Here is what the KICD curriculum design asks for in Circles, with a sample lesson plan, notes and an exit check you can read before you teach. In Fuma, the same lesson comes out of your own scheme of work, starting from the lesson your class has reached and dated to your term.
Aligned to the KICD curriculum designSample — review before you teach
What learners should be able to do
Specific learning outcomes, word for word from the KICD curriculum design.
a)work out the circumference of a circle in real-life situations
b)work out the length of an Arc of a circle in different situations
c)calculate the perimeter of a sector of a circle in different situations
d)promote use of circles in real-life situations
Key inquiry questions
How do we determine the circumference of a circle?
How do we use sectors of a circle in real-life situations?
A sample lesson plan: Exploring Circumference of Circles
This is a sample. Read it and change it for your class before you teach it. In Fuma, everything stays a draft until you approve it.
Grade 8 · Mathematics · 40 minutes
describe circumference as the distance around a circle and distinguish diameter from radius
measure the circumference and diameter of circular objects and calculate circumference using C = πd
appreciate the use of circles and accurate circumference measurements in real life
A sample lesson plan
Time
Teacher
Learners
Introduction5 min
Teacher:
Display circular objects: tin lid, bottle top, plate.
Ask learners to name and describe the shape.
Pose: How would you measure the distance around the edge?
Learners:
Look at objects and name them.
Discuss in pairs how to measure around the edge.
Share ideas: string, ruler, rolling.
Measuring around circular objects12 min
Teacher:
Distribute circular objects, string, and rulers to groups.
Instruct learners to wrap string around the object's edge once.
Guide learners to mark string, straighten, and measure length.
Ask learners to measure the distance across the widest part (diameter).
Record measurements in a table on the board.
Learners:
Wrap string tightly around circular object's edge.
Mark and straighten string; measure length with a ruler.
Measure diameter across the centre with a ruler.
Record distance around (C) and across (d) for three objects.
Discovering the circumference-diameter relationship10 min
Teacher:
Draw a table on board: object, circumference C, diameter d, C ÷ d.
Ask groups to complete table using their measured values.
Guide learners to calculate C ÷ d for each object.
Ask: What do you notice about the answers?
Learners:
Transfer measured values into class table on board.
Calculate C ÷ d for each object using a calculator.
Compare quotients; notice they are all about 3.14.
State conclusion: circumference is about 3 times diameter.
Using π to calculate circumference8 min
Teacher:
Introduce π as the constant ratio, approximately 3.14.
Write C = πd on the board; explain each term.
Work one example: a circular water tank has diameter 2 m; find C.
Ask learners to solve similar problems in pairs.
Learners:
Copy formula C = πd into exercise books.
Follow worked example: C = 3.14 × 2 = 6.28 m.
Solve near-identical problems: (i) d = 4 m, (ii) d = 0.5 m.
State answers and method.
Shown: the first 35 minutes of the 40-minute lesson.
Sample teaching notes
Teaching notes are for you at the board: the subject knowledge and what to watch for.
Content Mastery: The Mathematics Behind the Lesson
Why the ratio C ÷ d is constant for every circle. Every circle is a scaled copy of every other circle. If you double the diameter, you double the circumference; if you halve the diameter, you halve the circumference. Ratios that survive scaling like this are called invariant — and that invariant is what we call π. This is exactly why learners should get roughly the same quotient whether they measure a bottle top or a bicycle wheel: the objects differ in size, not in shape.
The two lengths, stated precisely. The diameter is a straight chord passing through the centre — the widest distance you can measure across the circle. The radius is a straight segment from the centre to any point on the circle. Therefore d = 2r and r = d ÷ 2. Circumference is a length measured along the curved edge, which is why string works and a ruler laid straight across does not.
Why the answer is never exactly the same in a classroom. π is irrational (about 3.14159...), and the learners are measuring with string and a 30 cm ruler. String stretches, it slips off the edge, rulers are read to the nearest millimetre, and objects are rarely perfect circles. Quotients of 2.9 to 3.3 are normal and healthy — that spread is evidence of measurement error, not evidence against the relationship. Tell learners this before they start so nobody thinks they have "failed" when their quotient is 3.2 instead of 3.14.
Misconceptions: What to Watch For and How to Correct Them
1. Learners measure the diameter and record it as the circumference — they confuse "across" with "around".
Why it forms: These are the first two lengths in the learners' experience that differ only in direction of travel, not in the object. Grade 7 length work trained them to lay a ruler from one point to another; string is a new tool and some learners will happily wrap the string across the middle of the lid, see a number on the ruler, and write it in the D column while thinking they have done the C column.
How to surface it during the activity: Walk round the groups during the first four minutes. A group whose circumference value is close to their diameter value (for example C = 10 cm, d = 10 cm for a tin lid) has done this. Ask them directly: "Show me again where that string started and ended. Did it travel along the edge or through the middle?"
A quick exit check, with answers
1.Which statement describes the circumference of a circular basin?
A. The distance around the basin
B. The distance across the basin through the centre
C. Half the distance across the basin
D. The distance from the centre to the edge
Show answer
A. The distance around the basin
2.For any circle, the diameter is twice the radius.
Show answer
True
3.A circular water tank has a diameter of 14 m. Taking π = 22/7, calculate its circumference. Show your working.
Show answer
C = πd = 22/7 × 14 = 44 m
4.(a) State the formula for calculating the circumference given the radius. (1 mark) (b) A circular mat has a radius of 7 cm. Taking pi = 22/7, calculate its circumference. (3 marks)
Show answer
(a) C = 2 x pi x r (or C = pi x d where d = 2r). (b) 44 cm.
Outcomes and inquiry questions are quoted from the KICD curriculum design. The lesson plan, notes and exit check are Fuma's draft. Fuma is built from the KICD designs; KICD has not endorsed it.