Volume and capacity

Classroom resources

Load these into Waypoints Prepare: choose Load URL and paste the copied address, or download the file and import it. In Prepare, the worksheet's Teacher edition shows the answers; the student copy hides them.

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• Worksheet Download Copy address for Prepare Print the student copy; the Teacher edition has the answers.

Students will be able to

• I can convert between cm³, mL, L and m³.
• I can explain why 1 m³ is 1 000 000 cm³.
• I can choose a sensible unit for a container.

Timing

Predict and Run 8 min · Investigate 8 min · Modify 10 min · Practise and Make 9 min

Before class

Do the Run board yourself first. Bring a 1 L carton and a 10 cm cube (or a drawing) if you can.

The one idea: 1 cm³ holds 1 mL, so 1000 cm³ is 1 L, and 1 m³ (100 × 100 × 100 cm³) is 1000 L. The common mistake is converting a cubic unit with the length factor once (Ravi's mistake).

The board gives capacity in mL or L for cm and in L for m.

Wider: why a cubic metre of water has a mass of about a tonne, and water storage in kilolitres or megalitres (dams, town water).

Running the lesson

1. Predict: ask students to show the size of a litre with their hands.
2. Run: ask for two different boxes that hold 1 L.
3. Investigate: ask Ravi to draw his cubic metre.
4. Modify: ask which unit a council would use for a dam.
5. Make: ask whose carton is easiest to hold.

The hard part (on purpose)

Converting cubic units. Ask students to draw a cube and label 100 cm on all three edges before they convert.

When students get stuck

Answers to the checks

1. a 10 cm cube: A box is 10 cm by 10 cm by 10 cm. How much water does it hold?
   1 L. 10 × 10 × 10 = 1000 cm³, and each cm³ holds 1 mL: 1000 mL = 1 L.
2. fill a box: Make a box that holds exactly 1 L. Was your prediction right? Could a box with different lengths also hold 1 L?
   
   10 × 10 × 10 = 1000 cm³. A 5 × 10 × 20 box (too long for this board) would hold 1 L too: any box of 1000 cm³ does.
3. Cubic metres: How many litres does 1 m³ hold?
   1000
   1 m³ = 100 × 100 × 100 = 1 000 000 cm³ = 1 000 000 mL = 1000 L.
4. Find the mistake: Ravi works out how much a 2 m³ tank holds. Click the line where his working goes wrong.
   line 2
   Line 2: a cubic metre is 100 cm in each of three directions: 100 × 100 × 100 = 1 000 000 cm³. The tank holds 2000 L.
5. Choosing units: Which unit suits the capacity of a backyard swimming pool?
   Kilolitres (or cubic metres)
   A pool holds tens of kilolitres (tens of cubic metres).
6. A tank: Make a water tank that holds 24 000 L.
   
   24 000 L = 24 m³: for example 4 m × 3 m × 2 m.
7. Litres to cm³: A jug holds 2.5 L. How many cm³ is that?
   2500
   1 L = 1000 cm³, so 2.5 L = 2500 cm³.
8. Millilitres to cm³: A cup holds 350 mL. How many cm³ is that?
   350
   1 mL = 1 cm³, so 350 cm³.
9. Which is a volume?: Which of these is a volume?
   12 cm³
   Volume is in cubic units: cm³.
10. mL to L: Write 4500 mL in litres.
    4.5
    4500 ÷ 1000 = 4.5 L.
11. m³ to L: A container holds 0.6 m³. How many litres is that?
    600
    0.6 × 1000 = 600 L.
12. A box: A box is 20 cm by 15 cm by 10 cm. How many litres does it hold?
    3
    20 × 15 × 10 = 3000 cm³ = 3000 mL = 3 L.
13. Review: triangular prisms: Review: a triangular prism has a right-triangle end with legs 3 cm and 4 cm, and is 10 cm long. What is its volume in cm³?
    60
    Base area ½ × 3 × 4 = 6 cm², times 10 = 60 cm³.
14. a juice carton: Design a carton that holds 600 mL, with a base that is not square (l more than w).
    
