Math lesson plan · 10th grade (Year 11 in England) · 45 minutes
Find missing lengths in similar triangles
Geometry
CCSS HSG.SRT.B.5England: GCSE Foundation GeometryEngland: GCSE Higher Geometry
Objective and success criteria
Students will: Find missing lengths in similar triangles.
- 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: Similar shapes
Leads to: Use length, area and volume scale factors
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 (Similar shapes). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- Triangles ABC and DEF are similar. AB = 5 cm, BC = 3 cm and DE = 7.5 cm. Find EF in cm. → 4.5Prompt: Find the scale factor from the matching sides AB and DE.
- Two similar solids have a length scale factor of 3. The smaller has volume 5 cm³. What is the volume of the larger, in cm³? → 135Prompt: Volumes scale by the cube of the length scale factor.
- Triangles ABC and DEF are similar. AB = 10 cm, BC = 8 cm and DE = 15 cm. Find EF in cm. → 12Prompt: Find the scale factor from the matching sides AB and DE.
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: Find missing lengths in similar triangles. 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 PQR are similar, with AB matching PQ and BC matching QR. AB = 7 cm, PQ = 28 cm and BC = 10 cm. Find QR.
- Step 1: k = 28 ÷ 7 = 4
- Step 2: QR = 10 × 4 = 40 cm
- Answer: 40
- 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 PQR are similar, with AB matching PQ and BC matching QR. AB = 10 cm, PQ = 25 cm and BC = 11 cm. Find QR. → 27.5Prompt: Find the scale factor from the matching pair you know.
- In triangle ABC, D is on AB and E is on AC with DE parallel to BC. AD = 3 cm, DB = 3 cm and DE = 2 cm. Find BC. → 4Prompt: Triangles ADE and ABC are similar (corresponding angles).
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.
- Maya is 1.8 m tall and casts a 3 m shadow. At the same moment a tree casts a 16 m shadow. How tall is the tree, to 1 decimal place? → 9.6Prompt: The sun's rays make two similar right triangles.
- Triangles ABC and PQR are similar, with AB matching PQ and BC matching QR. AB = 12 cm, PQ = 24 cm and BC = 6 cm. Find QR. → 12Prompt: Find the scale factor from the matching pair you know.
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: Similar shapes.
- 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: Use length, area and volume scale factors.
- 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-10.
Free lesson plan from eurekami.com/lesson-plan-builder