, I was seeing them everywhere in my life, and often I can use this understanding to help me to solve problems that I come across in my everyday life as well.

If you're ready to get started with this session, then let's get going.

So, we're gonna start today thinking about right angles, and by the end of this session today, you should be able to say that I can recall understanding and identification of right angles.

We've got one keyword we're going to be referring to throughout in this lesson.

I'll have a go at saying it first and then you can repeat it after me.

Are you ready? Here we go.

Right angle.

Your turn.

So, let's remind ourselves what we mean by a right angle.

A right angle is a quarter of a full turn.

It can also be known as a square corner.

This session today is broken down into two cycles.

The first cycle is identifying right angles and the second cycle is investigating right angles.

Let's get started with the first cycle.

Throughout the session today we're gonna be joined by both Jacob and Sam.

As always, they'll be sharing their thinking as well as any questions that they have throughout the lesson.

So, our lesson starts here.

Jacob and Sam have been drawing maps.

Jacob is saying to Sam that he's got a challenge for her.

He's saying, "Can you get from your house to the school by turning the least amount of right angles as possible?" Sam's asking, "What's a right angle again?" Good question, Sam.

Let's remind ourselves, shall we? A right angle is where two lines meet to make a square corner.

There we go.

We've got two lines that have met, and where they meet, we create a square corner.

They can be found on lots of different shapes.

For example, on a rectangle or on a square.

There can also be more than one in a shape as well.

Let's have a look at this square.

There we go.

There's another one and another one and another one.

So a square actually has four right angles, or four square corners.

So far in the examples we've looked at, all of our right angles have been made from a horizontal and vertical line.

However, right angles don't need to have to have vertical or horizontal lines.

Let's have a look.

There we go.

There's two lines which are a little bit more diagonal, aren't they? And these two here are still creating a right angle.

Here's another example.

And because of this, we know that they can also be found in irregular polygons.

Here we go.

Look at the lines we've drawn so far.

Now we've used those to create an irregular polygon.

This shape has six sides, so we can call it an irregular hexagon.

There we go.

That's helped Sam to remember now.

And she's now saying that she's seen lots of them in her everyday life as well.

For example, she's seen them on flags.

There's an example.

Can you see any others on this flag as well? Sam says that she has also seen them on computer screens.

Have a look at the computer screen.

Can you spot one? Yep, well done.

There's an example.

There might be a few more you can see as well.

And Sam's saying that she's also seen them within the human body when the human body is moving.

Let's have a look here.

Here's a picture of somebody running, and here we can see where the thigh bone joins the shin bone, we create another right angle.

So, we can extend our thinking of right angles to consider the size of a turn as well.

Jacob is saying a right angle can also be known as a quarter turn.

Here on the screen you can see a dial, and look where the arrow on the dial is pointing at the beginning.

We can show a quarter turn from where the dial starts to where the dial finishes.

Let's have a look.

There we go.

If we draw a line for where the dial started and a line to where the dial finished, we can see that we have turned a quarter turn, also known as a right angle.

Thinking back to the examples we had earlier on as well, the lines don't need to be horizontal and vertical, do they? A right angle can start from any point and can turn in any direction as well.

Have a look at the car.

Watch how the car is driving towards the T junction and then turns.

We can see that the car's original direction was drawn by a line and now the car's new direction is drawn by another line, and we can say that this car has turned in a right angle.

We could also describe it from this direction as well.

Watch how the car approaches the turning and then turns off.

Again, we can see that this car has also turned one right angle.

Jacob is saying that we can use a number of tools to help us identify right angles.

We can use what is known as an angle strip to help us identify the outside of an angle.

Here is an example of an angle strip, and we can see it's been placed around the corner of the square so we can see that we've got a right angle here.

We can also use a twice folded piece of paper to help us identify a right angle.

There we go.

You can see our twice folded piece of paper makes this shape here, and it gives us that corner that we need to identify a right angle, and we can see that we've now used that on the laptop to show that it is a square corner or a right angle.

Okay, so Sam thinks she's now ready to take on your challenge, Jacob.

So, let's have a go, shall we? We need to travel from Sam's house to the school with as few right angles as possible.

Why don't you have a quick go for yourself first? Let's have a look and see the journey that Sam came up with.

Here we go.

Sam is saying that she thinks she's found a way where she didn't have to turn any right angles at all.

Let's have a look at the turnings that she made.

