• Quick retrieval from earlier learning (Find missing lengths in similar triangles). Students answer on mini whiteboards.
• Show answers together and note who needs support in the main task.

1. Triangles ABC and PQR are similar, with AB matching PQ and BC matching QR. AB = 10 cm, PQ = 25 cm and BC = 10 cm. Find QR. → 25Prompt: Find the scale factor from the matching pair you know.
2. In triangle ABC, D is on AB and E is on AC with DE parallel to BC. AD = 7 cm, DB = 4 cm and DE = 9 cm. Find BC to 1 decimal place. → 14.1Prompt: Triangles ADE and ABC are similar (corresponding angles).
3. Lucia is 1.5 m tall and casts a 3 m shadow. At the same moment a tree casts a 21 m shadow. How tall is the tree, to 1 decimal place? → 10.5Prompt: The sun's rays make two similar right triangles.

• 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 length, area and volume scale factors. Read the success criteria together.

• Work through the example out loud, saying why you do each step, not just what you do.
• Example: Two similar shapes have lengths in the ratio 1 : 3. The smaller has area 14 cm². What is the area of the larger?
• Step 1: 14 × 3² = 14 × 9 = 126 cm²
• Answer: 126
• 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. Two similar shapes have lengths in the ratio 1 : 2. The smaller has area 23 cm². What is the area of the larger? → 92Prompt: Areas scale by the square of the length factor.
2. A model car is built to a length scale of 1 : 2 compared with a bigger model. The small model holds 25 cm³ of paint inside its body. How much would the bigger model hold? → 200Prompt: Volumes scale by the cube of the length factor.

• 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. Two similar shapes have lengths in the ratio 1 : 3. The smaller has area 8 cm². What is the area of the larger? → 72Prompt: Areas scale by the square of the length factor.
2. Two similar jugs have surface areas in the ratio 1 : 9. The smaller jug holds 5 ml. How much does the larger jug hold? → 135Prompt: Square-root the area ratio to get the length ratio.

Free online practice with hints and printable worksheets for this skill: eurekami.com/math/grade-10.