Math lesson plan · 8th grade (Year 9 in England) · 30 minutes
Interior and exterior angles of polygons
Geometry
CCSS 8.G.A.5England: KS3 GeometryEngland: GCSE Foundation Geometry
Objective and success criteria
Students will: Interior and exterior angles of polygons.
- 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; Polygons: sides and vertices
Leads to: Circle theorems; Interior angles of polygons
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 (Classify triangles; angles in a triangle; Polygons: sides and vertices). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- A triangle has one angle of 90°. What type of triangle is it? (scalene / isosceles / right-angled / equilateral) → right-angledPrompt: Equilateral: all sides equal. Isosceles: two equal. Scalene: none equal.
- A triangle has all three sides equal. What type of triangle is it? (right-angled / equilateral / isosceles / scalene) → equilateralPrompt: Equilateral: all sides equal. Isosceles: two equal. Scalene: none equal.
- A triangle has no equal sides. What type of triangle is it? (scalene / equilateral / right-angled / isosceles) → scalenePrompt: Equilateral: all sides equal. Isosceles: two equal. Scalene: none equal.
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: Interior and exterior angles of polygons. 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: What is the sum of the interior angles of a polygon with 12 sides, in degrees?
- Step 1: (12 − 2) × 180° = 1800°
- Answer: 1800
- 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.
- 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.
- Each exterior angle of a regular polygon is 45°. How many sides does it have? → 8Prompt: All the exterior angles add up to 360°.
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.
- Each exterior angle of a regular polygon is 72°. How many sides does it have? → 5Prompt: All the exterior angles add up to 360°.
- What is the sum of the interior angles of a polygon with 10 sides, in degrees? → 1440Prompt: Split the polygon into triangles from one vertex.
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
- Move on to: Circle theorems; Interior angles of polygons.
- 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-8.
Free lesson plan from eurekami.com/lesson-plan-builder