So, let's zoom in and have a look.

We can use our angle tools to help us here, can't we? We can see here that the first turning was made here, and this isn't a right angle, is it, because it's more than a quarter turn.

What about this one here? This was the second turn that had to be made.

Yep, again, this isn't a right angle, is it? This is less than a quarter turn.

Ah, this was the third corner, wasn't it? Have a look at this one.

Does this look a right angle to you? Jacob thinks it is, but Sam's disagreeing.

Sam's saying she doesn't think it is a right angle because the lines are different lengths and they're different thicknesses.

Well, Jacob disagrees.

Jacob is saying it doesn't matter.

The lines can be different in both length or thickness, but it still makes a right angle or shows a square corner.

Let's have a look.

Here's one example.

We've got a thicker vertical line and a thinner horizontal line and also the horizontal line is smaller than the vertical line, but as you can see, it still makes that right angle or that square corner.

Here's another example.

We've got a really small vertical line this time, haven't we? And a lot longer horizontal line.

The thicknesses are the same.

However, it still makes a square corner again, doesn't it? Well, the length of these lines were exactly the same as the example before, wasn't it? However, the horizontal line is a lot thicker this time, but once again, it still makes this square corner, doesn't it? There we go, Sam.

You weren't sure about that were you? But now you're feeling hopefully a bit more confident with that.

Let's continue on our journey.

So far we've met one right angle.

I wonder if there are any more.

Here's the next turning.

What do we think about this one? Is this one a right angle? Sam is saying it's definitely not a right angle because one of the lines isn't straight.

Well, let's have a look at this in a bit more detail as well.

Jacob is saying, "You're right for this example." in this example, the size of the angle would keep changing, wouldn't it, based on the curvy line.

However, Jacob is pointing out that the line doesn't always need to be straight.

In this example we can see that it doesn't make a right angle or a square corner, does it? Because there's a little bit of a gap between the line and our angle tool, isn't there? However, as long as the lines are straight at the point where they meet, then we can say that it was a right angle.

Let's have a look at this example.

There we go.

We can see that the line initially starts off being curvy, but as it goes towards the second line it straightens up, doesn't it? And now the lines are straight, and where these two straight lines meet, we've created a right angle, haven't we? Sam's now asking, what about if the straight part of the line was only really tiny? Well, let's have a look again, shall we? There we go.

What do you notice now? That's right, the straight part of the line has changed.

It was a lot longer before, whereas now it's a lot smaller.

Does it still make a right angle? That's right.

At the point at where these two lines meet, we have created a square corner or a right angle, haven't we? Great, that's what these lessons are all about, Sam, hopefully helping you to change your thinking a little bit more and develop your understanding about right angles.

Okay, time for us to check our understanding now.

A right angle must, A, be joined by two straight lines, B, be joined by two lines that are straight at the point that they meet, C, have the same size lines meeting each other, and D, start with a vertical line.

Take a moment to have a think for yourself.

That's right, it's B, isn't it? Right angles don't necessarily have to be joined by two straight lines.

What's important is that the lines are straight at the point where they meet, isn't it? And of course, we know that where these two straight lines meet, they have to create that square corner as well, don't they? Okay, and another quick check for understanding now.

Can you find three right angles on Jacob's map? Take a moment to have a think.

Okay, so there's one example you may have found, there's a second example you may have found, and there's a third example you may have found.

Notice there that on that third example, the lines are straight at the point at where they meet.

However, the vertical line veers off slightly to a curve, doesn't it? Okay, and now time for our first task for today.

Using the map then, can you find a way to avoid travelling through any right angles? A, the library to the park, B, the shops to the sports ground, or C, Jacob's house to school.

Good luck with that task, and when you're done, come back and we'll go through the answers.

Okay, let's have a quick look then, shall we? Here's an example that you may have taken from the library to the park.

Along this journey we had no right angles that we went through.

Here's an example from the shops to the sports ground.

Again, we travelled through no right angles this time.

And then finally, from Jacob's house to the school, did you manage to find a journey? No, it wasn't possible, was it? Sorry if I tricked you a bit there, but I wanted you to think about all the possibilities of how we could have travelled along that journey as well and to double check your understanding of right angles.

Okay, that's the end of cycle one.

Moving on to cycle two now then, we're gonna start thinking about investigating right angles.

Jacob and Sam have both been given a pinboard and they're making shapes on their pinboards.

