Lesson video

Welcome to the ninth lesson in the coordinates and shapes unit.

Today we'll be illustrating and naming parts of the circle.

You'll need quite a few pieces of equipment today, a pen, a pencil, a piece of string and a ruler, and something with a circular face to draw around like a glass or a tin.

Pause the video and get your equipment together.

So here's our agenda for the day.

We're going to be illustrating and naming parts of circles.

Then we'll look at circle properties, the parts of a circle, and the relationship between those parts.

Then you move on to some independent learning before completing a final quiz.

So let's start with your initial knowledge quiz.

So I would like you to write down everything you know about this shape.

Consider the things in pink at the side it's properties, how to draw it, the relationship between its parts, whether it's a polygon or not, and where you see it in real life.

Pause the video now, and make some notes.

So here are some things you may have noted down.

A circle has a 2-D shape.

It has one curved side.

It has no vertices.

One way of drawing a circle is using a pencil and a piece of string, which we will be doing shortly.

Another way is to use a piece of equipment called a pair of compasses.

It's not a polygon because it doesn't have straight sides.

Remember polygon must have straight sides.

And some places that you may see it in real life, a wheel, a coin, the base of a glass, the base of a tin, chocolate button, clock, or a slice of orange.

It's important to remember that not all of those examples are actual circles because a circle.

A real circle is 2-D And in fact, the wheel is a three D shape.

Because it has depth as well.

A wheel is a cylinder.

They're not entirely flat.

But we're talking about the surface of one of those objects that is circular.

So one of the faces of a coin is circular.

That actually a coin really is truly a cylinder.

Now we're going to practise using the string method to construct a circle.

So this is how you do it.

You follow the steps, they are very straightforward.

You tie the piece of string around the pointed end of your pencil, and then you hold onto the end of the piece of string and you hold it down to the piece of paper as shown in step two.

And then wherever the end of the string is on the paper, that will be where the centre of your circle is.

You use your finger to hold it in place, pull the string taut, which means tight and draw a circle around with the pencil, keeping hold of the string, as you draw the circle.

So have a practise of doing that.

You won't get it right straight away.

And then I'd like you to also try changing the length of the string and thinking about what you notice.

So pause the video while you construct some circles.

So you will have noticed, that changing the length of the string changes the size of the circle.

So the longer the string was, the bigger the circle was and the shorter the string length, the smaller the circle.

And you may also have noticed that the side of the circle is always the same distance from the middle of the circle.

The side is equidistant from the middle of the circle.

So let's use those diagrams to help label the parts of the circle.

Here is our first new piece of key vocabulary.

So when looking at the boundary of the circle, the boundary of the circle, as we just said, it's equidistant from the centre.

Which means it is in equal distance from the centre all the way around.

And the boundary of the circles of the distance all the way round is called the circumference.

So you can either use one of the circles that you have drawn or on a separate piece of paper draw around the circular object that you brought to the lesson so that you have a perfect circle and label the circumference on your circle so that you have it to use for later.

Now, the word circumference it has the root word, which is a Latin word 'circ' which means ring and the prefix 'circum' which means around.

There's always good to have an idea of where these words come from, because they usually give us a clue as to what the words mean.

So now if I were to measure the circumference of a circle, how do you think I could go about doing that? So the best way to measure the circumference of a circle is to use a piece of string and a ruler.

So if you place the piece of string all the way around the circumference of your circle.

And then you take a piece of string and measure it against the ruler.

You will see, that you did measurement of all the way around the boundary.

And you might need another person to help you hold the piece of string in place.

So, pause the video now and have a go at using a piece of string and a ruler to measure the circumference of the circles you have drawn.

Great work.

Let's look at our next part of the circle.

So I have a circle drawn below, and these lines are examples of the radius of the circle.

So have a think, how do you think you could define the radius of a circle? So here we have a diagram that shows us what this actually means.

So this is the radius.

This pink arrow.

Its showing us the part of the circle called the radius.

And it goes from the centre of the circle to the boundary.

The radius is the distance from the centre of the circle, out to the boundary.

And remember that this distance is the same all the way, all the way around the circle.

So all of these lines on this circle, are the same length, because the boundary of the circle is equidistant from the centre of the circle.

And the word radius This comes from the Latin radius, which means ray, but it also means the spoke of a chariot wheel.

So the spoke is this line here on the chariot wheel.

And that goes from the centre of the wheel out to the boundary.

So now you can add this label onto your labelled circle that you drew before, where you wrote on the circumference as well.

So how do you think you would construct a circle with a radius of five centimetres? How would you make sure that this radius was five centimetres? So you would use your piece of string and you would need to measure the piece of string, so that it's five centimetres from the centre to the pencil, and that will give you a circle with a radius of five centimetres.

So what you could do now, is have a practise of constructing circles with different length radius.

So measure the string, so that you know the distance from the centre to the boundary and construct circles with different radius sizes.

Okay, let's move on to our next part of the circle.

