Math lesson plan · 7th grade (Year 8 in England) · 30 minutes
Area and perimeter of semicircles and quarter circles
Geometry
CCSS 7.G.B.4England: KS3 Geometry and measuresEngland: GCSE Foundation Geometry and measures
Objective and success criteria
Students will: Area and perimeter of semicircles and quarter 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: Area of a circle; Link radius, diameter and circumference
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 · 4 min
- Quick retrieval from earlier learning (Area of a circle; Link radius, diameter and circumference). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- A circle has diameter 18 cm. Its area is kπ cm². What is k? → 81Prompt: Find the radius first: half the diameter.
- A circle has diameter 2 yd. Its area is kπ yd². What is k? → 1Prompt: Find the radius first: half the diameter.
- A circle has diameter 2 cm. Its area is kπ cm². What is k? → 1Prompt: Find the radius first: half the diameter.
Hook · 3 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: Area and perimeter of semicircles and quarter circles. Read the success criteria together.
I do: model it · 7 min
- Work through the example out loud, saying why you do each step, not just what you do.
- Example: A semicircle has diameter 8 cm. Find its perimeter (curved part + straight edge), to 1 decimal place.
- Step 1: π × 8 ÷ 2 = 12.566
- Step 2: + 8 = 20.566
- Step 3: ≈ 20.6 cm
- Answer: 20.6
- Pause after each step and ask a student to say what comes next.
We do: guided practice · 6 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 semicircle has diameter 22 cm. Find its perimeter (curved part + straight edge), to 1 decimal place. → 56.6Prompt: Curved part = half of π × d.
- A window is a 4 dm by 6 dm rectangle with a semicircle on top (the semicircle's diameter is the 4 dm side). Find the total area of glass in dm², to 1 decimal place. → 30.3Prompt: Rectangle area + semicircle area.
You do: independent practice · 7 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 6 questions are on the student sheet below, with answers in the key.
Exit ticket · 3 min
- Two questions on their own. Sort answers into got it / nearly / not yet to plan the next lesson.
- A window is a 12 dm by 9 dm rectangle with a semicircle on top (the semicircle's diameter is the 12 dm side). Find the total area of glass in dm², to 1 decimal place. → 164.5Prompt: Rectangle area + semicircle area.
- A semicircle has diameter 24 cm. Find its perimeter (curved part + straight edge), to 1 decimal place. → 61.7Prompt: Curved part = half of π × d.
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: Area of a circle.
- 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