Lesson video

Hello there.

My name is Mr. Tilstone.

I'm a teacher and I'm here today to teach you a lesson all about protractors.

You might have used a protractor before but forgotten how to use it.

You might have never used one before or you might have used one and you're really confident about using them.

Don't worry either way.

We're going to get through this lesson together.

So if you are ready, I'm ready.

Let's begin.

The outcome of today's lesson is I can use my knowledge of shape properties to draw shapes accurately using rulers and protractors.

And our keywords are my turn, protractor, your turn.

Hopefully you've got one of these in front of you right now.

You will need it for this lesson.

Here's what it is.

A protractor is an instrument used in measuring or drawing angles.

What can you notice about it? Can you remember something about the scales? Can you see it's got an outer scale that goes from zero to 180 and an inner scale that goes the opposite way.

Our lesson is split into two cycles.

The first will be drawing triangles accurately and the second drawing other shapes accurately.

So if you're already, let's start by focusing on triangles.

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

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

Alex and Sam are setting each other challenges.

Alex says, "Draw a triangle with a side length of 10 centimetres." So, Sam's got her ruler out and she's going to have a go at drawing that side length.

Let's see how she gets on.

Okay, look where she's starting.

Look where the pencil's starting.

Is that right? That's the line that she's drawn.

She's gone up to 10.

Hmm.

What do you think? No, she wasn't quite successful there, that wasn't accurate.

Sam's line didn't start exactly on the zero.

It's inaccurate.

She can have another go though, she will.

There we go, she's trying again.

This time is she starting on zero? Yes.

And that's where she's finished.

Hmm.

Would you say that's 10 centimetres? Is that accurate? No.

It started in the right place but it didn't finish in the right place.

It doesn't finish exactly on the 10 centimetres.

It's inaccurate.

It's close, but it's not accurate.

She's having another go.

Good on you, Sam.

Here we go.

Starting on zero.

Good start.

Oh, finishing on 10 this time.

Finishing exactly on the 10.

It's accurate.

Perfect.

Sam has drawn an accurate 10 centimetre side length.

Well done, Sam.

Sam says, "Now I just need to draw the other two sides of the triangle.

They can be any side length as long as the three sides join." Yeah, she's done the hard part now, hasn't she? At this point, the ruler is only there to make a straight line.

There's no need to consider the numbers.

There we go, that's the other job of a ruler, isn't it? Not just measuring accurately but making straight lines.

So there we go, it doesn't matter where it starts.

Make a line.

Make another line.

Join them together and you've got a triangle.

She's drawn, in fact, a scalene triangle.

What makes it scalene? All of the sides are different lengths.

"Okay, Alex" says Sam, "Draw a triangle with one side length of 10 centimetres and another side length of five centimetres." Hmm.

She's ramped up the challenge there.

He's got an extra thing to think about.

Let's see if he can succeed.

Here we go.

Well, there's his 10 centimetres.

Good start, Alex.

I'm just gonna draw another one.

Now look, this time he is starting on the zero.

Very good.

He knows he can use an acute angle for a vertex so he draws a second side of five centimetres.

There we go and it's an accurate five-centimeter line.

Alex has met Sam's requirements but has he finished the triangle? Not quite.

He needs to connect the two vertices with a final line and I think that's the easy job.

He doesn't need to worry about the numbers this time.

It's just a straight line he needs.

There we go.

Alex has drawn a different scalene triangle.

Again, the sides are not the same length as each other, none of them are, but it's different the other one.

"Okay," Sam says, "Alex, another triangle with one side length of 10 centimetres and another side length of five centimetres, but a different kind of triangle." Okay.

Right, that's harder still, isn't it? So it can't be scalene this time.

Hmm.

Here we go.

She learned from her previous mistakes, look, she's starting at zero.

It's exactly 10 centimetres, right? She's got to make a five centimetre one.

Ah, that's clever.

Can you see what she's doing? So she measured that exact accurate five centimetre line starting at zero, ending at five.

What kind of triangle is she making here? It's a right angle triangle and then she doesn't need to worry about the numbers, it's just a straight line that's needed to connect those together.

She's drawn a right angle scalene triangle.

So it's still scalene but it's slightly different because it's a right-angled scalene.

So well done, Sam.

Clever thinking.

There we go.

A right angle.

"Okay Alex," says Sam.

They like challenging each other, don't they these two? "Can you draw a triangle where one of the angles is 75 degrees?" Okay.

Right.

Well, a ruler is not going to do that, is it, a ruler alone? Something else is going to be needed here.

