Math lesson plan · 8th grade (Year 9 in England) · 30 minutes
Test whether a triangle is right-angled
Geometry
CCSS 8.G.B.6England: KS3 Geometry and measuresEngland: GCSE Foundation Geometry and measures
Objective and success criteria
Students will: Test whether a triangle is right-angled.
- 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: the next skill in this area.
Materials: Rulers and protractors, Squared or dotted paper, Shape cut-outs, Mini whiteboards and pens, Printed student sheet (below).
Warm-up · 4 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.
- Hana 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.
- Fatima 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.
- Noah 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.
Hook · 3 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: Test whether a triangle is right-angled. 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: A triangle has sides 6, 8 and 10. Is it a right triangle?
- Step 1: 36 + 64 = 100
- Step 2: 10² = 100
- Step 3: Equal: right triangle.
- Answer: Yes
- 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.
- A triangle has sides 10, 24 and 27. Is it a right triangle? (Yes / No) → NoPrompt: Check whether the two shorter sides squared add up to the longest side squared.
- Kwame builds a garden frame with sides 16 dm and 30 dm and wants a perfect right-angled corner. How long should the diagonal brace be, in dm? → 34Prompt: A right angle makes the diagonal the hypotenuse.
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.
- Ines builds a garden frame with sides 8 dm and 15 dm and wants a perfect right-angled corner. How long should the diagonal brace be, in dm? → 17Prompt: A right angle makes the diagonal the hypotenuse.
- A triangle has sides 21, 72 and 77. Is it a right triangle? (Yes / No) → NoPrompt: Check whether the two shorter sides squared add up to the longest side squared.
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
- 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