Math lesson plan · 10th grade (Year 11 in England) · 30 minutes
Find the angle or radius from an arc length or sector area
Geometry
CCSS HSG.C.B.5England: GCSE Higher Geometry
Objective and success criteria
Students will: Find the angle or radius from an arc length or 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: Arc length and sector area
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). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- A sector has radius 15 cm and angle 135°. Find the arc length in cm, rounded to 1 decimal place. → 35.3Prompt: Arc length = (θ/360) × 2πr.
- Find the area of a sector with radius 10 cm and angle 200°. Round to 1 decimal place. → 174.5Prompt: Sector area = (θ/360) × πr².
- A sector has radius 9 cm and angle 210°. Find the arc length in cm, rounded to 1 decimal place. → 33Prompt: Arc length = (θ/360) × 2πr.
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 angle or radius from an arc length or sector area. 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 sector of a circle with radius 3 cm has an arc length of 3Ï€ cm. Find the angle of the sector in degrees.
- Step 1: θ/360 = 3π ÷ 6π
- Step 2: θ = 180°
- Answer: 180
- 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 sector of a circle with radius 3 cm has an arc length of 1π cm. Find the angle of the sector in degrees. → 60Prompt: Arc length = (θ/360) × 2πr.
- A sector of radius 6 cm has area 18π cm². Find the angle of the sector in degrees. → 180Prompt: Sector area = (θ/360) × πr².
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 sector has angle 90° and arc length 2π cm. Find the radius. → 4Prompt: Arc length = (θ/360) × 2πr.
- A sector of radius 4 cm has area 2π cm². Find the angle of the sector in degrees. → 45Prompt: 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: 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-10.
Free lesson plan from eurekami.com/lesson-plan-builder