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Constructing a circle  

As I am teaching 13-year-old learners maths they should by now know what instrument is used to construct a circle.   

Learners should also have prior knowledge of the following:

Centre of a circle 

A circle is a simple closed shape. It is the set of all points in a plane that are at a given distance from a given point, the centre; equivalently it is the curve traced out by a point that moves so that its distance from a given point is constant.

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Centre of a circle

Radius:

The distance between any of the points and the centre is called the radius.

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Radius of a circle (r)

Using a pair of compasses to draw a circle:

A pair of compasses, also known simply as a compass, is a technical drawing instrument that can be used for inscribing circles or arcs.

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Compass for drawing a circle  

Diameter of a circle:

Diameter: a line segment whose endpoints lie on the circle and which passes through the centre; or the length of such a line segment, which is the largest distance between any two points on the circle. It is a special case of a chord, namely the longest chord, and it is twice the radius.

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Diameter of a circle (d)

Teachers can draw a circle like the one below on the board:

QS and PR are diameters that intersect at point T.

• Ask the learners these questions:

1. What do we call point T?
2. What do we call line segment TS?
3. How do we describe TS?

Your learners are expected to know that T is the centre and TS is a radius.  They should know that a radius is the line segment that joins the centre to a point on the curved line of a circle.

Constructing a circle:

Activity:

Teachers should do this activity with the learners, explaining it step by step.

CONSTRUCT A CIRCLE WITH CENTRE P AND A RADIUS OF 2CM

Step 1:

Use your compass and place the pointed tip on the zero line of your ruler.  Carefully widen the angle between the arms.  Move the pencil tip until it is exactly at 2cm as shown below

Step 1

Make sure that the pointed tip is still on zero.  Be careful not to change the gap once it is set to 2cm.

Step 2:

Mark a point, point A, in the middle of a blank sheet. Gently push the pointed tip into Point A.  Push just deep enough into the paper to keep it in place.  This will be the centre of your circle.

Step 3:

Hold the handle between the forefinger and thumb of your writing hand.  Keep you other hand out of the way.  Use only one hand when you draw a circle with a compass.

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Step 4:

Twist the handle between your thumb and forefinger.  If you are right-handed it is easiest to twist the compass clockwise.  If you are left-handed, turn anti-clockwise.  Let the pencil tip drag over the paper.  Don't push down too hard on the pencil,  Rather push down lightly on the pointed arm as you draw.  The pencil tip must move smoothly and easily.

                               

Drawing a circle with your left hand                                 

Drawing a circle with your right hand

Emphasize that constructions should be accurate.

Give your learners homework.  Let them draw patterns using a different size radius every time.

The following patterns can also be given to try on their own.

Pattern 1

Pattern 2

Pattern 3 - More advanced

Let learners try patterns of their own too. 

Try to make this lesson fun for your learners.