Length
millimetre (mm), centimetre (cm), metre (m), kilometre (km)
Learning Objectives
- choose suitable units for time, mass, length, temperature and capacity;
- convert between metric units;
- distinguish linear, square and cubic units;
- estimate measurements sensibly;
- check whether an answer has a reasonable unit.
Introduction
This lesson develops Units and Conversions from meaning and patterns before moving to calculations. Look for what the quantities, shapes or symbols represent, then connect that idea to the method.
Key Notes
Read the definitions and key facts below carefully. Each rule is most useful when you can explain why it fits the situation, not simply recall it.
Visual Exploration
Notice→Connect→Explain
Use the diagrams, tables or examples in this lesson to identify what changes, what stays fixed and which relationship connects the values.
Why Units Matter
A number without a unit often tells us very little. Saying a table is “2” long is incomplete. Is it 2 centimetres, 2 metres or 2 kilometres?
Key idea: The unit tells us the scale and meaning of a measurement.
Common Metric Units
Mass
milligram (mg), gram (g), kilogram (kg), tonne (t)
Capacity
millilitre (mL), litre (L)
Temperature
degrees Celsius (°C)
Length Conversion Ladder
km
m
cm
mm
1 km = 1000 m 1 m = 100 cm 1 cm = 10 mm
Moving to a smaller unit usually means multiplying. Moving to a larger unit usually means dividing.
Worked Example 1
Convert 3.75 m to centimetres.
1
1 m = 100 cm.
2
3.75 × 100 = 375.
3
3.75 m = 375 cm.
Area and Volume Units
Area measures surface coverage, so its units are squared. Volume measures space inside a solid, so its units are cubed.
Area: cm², m², km²
Volume: cm³, m³
Important: 1 m² is not 100 cm². Since both dimensions scale by 100, 1 m² = 10,000 cm².
Capacity and Volume
1 L = 1000 mL 1 cm³ = 1 mL 1000 cm³ = 1 L
🧠 Let’s Think Together
Before calculating, identify the information given, the result required and the mathematical relationship that connects them. Predict whether the answer should be larger, smaller or unchanged, then use that prediction to check the result.
Practice Questions
Foundation- Convert 4.6 km to metres.
- Convert 825 cm to metres.
- Convert 3.2 kg to grams.
- Convert 2.75 L to millilitres.
- Convert 2.4 m² to cm².
- Convert 7500 cm³ to litres.
- A journey lasts 2 hours 35 minutes. Express the time in minutes.
- A rectangular floor is 4.5 m by 320 cm. Find its area in m².
✅ Check Your Work
Show practice answers
- 4600 m
- 8.25 m
- 3200 g
- 2750 mL
- 24,000 cm²
- 7.5 L
- 155 minutes
- 320 cm = 3.2 m, so area = 4.5 × 3.2 = 14.4 m².
Common Mistakes
- Choosing a rule before identifying what the question describes.
- Skipping working or changing notation part-way through a solution.
- Accepting an answer without checking its size, sign or units.
Exam Focus
Show the mathematical relationship you are using, keep notation consistent and give a clear final answer. Use a quick estimate, diagram or inverse operation to check that the result is reasonable.
Summary
- Choose a unit that suits the size of the object.
- Linear, square and cubic units convert differently.
- 1 cm³ = 1 mL.
- Always attach the correct unit to the final answer.