Math lesson plan · 10th grade (Year 11 in England) · 45 minutes
Trigonometric ratios: SOH CAH TOA
Trigonometry
CCSS HSG.SRT.C.6CCSS HSG.SRT.C.8England: GCSE Foundation GeometryEngland: GCSE Higher Geometry
Objective and success criteria
Students will: Trigonometric ratios: SOH CAH TOA.
- 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: Pythagoras' theorem; Similar shapes
Leads to: Pythagoras and trigonometry in 3D; Find angles with inverse trig; Exact trig values (0°, 30°, 45°, 60°, 90°)
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 (Pythagoras' theorem; Similar shapes). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- Triangles ABC and DEF are similar. AB = 5 cm, BC = 12 cm and DE = 15 cm. Find EF in cm. → 36Prompt: Find the scale factor from the matching sides AB and DE.
- Triangles ABC and DEF are similar. AB = 5 cm, BC = 5 cm and DE = 15 cm. Find EF in cm. → 15Prompt: Find the scale factor from the matching sides AB and DE.
- Triangles ABC and DEF are similar. AB = 4 cm, BC = 4 cm and DE = 12 cm. Find EF in cm. → 12Prompt: Find the scale factor from the matching sides AB and DE.
Hook · 5 min
- Show a ramp or a ladder against a wall and ask how steep it is.
- Share the objective: Trigonometric ratios: SOH CAH TOA. 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: A ramp rises at 64° over a horizontal distance of 10 m. How high does it rise? Give 1 decimal place.
- Step 1: 10 × tan 64° = 20.503
- Step 2: ≈ 20.5 m
- Answer: 20.5
- 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.
- A ramp rises at 33° over a horizontal distance of 16 m. How high does it rise? Give 1 decimal place. → 10.4Prompt: You know the adjacent side and want the opposite: use tan.
- A ramp rises at 63° over a horizontal distance of 6 m. How high does it rise? Give 1 decimal place. → 11.8Prompt: You know the adjacent side and want the opposite: use tan.
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.
- A ramp rises at 41° over a horizontal distance of 23 m. How high does it rise? Give 1 decimal place. → 20Prompt: You know the adjacent side and want the opposite: use tan.
- A ramp rises at 50° over a horizontal distance of 24 m. How high does it rise? Give 1 decimal place. → 28.6Prompt: You know the adjacent side and want the opposite: use tan.
Watch out for
- Mixing up opposite and adjacent sides.
- Calculator in radians instead of degrees.
Support and stretch
Support
- Review first: Pythagoras' theorem.
- 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: Pythagoras and trigonometry in 3D; Find angles with inverse trig; Exact trig values (0°, 30°, 45°, 60°, 90°).
- 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