Jacob asked the question, "How many shapes could we create with at least one right angle using our pinboard?" Sam's feeling a lot more confident now about her understanding of right angles, and she says, "Let me have a go! Pass me the elastic bands to do that!" So, here's the first example she's come up with.

She says she knows that a square has four right angles, so she's created a square.

So there we go.

There's one shape that we've now got.

Hmm, can we think of any others? Sam's saying that she thinks she can make a different square.

Let's have a look.

Yep, there we go.

Good example, Sam.

That's a different square, isn't it? It still has four right angles, doesn't it? However, it's still a square though, isn't it? So we've still only got one shape at the moment.

Can we think of any other shapes? Hmm.

Sam thinks, "Ah, yes, of course! Rectangles also have four right angles, don't they?" So can we make any rectangles? Could you have a think about how we could put the elastic on the pinboard to make a rectangle? There we go.

Great example, Sam.

That certainly is a rectangle, isn't it? It's a shape with four straight sides, and the opposite lines in the shape are parallel, aren't they? Once again, we can see that we have four right angles, can't we? So there we go, that's two shapes.

And Sam thinks she can make several rectangles as well.

Let's have a look.

Look at all these rectangles we can make.

But as we know, they're all still rectangles, so that's just two shapes that we've got so far.

Jacob's now asking, "Do our shapes have to have four sides?" Hmm, Sam doesn't think so.

Let's see what she's now come up with.

Ah, yeah, great thinking, Sam.

She's now saying that she could lose one of her sides and join the points of the shape together, there we go, but she's still been able to keep one of her right angles, hasn't she? So we can make triangles, couldn't we, with a right angle.

How many of this type of triangle do you think we could have made? Well, let's have a look.

Well, we could have made seven of those triangles, couldn't we? That's amazing! So, so far we've got three shapes, haven't we? We've got a square, a rectangle, and a right-angled triangle.

Sam also thinks we could flip over this right-angled triangle.

Are you ready? Look at that.

Now we've flipped it over and we could do exactly the same with the rotations again.

We can have another seven of those right-angled triangles, couldn't we? But once again, it's still the same shape, isn't it? It's still a right-angled triangle and therefore we've still only got three shapes.

Okay, time for you to check your understanding again now then.

Can you create a shape with at least one right angle on this pinboard? Take a moment to have a think.

There we go.

There's an example of a right-angled triangle that we could have used.

Were there any others you could have come up with? Yep, you could have also made a square or a rectangle, couldn't you, for this example.

And another quick check.

True or false? This shape has two right angles.

Take a moment to think.

That's right, it's true, isn't it? And have a look at these two justifications here to help you reason why.

Great.

That's a really good justification there, isn't it? There are in fact two sets of straight lines that meet to make square corners.

So we can say that there are two square corners or there are two right angles in this shape.

Okay, onto some time for us to practise.

This time I've changed the pinboard so it has 12 pins around the outside of it.

I wonder how many different shapes you could create with at least one right angle in it.

Great question, Jacob, as well.

"How will you know that you've got all of the possible shapes?" Good luck with that task and I'll see you back here shortly.

Okay, let's see how you got on.

Here's one example that Jacob came up with.

He found a rectangle which would fit into this pinboard.

He also was able to create a square.

He also made a right-angled triangle like this, and he also made a right-angled triangle that looked a little bit like this.

Oh, look! And another right-angled triangle which looks like this.

So, so far that's five shapes.

Were there any more, Jacob? Wow, he's really thought about this a little bit more as well, hasn't he? Have a look here.

This time we've got a shape with six sides, haven't we? And yet we can still see that there are two right angles in this shape.

So, Jacob has managed to find six shapes altogether.

I wonder how many you managed to find and whether you found any others that Jacob didn't manage to find.

Okay, that's the end of our learning for today then.

Let's summarise what we've been thinking about in this lesson today.

We know that a right angle can be found where two straight lines meet each other to make a square corner.

The distance from where a quarter turn starts to where a quarter turn finishes is also known as a right angle.

And we know that right angles can be found in many regular and irregular shapes, as well as many everyday life examples.

That's the end of our learning for today.

Hopefully you're feeling more confident thinking about right angles once again, and that you might be ready to think about applying your understanding of right angles in everyday life.

Have a look around you now.

Can you see any? Take care, and I'll see you again soon.