Measurement
Convert and calculate without losing track of units
Length, area, volume, time, and mass — measurement problems require converting units before calculating.
See It in Action
The Problem
A rectangle is 2.5 m long and 80 cm wide. What is its area in cm²?
Common Mistake
2.5 × 80 = 200 cm².
Mixed units: length is in metres, width in centimetres. You cannot multiply 2.5 m by 80 cm and get a meaningful answer. Always convert first.
Correct Approach
Convert length to centimetres: 2.5 m = 250 cm. Area = 250 × 80 = 20,000 cm².
Answer: 20,000 cm²
250 cm × 80 cm = 20,000 cm². Sanity check: that's 2 m², which is 20,000 cm² (since 1 m² = 10,000 cm²). ✓
The Core Concept
Measurement problems fail in two predictable ways: wrong conversion factors, or calculating with mixed units. Both have the same fix: convert everything to the same unit before you calculate.
The critical conversions to know: length (mm, cm, m, km), mass (g, kg, t), volume (mL, L), time (seconds, minutes, hours). For area, remember that 1 m² = 10,000 cm² (not 100 cm² — because you square the conversion factor). This trips up many students.
For time, the 60-minute boundary is the most common trap. 2:45 + 35 minutes: don't just add 45 + 35 = 80. Think: 2:45 → 3:00 is 15 minutes, then 35 − 15 = 20 more minutes → 3:20. Always cross the hour mark in steps.
Common Mistakes to Avoid
Mixing units in a single calculation
You can't multiply metres by centimetres. Always identify all units in the problem and convert to one unit before calculating.
Forgetting that area conversions square the unit factor
1 m = 100 cm, so 1 m² = 100 × 100 = 10,000 cm². Many students write 1 m² = 100 cm², which is wrong.
Adding time by treating 60 like 100
1:50 + 20 minutes ≠ 1:70. Time resets at 60 minutes. 1:50 + 10 → 2:00, then + 10 more → 2:10.
Confusing perimeter and area
Perimeter is the total distance around (add all sides). Area is the space inside (multiply). They have different units: perimeter is in cm/m, area is in cm²/m².
Try It Yourself
A train departs at 8:47 am and arrives at 11:15 am. How long is the journey in hours and minutes?
Hint: Count in steps: 8:47 → 9:00, then 9:00 → 11:00, then 11:00 → 11:15.
Key Tips
Write the unit next to every number so you can see when units don't match.
For time problems, count in chunks (to the next hour, then between hours, then to the exact minute).
Area uses squared units (cm², m²). Always write ² so you remember it's area, not length.
Related Skills
Ready to practise Measurement?
Reading is the start. The Maths Gym has exercises designed around this skill — with instant feedback and progress tracking.