Lesson video

Hi there.

Welcome to today's lesson.

My name is Mr. Peters, and in this lesson today, we're gonna be thinking about a really valuable skill which will help us with our mathematics going forward.

We're gonna be learning to draw angles accurately using a protractor.

If you're ready to get started, let's get going.

So by the end of this lesson today, you should be able to say that, "I can draw angles accurately using a protractor." In this lesson today, we've got three keywords we're gonna be referring to throughout.

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

The first word is protractor, your turn.

The second word is angle, your turn.

And the third word is polygon, your turn.

Let's have think about what these words mean.

A protractor is an instrument or tool used to measure angles.

An angle is a measure of turn, and a polygon is a 2D shape made up with three or more straight lines.

This lesson today has got two cycles.

The first cycle is drawing angles, and the second cycle is constructing shapes.

When you're ready, let's get going.

Throughout our lesson today, you'll also meet Aisha and Sofia.

As always, they'll share their thinking as well as any questions that they have to support us and develop our thinking along the way.

So our lesson starts here with Aisha wanting to draw an angle of 75 degrees.

Which steps could she take to do this I wonder? Well, in order to draw an angle, we should start by using a ruler to draw a straight line.

There we go.

Now that we've drawn a straight line, this will act as one of the lines of the angle.

We can now place the middle spot of the protractor on one end of the line.

Because we've placed it on the left-hand end of the line, we can see that the zero is in fact on the internal scale of the protractor.

So we can now work with the inside scale and follow that around to find 75 degrees.

I'm gonna place a little mark here at the edge of the protractor to show us where 75 degrees would be marked on the inside scale of our protractor.

Now that we've done this, we can use our ruler to draw the mark for 75 degrees and to connect that to the other line, creating the angle itself or creating a vertex.

There we go.

To finish off, we can mark on our angle using an arc and also label the angle with the correct size.

So in this case, this angle here is now 75 degrees.

Sofia, on the other hand, wants to draw an angle of 285 degrees this time.

Hmm, how could we go about doing this? Well, Sofia knows that a full turn is 360 degrees.

So we could subtract the size of the angle that we need to measure from 360 degrees to help us identify the size of the angle that we don't need.

That angle would be 75 degrees.

So what we could do here is in fact draw a 75-degree angle again.

That would mean drawing a straight line, placing the middle spot of the protractor on one end of the line, choosing the correct scale, and then marking the 75-degree mark and then joining these lines together.

So what you can now see is we've created a 75-degree angle.

If we know that this angle here is 75 degrees, that means that the outside angle must therefore be 285 degrees.

And we know that because 285 degrees and 75 degrees would be equivalent to 360 degrees, which is the size of a full turn.

So one strategy for drawing a reflex angle would be to draw the size of the internal angle, which adds up to 360 degrees, and then just mark the outside of that angle with the size of the reflex angle.

Time for us to check our understanding now.

Sofia wants to draw an angle of 52 degrees and she's drawn her first line.

Which diagram shows her protractor in the correct position.

Take a moment to have a think.

That's right.

It's the first diagram and the last diagram, isn't it? And why is that the case? That's right.

We need to place the middle spot of the protractor on one end of the line.

You could do this on the left end of the line or the right end of the line.

You can see in the middle example that the middle spot of the protractor is in fact in the middle of the line, which can be a strategy in order to draw an angle.

However, the vertex would be in the middle of that line rather than at one end of the line.

Okay, and another example here, Sofia attempts to draw an angle of 52 degrees.

Is her drawing correct? Take a moment to explain your thinking.

How did you get on? What was your thinking here? Sofia was in fact wrong, wasn't she? She used the wrong scale, didn't she, to find the angle.

She's actually drawn an obtuse angle here, which would be a lot larger.

And we know that obtuse angles are greater than 90 degrees.

So 52 degrees for this angle would not be correct.

Okay, onto our first task for today then.

What I'd like you to do is draw the angles for the following sizes.

And as always, make sure you check your drawings afterwards to check if they're accurate.

It might be a good idea as Sofia is suggesting to check and see if you're expecting the angle to be acute, obtuse, or reflex.

And then for task two, what I'd like you to do is draw the three angles for each of these here and think about how could you potentially have drawn these more efficiently each time? Good luck with that task, and I'll see you back here shortly.

Okay, welcome back.

I'll give you a moment to have a look and see how your angles compare to these angles here on the screen.

Now remember, some of your angles may be facing the other way around, which is equally fine.

However, what's important is that you've marked on the angle correctly and you've got the exact value in the right place for each one.

We know that angle A and angle B would've been acute angles.

Angle C would've been an obtuse angle and angles D, E, and F were in fact all reflex angles.

And for task two then.

Sofia is suggesting that actually she only needs to draw one angle to be able to draw all of the other angles.

Let's have a look about how she did it.

First of all, she drew her 37-degree angle, and of course if this is 37 degrees, then the outside of this shape would've been 323 degrees, 'cause 323 and 37 is equal to 360 degrees.

And finally, to draw the 143 degrees, well, actually that would just sum to the angle on a straight line, wouldn't it? 143 degrees plus 37 degrees will be equal to 180 degrees, which of course, as we know, is the size of the angles on a straight line.

Okay, that's the end of cycle one.

Moving on to cycle two now then, constructing shapes.

So we're gonna start here thinking about whether we can construct a polygon with an angle of 35 degrees.

And Aisha's saying, "Well, now that I know how to draw angles, it should be relatively easy for us to be able to draw polygons with these angles as well." We're gonna draw a line to start us off with, and then I'm gonna place our protractor on, and I'm gonna mark the 35-degree angle.

There we go.

