You will learn
- Count unit cubes.
- Use V = l × w × h.
- Find a missing dimension.
- Solve volume problems.
Version 0.2 · expanded edition · built from cited public sources Content is based on the official frameworks and sources listed under Sources and standards. No official endorsement is claimed. Written in the style of common primary school assessments. No exam result is promised.
Student lesson
- Volume is the space inside a solid.
- Volume of a prism = l × w × h.
- Volume = base area × height.
- Volume is in cubic units.
Words to know
Space inside.
Unit of volume.
Solid with equal cross-section.
Length, width or height.
1. Discover: filling a box
A box is 5 cm long, 4 cm wide and 3 cm high. How many 1 cm cubes fill it?
2. Understand: volume
- V = l × w × h = 5 × 4 × 3 = 60 cm³.
- 8 × 3 × 2 = 48; a 10 cm cube holds 10 × 10 × 10 = 1,000.
- Base area 30 cm² and volume 90 cm³ give height 3 cm.
- Volume uses cubic units: cm³.
Idea 1: Formula
5 by 4 by 3: 5 × 4 × 3 = 60 cm³. 8 by 3 by 2: 48 cm³.
Idea 2: Cube
Cube of side 10: 10 × 10 × 10 = 1,000 cm³.
Idea 3: Missing
V = 90, base area 30: h = 90 ÷ 30 = 3 cm.
Why cubic? We count unit cubes that fill the space.
3. Worked examples
Example 1 (I show you): Volume
5 by 4 by 3
- 5 × 4 = 20.
- 20 × 3.
Answer: 60 cm³
Example 2 (We do it together): Cube
Side 10
- 10 × 10 × 10.
Answer: 1,000 cm³
Example 3 (You try): Height
V = 90, base 30
Show the steps and answer
- 90 ÷ 30.
Answer: 3 cm
Did you know?
1 cm³ holds exactly 1 mL of water.
Why this matters
Volume tells how much a box, tank or room can hold.
4. Explore: volume
You need paper.
- Multiply l × w.
- Multiply by h.
- Write cm³.
- Check.
Think about it: what did you notice?
60 cm³.
5. Practise
Say it in a sentence
Use these starters when you talk about the lesson. Say them out loud.
- Base area = ___ × ___ = ___.
- Volume = ___ × ___ = ___.
- The unit is ___.
- The missing dimension is ___.
Guided practice
Question 1. 5 × 4 × 3?
60.
Question 2. 10 × 10 × 10?
1,000.
Question 3. Height if V = 90, base 30?
3.
Independent practice
Level 1: Start
- 5 by 4 by 3
- 8 by 3 by 2
- Cube of side 10
- Height if V = 90, base area 30
- Unit of volume
Level 2: Grow
- 6 by 3 by 2
- 10 by 5 by 4
- Cube of side 4
Level 3: Stretch
- Height if V = 120, base area 24
- A tank 2 m by 1.5 m by 1 m
- Ben says 5 by 4 by 3 has volume 12. What is wrong?
Answers are in the answer key below. Try first, then check.
6. Apply: everyday mathematics
A box is 5 by 4 by 3 cm. How many 1 cm cubes?
Show a sample answer
60.
Another one. A box is 7 cm by 2 cm by 3 cm. How many 1 cm cubes fill it?
Show a sample answer
42
7. Common mistakes
Fix: Multiply them.
Fix: Multiply them.
Fix: Use cm³.
8. Lesson summary and revision card
- I can count unit cubes.
- I can use V = l × w × h.
- I can find a missing dimension.
- I can solve volume problems.
9. Check and master
Answer all 14 questions. You will see feedback after each one.
Your result appears here after you answer every question.
10. Key takeaways
- V = l × w × h.
- Cubic units.
- Divide to find a missing side.
11. Next lesson
Next lesson: Surface area using nets. Keep going with the next idea in this course.
Exam practice
These questions are written in the style of common school and international primary assessments. Try them on your own, without looking back. Then check your answers in the marking guide. The marks are shown in brackets.
- Find the volume of a box 5 cm by 4 cm by 3 cm. [3 marks]
- Find the volume of a box 8 cm by 3 cm by 2 cm. [2 marks]
- Find the volume of a cube of side 10 cm. [2 marks]
- A prism has volume 90 cm³ and base area 30 cm². Find the height. [2 marks]
- Ali says the volume of a 5 by 4 by 3 box is 12 because 5 + 4 + 3 = 12. Is he right? Explain. [3 marks]
Total: 12 marks.
