Math lesson plan · 8th grade (Year 9 in England) · 45 minutes
Use Pythagoras to find the hypotenuse
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 the hypotenuse.
- 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; Square roots of fractions and decimals
Leads to: Use Pythagoras to find a shorter side; Test whether a triangle is right-angled; Distance between two points with Pythagoras
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 (Pythagoras' theorem; Square roots of fractions and decimals). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- Find √(81/64). → 9/8 (1 1/8)Prompt: Take the square root of the top and of the bottom.
- Find √(1/16). → 1/4Prompt: Take the square root of the top and of the bottom.
- Find √(64/121). → 8/11Prompt: Take the square root of the top and of the bottom.
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 the hypotenuse. 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: Diego says the hypotenuse of a right triangle with legs 6 and 8 is 14, because you add the legs. What is it really?
- Step 1: √(6² + 8²) = √100 = 10
- Answer: 10
- 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.
- Ben says the hypotenuse of a right triangle with legs 10 and 24 is 34, because you add the legs. What is it really? → 26Prompt: Pythagoras adds the SQUARES of the legs.
- Priya says the hypotenuse of a right triangle with legs 6 and 8 is 14, because you add the legs. What is it really? → 10Prompt: Pythagoras adds the SQUARES of the legs.
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.
- Ethan says the hypotenuse of a right triangle with legs 7 and 24 is 31, because you add the legs. What is it really? → 25Prompt: Pythagoras adds the SQUARES of the legs.
- Lucia says the hypotenuse of a right triangle with legs 16 and 30 is 46, because you add the legs. What is it really? → 34Prompt: Pythagoras adds the SQUARES of the legs.
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: Pythagoras' theorem.
- 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: Use Pythagoras to find a shorter side; Test whether a triangle is right-angled; Distance between two points with Pythagoras.
- 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