Math lesson plan · 10th grade (Year 11 in England) · 30 minutes
Circle theorems
Geometry
CCSS HSG.C.A.2CCSS HSG.C.A.3England: GCSE Higher Geometry
Objective and success criteria
Students will: Circle theorems.
- 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: Interior and exterior angles of polygons; Angles with parallel lines
Leads to: Circle theorems: angle at the centre and angle in a semicircle; Circle theorems: cyclic quadrilaterals and angles in the same segment; Circle theorems: tangents and radii
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 (Interior and exterior angles of polygons; Angles with parallel lines). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- A line crosses two parallel lines. One angle is 32°. What is the corresponding angle to it, in degrees? → 32Prompt: Alternate angles are equal (Z shape). Corresponding angles are equal (F shape).
- What is the sum of the interior angles of a polygon with 7 sides, in degrees? → 900Prompt: Split the polygon into triangles from one vertex.
- A line crosses two parallel lines. One angle is 114°. What is the alternate angle to it, in degrees? → 114Prompt: Alternate angles are equal (Z shape). Corresponding angles are equal (F shape).
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: Circle theorems. 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: ABCD is a cyclic quadrilateral. Angle A = 110°. What is angle C?
- Step 1: Opposite angles in a cyclic quadrilateral add up to 180°.
- Step 2: 70°
- Answer: 70
- 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.
- The angle at the circumference is 39°, standing on the same arc as the angle at the centre. What is the angle at the centre? → 78Prompt: The angle at the centre is twice the angle at the circumference.
- Two angles at the circumference stand on the same arc. One is 72°. What is the other? → 72Prompt: Angles in the same segment are equal.
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.
- Two angles at the circumference stand on the same arc. One is 43°. What is the other? → 43Prompt: Angles in the same segment are equal.
- ABCD is a cyclic quadrilateral. Angle A = 110°. What is angle C? → 70Prompt: Opposite angles in a cyclic quadrilateral add up to 180°.
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: Interior and exterior angles of polygons.
- 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: Circle theorems: angle at the centre and angle in a semicircle; Circle theorems: cyclic quadrilaterals and angles in the same segment; Circle theorems: tangents and radii.
- 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