Math lesson plan · 7th grade (Year 8 in England) · 45 minutes
Solve real problems with circles
Geometry
CCSS 7.G.B.4England: KS3 Geometry and measuresEngland: GCSE Foundation Geometry and measures
Objective and success criteria
Students will: Solve real problems with circles.
- 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: Link radius, diameter and circumference; Area of a circle
Leads to: the next skill in this area.
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 (Link radius, diameter and circumference; Area of a circle). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- A circle has circumference 52π cm. What is its diameter, in cm? → 52Prompt: C = πd = 2πr.
- A circle has circumference 52π cm. What is its radius, in cm? → 26Prompt: C = πd = 2πr.
- A circle has circumference 22π cm. What is its diameter, in cm? → 22Prompt: C = πd = 2πr.
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: Solve real problems with circles. 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: A bike wheel has diameter 50 cm. How far does the bike travel, in metres, when the wheel turns 91 times? Round to 1 decimal place.
- Step 1: π × 50 = 157.08 cm
- Step 2: × 91 = 14294.2 cm
- Step 3: ≈ 142.9 m
- Answer: 142.9
- 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.
- A bike wheel has diameter 72 cm. How far does the bike travel, in metres, when the wheel turns 98 times? Round to 1 decimal place. → 221.7Prompt: One turn moves the bike one circumference.
- A 24 cm pizza and a 32 cm pizza have the same thickness. How many times as much pizza is in the larger one? Round to 2 decimal places. → 1.78Prompt: Compare the areas, not the diameters.
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.
- A 24 cm pizza and a 30 cm pizza have the same thickness. How many times as much pizza is in the larger one? Round to 2 decimal places. → 1.56Prompt: Compare the areas, not the diameters.
- A bike wheel has diameter 60 cm. How far does the bike travel, in metres, when the wheel turns 89 times? Round to 1 decimal place. → 167.8Prompt: One turn moves the bike one circumference.
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: Link radius, diameter and circumference.
- 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
- 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-7.
Free lesson plan from eurekami.com/lesson-plan-builder