Lesson video

Hello, my name is Dr.

Rowaldson, and I'm excited to be guiding you through today's lesson.

Let's get started.

Welcome to today's lesson from the unit of constructions.

This lesson is called "Checking Compass Skills".

And by end of today's lesson we'll feel confident in using a pair of compasses to draw circles and arcs.

Here are some previous keywords that you may be familiar with and we will be reusing again in today's lesson.

So you may wanna pause the video at this point while you remind yourself the meanings of these words before pressing play to continue.

And here is a new keyword or key phrase that we'll be introducing in today's lesson, that is a pair of compasses.

A pair of compasses is a tool which can be used to draw circles and arcs.

And we say a pair of compasses in the same way we say a pair of scissors or a pair of trousers because it's two things that are stuck together and come together as a pair.

But also just like how we sometimes just say scissors rather than a pair of scissors or just say trousers rather than a pair of trousers, we sometimes refer to a pair of compasses just as a compass.

So you may hear people say a pair of compasses or just a compass, means the same thing.

This lesson contains two learn cycles.

In the first learn cycle we'll be drawing circles and the second learn cycle will be drawing arcs or drawing circles that have a particular radius.

But let's start off with drawing circles.

Here's a challenge for you, I'd like you to take a plain piece of paper and mark a cross somewhere near the middle of the page.

It doesn't have to be exactly the middle, but just make sure you've got plenty of space around the cross.

I'd like you to try and draw a circle where the cross is at the centre of your circle and try and do it freehand.

Pause the video while you do that.

Okay, now you drawn your circle.

I'd like you to draw a two radii from the centre of your circle to the edge and do that with a ruler.

Pause the video while you do that.

Now, once you've done that, I'd like you to use your ruler to accurately measure the length of each radius and measure it as accurately as you possibly can.

Pause the video while you do that.

Okay, are the two radii in your circle exactly the same length? If they are, then maybe draw another radius and measure that one, and maybe draw another one and measure that one and see how many you draw until you find a radius that is not equal to the others.

If they're not equal, don't worry, I think most people will probably be in a similar position to you.

But if your radii are not equal, what does that say about your circle? Hmm? A circle remember is a shape such that every point on a circumference is equidistant to its centre.

For example, the image on the left is a circle and we can see that those two radii that are drawn there, they are both the same length, they're both 3.

2 centimetres.

If I drew a radius in any other direction on that circle, it would also be 3.

2 centimetres.

because every point on that circle is the same distance away from the centre.

But the image on the right is not a circle.

And we can see that because there are two measurements drawn from the centre to the edge, and one of them is 3.

2 centimetres and the other one is 3.

7 centimetres.

So not every point on that curve is the same distance away from the centre.

So it's not a circle.

Now circles are difficult to draw accurately freehand, and you may have experienced that in our last little activity.

So what equipment could be used to draw circles more accurately? Pause the video while you think about this and maybe think about a few examples before pressing play to continue.

Here we have Lucas, Lucas draws a circle by tracing around his protractor twice.

Now if Lucas did that, would it draw a circle, and what problems might there be with Lucas's method? Pause the video while you think about this and press play when you're ready to continue.

See how Lucas does? He draws round a protractor on one side, he turns his protractor around and draws around it on the other side.

So he is got something that looks a bit like a circle, but he says, "My protractor is a fixed size "so I cannot draw circles of different sizes." He is stuck with this particular size, he can't draw a smaller circle or a bigger circle using his protractor in the same way.

But then he also notices something else.

He says, "Also, my shape "has two straight line segments in it, "so it's not a circle." And that's because at the bottom of the protractor it's straight on either side just for a little tiny bit.

So that's why Lucas has these two small straight line segments on the top and bottom of his image.

So it's not quite a circle.

Here's Laura, Laura draws a circle by tracing around a coin.

Now would this draw a circle, and what problems might Laura have with using this method to draw circles? Pause the video while you think about it and press play to continue.

Well, here's Laura's circle she traces around the coin.

It does look like a circle.

So Laura says, "My circle is good, but it's very small.

And also, 'cause a coin is a thick size, it means that she cannot draw circles of different sizes, she's stuck with that particular size circle.