These lines on this circle are all examples of the diameter of a circle.

So how would we define the diameter of a circle? Well, here it is on our labelled diagram.

The diameter is the distance from boundary to boundary, but it's very important.

This part, it must go through the centre.

So I can draw a line from boundary to boundary from boundary to boundary there, but that is not as an example of the diameter because it doesn't go through the centre point.

It has to go through the centre and diameter is derived from the Greek diametros which means diameter of a circle and from the word dia, which means across or through and metron which means measurement.

So it's the measurement across the circle, through the centre point.

So add that now onto your label diagram, so that you have got this image to go back and look at to help you with your questions later on.

So now let's have a look at the relationship between the diameter and the radius.

So we can see that if the diameter goes from boundary to boundary through the centre and the radius goes from centre to boundary, we can see that the diameter is double the length of the radius.

So the diameter is the radius times two.

And therefore we can use the inverse to say that the radius is half of the diameter.

So the radius is the diameter divided by two.

So these are very important rules to remember.

So then remember that the radius is half of the diameter.

If the radius is three centimetres, what is the length of the diameter? So I want to work out the diameter.

So I know that diameter equals radius times two.

And I know that the radius here is three centimetres.

So three times two.

So the diameter is equal to six centimetres.

So I'll just draw a very rough sketch of this on here.

And when I say very rough, I mean, super rough, there we go.

So I put my rough centre point in, is it going to let me, there we go.

So the radius is three centimetres.

So the diameter must be double that, which is six centimetres.

I can actually show you that in a better way.

Sorry my circles are getting worse though.

The dia.

The radius is three centimetres and I put another radius on there.

With three centimetres, that whole diameter is six centimetres.

Let's have a look at some more examples.

So we'll do the first one together.

So we're going to fill in the empty boxes and we've got the rules up at the top.

So the first example, the radius is 4.

5 centimetres, what's the diameter? So to get from radius to diameter, I multiply by two to get from diameter to radius I divide by two.

So I know that 4.

5 multiplied by two is nine centimetres.

And if I show that using a diagram, so I draw my circle and then I put my centre point in.

Remember, this is a rough diagram.

I know that the radius is 4.

5 centimetres, and if I added another radius measurement in to show the diameter now it's 4.

5 plus 4.

5, which is nine centimetres.

So can you pause the video now and find the other three blank measurements.

So looking at this one, we need it to get from the diameter to the radius.

We divide by two, because the radius is half of the diameter.

14 divided by two is seven centimetres.

Again, we're dividing by two 27 divided by two is 13.

5 centimetres.

And then we're going the other way, because the diameters double the radius, we're going to multiply 72 by two, which is 144 centimetres.

Okay it's time for some independent learning.

So pause the video now to complete your task and click re-start once you're finished so that we can go through the answers together.

Great work.

So your first job was to label the parts of the circle, and yet I gave you the key vocabulary at the side so that you would need to put them in the correct place.

So your first one is the radius.

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

Your second one was diameter, and that's the measurement from boundary to boundary going through the centre of the circle.

And the relationship that is that the diameter is double the radius, or the radius is half of the diameter.

And then your final one was the distance all the way around the boundary, which is the circumference.

Now using your knowledge of the relationship between diameter and radius, you were asked to calculate the radius.

So I know that the radius is half of the diameter.

So diameter divided by two is equal to the radius.

So all I needed to do was divide each of these measurements by two to find the radius.

So 17 divided by two, I can put on my radius there is 8.

5 centimetres.

25 divided by two, put on my radius is 12.

5 centimetres 46 divided by two is 23 centimetres and 73 divided by two is 36.

5 centimetres.

Now you have to match the key vocabulary to the definition.

So the circumference remember is all the way around the circle.

So it's the boundary enclosing the circle.

The radius, and thinking back the radius meant ray and also the spoke of a chariot wheel.

And that was from the point to the boundary.

So it's the straight line from a point on the circumference to the centre.

The diameter that one passed all the way through the centre of the circle, from one point on the circumference to another, and then the centre is the middle of the circle.

Now you were to use the given radius to calculate the diameter.

And we know that radius multiplied by two is equal to the diameter.

So all you needed to do here was to either multiply the radius by two or use repeated addition to find the diameter.

So this one was 6.

8 centimetres, and then another 7.

1, this 14.

2 centimetres.

And then another that 8.

7 is 17.

4 centimetres.

And then your final question, you were asked to draw a circle with radius three centimetres, and then another one with diameter eight centimetres.

So for this one, you needed a piece of string, which was three centimetres from the centre to the pencil.

And for this one, you needed to have a piece of string, which was four centimetres from centre to pencil because you needed to use the radius measurement for your piece of string.

Okay Pause the video and complete your final quiz and then click re-start once you're finished.

Great work today! I really love circles, so I enjoyed that lesson.

In our next lesson, we will be solving problems involving circles.

And if you could have the same equipment as today, that will be really helpful.

I'll see then!.