"I'll start by drawing one side of my triangle so I can create a vertex, which will be the angle." Okay, don't need to worry this time about the side length, can be any side length, that wasn't specified.

I'll place my protractor, that's a tool that's needed for this, at one end of my line, measures 75 degrees, and mark a point on my page.

So let's have a look at what he does.

Here we go.

Look.

He has used a centre point sometimes called the origin and he's lined up the baseline.

He's doing everything right and all he's gotta do now is starting at zero, so he's using the inner scale for this one going up to 75 degrees, and he's marking that point on the page.

"I'll then use my ruler," he says, "to make another side of any length.

It must go through the mark that I drew." So it didn't really matter how long it is but it's gotta go through it.

Here we go.

So again, we're not worrying about the numbers on the ruler but it's got to go through that mark.

There we go.

"75 degrees is an acute angle.

This angle looks right to me." It's a good tip to use your instinct.

So, I know that 75 degrees is less than a right angle and that's less than a right angle.

So that suggests that the right side of the protractor's been used the right scale.

"Next, I'll mark and label my angle." Here we go.

That's a 75-degree vertex.

That's the angle there.

"Now we just have to make one more side." He's done the hard work, hasn't he? And again, not worrying about the numbers, just using the straight line.

There we go.

Let's join them together.

Now, he's got a triangle with a 75-degree vertex.

"Well done, Alex.

Remember you could have made a vertex of 75 degrees from either end of your first side." "I'd need to use the outer scale of the protractor this time, not the inner scale." Shall we have a look at that? Here we go.

So that's that straight line again.

And this time he's gone to the other side of the straight line.

Can you see? So this time he's using the outer scale to make that 75-degree angle.

He's put his mark on just like before and he's gone through it and joined those together.

So he is made a triangle with a 75-degree vertex once again.

"Okay Sam," says Alex.

"Let's combine side length and angle size.

A triangle with a side length of seven centimetres and a 100 degree angle." Okay, now it's getting tough, isn't it? Let's see if Sam's up for this.

"I think I can do that." Good for you, Sam.

"I just need to use the ruler and the protractor." Gonna combine those skills.

Here we go.

So that's our seven-centimeter side length.

She's not making that mistake again, is she, about where to start the line and where to end the line? She's good at that now, she's learned.

It's not almost seven centimetres.

It's not a little bit less or a little bit more.

It is seven centimetres.

It's accurate.

Here we go, the ruler can be taken away for a second.

Now we make our angle and remember, it could be from either side, doesn't matter.

Going from the right hand side of the line this time so we can use the outer scale.

We're making that 100-degree angle.

Going to put a little mark just there.

Protractor can come away now.

Now we make a line and now we mark the angle, and finally join the sides together to make the triangle.

There we go.

Brilliant, she did it.

Let's have a quick check for understanding.

Is Sam correct? Explain.

Let's see what Sam's got to say.

She says, "My triangle has a side length of eight centimetres and a 93-degree angle." Are both of those things right? Are both of those things wrong? Is one right, one wrong? What do you think? Have a look, see what you can notice, and pause the video.

Did you spot anything there? Well, let's have a look.

No.

She's not started her line at zero centimetres and she's used the wrong protractor scale.

She in fact it's got angle of 87 degrees.

So well done if you spotted those things and well done if you were able to figure out where she'd gone wrong.

It's time for some practise.

Here is a sketch of a triangle.

It's not to scale.

Draw the full size triangle accurately using a ruler and a protractor.

So you're going to draw a triangle.

It's a right-angled triangle with a 10 centimetre line and a 38-degree angle.

You'll need your ruler, you'll need your protractor.

Number two, draw a triangle where one side is seven centimetres and only one of the interior angles is 45 degrees.

Use your ruler and protractor again.

And number three, if you've got dice, roll the dice.

If not, just pick some random numbers to six, three of them.

Roll three dice to give you some shape criteria.

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

So roll number one will be the kind of triangle, roll number two will be the side length, and role number three will be the angle that's required.

See which ones you can and can't sketch.

Have fun with that.

Remember to be nice and accurate and I'll see you soon for some feedback.

Welcome back.

How did you get on with that? Were you accurate? Let's have a look.

So number one.

10-centimeter line.

Using our protractor to make that 38-degree angle.

There we go, take the protractor away.

Draw a line through the mark.

Then if you remember, it was a right angle triangle, isn't it? So there we go, there's our right angle and then we just need to make a little alteration, get rid of the end of that line.

And there we go.

Voila.

There's our right-angled triangle that's 38 degrees for one of the vertices and a 10-centimeter line.

Draw a triangle where one side is seven centimetres and only one of the interior angles is 45 degrees.

