Primary 6 Maths: Circumference and Area of a Circle

Primary 6 Maths: Circumference and Area of a Circle — Tutor Lesson Plan

2026-10-27

Tutor lesson-prep guides · Primary maths

The two formulas differ by one r, and students love substituting the diameter into the area. Measuring a rim with string shows where pi comes from; two colours keep the formulas apart.

Objectives — the student can explain that circumference is about 3.14 diameters, use C = pi d and A = pi r² correctly, and handle a semicircle (adding the diameter to its boundary).

01 Prerequisites (3-minute check)

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

Skill	Quick check	Pass mark
Radius and diameter	d = 12, r = ?	6
Squares	7²	49
Decimal multiplication	3.14 × 6	18.84

02 Lesson flow (50 minutes)

Time	Stage	Tutor does	Student does
0-8 min	Measure	Wrap string around a cup and straighten it	Measure and compare with the diameter
8-18 min	Pi and circumference	C = pi d with d = 14 and 22/7	One alone
18-30 min	Area	A = pi r², radius first	r = 7
30-40 min	Semicircle	Boundary = half the circle plus the diameter	One alone
40-46 min	Fix errors	Board the diameter-in-area error	Say which value they used
46-50 min	Exit check	Three questions marked at once	Finish alone

03 Teaching script (read it out)

Scene 1: Pi is a measured ratio

Wrap string once around a cup and straighten it: about three times the diameter.
That ratio is pi, about 3.14 or 22/7. So circumference = pi × diameter.

Repeat: “the circumference is pi times the diameter”.

Scene 2: Area needs the radius

Area = pi × radius × radius. With diameter 14, halve first to get r = 7, then 22/7 × 49 = 154 cm².
Using 14 instead gives an answer four times too big.

Student does r = 3.5, area 38.5 cm².

Scene 3: Semicircle: add the diameter

The boundary of a semicircle is half the circumference plus the diameter.
Many students forget the straight edge. The area is simply half the circle.

Warn: boundary and area are handled differently; keep them separate.

04 Question types and worked steps

Type	Example	Steps	Answer
Circumference (22/7)	r = 7	2 × 22/7 × 7	44 cm
Circumference (3.14)	d = 20	3.14 × 20	62.8 cm
Area	r = 7	22/7 × 49	154 cm²
Semicircle boundary	r = 7	44 ÷ 2 + 14	36 cm

Sanity check (teach this): For the same radius the area number is larger than the circumference number (154 against 44); a smaller area usually means the square was dropped.

05 Independent practice (3 questions)

Question	Answer	What to watch
Circumference, r = 3.5	22 cm	Using r, not d
Area, r = 3.5	38.5 cm²	Squaring the radius
Semicircle boundary, r = 7	36 cm	Adding the diameter

06 Common mistakes and what to say

Mistake	Student writes	Say this
Diameter used in the area	A = 22/7 × 14²	Halve the diameter first.
No square	A = 22/7 × 7 = 22	Area needs r twice.
Semicircle boundary short by the diameter	answers 22 cm	Add the straight edge.
Changing pi mid-question	22/7 then 3.14	Use one value throughout, usually the one given.

07 Homework (paper, section and question numbers)

Primary 6 first-term paper — Section C, questions 1 to 5
Primary 6 first-term paper — Section E, questions 5 and 6

08 Exit check (last 5 minutes)

Question	Answer	Decision
Circumference, r = 3.5	22 cm	All right: move to speed
Area, r = 3.5	38.5 cm²	One wrong: re-teach r against d
Semicircle boundary, r = 7	36 cm	Two wrong: repeat the measuring activity

09 Tutor FAQ

22/7 or 3.14?

Use whichever the question states; with no instruction use 3.14 and do not switch.

Do you derive the area formula?

No derivation, but the “many sectors make a rectangle” picture is worth one sentence.

Semicircles keep going wrong.

Draw it and label the arc and the diameter before adding anything.

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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.