Math lesson plan · 8th grade (Year 9 in England) · 60 minutes
Dilations (enlargements) from the origin
Geometry
CCSS 8.G.A.3CCSS 8.G.A.4England: KS3 Geometry and measuresEngland: GCSE Foundation Geometry and measures
Objective and success criteria
Students will: Dilations (enlargements) from the origin.
- 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: Scale factors and enlargement; Coordinates in all four quadrants
Leads to: Find missing sides in similar shapes
Materials: Rulers and protractors, Squared or dotted paper, Shape cut-outs, Mini whiteboards and pens, Printed student sheet (below).
Warm-up · 6 min
- Quick retrieval from earlier learning (Scale factors and enlargement; Coordinates in all four quadrants). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- A 6 cm by 12 cm rectangle is enlarged by scale factor 4. What is the new length in cm? → 24Prompt: Every length is multiplied by the scale factor.
- A side of 9 cm becomes 45 cm after an enlargement. What is the scale factor? → 5Prompt: Scale factor = new length ÷ old length.
- A 6 cm by 16 cm rectangle is enlarged by scale factor 0.5. What is the new width in cm? → 8Prompt: Every length is multiplied by the scale factor.
Hook · 6 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: Dilations (enlargements) from the origin. Read the success criteria together.
I do: model it · 12 min
- Work through the example out loud, saying why you do each step, not just what you do.
- Example: Dilate (−3, −5) by a scale factor of 4 with centre the origin. Type the image like (2, −3).
- Step 1: (−12, −20)
- Answer: (−12, −20)
- Pause after each step and ask a student to say what comes next.
We do: guided practice · 12 min
- Do these together. Students try each step on whiteboards before you reveal it.
- Use the hints as prompts rather than giving the answer.
- Dilate (5, 5) by a scale factor of 4 with centre the origin. Type the image like (2, −3). → (20, 20)Prompt: Multiply both coordinates by the scale factor.
- A(−16, 16) is dilated about the origin to A′(−4, 4). What is the scale factor? Give a fraction or decimal. → 1/4Prompt: Divide an image coordinate by the matching original coordinate.
You do: independent practice · 17 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 8 questions are on the student sheet below, with answers in the key.
Exit ticket · 7 min
- Two questions on their own. Sort answers into got it / nearly / not yet to plan the next lesson.
- A(4, −8) is dilated about the origin to A′(6, −12). 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.
- Dilate (−1, 5) by a scale factor of 3 with centre the origin. Type the image like (2, −3). → (−3, 15)Prompt: Multiply both coordinates by the scale factor.
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: Scale factors and enlargement.
- 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: Find missing sides in similar shapes.
- 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