So here's Aisha's method.

Aisha ties a piece of string around a pencil and pins the other end of the string to the page.

So would this draw a circle, and what problems might Aisha have with this method? Pause the video while you think about this and press play to continue.

So Aisha keeps one part of the string pinned to the paper and than she uses a pencil and draws a pretty good looking circle.

She says, "My circle is good "and I can adjust the size of it "by varying the length of the string." She can just put the pin further up the string closer to the pencil to make the circle smaller, or further away from the pencil to make this circle bigger.

But she says it's difficult to keep the string taut all the way around.

So it's a bit of a fiddly method for drawing a circle.

So here we have a pair of compasses.

A pair of compasses can be used to draw a circle accurately.

That's because it's got a few parts that helps us.

So let's take a look at this now.

Here we have two arms or two legs, which are compasses, they are joined together at the top.

Above that we have a handle for holding.

We have a pencil holder and it's got a screw in it so you can tighten your pencil into it.

So it stays still while it's in there.

And we have a needle at the bottom as well.

Need to be very careful that we don't hurt ourselves with that.

Now pairs or compasses can vary and may contain different features.

Here we have three different pairs of compasses.

Now how do these pairs of compasses differ to each other? Pause the video while you look at this and then press play to continue when you're ready.

The one on that left is probably the most standard one you'll see in a school.

You may see it made out of plastic or metal, but it's got the usual standard features; a needle and a pencil holder.

Now you might notice that the one in the middle has this little extra thing here by the hinge, and that is to help you open and close the compasses in a steady and controlled way.

Now the one on the right doesn't have a pencil holder, it has two needles instead.

This one is sometimes referred to as dividing compass or just a divider, but it looks a lot like a pair of compasses that you may see in a pencil case.

You might be thinking, "Why is it not got a pencil holder?" Well, that's because it's used for different purposes to a pair of compasses that have a pencil.

For example, it can be used to measure objects, 3D objects that don't have a straight side on them, so you can't get a ruler to 'em.

Or it can be used to measure out distances on a map.

And sometimes it's used for technical drawing such as enlarging a shape of some sort.

So let's take our pair of compasses now, place a pencil into the pencil holder.

Now it should not matter how close the pencil tip is to the needle, but it's easiest to draw when the pencil and the needle tips are aligned.

Technically it shouldn't make a difference, but people tend to say it's easier and find it easier with the middle configuration there.

So to draw a circle accurately with a pair of compasses, open up your pair compasses, maybe about midway, place the needle at the point where the centre of the circle will be.

That needle will be a fixed point that will not move and that'll stay where the centre of the circle will be.

Rest a pencil gently on the paper and use it to draw the circle, and do that by rotating the pencil around the needle.

You wanna keep that needle firmly in place and gently rotate that pencil around it to draw a circle.

Let's watch a couple of demonstrations of this.

Here's method one.

Place the needle down on the paper, hold the handle at the top, and just hold it between a couple of fingers, and rotate the handle between your fingertips.

Now that is probably the most ideal way of using a pair of compasses, but sometimes people find that a little bit tricky, especially to begin with.

So here's a different method if you are finding the first one a little bit tricky to do, and that is to hold the pair compasses near the needle and rotate the paper instead.

If you're doing this, make sure you keep the needle very, very firmly in the same position.

Let's watch.

Whichever way you use your pair compasses just avoid holding both compasses while you're drawing your circle because that can cause 'em to open and close midway around, meaning your circle will not be the same distance from the centre all the way round.

So do not hold both of those legs.

So let's check what you've learned so far.

Which way of holding a pair of compasses should be avoided while drawing a circle? Pause the video while you choose either a, b, or c and press play when you're ready for an answer.

The answer is c.

Do not hold both compasses while you are drawing your circle.

Let's check how well we can draw a circle with a pair of compasses now.

So take a plain piece of paper and mark a cross in it, somewhere near the middle of the page, like we did before, and this time, using a pair compasses draw a circle with the cross at the centre.

Now if this is the first time you are using a pair of compasses, you may find it tricky to begin with and you may not draw a perfect circle first time.

And that's okay, you'll get better with practise.

