• Quick retrieval from earlier learning (Dilations (enlargements) from the origin). Students answer on mini whiteboards.
• Show answers together and note who needs support in the main task.

1. Dilate (2, 2) by a scale factor of 3 with centre the origin. Type the image like (2, −3). → (6, 6)Prompt: Multiply both coordinates by the scale factor.
2. A(−16, −4) is dilated about the origin to A′(−24, −6). What is the scale factor? Give a fraction or decimal. → 3/2 (1 1/2)Prompt: Divide an image coordinate by the matching original coordinate.
3. A 6 by 6 rectangle is dilated by scale factor 2. What is the area of the image? → 144Prompt: Every length is multiplied by the scale factor.

• 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: Find missing sides in similar shapes. Read the success criteria together.

• Work through the example out loud, saying why you do each step, not just what you do.
• Example: Two triangles are similar. The small one has sides 7 cm and 8 cm. The matching side to 7 cm on the large triangle is 14 cm. How long is the side matching 8 cm?
• Step 1: k = 2
• Step 2: 8 × 2 = 16 cm
• Answer: 16
• 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 triangles are similar. The small one has sides 6 cm and 9 cm. The matching side to 6 cm on the large triangle is 24 cm. How long is the side matching 9 cm? → 36Prompt: Find the scale factor from the matching pair.
2. Yuki is 1.5 m tall and casts a 2 m shadow. At the same moment a tree casts a 11 m shadow. How tall is the tree, in m? Round to 1 decimal place if needed. → 8.3Prompt: The sun's rays make similar triangles.

• 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.

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

1. Ben is 2.5 m tall and casts a 1.5 m shadow. At the same moment a tree casts a 20 m shadow. How tall is the tree, in m? Round to 1 decimal place if needed. → 33.3Prompt: The sun's rays make similar triangles.
2. Two triangles are similar. The small one has sides 3 cm and 2 cm. The matching side to 3 cm on the large triangle is 4.5 cm. How long is the side matching 2 cm? → 3Prompt: Find the scale factor from the matching pair.

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