Math lesson plan · 10th grade (Year 11 in England) · 60 minutes
Circle theorems: angle at the centre and angle in a semicircle
Geometry
CCSS HSG.C.A.2England: GCSE Higher Geometry
Objective and success criteria
Students will: Circle theorems: angle at the centre and angle in a semicircle.
- 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: Circle theorems
Leads to: Name the circle theorem that justifies a step
Materials: Rulers and protractors, Squared or dotted paper, Shape cut-outs, Mini whiteboards and pens, Printed student sheet (below).
Warm-up · 6 min
- Quick retrieval from earlier learning (Circle theorems). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- A tangent meets a radius at the point of contact. A triangle formed with the centre has an angle of 48° at the centre. What is the angle between the tangent and the line to the centre (the third angle)? → 42Prompt: A tangent is perpendicular to the radius at the point of contact.
- Two angles at the circumference stand on the same arc. One is 46°. What is the other? → 46Prompt: Angles in the same segment are equal.
- The angle at the circumference is 43°, standing on the same arc as the angle at the centre. What is the angle at the centre? → 86Prompt: The angle at the centre is twice the angle at the circumference.
Hook · 6 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: Circle theorems: angle at the centre and angle in a semicircle. Read the success criteria together.
I do: model it · 12 min
- Work through the example out loud, saying why you do each step, not just what you do.
- Example: O is the centre of a circle. A, B and C are on the circle, with C on the major arc. ∠ACB = 49°. Find ∠AOB.
- Step 1: ∠AOB = 2 × 49° = 98°
- Answer: 98
- Pause after each step and ask a student to say what comes next.
We do: guided practice · 12 min
- Do these together. Students try each step on whiteboards before you reveal it.
- Use the hints as prompts rather than giving the answer.
- O is the centre of a circle. A, B and C are on the circle, with C on the major arc. ∠ACB = 58°. Find ∠AOB. → 116Prompt: Both angles stand on the same arc AB.
- O is the centre. ∠AOB = 68° and C is on the major arc. Find ∠ACB. → 34Prompt: Angle at centre = 2 × angle at circumference.
You do: independent practice · 17 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 · 7 min
- Two questions on their own. Sort answers into got it / nearly / not yet to plan the next lesson.
- O is the centre of a circle. A, B and C are on the circle, with C on the major arc. ∠ACB = 68°. Find ∠AOB. → 136Prompt: Both angles stand on the same arc AB.
- AB is a diameter of a circle and C is a point on the circle. ∠CAB = 36°. Find ∠CBA. → 54Prompt: What is the angle at C, in a semicircle?
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: Circle theorems.
- 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: Name the circle theorem that justifies a step.
- 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