Math lesson plan · 7th grade (Year 8 in England) · 60 minutes
Volume of prisms
Geometry
CCSS 7.G.B.6England: KS3 GeometryEngland: GCSE Foundation Geometry
Objective and success criteria
Students will: Volume of prisms.
- 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 cuboids (rectangular prisms); Area of triangles
Leads to: Volume of cylinders, cones and spheres; Volume of triangular and other prisms; Volume of a cylinder
Materials: Rulers and protractors, Squared or dotted paper, Shape cut-outs, Mini whiteboards and pens, Printed student sheet (below).
Warm-up · 6 min
- Quick retrieval from earlier learning (Volume of cuboids (rectangular prisms); Area of triangles). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- A box is 10 m long, 7 m wide and 3 m high. What is its volume, in m³? → 210Prompt: Volume = length × width × height.
- A box is 10 ft long, 8 ft wide and 5 ft high. What is its volume, in ft³? → 400Prompt: Volume = length × width × height.
- A box is 8 ft long, 2 ft wide and 3 ft high. What is its volume, in ft³? → 48Prompt: Volume = length × width × height.
Hook · 6 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 prisms. Read the success criteria together.
I do: model it · 12 min
- Work through the example out loud, saying why you do each step, not just what you do.
- Example: A triangular prism has a triangular end with base 10 ft and height 12 ft. The prism is 4 ft long. What is its volume, in ft³?
- Step 1: ½ × 10 × 12 = 60
- Step 2: 60 × 4 = 240 ft³
- Answer: 240
- Pause after each step and ask a student to say what comes next.
We do: guided practice · 12 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 triangular prism has a triangular end with base 3 cm and height 2 cm. The prism is 9 cm long. What is its volume, in cm³? → 27Prompt: Volume of a prism = area of cross-section × length.
- A prism has a cross-section of area 32 cm² and length 16 cm. What is its volume, in cm³? → 512Prompt: Volume = cross-section area × length.
You do: independent practice · 17 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 · 7 min
- Two questions on their own. Sort answers into got it / nearly / not yet to plan the next lesson.
- A prism has a cross-section of area 52 yd² and length 17 yd. What is its volume, in yd³? → 884Prompt: Volume = cross-section area × length.
- A triangular prism has a triangular end with base 7 m and height 8 m. The prism is 3 m long. What is its volume, in m³? → 84Prompt: Volume of a prism = area of cross-section × length.
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 cuboids (rectangular prisms).
- 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: Volume of cylinders, cones and spheres; Volume of triangular and other prisms; Volume of a cylinder.
- 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