Math lesson plan · 8th grade (Year 9 in England) · 30 minutes
Pythagoras' theorem
Geometry
CCSS 8.G.B.6CCSS 8.G.B.7England: GCSE Foundation GeometryEngland: GCSE Higher Geometry
Objective and success criteria
Students will: Pythagoras' theorem.
- 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: Square roots and cube roots; Classify triangles; angles in a triangle
Leads to: Distance and midpoint between points; Pythagoras and trigonometry in 3D; Trigonometric ratios: SOH CAH TOA
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 (Square roots and cube roots; Classify triangles; angles in a triangle). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- What is √324? → 18Prompt: Which number multiplied by itself gives this?
- √120 lies between which two whole numbers? (10 and 11 / 11 and 12 / 8 and 9 / 9 and 10) → 10 and 11Prompt: List the square numbers near it.
- What is √81? → 9Prompt: Which number multiplied by itself gives this?
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: Pythagoras' theorem. 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 ladder leans against a wall. Its foot is 8 m from the wall and it reaches 3 m up the wall. How long is the ladder? Round to 1 decimal place.
- Step 1: 8² + 3² = 73
- Step 2: √73 = 8.544…
- Step 3: ≈ 8.5 m
- Answer: 8.5
- 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 rectangular park is 3 m by 9 m. How long is the diagonal path across it? Round to 1 decimal place. → 9.5Prompt: Spot the right angle: the unknown is the hypotenuse.
- A rectangular park is 5 m by 7 m. How long is the diagonal path across it? Round to 1 decimal place. → 8.6Prompt: Spot the right angle: the unknown is 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.
- A rectangular park is 9 m by 2 m. How long is the diagonal path across it? Round to 1 decimal place. → 9.2Prompt: 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.
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: Square roots and cube roots.
- 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: Distance and midpoint between points; Pythagoras and trigonometry in 3D; Trigonometric ratios: SOH CAH TOA.
- 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