Hmm.

Well, let's have a go.

So seven centimetres side.

Now let's think about the angle.

Put our protractor on, make that 45 degree angle mark.

Draw a line through it.

Mark our angle on, then we can just join them together.

Doesn't have to be a right angle this time, can be any.

So well done if you've got something like that, your triangle might look slightly different but it needs that angle and that side length.

And then you are rolling your three dice or picking the random numbers.

So there's an example.

So three and a two and a five gives you a scalene triangle with one side of six centimetres and one interior angle of 108 degrees.

Well, here we go.

There's your six-centimeter line.

There is your 108-degree angle.

A line through it, want your angle on and join them together.

There we go.

That's possible.

But not all combinations are possible.

Here's an example.

A four and a six and a five wouldn't have been possible.

All triangles have angles which sum to 180 degrees.

So not everything was possible there.

Similarly, if you rolled a one for the triangle type, the only angle that would've been possible was 60 degrees.

This is a size of all three angles in any equilateral triangle.

Are you ready for the next cycle that's drawing other shapes accurately? Let's go.

When Alex drew this angle, it was one of the vertices of a triangle, if you remember.

Could it have been the vertex though of a different polygon? Could he finish that shape in a different way? "How about," he says, "a quadrilateral?" What do you think? Could he turn that into a four-sided shape? Yes.

Alex now has a trapezium with a 75-degree angle.

Sam says, "I challenge you now to draw a quadrilateral with an angle of 45 degrees and a different angle of 120 degrees." Alex recently learned that when drawing a quadrilateral with two right angles, you should draw the right angles first.

You might have done this yourself recently.

Just like that and then join them together.

He wonders if this will help when plotting in a pair of other angles.

He plots his two angles, 45 degrees and 120 degrees, on a straight horizontal line.

That's a good starting point.

Let's have a look.

So here's his horizontal line and he's going to plot the angles onto that.

So here's his 45-degree angle, same as before.

And he's going to go to the other side of the line and make his 120 degree angle, which is just there.

And again, draw a line through that mark.

He decides to make the final line parallel to one of the other lines.

He didn't have to, that's what he decided.

That will form a trapezium.

There we go.

It's got one pair of parallel sides, it's a trapezium.

Let's do a check.

Explain to a partner how you would go about drawing a hexagon with a side length of 10 centimetres, an angle of 50 degrees, and another angle of 110 degrees.

So as clearly and simply as you can, how would you go about that? Pause the video.

Let's have a look.

You could have said something like this.

Measure the straight 10-centimeter line with a ruler.

Measure the 50-degree angle with the inner scale of a protractor.

Like so.

Draw a straight line that goes through that mark.

Measure the 110-degree angle with the outer scale of the protractor this time 'cause it's on the other side of the line.

Draw a straight line through it.

Then add the remaining three lines, this is the easy part, really.

One, two and as long as the last one joins up to this other one.

There we go, number three.

Now we've got a hexagon, a six-sided shape.

It's got a side length of 10 centimetres and an angle of 50 degrees, and an angle of 110 degrees.

Well done if you explain that clearly.

And it's time for some final practise.

This time, roll four dice or the same dice four times to give you some shape criteria.

Explore whether it's possible to sketch a shape that matches the criteria and repeat.

So a bit like before but we've got some new things to think about.

So roll one will be the shape, roll two, a side length, roll three, an angle, and then roll four, a different angle.

And once again, some of those will be possible and some of those won't be possible.

So keep doing it.

Do as many as you can in the time that you've got.

Pause the video and have fun.

Welcome back.

How'd you get on? Were you accurate? Which ones were possible? Which ones were not possible? Let's have a look.

Well, this is a Pentagon with a 12.

5 centimetre side length and angles of 105 degrees and 95 degrees.

Let's have a look.

Here's the line.

There's angle one.

There's angle two.

And there's the remaining sides.

To make it a five-sided shape.

That's possible.

We've come to the end of the lesson.

Today's lesson has been using knowledge of shape properties to draw shapes accurately using rulers and protractors, and that word accurately has been key today.

Protractors and rulers can be used to draw accurate polygons with specific angles and specific side lengths.

You have to be really careful and make sure you're accurate.

Remember to start from zero, both when measuring out the angle and when measuring out the line.

Well done on your accomplishments and your achievements today.

It's been a real pleasure working with you.

Give yourself a little pat on the back, it's well-deserved.

Hopefully I'll get the chance to spend another math lesson with you in the near future and we can explore something else, maybe shapes, maybe something different.

Until then, take care.

Enjoy the rest of your day, whatever you've got in store and goodbye.