Math lesson plan · 9th grade (Year 10 in England) · 45 minutes
Similar shapes
Geometry
CCSS 8.G.A.4CCSS HSG.SRT.A.2CCSS HSG.SRT.B.5England: GCSE Foundation GeometryEngland: GCSE Higher Geometry
Objective and success criteria
Students will: Similar shapes.
- 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; Proportional relationships
Leads to: Trigonometric ratios: SOH CAH TOA; Decide whether two triangles are similar; Find missing lengths in similar triangles
Materials: Rulers and protractors, Squared or dotted paper, Shape cut-outs, Mini whiteboards and pens, Printed student sheet (below).
Warm-up · 5 min
- Quick retrieval from earlier learning (Scale factors and enlargement; Proportional relationships). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- A 10 cm by 6 cm rectangle is enlarged by scale factor 2. What is the new width in cm? → 12Prompt: Every length is multiplied by the scale factor.
- Is this relationship proportional? x: 3, 6, 9 → y: 18, 36, 54 (Yes, proportional / No, not proportional) → Yes, proportionalPrompt: Find y ÷ x for each pair.
- A side of 2 cm becomes 10 cm after an enlargement. What is the scale factor? → 5Prompt: Scale factor = new length ÷ old length.
Hook · 5 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: Similar shapes. Read the success criteria together.
I do: model it · 10 min
- Work through the example out loud, saying why you do each step, not just what you do.
- Example: Triangles ABC and DEF are similar. AB = 3 cm, BC = 8 cm and DE = 9 cm. Find EF in cm.
- Step 1: k = 9 ÷ 3 = 3
- Step 2: EF = 8 × 3 = 24 cm
- Answer: 24
- Pause after each step and ask a student to say what comes next.
We do: guided practice · 10 min
- Do these together. Students try each step on whiteboards before you reveal it.
- Use the hints as prompts rather than giving the answer.
- Triangles ABC and DEF are similar. AB = 9 cm, BC = 4 cm and DE = 18 cm. Find EF in cm. → 8Prompt: Find the scale factor from the matching sides AB and DE.
- Two similar shapes have a length scale factor of 5. The smaller has area 11 cm². What is the area of the larger, in cm²? → 275Prompt: Areas scale by the square of the length scale factor.
You do: independent practice · 10 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 · 5 min
- Two questions on their own. Sort answers into got it / nearly / not yet to plan the next lesson.
- Triangles ABC and DEF are similar. AB = 5 cm, BC = 7 cm and DE = 15 cm. Find EF in cm. → 21Prompt: Find the scale factor from the matching sides AB and DE.
- Two similar shapes have a length scale factor of 4. The smaller has area 7 cm². What is the area of the larger, in cm²? → 112Prompt: Areas scale by the square of the length 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: Trigonometric ratios: SOH CAH TOA; Decide whether two triangles are similar; Find missing lengths in similar triangles.
- 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-9.
Free lesson plan from eurekami.com/lesson-plan-builder