Math lesson plan · 8th grade (Year 9 in England) · 45 minutes
Use Pythagoras to find a shorter side
Geometry
CCSS 8.G.B.7England: KS3 Geometry and measuresEngland: GCSE Foundation Geometry and measures
Objective and success criteria
Students will: Use Pythagoras to find a shorter side.
- 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: Use Pythagoras to find the hypotenuse
Leads to: Pythagoras in real life: ladders, screens, shortcuts and boxes
Materials: Rulers and protractors, Squared or dotted paper, Shape cut-outs, Mini whiteboards and pens, Printed student sheet (below).
Warm-up · 5 min
- Quick retrieval from earlier learning (Use Pythagoras to find the hypotenuse). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- Luis says the hypotenuse of a right triangle with legs 5 and 12 is 17, because you add the legs. What is it really? → 13Prompt: Pythagoras adds the SQUARES of the legs.
- Felix says the hypotenuse of a right triangle with legs 5 and 12 is 17, because you add the legs. What is it really? → 13Prompt: Pythagoras adds the SQUARES of the legs.
- Ben says the hypotenuse of a right triangle with legs 8 and 15 is 23, because you add the legs. What is it really? → 17Prompt: Pythagoras adds the SQUARES of the legs.
Hook · 5 min
- Show a photo of a building, a tile pattern or a road sign and ask what shapes and angles students can spot.
- Share the objective: Use Pythagoras to find a shorter side. 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 right triangle has hypotenuse 17 cm and one leg 4 cm. Find the other leg, to 1 decimal place.
- Step 1: 289 − 16 = 273
- Step 2: √273 ≈ 16.5 cm
- Answer: 16.5
- 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 right triangle has hypotenuse 9 cm and one leg 6 cm. Find the other leg, to 1 decimal place. → 6.7Prompt: Subtract the square of the known leg from the square of the hypotenuse.
- A right triangle has hypotenuse 12 cm and one leg 5 cm. Find the other leg, to 1 decimal place. → 10.9Prompt: Subtract the square of the known leg from the square of the hypotenuse.
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 right triangle has hypotenuse 14 cm and one leg 8 cm. Find the other leg, to 1 decimal place. → 11.5Prompt: Subtract the square of the known leg from the square of the hypotenuse.
- A right triangle has hypotenuse 15 cm and one leg 4 cm. Find the other leg, to 1 decimal place. → 14.5Prompt: Subtract the square of the known leg from the square of the hypotenuse.
Watch out for
- Thinking a square turned on its corner is no longer a square.
- Reading the wrong scale on a protractor.
Support and stretch
Support
- Review first: Use Pythagoras to find the hypotenuse.
- Use concrete materials: rulers and protractors.
- 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 in real life: ladders, screens, shortcuts and boxes.
- 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-8.
Free lesson plan from eurekami.com/lesson-plan-builder