Math lesson plan · 11th grade (Year 12 in England) · 30 minutes
Decide which rule solves a triangle
Trigonometry
CCSS HSG.SRT.D.10CCSS HSG.SRT.D.11England: GCSE Higher Geometry
Objective and success criteria
Students will: Decide which rule solves 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: Find a side with the sine rule; Find a side with the cosine rule
Leads to: the next skill in this area.
Materials: Scientific calculators, Protractors and rulers, Right-triangle diagrams, Mini whiteboards and pens, Printed student sheet (below).
Warm-up · 4 min
- Quick retrieval from earlier learning (Find a side with the sine rule; Find a side with the cosine rule). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- In triangle ABC, A = 67°, B = 80° and a = 6 cm. Find b to 1 decimal place. → 6.4Prompt: a/sin A = b/sin B.
- In triangle ABC, b = 6 cm, c = 20 cm and A = 113°. Find a to 1 decimal place. → 23Prompt: a² = b² + c² − 2bc cos A.
- In triangle ABC, A = 40°, C = 91° and a = 7 cm. Find b to 1 decimal place. → 8.2Prompt: You need angle B, opposite b. Use the angle sum first.
Hook · 3 min
- Show a ramp or a ladder against a wall and ask how steep it is.
- Share the objective: Decide which rule solves a triangle. 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: You know two sides and an angle opposite one of them; find another angle. Which is the most direct method?
- Step 1: Sine rule
- Answer: Sine rule
- 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.
- You know two sides and an angle opposite one of them; find another angle. Which is the most direct method? (Sine rule / Cosine rule / SOH CAH TOA (right angle)) → Sine rulePrompt: Is there a right angle? If so, basic trigonometry is enough.
- You know all three sides; find an angle. Which is the most direct method? (Sine rule / Cosine rule / SOH CAH TOA (right angle)) → Cosine rulePrompt: Is there a right angle? If so, basic trigonometry is enough.
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 5 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.
- You know two angles and a side; find another side. Which is the most direct method? (Sine rule / Cosine rule / SOH CAH TOA (right angle)) → Sine rulePrompt: Is there a right angle? If so, basic trigonometry is enough.
- You know all three sides; find an angle. Which is the most direct method? (Sine rule / Cosine rule / SOH CAH TOA (right angle)) → Cosine rulePrompt: Is there a right angle? If so, basic trigonometry is enough.
Watch out for
- Mixing up opposite and adjacent sides.
- Calculator in radians instead of degrees.
Support and stretch
Support
- Review first: Find a side with the sine rule.
- Use concrete materials: scientific calculators.
- 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-11.
Free lesson plan from eurekami.com/lesson-plan-builder