Math lesson plan · 11th grade (Year 12 in England) · 30 minutes
The unit circle and radians
Trigonometry
CCSS HSF.TF.A.1CCSS HSF.TF.A.2
Objective and success criteria
Students will: The unit circle and radians.
- 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: Exact trig values (0°, 30°, 45°, 60°, 90°); Arc length and sector area
Leads to: Graphs of sine and cosine: amplitude and period; Solve trigonometric equations; Trigonometric identities
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 (Exact trig values (0°, 30°, 45°, 60°, 90°); Arc length and sector area). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- What is the exact value of cos 90°? (0 / √3 / 1 / √2/2) → 0Prompt: Use the 30-60-90 triangle (sides 1, √3, 2) or the 45-45-90 triangle (sides 1, 1, √2).
- A sector has radius 14 cm and angle 150°. Find the arc length in cm, rounded to 1 decimal place. → 36.7Prompt: Arc length = (θ/360) × 2πr.
- Find the area of a sector with radius 6 cm and angle 200°. Round to 1 decimal place. → 62.8Prompt: Sector area = (θ/360) × πr².
Hook · 3 min
- Show a ramp or a ladder against a wall and ask how steep it is.
- Share the objective: The unit circle and radians. 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: Convert π/6 radians to degrees.
- Step 1: π/6 = 30°
- Answer: 30
- 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.
- Convert 150° to radians (in terms of π). (π/6 / 2π/3 / 5π/6 / π) → 5π/6Prompt: A half turn is π radians.
- Is cos 180° positive, zero or negative? (Positive / Zero / Negative) → NegativePrompt: On the unit circle, cos is the x-coordinate and sin is the y-coordinate.
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.
- Is sin 210° positive, zero or negative? (Positive / Zero / Negative) → NegativePrompt: On the unit circle, cos is the x-coordinate and sin is the y-coordinate.
- Convert 135° to radians (in terms of π). (π/3 / π/2 / 3π/4 / 2π/3) → 3π/4Prompt: A half turn is π radians.
Watch out for
- Mixing up opposite and adjacent sides.
- Calculator in radians instead of degrees.
Support and stretch
Support
- Review first: Exact trig values (0°, 30°, 45°, 60°, 90°).
- 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: Graphs of sine and cosine: amplitude and period; Solve trigonometric equations; Trigonometric identities.
- 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