Primary 5 Maths: Properties of Circles — Tutor Lesson Plan (centre, radius, diameter)

2026-10-27

Tutor lesson-prep guides · Primary maths

Students can draw a circle but cannot say every point is the same distance from the centre. The compass draws that definition for them.

Objectives — the student can name the centre, radius and diameter, explain why every point on the circle is the same distance from the centre, use d = 2r in both directions, and state that a circle has infinitely many lines of symmetry.

01 Prerequisites (3-minute check)

If any of these fails, fix it before the lesson starts.

Skill	Quick check	Pass mark
Using compasses	Draw a circle of radius 3 cm	Needle fixed, 3 cm measured
Multiplication	7 × 2	14
Symmetry	How many lines of symmetry has a square?	4

02 Lesson flow (45 minutes)

Time	Stage	Tutor does	Student does
0-6 min	Draw	Draw a circle and mark the needle hole	Draw one and mark the centre
6-16 min	Radius	Draw three radii and measure them	Measure and find them equal
16-26 min	d = 2r	Convert radius to diameter and back	Do four conversions
26-36 min	Symmetry	Fold the circle several ways	Conclude there are infinitely many
36-42 min	Fix errors	Board “diameter halved by doubling”	Name their own slip
42-45 min	Exit check	Three questions marked at once	Finish alone

03 Teaching script (read it out)

Scene 1: The centre is the needle hole

Where the compass needle sits is the centre; the pencil traces the circle.
So every point on the circle is the same distance from the centre: the compass width.

Student measures three radii in different directions.

Scene 2: Radius and diameter

A radius runs from the centre to the circle; a diameter passes through the centre and touches both sides.
So d = 2r and r = d ÷ 2.

Student converts r = 3.5 to d = 7, and d = 9 to r = 4.5.

Scene 3: Infinitely many lines of symmetry

Fold the circle in half: the halves match. Fold along another direction: they match again.
Every direction works, so there are infinitely many. A square has only four.

Note: every line of symmetry passes through the centre.

04 Question types and worked steps

Type	Example	Steps	Answer
Radius to diameter	r = 7	7 × 2	d = 14 cm
Diameter to radius	d = 9	9 ÷ 2	r = 4.5 cm
Distance on the circle	point to centre when r = 3	equals the radius	3 cm
Symmetry	a circle	any line through the centre	infinitely many

Sanity check (teach this): The diameter is twice the radius and always longer; an answer of r = 18 from d = 9 means the operation went the wrong way.

05 Independent practice (3 questions)

Question	Answer	What to watch
r = 6, find d	12 cm	Multiplying by 2
d = 9, find r	4.5 cm	Dividing by 2
Lines of symmetry of a circle	infinitely many	Understanding the fold test

06 Common mistakes and what to say

Mistake	Student writes	Say this
Radius and diameter confused	d = 9 written as r = 9	The diameter spans the whole circle; the radius is half.
Doubling instead of halving	d = 9 gives r = 18	Half of 9 is 4.5.
Fixed number of symmetry lines	answers 4 or 8	Any fold through the centre works.
Units missing	answers 12	Length needs a unit.

07 Homework (paper, section and question numbers)

Primary 5 first-term paper — Section C, questions 14 to 16
Primary 5 second-term paper — Section C, questions 8 to 10

08 Exit check (last 5 minutes)

Question	Answer	Decision
d = 20, find r	10 cm	All right: move to percentages
r = 2.5, find d	5 cm	One wrong: re-teach d = 2r
Lines of symmetry of a circle	infinitely many	Two wrong: repeat scene 3

09 Tutor FAQ

Is circumference in this lesson?

No. Circumference and area come in Primary 6; here we only build centre, radius, diameter and symmetry.

What if there are no compasses?

A piece of string and a pencil draw a circle just as well; the string length is the radius.

Do we need pi?

Not at all in this lesson.

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A TutorZone lesson-prep guide. Written by the TutorZone team; questions and lesson flow are original and are not taken from any school or publisher material.