Math lesson plan · 10th grade (Year 11 in England) · 60 minutes
Use the exterior angle of a triangle
Geometry
CCSS HSG.CO.C.10CCSS 8.G.A.5England: GCSE Foundation Geometry
Objective and success criteria
Students will: Use the exterior angle of a triangle.
- 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: Classify triangles; angles in a triangle
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 · 6 min
- Quick retrieval from earlier learning (Classify triangles; angles in a triangle). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- A triangle has no equal sides. What type of triangle is it? (scalene / equilateral / isosceles / right-angled) → scalenePrompt: Equilateral: all sides equal. Isosceles: two equal. Scalene: none equal.
- An isosceles triangle has two equal base angles of 84° each. What is the third angle, in degrees? → 12Prompt: The three angles add to 180°.
- A triangle has all three sides equal. What type of triangle is it? (equilateral / scalene / isosceles / right-angled) → equilateralPrompt: Equilateral: all sides equal. Isosceles: two equal. Scalene: none equal.
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: Use the exterior angle of a triangle. 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: A triangle has interior angles 26° and 76°. One side is extended at the third vertex. What is the exterior angle there?
- Step 1: 26° + 76° = 102°
- Answer: 102
- 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.
- A triangle has interior angles 21° and 53°. One side is extended at the third vertex. What is the exterior angle there? → 74Prompt: An exterior angle equals the sum of the two opposite interior angles.
- An exterior angle of a triangle is (3x + 17)°. The two opposite interior angles are 2x° and 45°. Find x. → 28Prompt: Exterior angle = sum of the opposite interior angles.
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.
- An exterior angle of a triangle is (2x + 1)°. The two opposite interior angles are x° and 28°. Find x. → 27Prompt: Exterior angle = sum of the opposite interior angles.
- An exterior angle of a triangle is 73°. One of the two opposite interior angles is 49°. Find the other. → 24Prompt: An exterior angle equals the sum of the two opposite interior angles.
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: Classify triangles; angles in a triangle.
- 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