Primary 6 Maths | Circle Circumference And Area Lesson-Prep Guide (for Tutors) | Pi, C = Pi D, A = Pi R Squared

Primary 6 Maths | Circle Circumference and Area Lesson-Prep Guide (for tutors) | pi, C = pi d, A = pi r squared

2026-11-11

Tutor lesson-prep guides · Primary Maths

A circle is the first shape that needs a constant. Pupils rarely fail on the formula; they fail by putting the diameter where the radius belongs, or by giving a semicircle the arc only. This lesson builds every formula from what pi means.

Objectives — Pupils can: (1) explain pi as “the circumference is about 3.14 diameters”; (2) find a circumference with C = pi x d or 2 x pi x r and an area with A = pi x r squared; (3) add the straight edge when finding a semicircle or quarter-circle perimeter; (4) say that doubling the diameter doubles the circumference but quadruples the area.

01 Prerequisites (3-minute check)

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

Skill	Quick check	Pass mark
Diameter and radius	A circle has diameter 14 cm. What is the radius?	7 cm, half of the diameter
Multiplying decimals	Roughly what is 3.14 x 14?	About 43.96
What squaring means	What is 7 squared?	49, that is 7 x 7 and not 7 x 2

02 Lesson flow (45 minutes)

Time	Stage	Tutor does	Student does
0-6 min	Wrap a string round a circle	Wrap string round a cup, straighten it and measure; measure the diameter; let pupils notice the circumference is a bit more than three diameters	Do it and record both numbers
6-16 min	pi and C = pi d	Write C = pi x d, work 3.14 x 14 = 43.96 cm, then check with 2 x pi x r	Compute with both forms
16-26 min	A = pi r squared	The square applies to the radius only; r = 7 gives 3.14 x 49 = 153.86 cm squared; show what happens if the diameter is squared instead	Decide whether the question gave d or r
26-34 min	Semicircles and quarter circles	Semicircle perimeter is arc plus diameter: 3.14 x 7 + 14 = 35.98 cm; area is 76.93; a quarter circle of r = 10 has arc 15.7, perimeter 35.7, area 78.5	Mark the straight edges on a sketch
34-40 min	Doubling the diameter	d from 14 to 28: circumference 43.96 to 87.92 (x2), area 153.86 to 615.44 (x4)	Explain why area goes up fourfold
40-45 min	Exit check	Three quick questions on circumference, area and semicircle perimeter	Answer orally

03 Teaching script (read it out)

Scene 1: pi is a ratio, not a formula

Circumference divided by diameter is always about 3.14, however big the circle. Know the diameter and you know the circumference.

d = 14 gives 43.96; d = 28 gives 87.92

Scene 2: Area uses the radius, squared

A = pi r squared puts the square on the radius alone, never on pi x r. Halve the diameter first.

r = 7 gives 3.14 x 49 = 153.86 cm squared

Scene 3: A semicircle has a straight edge

Its boundary is the arc plus one diameter, so the arc alone loses 14 cm.

3.14 x 7 + 14 = 35.98 cm

Scene 4: Double the length, quadruple the area

Area multiplies two lengths, so doubling each length multiplies area by 2 x 2 = 4.

153.86 x 4 = 615.44 cm squared

04 Question types and worked steps

Type	Example	Steps	Answer
Find the circumference	A round flower bed has diameter 14 m. How much fencing goes round it? (pi = 3.14)	(1) Recognise circumference; (2) 3.14 x 14; (3) 43.96 m	43.96 m
Find the area	What is the area of the same bed?	(1) Radius 14 / 2 = 7; (2) 3.14 x 7 squared; (3) 153.86 square metres	153.86 square metres
Semicircle perimeter	A semicircular plot has radius 7 m. What is its perimeter?	(1) Arc 3.14 x 7 = 21.98; (2) add diameter 14; (3) 35.98 m	35.98 m

Sanity check (teach this): Check four things: the circumference must be a little over three diameters (43.96 against 14); an area unit must be squared (cm squared, never cm); a semicircle perimeter must exceed half the circumference (35.98 over 21.98, because of the diameter); doubling the diameter quadruples the area, not doubles it.

05 Independent practice (3 questions)

Question	Answer	What to watch
A round pool has diameter 42 m. Find the circumference using 22/7.	22/7 x 42 = 132 m, almost the same as 131.88 with 3.14	Check the 22/7 line is written out
A quarter circle has radius 10 cm. What is its perimeter?	Arc 15.7 plus two radii 20, giving 35.7 cm	Check both radii are added
A circle radius grows from 5 cm to 15 cm. How many times larger is the area?	Three times the radius, so nine times the area	Check the squaring: nine times, not three

06 Common mistakes and what to say

Mistake	Student writes	Say this
Putting the diameter into pi r squared	“The question says 14, so 3.14 x 14 squared.”	Write r = 14 / 2 = 7 before substituting; using d makes the area four times too big
Giving only the arc for a semicircle	“Half a circle is half the circumference, so 21.98.”	Add the diameter: 21.98 + 14 = 35.98
Writing an area in cm	“153.86 cm.”	Areas take square units; a right number with a wrong unit still loses marks
Thinking doubling the diameter doubles the area	“14 to 28, so 153.86 to 307.72.”	Area goes up 2 x 2 = 4, so 615.44; show it by tiling small squares

07 Homework (paper, section and question numbers)

Primary 6 maths test paper, Part A, circles question 6 — Part A, Q6
Primary 6 maths test paper, Part B, area applications question 11 — Part B, Q11
Primary maths chapter index (revise the area chapters) — Chapter index

08 Exit check (last 5 minutes)

Question	Answer	Decision
A circle has diameter 20 cm. What is the circumference?	62.8 cm (3.14 x 20)	If wrong, rewrite C = pi d and label d
A circle has radius 6 cm. What is the area?	113.04 cm squared (3.14 x 36)	If wrong, check the squaring and the unit
A semicircle has radius 5 cm. What is its perimeter?	25.7 cm (15.7 + 10)	If they answer 15.7, sketch it and mark the diameter

09 Tutor FAQ

Should pupils use 3.14 or 22/7?

Use whichever the question gives; 22/7 is quicker and exact when the diameter is a multiple of 7.

Is memorising the formulas enough?

No. They should be able to rebuild C = pi d from “three diameters and a bit”, or they will swap d and r under pressure.

Is there a matching worksheet?

Parts A and B of the Primary 6 maths test paper both carry circle questions, cited in the homework box.

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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.