You will learn
- Count faces, edges and vertices.
- Match nets to solids.
- Picture views.
- Visualise rotations.
Version 0.1 · published for early use · expert review pending Standards alignment: pending verification. Not yet reviewed against the Courseversity scorecard.
Student lesson
Words to know
Flat surface.
Where faces meet.
Corner.
Flat pattern of a solid.
1. Discover: unfold a box
If you cut a cardboard box along its edges and lay it flat, what do you get?
2. Understand: 3D shapes
- A cube has 6 faces, 12 edges and 8 vertices.
- A triangular prism has 5 faces, 9 edges, 6 vertices.
- A net of a cube has 6 squares joined edge to edge.
- A 2 × 2 × 2 block of small cubes holds 8 cubes.
3. Explore: count
You need a box.
- Count faces.
- Count edges.
- Count corners.
- Check with Euler.
Think about it: what did you notice?
6, 12, 8.
4. Practise
Guided practice
Question 1. Faces of a cube?
6.
Question 2. Edges of a cube?
12.
Question 3. Vertices of a cube?
8.
Independent practice
- Faces of a triangular prism
- Edges of a triangular prism
- Vertices of a triangular prism
- Squares in a cube net
- Cubes in a 2 × 2 × 2 block
Answers are in the answer key below. Try first, then check.
5. Apply: everyday mathematics
How many small cubes fill a 2 × 2 × 2 box?
Show a sample answer
8.
6. Common mistake
Fix: Count all six.
7. Check and master
Answer all questions. You will see feedback after each one.
Your result appears here after you answer every question.
8. Key takeaways
- Count carefully.
- Nets fold into solids.
- Volume counts cubes.
9. Next lesson
Next lesson: Metric conversions. Keep going with the next idea in this course.
Printable worksheet
- Faces of a triangular prism
- Edges of a triangular prism
- Vertices of a triangular prism
- Squares in a cube net
- Cubes in 2 × 2 × 2
Homework
Build a cube net from paper and fold it.
Answer key and marking scheme
| Question | Expected response | Marks |
|---|---|---|
| Faces of a triangular prism | 5 | 2 |
| Edges of a triangular prism | 9 | 2 |
| Vertices of a triangular prism | 6 | 2 |
| Squares in a cube net | 6 | 2 |
| Cubes in 2 × 2 × 2 | 8 | 2 |
| Total | 10 |
Practice answers: Worksheet: 1 5; 2 9; 3 6; 4 6; 5 8.
Quiz answers: 1 A, 2 B, 3 C, 4 A, 5 B, challenge C.
Mastery and remediation
| Objective | Bronze (Developing) | Silver (Proficient) | Gold (Advanced) |
|---|---|---|---|
| O1 Count faces, edges and vertices | Shows this with help from an adult or a picture | Does this independently and explains how they know | Explains it clearly and uses it in a new situation |
| O2 Match nets to solids | Shows this with help from an adult or a picture | Does this independently and explains how they know | Explains it clearly and uses it in a new situation |
| O3 Picture views | Shows this with help from an adult or a picture | Does this independently and explains how they know | Explains it clearly and uses it in a new situation |
| O4 Visualise rotations | Shows this with help from an adult or a picture | Does this independently and explains how they know | Explains it clearly and uses it in a new situation |
Proposed Courseversity thresholds for this page: Bronze = at least 3 of 5 core questions correct; Silver = all 5; Gold = all 5 plus the challenge. A badge is never a full record of progress.
If a learner struggles
- Find the misconception: Counting hidden faces. Count all six.
- Explain another way: use real objects first, then pictures.
- Show a simpler example: Shape names.
- Guided practice: work through one example together and let the learner try the next one.
- Reassess: use the quiz again or the worksheet.
- Move on when the learner shows Silver-level evidence independently.
Teacher package
1–5. Objectives, prerequisites, materials, preparation, duration
Lesson objectives. Learners will: count faces, edges and vertices; match nets to solids; picture views; visualise rotations.
Prerequisite knowledge. Lesson 5.
Materials. Counters (stones, seeds or bottle tops), paper, pencils, board or chalkboard. Low-resource options: use stones, seeds, sticks, bottle tops or drawings in the sand or on the board instead of printed materials.
Preparation. Gather the counters and draw the example pictures on the board before the lesson.
Suggested duration. 35–45 minutes.
6–9. Teaching procedure, explanation notes, guided and independent activities
Introduction (5 min). Start with the Discover situation and let learners suggest ideas before you teach.
Explanation (10 min). Teach the Understand section with real objects first, then pictures, then symbols and words.
Guided activity (10 min). You need a box. Learners follow the Explore steps in pairs.
Independent activity (10 min). Learners complete the independent practice and the worksheet.
Assessment and reflection (5 min). Ask each learner to say one thing they learned and how they know it.
Teacher explanation notes. Use the concrete, pictorial, abstract order: real objects first, then pictures, then symbols and words. Return to real objects whenever a learner needs support.
10–12. Differentiation, formative assessment, common misconceptions
Support. Use real objects and work with a partner; say each step aloud together. Extension. Ask learners to make up their own example and explain it to a partner.
Formative assessment. Listen to learner explanations, ask “how do you know?”, and check the independent work.
Misconceptions. Counting hidden faces. Count all six.
13–15. Assessment questions, answer keys, marking scheme
Use the quiz and worksheet on this page. The 10-mark scheme and all answers are in the answer key above. Re-check every answer and the marking scheme before publication.
16–19. Remediation, enrichment, homework, teacher reflection
Remediation. Shape names. Enrichment. Invite learners to find or create three more examples at home or in the classroom and explain them. Homework. See above.
Teacher reflection. After teaching, record: which concepts learners understood; which misconceptions occurred; which activities worked; which learners need more practice; and what to improve next time.
Sources and standards
Alignment is pending verification and no external endorsement is claimed. Reference starting points named in the Courseversity standard: Common Core State Standards for Mathematics, Cambridge Primary and the IB Primary Years Programme. Specific standard codes will be added once checked against the official documents.