You will learn
- Choose perimeter, area or volume.
- Convert units in a problem.
- Solve multistep problems.
- Check sense.
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
Words to know
Distance around.
Surface covered.
Space inside.
How much a container holds.
1. Discover: a fish tank
A tank is 50 cm long, 40 cm wide and 30 cm high. How many litres of water does it hold?
2. Understand: measurement applications
- Volume = 50 × 40 × 30 = 60,000 cm³.
- 1,000 cm³ = 1 litre, so the tank holds 60 L.
- Fence a 12 m by 8 m garden: perimeter 40 m.
- Tile a 4 m by 3 m floor with 1 m² tiles: area 12 tiles.
Idea 1: Tank
Tank 50 × 40 × 30 = 60,000 cm³. 60,000 ÷ 1,000 = 60 L.
Idea 2: Perimeter and area
Fence for 12 by 8: 2 × 20 = 40 m. Tiles for a 4 by 3 floor: 12.
Idea 3: Choose
Paint a wall needs area. Fence needs perimeter. Water needs volume.
Why choose first? The right measure gives the right answer.
3. Worked examples
Example 1 (I show you): Volume
50 × 40 × 30 cm
- Multiply.
Answer: 60,000 cm³
Example 2 (We do it together): Litres
60,000 cm³
- ÷ 1,000.
Answer: 60 L
Example 3 (You try): Fence
12 m by 8 m
Show the steps and answer
- 2 × (12 + 8).
Answer: 40 m
Did you know?
Capacity is the volume of liquid a container can hold.
Why this matters
Real jobs need the right measure: fencing, painting, filling.
4. Explore: choose
You need paper.
- Decide what is measured.
- Use the formula.
- Convert units.
- Check sense.
Think about it: what did you notice?
60 L.
5. Practise
Say it in a sentence
Use these starters when you talk about the lesson. Say them out loud.
- This needs perimeter / area / volume because ___.
- I convert ___ to ___.
- The calculation is ___.
- The answer is ___.
Guided practice
Question 1. 50 × 40 × 30?
60,000.
Question 2. Litres?
60 L.
Question 3. Fence for 12 by 8?
40 m.
Independent practice
Level 1: Start
- Tank 50 × 40 × 30 in cm³
- Tank in litres
- Fence 12 by 8 garden
- Tiles for 4 by 3 floor
- Perimeter, area or volume for paint
Level 2: Grow
- Fence round 15 m by 10 m
- Tiles for a 6 by 5 floor
- Paint for a wall needs
Level 3: Stretch
- A tank 1 m by 50 cm by 40 cm in litres
- 4 walls of a 5 by 4 room, 2.5 m high. Area to paint
- Ben says painting a wall needs perimeter. What is wrong?
Answers are in the answer key below. Try first, then check.
6. Apply: everyday mathematics
A tank is 50 by 40 by 30 cm. How many litres?
Show a sample answer
60 L.
Another one. A tank is 20 cm by 10 cm by 10 cm. How many litres does it hold?
Show a sample answer
2 L
7. Common mistakes
Fix: Fence needs perimeter.
Fix: Surface: area; inside: volume.
Fix: Use the same unit throughout.
8. Lesson summary and revision card
- I can choose perimeter, area or volume.
- I can convert units in a problem.
- I can solve multistep problems.
- I can check sense.
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
- Pick the right measure.
- Convert units.
- Check sense.
11. Next lesson
Next lesson: Statistical questions. 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 tank 50 cm by 40 cm by 30 cm. [2 marks]
- Write the tank volume in litres. [2 marks]
- Find the length of fence for a garden 12 m by 8 m. [2 marks]
- How many 1 m² tiles cover a floor 4 m by 3 m? [2 marks]
- Ali says painting a wall needs the perimeter. Is he right? Explain. [3 marks]
Total: 11 marks.
Marking guide and model answers
- 50 × 40 × 30 [1]; 60,000 cm³ [1]
- 1,000 cm³ = 1 L [1]; 60 L [1]
- 2 × (12 + 8) [1]; 40 m [1]
- 4 × 3 [1]; 12 tiles [1]
- No [1]. Paint covers a surface [1]. Use area [1].
Score guide: 10 to 11 = secure. 7 to 9 = nearly there, revise the parts you missed. Under 7 = work through the lesson again with a grown-up.
Printable worksheet
- Tank in cm³
- Tank in litres
- Fence 12 by 8
- Tiles for 4 by 3 floor
- Painting a wall needs
- Tank 50 × 40 × 30 in cm³
- Tank in litres
- Fence 12 by 8
- Tiles for 4 by 3 floor
- Paint for a wall needs
Homework
Find the capacity of a bucket or tank.
Answer key and marking scheme
| Question | Expected response | Marks |
|---|---|---|
| Tank in cm³ | 60,000 | 2 |
| Tank in litres | 60 | 2 |
| Fence 12 by 8 | 40 | 2 |
| Tiles for 4 by 3 floor | 12 | 2 |
| Painting a wall needs | area | 2 |
| Total | 10 |
Practice answers: Worksheet: 1 60,000; 2 60; 3 40; 4 12; 5 area.
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 60,000; 7 60 L; 8 40 m; 9 12; 10 area.
Independent practice answers. Level 1: 1 60,000 cm³; 2 60 L; 3 40 m; 4 12 tiles; 5 area. Level 2: 1 50 m; 2 30; 3 area. Level 3: 1 200 L; 2 45 m²; 3 Paint covers a surface: area..
Mastery and remediation
| Objective | Bronze (Developing) | Silver (Proficient) | Gold (Advanced) |
|---|---|---|---|
| O1 Choose perimeter, area or volume | 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 Convert units in a problem | 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 Solve multistep 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 |
| O4 Check sense | 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: Using area for a fence. Fence needs perimeter.
- Explain another way: use real objects first, then pictures.
- Show a simpler example: Perimeter and area.
- 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 uses perimeter, area and volume in real tasks. You do not need to be good at mathematics to help.
- Plan how much paint a room needs.
- Ask: perimeter, area or volume?
- Check the units.
- 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: choose perimeter, area or volume; convert units in a problem; solve multistep problems; check sense.
Prerequisite knowledge. Lessons 2–7.
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. Around, surface or inside? Same units?
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. Using area for a fence. Fence needs perimeter.
13–15. Assessment questions, answer keys, marking scheme
Use the quiz and worksheet on this page. The 11-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. Perimeter and area. 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 6.G.A.1 and 6.G.A.2; Cambridge Primary Mathematics Stage 6 (measurement problems). These sources informed the lesson.