Marking guide and model answers
- V = l × w × h [1]; 5 × 4 × 3 [1]; 60 cm³ [1]
- 8 × 3 × 2 [1]; 48 cm³ [1]
- 10 × 10 × 10 [1]; 1,000 cm³ [1]
- Height = V ÷ base area [1]; 3 cm [1]
- No [1]. Multiply the three dimensions [1]. The volume is 60 cm³ [1].
Score guide: 11 to 12 = secure. 8 to 10 = nearly there, revise the parts you missed. Under 8 = work through the lesson again with a grown-up.
Printable worksheet
- 5 by 4 by 3
- 8 by 3 by 2
- Cube of side 10
- Height if V = 90, base 30
- Unit of volume
- 5 by 4 by 3
- 8 by 3 by 2
- Cube of side 10
- Height if V = 90, base 30
- Volume is measured in
Homework
Find the volume of a box at home.
Answer key and marking scheme
| Question | Expected response | Marks |
|---|---|---|
| 5 by 4 by 3 | 60 | 2 |
| 8 by 3 by 2 | 48 | 2 |
| Cube of side 10 | 1,000 | 2 |
| Height if V = 90, base 30 | 3 | 2 |
| Unit of volume | cubic units | 2 |
| Total | 10 |
Practice answers: Worksheet: 1 60; 2 48; 3 1,000; 4 3; 5 cubic units.
Quiz answers: 1 A, 2 B, 3 C, 4 A, 5 B, 6 A, 7 B, 8 C, 9 A, 10 B, 11 C, 12 A, Challenge 1 C, Challenge 2 C.
Extra worksheet answers (items 6 onward): 6 60 cm³; 7 48 cm³; 8 1,000 cm³; 9 3 cm; 10 cubic units.
Independent practice answers. Level 1: 1 60 cm³; 2 48 cm³; 3 1,000 cm³; 4 3 cm; 5 cubic units. Level 2: 1 36 cm³; 2 200 cm³; 3 64 cm³. Level 3: 1 5 cm; 2 3 m³; 3 Multiply: 5 × 4 × 3 = 60 cm³..
Mastery and remediation
| Objective | Bronze (Developing) | Silver (Proficient) | Gold (Advanced) |
|---|---|---|---|
| O1 Count unit cubes | 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 Use V = l × w × h | 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 Find a missing dimension | 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 Solve volume problems | 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 |
Courseversity badge thresholds (overall quiz score): Gold = 90–100%; Silver = 80–89.9%; Bronze = 70–79.9%. A badge is never a full record of progress.
If a learner struggles
- Find the misconception: Adding the dimensions. Multiply them.
- Explain another way: use real objects first, then pictures.
- Show a simpler example: Unit cubes.
- 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.
For parents and guardians
In this lesson your child finds the volume of boxes. You do not need to be good at mathematics to help.
- Pack boxes with small blocks.
- Ask: how many layers?
- Fill a box with sugar cubes.
- Ask “how do you know?” after each answer, and listen.
- Praise effort, not only right answers. Mistakes are how we learn.
- Ten to fifteen minutes a day is better than one long session.
Teacher package
1–5. Objectives, prerequisites, materials, preparation, duration
Lesson objectives. Learners will: count unit cubes; use V = l × w × h; find a missing dimension; solve volume problems.
Prerequisite knowledge. Grade 5 volume.
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. 45–60 minutes. It can be split into two shorter sessions.
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 paper. 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.
Key questions. What is the base area? How many layers?
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. Adding the dimensions. Multiply them.
13–15. Assessment questions, answer keys, marking scheme
Use the quiz and worksheet on this page. The 12-mark exam practice scheme, the 10-mark scheme and all answers are in the answer sections above. Re-check every answer and the marking scheme before publication.
16–19. Remediation, enrichment, homework, teacher reflection
Remediation. Unit cubes. 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
This lesson is based on the sources below, and no official 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. Where a standard code is named, it points to the official framework.
Official standards for this topic area. Common Core State Standards for Mathematics (official site): Grade 6 » Ratios & Proportional Relationships; Grade 6 » Geometry. These pages list the standards that cover this topic area; read them alongside the lesson.
Research used to shape this lesson. Common Core 5.MD.C.5 and 6.G.A.2; Cambridge Primary Mathematics Stage 6 (volume). These sources informed the lesson.