The circumference is also the radius of a circle

The circumference is the area of the circle

The circumference is the distance around a circle

Complete the sentence. The diameter of a circle is...

The radius of my circle is 8.5cm. What is the diameter of the circle?

Exploring circles

Key Stage 3

Maths

Constructing triangles and quadrilaterals

﻿In this lesson you will be able to name the basic features of circles and also their reasoning. Using the properties of circles. You would also be able to draw circles using a pair of compasses. So again, if you do not have your compass, please could you get one as it will be very beneficial for this lesson. let's move on to our, Try this activity. Our student here is saying, with one straight cut, she can chop a circle into at most the maximum she can chop a circle to with one cut is two pieces. Now, the question you want to answer is what is the maximum number of pieces you can chop a circle into with two cuts? With three cuts and with four cuts? If I chop a circle with two cuts, what's the maximum number of pieces my circle would become? And with three cuts and with four straight cuts? Pause your screen now and complete this task and then when you're ready, press resume to carry on with the lesson. The answers are on the board for you to try this task. We have one cut as we saw. I can chop my circle into two pieces, piece one and piece two. With two cuts here and there, I can chop my circle into four pieces. With three cuts, I can chop my circle into seven pieces, and with full cuts one, two, three, four, I can chuck my circles into 11 sections. What did you get? Were you able to get the answers on your screen right now? For our Connect task, I am going to show you an image and when I show you the image, I want you to generate a sentence in your book to describe which each term means. And then once you've done that, the second thing I want you to do is to generate some examples and some non-examples. Examples being, this works for this term, and non-examples being, this is not correct for this term. So let's do an example. A circumference. I am saying that a circumference is, if I go round my circle, that is the circumference. Now, I could say my sentence could be, a circumference is the distance around the circle. And an example would be, this pink circle I've drawn over here 'coz it's highlighting the distance around the circle. And then this would be a non-example 'coz it's showing just a straight line going from one end to the other. So, this is not an example of a circumference. So now, if I show you this picture of a diameter, an arc and the radius. Can you write a sentence in your book to describe what each term mean and generate some examples and some non-examples Pause your screen now and proceed with this task. Once you're ready, press play to continue with the lesson. Here are some of the examples I wrote. I'm going to read each one for you. A diameter is a straight line from one side of the circumference. this is the one side of the circumference to the other, going through the centre. The diameter goes through the centre of the circle from one end of the circumference to the other end of the circumference. Notice how this is different to this non-example here. This line isn't going through the centre. This is not a diameter. This is a diameter. and an arc, I have written that an arc is a part of a circle. Right here. Just part of the circle. And a radius is a straight line from the centre of the circle to the circumference of the circle. I could either draw my radius from this point, from the centre here to that end of the circumference, or from the centre here to this end of the circumference, it doesn't matter. The radius is a straight line from the centre of the circle to the circumference of the circle. There are three things going on here. I'm talking, you're watching a video, and they're also be some obstruction that'll be on your screen over here. If at any point you think this is a bit much, just pause the video, so you can understand this every single step. Take your time when you're doing this, and then proceed at your own pace. Let's proceed . First thing I want you to do is, you would see in the video, I want you to choose your own radius length. I chose a length of two centimetre. I'm going to pause the video there, if it pauses. First thing I want you to do is choose your own radius length. Your length can be of any centimetre, any value. So I went for two centimetre. Next step. Once you've chosen your own length, you're going to use your compass to measure the length you drew on your paper, Okay? It should be two centimetres for me. My measurement on my compass came to two centimetre because my radius length was two centimetre. So I'm going to play the video now. You're going to see what I mean by that. I am measuring my length on my paper. Now you are going to draw a circle. When you're drawing your circle, the sharp point of your compass is at one end of your line, the sharp point of your compass is at one end of your line and it stays on that end of the line and you rotate. So your hand is on this black tip of your compass and you rotate it round your page, like so. Okay, so I'm going to show you the video you're going to see what I mean by that. There you go. Pause the video and try this activity now. First step, Choose Your Own radius length. Second step, use your compass to measure the length on your piece of paper. Third step, using the same length you measured, put your sharp point on one end of the line and draw a circle around that line. Pause the video now, attempt that, come back, and we'll carry on with the lesson. I hope you were able to draw your circle. If you weren't, then keep trying until you do. Don't give up. It is a tricky skill to learn but it is very possible to learn, so keep trying until you get it. Now the third question is, what point should I connect on my circle, if I want to draw this shape? If I want to draw this triangle. What point should I connect On my circle, if I want to draw this shape? I want to connect, I've drawn the radius. Notice, remember, we said the radius goes from the centre of the circle to, from the centre of the circle here , to the end of the circumference. But if you notice from this triangle, I don't just have the radius, I have the diameter, and the radius is therefore twice, the diameter is therefore twice the radius. I'm going to stretch my line to meet the other end of my circumference. Now, I have the diameter and to connect up to draw this triangle, I'm just going to go from one end to the middle point there, and from another end over here. And I've done that circle. Now what if I want to draw the shape? What do you think I should do? Take about five seconds to think about it. If I want to draw the shape, what do I need? What can you see? And what would I need to do? Again, I think it'll better if I show you a video as I learn things through visualisation. I think it would help you if I show you through a video how I went about how to construct a shape like this. Let us start. The question is, how many circles would I need to construct the shape on your screen right here? Let us start. First thing I did, like before I measured my radius. I started with a radius of two centimetre. Then I am going to measure, making sure my compass is also at a length