But let's see how well we can do it right now at this first attempt.

Pause the video while you have a go and press play when you're done.

Okay, now let's check our circles.

So like we did before, draw two radii in your circle, use a ruler to accurately measure the length of each radius, and check are the two radii in your circle exactly the same length.

You can pause while you check that, and then press play to continue.

Hopefully what you're seeing is that your radii are at least more equal now than they were previously and they will get more and more equal with more practise.

Some more advice for using a pair of compasses.

So firstly, make sure you press the needle firmly onto the paper to prevent it from slipping.

Don't press so hard that the paper slips, but press hard enough so that the needle doesn't slip.

You wanna apply pressure through that compass into the needle onto the paper.

And then when you're resting the pencil on the paper, rest it gently on the paper because if you push hard onto the pencil then it's likely to open or close the compasses or cause a needle to slip.

So just rest it gently, and it's okay if your if your circle is quite faint on the page, that's okay.

And then while you're drawing your circle, tilt the pair of compasses ever so slightly so that the pencil brushes against the paper like a paintbrush.

So rather than the pencil going straight down perpendicular to the paper where it'll sort of bounce up and down on top of the page, just tilt it ever so slightly and imagine that you are painting with a paintbrush instead.

And be careful not to adjust the angle between the compasses midway around a circle, you wanna to keep those compasses at a fixed distance all the way round.

And finally, you may wanna rest your paper on top of something to stop that from slipping on the table.

And also to just to put a little bit of padding slightly underneath, so it's for your needle to go into.

And that'll just keep things in place a bit more.

Maybe another piece of paper to go underneath it or a book or something like that.

Okay, over to you now for "Task A".

And this task contains two questions, and it's all about practising using your pair of compasses and hopefully you'll get better and better each time.

In question one, I'd like you to use a pair of compasses to draw five circles of different sizes using this cross as a centre point for all five of your circles.

Pause the video while you have a go at this and press play when you're ready to continue.

And here is question two.

"For each of these questions, use a pair of compasses "to draw a circle between the two circles "that have already been provided." So you can see in a, you've got quite a bit of room between the small circle and the big circle and I'd like you to draw your circle in between those two.

In b, you can see those two lines, those two circles are getting closer together so you've got less room and need to be a bit more careful in b.

And then c, those two circles are very close together.

So if you wanna draw your circle in between those, you've got to be super careful.

All right, pause the video while you have a go at these and press play when you're ready to continue.

Okay, big well done with that.

So hopefully you've drawn five circles and you might have something looked a bit like this, probably not quite as neatly done as on a computer, but your five circles should be of different sizes.

What you may wanna think about at this point is, which circles did you find easier to draw than others? Did you find it easier to draw small circles where the compasses were close together or really big circles? Was it easy to draw with a pair of compasses when they were really wide apart or did you find it easiest when the compasses were kind of open midway and you're drawing medium-sized ones? I think a lot of people tend to say they find it easier to use a pair of compasses when they're open sort of midway rather than at the extreme small or extreme large end.

And for question two, hopefully we've drawn a circle in between each of those pairs of circles in a, b and c.

Fantastic work so far.

Now in the first learn cycle we just drew circles of any size.

In the second learn cycle, we're gonna draw circles of particular sizes and also draw some arcs as well.

Before we continue, let's us recap the parts of a circle.

Which parts of a circle can you remember the names for? Pause the video while you write these down and press play when you're ready to continue.

Okay, let's see which ones we can think of.

The circumference is the distance around the edge of a circle, bit like the perimeter of a shape.

The radius is the distance from the centre of the circle to its edge.

And the diameter is the furthest distance from one side of the circle to the other, and that goes through the centre.

We also have an arc, which is part of a circle or part of its circumference.

Now an arc in general is part of a curve, but an arc of a circle is part of the circle circumference, and a pair of compasses could be used to draw an arc.

You place your pair of compasses down, in the same way you do for drawing a circle, but you don't go all the way around, you just go part the way around and you've got an arc of a circle.

So let's check what we've learned there.

Which part of the circle is indicated by the arrow? Pause the video while you write down the word and then press play when you're ready to continue.

The part of the circle there is the radius, that is the distance from the centre to the edge of the circle.

