Math lesson plan · 9th grade (Year 10 in England) · 45 minutes
Arc length and sector area
Geometry
CCSS HSG.C.B.5England: GCSE Foundation GeometryEngland: GCSE Higher Geometry
Objective and success criteria
Students will: Arc length and sector area.
- 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: Area of a circle
Leads to: The unit circle and radians; Find the angle or radius from an arc length or sector area; Find the perimeter of a sector
Materials: Rulers and protractors, Squared or dotted paper, Shape cut-outs, Mini whiteboards and pens, Printed student sheet (below).
Warm-up · 5 min
- Quick retrieval from earlier learning (Area of a circle). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- A circle has diameter 20 cm. Its area is kπ cm². What is k? → 100Prompt: Find the radius first: half the diameter.
- What is the area of a semicircle with radius 9 m? Round to 1 decimal place. → 127.2Prompt: Find the area of the whole circle first.
- A circle has diameter 4 yd. Its area is kπ yd². What is k? → 4Prompt: Find the radius first: half the diameter.
Hook · 5 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: Arc length and sector area. Read the success criteria together.
I do: model it · 10 min
- Work through the example out loud, saying why you do each step, not just what you do.
- Example: A sector has radius 11 cm and angle 30°. Find the arc length in cm, rounded to 1 decimal place.
- Step 1: (30/360) × 2 × π × 11
- Step 2: ≈ 5.8 cm
- Answer: 5.8
- Pause after each step and ask a student to say what comes next.
We do: guided practice · 10 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 sector has radius 4 cm and angle 30°. Find the arc length in cm, rounded to 1 decimal place. → 2.1Prompt: Arc length = (θ/360) × 2πr.
- Find the area of a sector with radius 3 cm and angle 120°. Round to 1 decimal place. → 9.4Prompt: Sector area = (θ/360) × πr².
You do: independent practice · 10 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 8 questions are on the student sheet below, with answers in the key.
Exit ticket · 5 min
- Two questions on their own. Sort answers into got it / nearly / not yet to plan the next lesson.
- A sector has radius 10 cm and angle 270°. Find the arc length in cm, rounded to 1 decimal place. → 47.1Prompt: Arc length = (θ/360) × 2πr.
- Find the area of a sector with radius 9 cm and angle 200°. Round to 1 decimal place. → 141.4Prompt: Sector area = (θ/360) × πr².
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: Area of a circle.
- 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
- Move on to: The unit circle and radians; Find the angle or radius from an arc length or sector area; Find the perimeter of a sector.
- 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-9.
Free lesson plan from eurekami.com/lesson-plan-builder