Math lesson plan · 10th grade (Year 11 in England) · 45 minutes
Exact trig values (0°, 30°, 45°, 60°, 90°)
Trigonometry
CCSS HSF.TF.A.3England: GCSE Higher Geometry
Objective and success criteria
Students will: Exact trig values (0°, 30°, 45°, 60°, 90°).
- 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: Trigonometric ratios: SOH CAH TOA; Simplify surds (radicals)
Leads to: The unit circle and radians; Find exact side lengths using 30°, 45° and 60°; Read exact coordinates on the unit circle
Materials: Scientific calculators, Protractors and rulers, Right-triangle diagrams, Mini whiteboards and pens, Printed student sheet (below).
Warm-up · 5 min
- Quick retrieval from earlier learning (Trigonometric ratios: SOH CAH TOA; Simplify surds (radicals)). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- Simplify √75. It can be written as k√3. What is k? → 5Prompt: Look for the largest square number that divides it.
- Simplify √294. It can be written as k√6. What is k? → 7Prompt: Look for the largest square number that divides it.
- Simplify √28. It can be written as k√7. What is k? → 2Prompt: Look for the largest square number that divides it.
Hook · 5 min
- Show a ramp or a ladder against a wall and ask how steep it is.
- Share the objective: Exact trig values (0°, 30°, 45°, 60°, 90°). 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 the exact value of tan 30°?
- Step 1: tan 30° = √3/3
- Answer: √3/3
- 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 the exact value of sin 0°? (1 / 0 / √3/2 / √3/3) → 0Prompt: Use the 30-60-90 triangle (sides 1, √3, 2) or the 45-45-90 triangle (sides 1, 1, √2).
- What is the exact value of sin 60°? (√3/3 / √3/2 / 0 / 1/2) → √3/2Prompt: Use the 30-60-90 triangle (sides 1, √3, 2) or the 45-45-90 triangle (sides 1, 1, √2).
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 the exact value of sin 30°? (√3/3 / 1/2 / 0 / √3) → 1/2Prompt: Use the 30-60-90 triangle (sides 1, √3, 2) or the 45-45-90 triangle (sides 1, 1, √2).
- What is the exact value of sin 60°? (1 / √3/3 / 1/2 / √3/2) → √3/2Prompt: Use the 30-60-90 triangle (sides 1, √3, 2) or the 45-45-90 triangle (sides 1, 1, √2).
Watch out for
- Mixing up opposite and adjacent sides.
- Calculator in radians instead of degrees.
Support and stretch
Support
- Review first: Trigonometric ratios: SOH CAH TOA.
- 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
- Move on to: The unit circle and radians; Find exact side lengths using 30°, 45° and 60°; Read exact coordinates on the unit circle.
- 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