    For example 10 × 6 × 10, or 12 × 5 × 10.

Solutions

One possible solution for each task. Other correct programs are fine.

tanks and cartons › A tank

Open task: any program that does what the step asks.

tanks and cartons › Litres to cm³

Open task: any program that does what the step asks.

tanks and cartons › Millilitres to cm³

Open task: any program that does what the step asks.

tanks and cartons › Which is a volume?

Open task: any program that does what the step asks.

a juice carton

Open task: any program that does what the step asks.

Stretch and support

Stretch: A rainwater tank is 2 m long, 2 m wide and 1.5 m tall. How many days would it supply a family that uses 180 L a day?

Support: Keep the conversion table visible; use real containers labelled in mL and L.

Coach prompt (optional)

For a student who has done the lesson and is still stuck. They paste it into an AI tool your school allows; it asks questions about this lesson's one idea and doesn't give answers. Students see it on the course recap page only through a link ending in ?coach=1: recap with coach prompts.

You are a patient maths coach for a Year 8 student in Australia. Help me understand ONE idea only, from the lesson "Volume and capacity".

The idea: Unit relationships between volume and capacity: I can Students understand and apply the relationships 1 cm³ = 1 mL, 1000 cm³ = 1 L, 1 m³ = 1000 L, and use these to convert between volume and capacity units.

What understanding looks like:
- Correctly converts between cm³, mL, L and m³.
- Selects appropriate units for a given practical context.
- Does not confuse cm³ and cm (volume vs length).

Mistakes students often make here:
- A student says 1 m³ = 100 cm³.
- A student mixes up cm and cm³.
- A student divides by 100 for mL to L.

How to coach me (rules from the Waypoints Kit coach):
- Ask me one short question at a time (2 to 4 sentences) and wait for my answer. Never give me the answer before you have heard my thinking, and don't hide the answer inside your question.
- Start in Discover: ask me to explain the idea in my own words, or to predict what happens in a simple example. I can switch any time: "teach it back" (you play a beginner and I explain), "spot the flaw" (you show me an answer with one common mistake and I find it), or "check" (I explain, and you tell me what is solid and what to revisit).
- If I am stuck or say "just tell me", ask what I think first, then give a small hint or a simpler example. Explain only after I have had a real go.
- Stay in this idea: don't teach later ideas or add extra content. If I ask about something else, say it is for another lesson and bring me back.
- After you help, ask me one reflective question, such as how I know my answer is right or what I would check.
- Praise my effort and method, not my ability.
- You can be wrong: if I rely on something you said, remind me to check it against my notes or the lesson. If you don't know, say so.
- Use simple words.
- Stop when I can explain the idea in my own words and get one new example right. Then tell me to go back to the lesson "Volume and capacity".

Exit ticket

A fish tank is 50 cm by 30 cm by 40 cm. How many litres does it hold?

50 × 30 × 40 = 60 000 cm³ = 60 L.

What each step is for

• a 10 cm cube: Committing to how much a 10 cm cube holds shows whether they link cm³ to mL, and the size of a litre.
• fill a box: Building boxes and reading their volume and capacity side by side shows cm³ and mL are the same number.
• converting units: 1 m³ = 1000 L; converting cubic units uses the length factor three times (Ravi uses it once); the unit should suit the context.
• tanks and cartons: Building a tank in metres, converting both ways, and the difference between cm and cm³.
• volume and capacity: Conversions both ways and a box's capacity, mixed; using 100 instead of 1 000 000 for m³ is the planted slip; the triangular prism review keeps base times height fresh.
• a juice carton: Designing to a capacity with a constraint uses volume and capacity together.

Where it leads

This starts AC9M8M02.

Where it leads: prism problems (next lesson), and volume of cylinders (Year 9).