Math lesson plan · 7th grade (Year 8 in England) · 60 minutes
Describe cross-sections of solids
Geometry
CCSS 7.G.A.3England: KS3 Geometry and measures
Objective and success criteria
Students will: Describe cross-sections of solids.
- 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: Faces, edges and vertices of 3D shapes
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 (Faces, edges and vertices of 3D shapes). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- How many faces does a triangular pyramid (tetrahedron) have? → 4Prompt: Faces are flat surfaces, edges are where two faces meet, vertices are corners.
- How many edges does a cuboid have? → 12Prompt: Faces are flat surfaces, edges are where two faces meet, vertices are corners.
- How many faces does a triangular prism have? → 5Prompt: Faces are flat surfaces, edges are where two faces meet, vertices are corners.
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: Describe cross-sections of solids. 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 cube is sliced parallel to one face. What shape is the cut face (cross-section)?
- Step 1: The cross-section is a square.
- Answer: Square
- 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 square-based pyramid is sliced parallel to its base. What shape is the cut face (cross-section)? (Square / Pentagon / Circle / Triangle) → SquarePrompt: Imagine cutting the solid with a flat knife.
- A prism has a quadrilateral at each end. It is sliced parallel to the ends. How many sides does the cross-section have? → 4Prompt: A prism has the same cross-section all the way along.
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 cone standing on its base is sliced straight down through its tip. What shape is the cut face (cross-section)? (Rectangle / Circle / Pentagon / Triangle) → TrianglePrompt: Imagine cutting the solid with a flat knife.
- A prism has a octagon at each end. It is sliced parallel to the ends. How many sides does the cross-section have? → 8Prompt: A prism has the same cross-section all the way along.
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: Faces, edges and vertices of 3D shapes.
- 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