Math lesson plan · 7th grade (Year 8 in England) · 60 minutes
Volume of triangular and other prisms
Geometry
CCSS 7.G.B.6England: KS3 Geometry and measuresEngland: GCSE Foundation Geometry and measures
Objective and success criteria
Students will: Volume of triangular and other 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 prisms; Area of triangles
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 · 6 min
- Quick retrieval from earlier learning (Volume of prisms; Area of triangles). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- A triangular prism has a triangular end with base 6 ft and height 2 ft. The prism is 15 ft long. What is its volume, in ft³? → 90Prompt: Volume of a prism = area of cross-section × length.
- A prism has a cross-section of area 39 ft² and length 11 ft. What is its volume, in ft³? → 429Prompt: Volume = cross-section area × length.
- A triangular prism has a triangular end with base 6 yd and height 12 yd. The prism is 14 yd long. What is its volume, in yd³? → 504Prompt: Volume of a prism = area of cross-section × length.
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 triangular and other 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 prism has a cross-section shaped like a pentagon with area 22 cm². It is 7 cm long. What is its volume, in cm³?
- Step 1: 22 × 7 = 154 cm³
- Answer: 154
- 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 prism has a cross-section shaped like a pentagon with area 36 cm². It is 19 cm long. What is its volume, in cm³? → 684Prompt: The shape of the cross-section does not matter once you know its area.
- A tent is a triangular prism. Its triangular end has base 12 m and height 9 m. The tent holds 648 m³ of air. How long is the tent, in m? → 12Prompt: Find the area of the triangle.
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 tent is a triangular prism. Its triangular end has base 4 m and height 4 m. The tent holds 80 m³ of air. How long is the tent, in m? → 10Prompt: Find the area of the triangle.
- A prism has a cross-section shaped like a trapezium with area 57 cm². It is 20 cm long. What is its volume, in cm³? → 1140Prompt: The shape of the cross-section does not matter once you know its area.
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 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
- 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