• 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 18 cm and one leg 7 cm. Find the other leg, to 1 decimal place. → 16.6Prompt: Subtract the square of the known leg from the square of the hypotenuse.
2. A right triangle has hypotenuse 15 cm and one leg 11 cm. Find the other leg, to 1 decimal place. → 10.2Prompt: Subtract the square of the known leg from the square of the hypotenuse.
3. A right triangle has hypotenuse 15 cm and one leg 8 cm. Find the other leg, to 1 decimal place. → 12.7Prompt: 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 103 m long and 56 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. → 42Prompt: Find the diagonal with Pythagoras.
2. A box is 18 cm by 18 cm by 21 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 75 m long and 52 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. → 36Prompt: Find the diagonal with Pythagoras.
2. A box is 4 cm by 6 cm by 12 cm. What is the length of the longest straight rod that fits inside, from one corner to the opposite corner, in cm? → 14Prompt: 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.