Math lesson plan · 10th grade (Year 11 in England) · 45 minutes
Label hypotenuse, opposite and adjacent sides
Trigonometry
CCSS HSG.SRT.C.6England: GCSE Foundation Geometry
Objective and success criteria
Students will: Label hypotenuse, opposite and adjacent sides.
- 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
Leads to: Choose sine, cosine or tangent for a problem
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). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- A rectangular park is 4 m by 12 m. How long is the diagonal path across it? Round to 1 decimal place. → 12.6Prompt: Spot the right angle: the unknown is the hypotenuse.
- A ladder leans against a wall. Its foot is 10 m from the wall and it reaches 9 m up the wall. How long is the ladder? Round to 1 decimal place. → 13.5Prompt: Spot the right angle: the unknown is the hypotenuse.
- A rectangular park is 5 m by 12 m. How long is the diagonal path across it? Round to 1 decimal place. → 13Prompt: Spot the right angle: the unknown is the hypotenuse.
Hook · 5 min
- Show a ramp or a ladder against a wall and ask how steep it is.
- Share the objective: Label hypotenuse, opposite and adjacent sides. 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: In triangle YPN, the right angle is at P. Using angle Y, which side is the adjacent?
- Step 1: YP
- Answer: YP
- 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.
- In triangle ZNR, the right angle is at N. Using angle Z, which side is the opposite? (NR / ZN / ZR) → NRPrompt: Sketch the triangle and mark the right angle.
- In triangle QYP, the right angle is at Y. Using angle Q, which side is the opposite? (QY / YP / QP) → YPPrompt: Sketch the triangle and mark the right angle.
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.
- In triangle YPR, the right angle is at P. Using angle Y, which side is the opposite? (YR / YP / PR) → PRPrompt: Sketch the triangle and mark the right angle.
- In triangle MPR, the right angle is at P. Using angle M, which side is the opposite? (MP / PR / MR) → PRPrompt: Sketch the triangle and mark the right angle.
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: Choose sine, cosine or tangent for a problem.
- 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