Math lesson plan · 8th grade (Year 9 in England) · 45 minutes
Volume of spheres and hemispheres
Geometry
CCSS 8.G.C.9England: KS3 Geometry and measuresEngland: GCSE Foundation Geometry and measures
Objective and success criteria
Students will: Volume of spheres and hemispheres.
- 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: Volume of a cylinder
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 (Volume of a cylinder). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- A cylinder has radius 9 cm and height 8 cm. Find its volume in cm³, to 1 decimal place. → 2035.8Prompt: A cylinder is a prism with a circular cross-section.
- A cylinder has radius 6 m and height 6 m. Its volume is kπ m³. What is k? → 216Prompt: V = πr²h. Leave π as a symbol.
- A water bottle is a cylinder 12 cm across and 8 cm tall. How many litres does it hold? (1 litre = 1000 cm³.) Round to 2 decimal places. → 0.9Prompt: Radius = 12 ÷ 2.
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: Volume of spheres and hemispheres. 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 sphere has radius 3 cm. Its volume is kπ cm³. What is k?
- Step 1: ⁴⁄₃ × 27 = 36
- Step 2: 36π cm³
- Answer: 36
- 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 sphere has radius 12 cm. Its volume is kπ cm³. What is k? → 2304Prompt: V = ⁴⁄₃πr³.
- Find the volume of a hemisphere (half a sphere) with radius 4 cm, to 1 decimal place. → 134Prompt: V(sphere) = ⁴⁄₃πr³.
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 sphere has radius 9 cm. Its volume is kπ cm³. What is k? → 972Prompt: V = ⁴⁄₃πr³.
- A table-tennis ball has a diameter of about 4 cm. Estimate the volume of air inside, in cm³, to the nearest whole number. → 34Prompt: Halve the diameter to get the radius.
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: Volume of a cylinder.
- 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-8.
Free lesson plan from eurekami.com/lesson-plan-builder