Which part of this circle is highlighted? Pause the video while you write down the word and then press play when you're ready to continue.

This is part of the circumference, so it's an arc.

Now the distance between the needle and the pencil tip of a pair compasses is equal to the radius of the circle.

We can see that here.

The needle is at the centre of the circle and the pencil is at the edge of the circle, then the distance between those must be the radius.

So how could this fact be used to draw circles with specific radii? Hmm.

Pause the video while you think about this, and press play when you're ready to continue.

Well, let's try that now.

Let's take a plain piece of paper, mark a cross on it somewhere and draw a circle with a radius of four centimetres.

So to do that, open up your pair of compasses, so that the distance between the needle and the pencil tip is four centimetres.

Now you may find it easier to draw a line segment on the page first that is exactly four centimetres, and then use the line segment to open up your pair of compasses to the correct distance instead.

Whichever way you do it, then move the needle tip onto the centre point of the circle and draw a circle around it.

The radius of your circle should be four centimetres in every direction.

Let's check what we've learned there.

"Jacob has got a pair of compasses ready to draw a circle.

"Which of these statements will be true? "Is it a: the circumference will be seven centimetres, "b: the diameter will be seven centimetres, "or c: the radius will be seven centimetres?" Pause the video while you have a go at this and press play when you're ready to continue.

The answer is c.

The radius will be seven centimetres because the needle will be at the centre of the circle and the pencil tip will be at the edge of the circle.

Let's now check again how well we can draw a circle with a specific radius.

So take a plain piece of paper and mark a cross somewhere in the middle of the page.

Now use a pair of compasses, draw a circle with a radius of six centimetres and with a cross at the centre.

Pause the video while you have a go at this, and then press play when you're ready to check it.

So to check our circle, draw two radii in it, preferably not in the same direction as where you first started, in different directions.

And use your ruler to accurately measure the length of each radius and check are both of the radii of your circle six centimetres.

Pause the video while you check that and then press play when you're ready to continue.

Okay, it's over to you now for "Task B".

In this task, you need to take your pair of compasses to draw four circles all with the radii that are specified below.

So your first circle will have a radius of five centimetres, your second circle will have a radius of eight centimetres and we'll wrap around the first one, and then 10 centimetres, and then two centimetres.

Each of your circles need to be around the same cross for the centre point.

While you're doing this, you may wanna think about which questions feel more comfortable than others.

Is it when the compasses are open far apart, or is it when they're close together, or is it when it's in the mid-range? Okay, pause a video while you have a go at this, and press play when you're ready for question two.

Here is question two, and don't we have a treat for you here? This is like a steady hand game.

So working from left to right,, draw a set of connecting arcs staying between the lines provided at all times.

So use the first cross on the left, put your needle there, put the pencil on the start line, draw an arc until you can't go any further.

And then move the needle to the second cross, draw another art that connects to the first one until, and keep doing it until you get all the way around to the finish line.

And you'll notice that the lines are getting closer and closer together as they go.

So you'll need to be more and more precise as you get closer to the finish line.

Have fun with this one.

Pause while you have a go, and press play when you're ready to continue.

Okay, here is what question one should look like when you're finished.

Yours might not be quite as as perfect as these ones 'cause these will draw on a computer, but should give you a general gist of what they look like.

And how have you got on with question two? Our final answers should look like something a bit like this.

Now you might have your arcs crossing over at the different points where they join, but hopefully you might just stay between the lines all the way.

If you didn't, don't worry, just keep practising , you can always have another go at this one.

And the more you practise on this particular activity, the the steadier you'll get with using a pair of compasses.

Fantastic work today.

Great job.

Let's summarise what we've learned in this lesson.

Firstly, a pair of compasses can be used to draw any circle, so long as the compasses can open wide enough to draw it.

A pair of compasses can also be used to draw a circle with a specific radius.

You just need to measure distance between the needle and the pencil tip because that will be equal to the radius of the circle.

And a pair of compasses can also be used to draw an arc rather than an entire full circle.

But drawing with a pair of compasses can be tricky to begin with.

But like anything, the more we practise the easier we'll find it over time.

Well done today.