of two centimetre. Then I am going to put the sharp edge of my compass at one end of the line and draw a circle. As I said before, it is quite a fiddly tool. And it takes quite a few practises before you can get the hang of it. Now, watch how I put my compass at the other end of my line. So, the compass is now at the other end of my line. I started with the compass being on that and now I'm starting on the sharp point of my compass being on the other edge of my line. I'm just going to go back a few seconds. The compass is now on the few edge of my line and I'm going to now draw a circle again. What do you notice about the two circles that I've drawn? What do you notice about this circle here and that circle here? Well, they intersect at these two points over here, that will come in handy later on. So keep that in mind. Now I am going to connect the ends of my line to one point of intersection and I'm choosing the top intersection point. Notice how I made a mistake here. I'm going to extend my line. Even though I started at two centimetres, I am adjusting my line because my circle was not quite perfect. And you would notice the difference that I made in my measurement. I started with two centimetres and now I am at 2.5 centimetres. I am now measuring the other length of my triangle and I noticed or I measured that each length was also 2.5 centimetre. What type of triangle is that? An equilateral triangle. And to construct an equilateral triangle, I needed two circles. Now it's your turn. I want you to name the shaded polygon below. And how many features can you describe? So for this one, I could say, this is an equilateral triangle, because the radiuses are the same each time. I could say this is an isosceles triangle, because these two side lengths are the same. What is the shaded polygon on this shape and on this shape, and how many of its features can you describe? And I want you to explain your reasoning as well. Pause the video now, make right a couple of sentences, naming the polygon and explaining its features too. Let's come back and discuss this. As I mentioned, this is an isosceles triangle because two sides have an equal length to the radius. This from here to here, the radius is the same, from here to here is the radius and from here to here is the radius, and they both have equal length to the radius. This is a regular hexagon, as the circles, they all share the same radius and all the six sides, therefore, because they all share the same radius, the six sides have equal length to the radius as well. And you can see the lines of symmetry too, on the hexagon. The lines of symmetry, also show that it is a hexagon. They have three lines of symmetry, and all three sides have equal length to the radius as well. The length from here to here is the same as the length from here to here, and the length from here to here. Remember what I said, that as long as the line goes from the centre of the circle to any point of our circumference, it is a radius. This line goes from the centre of the circle here, to the end of our radius, and from the centre of the circle to the end of our radius of the centre of a circle, this circle to the end of our radius, They all have equal length. It is now time for your independent task. Pause the video now and attempt the questions. Once you're done, come back and we'll go over the answers together. Your explore task. Construct each image, So, that means you have to use your compass to construct this image, where the diameter of the largest circle, for the circle one the diameter is 24 centimetre, for circle two the diameter is 24 centimetre. Mark on any lines of symmetry and state the order of rotation of symmetry as well. Just to say that again, you are to construct each of these circles, mark out any lines of symmetry for both this and this and also the order of rotation of symmetry for both images. If you need some support, carry on watching the video, and I'll provide you some support. However, if you're confident and know what to do, pause the video now and attempt this task. once you're done, come back and we can discuss this. For your support, well, if the diameter here is 24 centimetre, the diameter here would also be 24 centimetre. If the diameter going along here is 24 centimetre, what would be the radius from this point from this centre to the end of the circumference? The radius is half of the diameter. So, the radius from the centre of the circle to this point, the radius from here to here would be 12 centimetre, wouldn't it? And, it would also be 12 centimetre there. If this is 12 centimetre, what would be the radius of this circle here? Will be six centimetre, wouldn't it? And if this Six centimetre, what would be the radius of this circle over here? It would be three centimetre. You're starting with a radius of 12 centimetre, you're measuring that drawing a circle. And then you'll go into six centimetre drawing a circle, three centimetre drawing a circle. If we move on to this one, the diameter is 24 centimetre. So if the diameter is 24 centimetre, what would be the diameter of each circle? What times three, 'coz they're three circles, would give me 24? It's eight, right? This diameter will be eight, this diameter will be eight, and this diameter will be eight. Eight plus eight plus eight is 24. Therefore the radius of this circle is the radius is Four centimetre. Use that support I've just provided to help you draw this circle. Let's go through this together. You are given the diameter over here is 24 centimetre. So, if this is 24 centimetre from this point, we use another colour from this point here to this point, what would be the diameter? Where would be half of the full circle of the biggest circle, wouldn't it? That will be 12 centimetre. If this is therefore 12 centimetre using another colour what would be the diameter of this circle? It would be six, wouldn't it? The diameter would be six centimetre. How can I go about drawing the circle? Well, that means for the biggest circle, I would have drawn a radius of 12' The next circle I would have drawn a radius of six and for the smallest circle, I would have drawn a radius of three centimetre and marking on the lines of symmetry, it has the same symmetry as a rectangle and an order of rotation too For this one then, the diameter from here to here were given as 24 and is the same from here to here. If the diameter is 24, what would be the diameter for each circle? I need three numbers that if I add together would give me 24. So each diameter for each circle would be eight centimetre. So therefore, the radius for the smaller circles would be four centimetre. So I would have drawn a radius of 12 centimetre for bigger circle and then a radius of four centimetre, for the little circles, and you would see that it has the same symmetries as a square, and therefore an order of rotation of four. we've now reached the end of today's lesson. Well done, it was quite a tricky subject, especially using a compass. I do hope you will practise lots more even after this lesson. And I also hope that you've learned how to name some features of a circle such as the arc, the diameter, the radius and the circumference. I will see you at the next lesson.

Exploring circles

Exploring circles

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UnitMaths / Constructing triangles and quadrilaterals

Maths