Math lesson plan · 8th grade (Year 9 in England) · 60 minutes
Use the exterior angle of a triangle
Geometry
CCSS 8.G.A.5England: KS3 Geometry and measuresEngland: GCSE Foundation Geometry and measures
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: Missing angles in triangles, including isosceles and algebra
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 (Missing angles in triangles, including isosceles and algebra). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- The angles of a triangle are 3x, 4x and 5x. What is the largest angle, in degrees? → 75Prompt: They add to 180°: 12x = 180.
- In a triangle, two angles are 68° and 75°. One side is extended to make an exterior angle next to the third angle. How big is that exterior angle? → 143Prompt: Find the third angle first, then use the straight line.
- The angles of a triangle are x, 3x and 5x. What is the largest angle, in degrees? → 100Prompt: They add to 180°: 9x = 180.
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: An exterior angle of a triangle is 106°. One of the two opposite interior angles is 44°. Find the other opposite interior angle.
- Step 1: 106° − 44° = 62°
- Answer: 62
- 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.
- An exterior angle of a triangle is 92°. One of the two opposite interior angles is 26°. Find the other opposite interior angle. → 66Prompt: The exterior angle equals the sum of the two opposite interior angles.
- In a triangle the two opposite interior angles are (x + 9)° and (2x + 12)°. The exterior angle is 108°. Find x. → 29Prompt: Exterior angle = sum of the two 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.
- In a triangle the two opposite interior angles are (x + 12)° and (2x + 11)°. The exterior angle is 104°. Find x. → 27Prompt: Exterior angle = sum of the two opposite interior angles.
- An exterior angle of a triangle is 79°. One of the two opposite interior angles is 30°. Find the other opposite interior angle. → 49Prompt: The 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: Missing angles in triangles, including isosceles and algebra.
- 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