• Quick retrieval from earlier learning (Use Pythagoras to find a shorter side). Students answer on mini whiteboards.
• Show answers together and note who needs support in the main task.

1. A right triangle has hypotenuse 9 cm and one leg 7 cm. Find the other leg, to 1 decimal place. → 5.7Prompt: Subtract the square of the known leg from the square of the hypotenuse.
2. A right triangle has hypotenuse 13 cm and one leg 11 cm. Find the other leg, to 1 decimal place. → 6.9Prompt: Subtract the square of the known leg from the square of the hypotenuse.
3. A right triangle has hypotenuse 13 cm and one leg 2 cm. Find the other leg, to 1 decimal place. → 12.8Prompt: Subtract the square of the known leg from the square of the hypotenuse.

• 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 in real life: ladders, screens, shortcuts and boxes. Read the success criteria together.

• Work through the example out loud, saying why you do each step, not just what you do.
• Example: A rectangular park is 110 m long and 67 m wide. Instead of walking along two sides, you cut across the diagonal. How many metres shorter is the shortcut? Round to the nearest metre.
• Step 1: √(110² + 67²) ≈ 128.8 m
• Step 2: 177 − 128.8 ≈ 48 m
• Answer: 48
• Pause after each step and ask a student to say what comes next.

• Do these together. Students try each step on whiteboards before you reveal it.
• Use the hints as prompts rather than giving the answer.

1. A rectangular park is 92 m long and 36 m wide. Instead of walking along two sides, you cut across the diagonal. How many metres shorter is the shortcut? Round to the nearest metre. → 29Prompt: Find the diagonal with Pythagoras.
2. A box is 6 cm by 18 cm by 27 cm. What is the length of the longest straight rod that fits inside, from one corner to the opposite corner, in cm? → 33Prompt: First find the diagonal of the base with Pythagoras.

• 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.

• Two questions on their own. Sort answers into got it / nearly / not yet to plan the next lesson.

1. A rectangular park is 113 m long and 41 m wide. Instead of walking along two sides, you cut across the diagonal. How many metres shorter is the shortcut? Round to the nearest metre. → 34Prompt: Find the diagonal with Pythagoras.
2. A box is 4 cm by 4 cm by 7 cm. What is the length of the longest straight rod that fits inside, from one corner to the opposite corner, in cm? → 9Prompt: First find the diagonal of the base with Pythagoras.

Free online practice with hints and printable worksheets for this skill: eurekami.com/math/grade-8.