Mathematics
Advanced
50 mins
Teacher/Student led
+65 XP
Teacher-led from the board — pupils need no device
What you need:
IWB/Projector/Large Screen
Compass

Constructing Circles and Exploring Their Parts

Construct circles using a compass, learn to label the centre, radius, diameter, chord, arc and circumference, and discover why the diameter is always twice the radius.

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    1 - Getting Started ~4 mins

    Illustration for Getting StartedHere are two circles. One was drawn freehand with a pencil. The other was drawn with a compass.

    Look closely: which one is a true circle, and what makes it perfect all the way round?

    2 - Watch and Notice ~9 mins

    Watch three circles on the board, each labelled with its parts. Look for where the centre sits and how far the radius reaches. The circumference is the whole distance all the way around the edge. The diameter goes right across through the centre, and it is made of two radii laid end to end, so it is always exactly twice the radius.

    Now a second circle, smaller than the first. The radius is shorter this time. Notice what has happened to the diameter now that the radius is shorter.

    The last circle brings in two new names. One is a straight line joining two points on the edge, and the other is a piece of the edge itself. Watch where each one sits, and decide whether that straight line could be called a diameter.

    3 - Try It Together ~7 mins

    Key point

    Today we work through three circles together, with one pupil setting each one at the board while the rest of the class predicts aloud. The first two give you the radius and ask you for the diameter, and the last one turns it around: you are given the diameter and you have to work the radius back out. Each time, say your answer out loud before we check it on the screen.

    Set the radius, name the parts

    4 - Construct a Circle in Your Copy ~3 mins

    COPYBOOK MOMENT

    In your maths copy, construct a circle of radius 5 cm with your own compass. Label the centre, the radius, the diameter and a chord. Then write down the length of the diameter.

    5 - Class Challenge ~9 mins

    Key point

    Work out the radius the compass needs each time before you set it.

    Now you build circles to match a target on the screen. The first two targets give you the radius straight out, so you can set it and check. The last two give you the diameter instead, which means you have to halve it yourself before the compass goes anywhere near the right size.

    Match the circle

    Pupil practice
    Module 7 · 2D Shape, 3D Shape and Angles Shape & Space
    Lesson 83 · Constructing Circles and Exploring Their Parts
    Download Activity Book page (PDF)
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