Math lesson plan · 8th grade (Year 9 in England) · 45 minutes
Exterior angles of regular polygons
Geometry
CCSS 8.G.A.5England: KS3 Geometry and measuresEngland: GCSE Foundation Geometry and measures
Objective and success criteria
Students will: Exterior angles of regular 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: Interior angles of polygons
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 · 5 min
- Quick retrieval from earlier learning (Interior angles of polygons). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- A 8-sided polygon has angles 134°, 129°, 141°, 133°, 135°, 129°, 136° and x°. Find x. → 143Prompt: The interior angles add to (8 − 2) × 180°.
- A 7-sided polygon has angles 135°, 125°, 132°, 127°, 123°, 129° and x°. Find x. → 129Prompt: The interior angles add to (7 − 2) × 180°.
- A 8-sided polygon has angles 139°, 141°, 131°, 134°, 134°, 130°, 135° and x°. Find x. → 136Prompt: The interior angles add to (8 − 2) × 180°.
Hook · 5 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: Exterior angles of regular polygons. Read the success criteria together.
I do: model it · 10 min
- Work through the example out loud, saying why you do each step, not just what you do.
- Example: What is each exterior angle of a regular polygon with 10 sides?
- Step 1: 360 ÷ 10 = 36°
- Answer: 36
- Pause after each step and ask a student to say what comes next.
We do: guided practice · 10 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 each exterior angle of a regular polygon with 9 sides? → 40Prompt: The exterior angles of any polygon add to 360°.
- Each exterior angle of a regular polygon is 12°. How many sides does it have? → 30Prompt: Divide 360° by the exterior angle to get the number of sides.
You do: independent practice · 10 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 · 5 min
- Two questions on their own. Sort answers into got it / nearly / not yet to plan the next lesson.
- What is each exterior angle of a regular polygon with 20 sides? → 18Prompt: The exterior angles of any polygon add to 360°.
- Each exterior angle of a regular polygon is 10°. How many sides does it have? → 36Prompt: Divide 360° by the exterior angle to get the number of sides.
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 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
- 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