Math lesson plan · 11th grade (Year 12 in England) · 30 minutes
Find the area of a circular segment
Geometry
CCSS HSG.C.B.5CCSS HSG.SRT.D.9England: GCSE Higher GeometryEngland: A-level Pure Mathematics
Objective and success criteria
Students will: Find the area of a circular segment.
- I can answer questions on today's skill on my own, without help.
- I can explain each step and say why it works.
- I can check my answer and spot a mistake.
Before and after
Needs first: Arc length and sector area; Area of a triangle: ½ab sin C
Leads to: the next skill in this area.
Materials: Rulers and protractors, Squared or dotted paper, Shape cut-outs, Mini whiteboards and pens, Printed student sheet (below).
Warm-up · 4 min
- Quick retrieval from earlier learning (Arc length and sector area; Area of a triangle: ½ab sin C). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- A sector has radius 11 cm and angle 30°. Find the arc length in cm, rounded to 1 decimal place. → 5.8Prompt: Arc length = (θ/360) × 2πr.
- Two sides of a triangle are 10 cm and 13 cm with an angle of 102° between them. Find the area to 1 decimal place. → 63.6Prompt: Area = ½ab sin C, where C is the angle between a and b.
- Find the area of a sector with radius 8 cm and angle 90°. Round to 1 decimal place. → 50.3Prompt: Sector area = (θ/360) × πr².
Hook · 3 min
- Show a photo of a building, a tile pattern or a road sign and ask what shapes and angles students can spot.
- Share the objective: Find the area of a circular segment. Read the success criteria together.
I do: model it · 7 min
- Work through the example out loud, saying why you do each step, not just what you do.
- Example: A chord cuts off a minor segment of a circle of radius 15 cm. The chord subtends 50° at the centre. Find the area of the segment to 1 decimal place.
- Step 1: 50/360 × π × 15² − ½ × 15² × sin 50°
- Step 2: ≈ 12 cm²
- Answer: 12
- Pause after each step and ask a student to say what comes next.
We do: guided practice · 6 min
- Do these together. Students try each step on whiteboards before you reveal it.
- Use the hints as prompts rather than giving the answer.
- A chord cuts off a minor segment of a circle of radius 13 cm. The chord subtends 40° at the centre. Find the area of the segment to 1 decimal place. → 4.7Prompt: Segment = sector − triangle.
- A segment of a circle of radius 2 cm has angle 1.1 radians at the centre. Find its area to 2 decimal places. → 0.42Prompt: In radians: segment area = ½r²(θ − sin θ).
You do: independent practice · 7 min
- Students work on the student sheet. Circulate and check the first two answers of every student early.
- Students who finish: write a question of their own for a partner, with the answer.
The 6 questions are on the student sheet below, with answers in the key.
Exit ticket · 3 min
- Two questions on their own. Sort answers into got it / nearly / not yet to plan the next lesson.
- A chord cuts off a minor segment of a circle of radius 15 cm. The chord subtends 110° at the centre. Find the area of the segment to 1 decimal place. → 110.3Prompt: Segment = sector − triangle.
- A segment of a circle of radius 5 cm has angle 0.6 radians at the centre. Find its area to 2 decimal places. → 0.44Prompt: In radians: segment area = ½r²(θ − sin θ).
Watch out for
- Thinking a square turned on its corner is no longer a square.
- Reading the wrong scale on a protractor.
Support and stretch
Support
- Review first: Arc length and sector area.
- Use concrete materials: rulers and protractors.
- Give the first step of each question, or a partly worked example to finish.
- Pair with a confident partner for the guided practice.
Stretch
- Explain a common mistake in writing and how to fix it.
- Write a word problem that uses today's skill, then solve a partner's.
Homework and more practice
Free online practice with hints and printable worksheets for this skill: eurekami.com/math/grade-11.
Free lesson plan from eurekami.com/lesson-plan-builder