Now we can see that we've drawn an angle of 35 degrees.

Does it matter that the lines are different lengths? No, it doesn't, does it? And that's gonna be part of what we need to understand when we're drawing polygons.

All the lines in a polygon don't always need to be the same length either, do they? We can now join these lines together using our ruler.

And there you go.

We've now created a polygon, haven't we? We've created a triangle with one angle of 35 degrees.

Hmm, Aisha thinks she could have also drawn a quadrilateral instead of a triangle.

I wonder what that would've looked like.

Let's see.

Instead of drawing these two lines together, Aisha could have drawn a separate line, for example, one like this, and then join these two lines here together.

And therefore we've also created a quadrilateral as well, which of course has an angle of 35 degrees in it as well.

Okay, so now we can extend this to ask ourselves the question, "Could we draw a polygon with a 35-degree angle and a 125-degree angle?" Well, Aisha's saying she could have kept her original angle here.

So you can see we've got a 35-degree angle already.

And now what she needs to do is mark on a 125-degree angle.

So to do that, she needs to choose a line to create the other angle with.

So we're gonna choose the horizontal line at the bottom here, and you can see that we've placed the middle spot of the protractor at the end of that line.

We can now use the outside scale to find the 125 degrees, which we would mark as here.

And now we can start thinking about drawing a line at this angle here.

But what do you notice I've done here? That's right.

We actually haven't drawn it all the way up to the line where we marked it.

And does that matter? No, it doesn't matter.

The angle still remains the same no matter the length of the line we draw.

So we don't actually need to draw all the way up to the little mark that we created as long as it is in line with the mark that we've created.

So we can now mark on the 125-degree angle that we've made and rub out the little mark that we created to show where the 125-degree angle line would need to be.

And now we can join these two lines together again, and we've created ourselves a quadrilateral again, both with a 125-degree angle and a 35-degree angle.

Okay, this time we're extending it even further.

Can we draw a polygon with a 35-degree angle, a 125-degree angle, and a 54-degree angle? Well, we could use what we had already so far, as always, and now we need to think about what shapes we could create with this.

Well, if we use a 54-degree angle as well, we wouldn't be able to create a triangle, would we? Why wouldn't we be able to create a triangle? That's right.

We know that all of the angles in the triangle sum to 180 degrees, don't they? Now, if we were to add 35 plus 125 plus 54 together, that would actually be greater than 180 degrees, therefore, we know it has to be at least a quadrilateral that we're going to be drawing.

So we need to choose a line to start us off with to identify where we're going to draw the angle from.

Let's use this top line here.

We've put the middle spot on the line and we're gonna mark on the 54.

There we go.

So you can see where the 54 mark would be.

Oh, and look, I can now join this shape up.

There we go.

No problem at all.

So we've now created a quadrilateral with a 54-degree angle as well.

Okay, time for you to check your understanding now.

Can you draw a polygon with an angle of 48 degrees? Take some time to have a go.

You might like to pause the video.

Okay, let's see how you got on.

Here's an example here.

Yours may look completely different to this one, and that's absolutely fine, but as long as you know that you've got the angle absolutely spot on with the size of it.

And you can look at the size of the angle that we've created here and take a quick estimate.

Does yours look very similar to that one there? Okay, and another quick check now then.

Sofia has drawn a polygon with a 36-degree, a 32-degree, and a 240-degree angle.

One of the angles is incorrect.

Can you correct the polygon? Take some time to have a think.

You might like to redraw it to help you.

Okay, let's see if you managed to spot it.

It was in fact the 32-degree angle that was incorrect.

This angle is a lot bigger than 32 degrees, so we'd need to shrink this angle slightly, which would mean our line would join up to here.

And as a result of that, we can also shrink the other line as well.

And there we go.

You can now see how our polygon has changed its shape according to the size of the angle that needed changing.

Well done if you managed to do that for yourself too.

Okay, and onto our final tasks for today then.

For task one, what I'd like you to do is draw a polygon with A, a 47-degree angle, B, a 47 and 126-degree angle, and C, a 47, 126, and 208-degree angle.

And as Sofia's pointing out, make sure that you label each of the angles as well.

Once you've done that, what do you notice as you're creating those polygons? And then for task two, what I'd like you to do is to create some triangles based on each one of these lines here.

And where the dot is, I'd like you to draw an angle of 34 degrees each time.

Can you make each triangle look different as you do so? Good luck with those two tasks, and I'll see you back here shortly.

Okay, welcome back.

Let's see how you got on with the first task then.

So here's a polygon with a 47-degree angle as you can see here.

Here's my example of a polygon with a 47-degree angle and a 126-degree angle.

And then as well, here's an example of a polygon with a 47, 126, and 208-degree angle.

And that's right, Sofia.

The final polygon had to be a type of pentagon, didn't it? Because the angles in the quadrilateral sum to 360 degrees and the angles that we had been asked to use for these three angles were in fact greater than 360 degrees.

So it would've needed to have been at least an irregular pentagon for us to be able to create a shape, which would work for that.

Okay, and for task two then here, you can see where we've drawn the 34-degree angles each time.

And the trick here would've been for you to practise in order making sure that you're lining up your protractor in the correct way, to enable you to draw the 34-degree angle consistently for each one.

Well done if you managed to do all of those too.

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

To summarise what we've been learning, we can say that you can use a protractor to draw an angle.

It's important to read the correct scale when identifying the correct angle size.

And it can also be useful to mark the angle you are wanting to draw, and then join the mark with the line end with a ruler.

That's the end of our learning for today.

Make sure you spend some extra time practising , drawing lots of different angles and lots of different polygons with your new knowledge of how to use a protractor.

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