Choose units and use scale factors consistently
Convert units before combining quantities · Distinguish length, area and volume conversions · Interpret a scale and define useful quantities
Section Paper 2 · Historical Extended · non-calculator
Exam scope and assessment notes
Core and Extended foundations. Historical study of Cambridge IGCSE Mathematics (US) 0444, 2025 Version 2. The final assessment was June 2025; the syllabus was available only to schools in Arizona, USA. This is not a current exam-entry option. Original self-check teaching and explained practice are not Cambridge papers, official marks or predicted grades. Linked teaching foundations do not establish full syllabus mastery. Calibrated cumulative assessment, reliable drawn-work review and qualified mathematics-teacher review remain unfinished.
Before you begin
- Metric units
- Ratio
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
What should you establish before applying the method in this lesson?
What you will learn
- Convert units before combining quantities
- Distinguish length, area and volume conversions
- Interpret a scale and define useful quantities
Identify the quantity
A length, area, volume, duration or money amount needs a suitable unit. Convert unlike units before adding quantities. Prefix conversions for length are multiplied twice for area and three times for volume: 1 m = 100 cm, so 1 m² = 10000 cm² and 1 m³ = 1000000 cm³.
Use a consistent scale
A map scale 1:25000 compares map length with real length in the same unit. Multiply map distance by 25000, then convert to a useful real unit. Define the quantities needed in a multi-step problem before calculating; a numerical answer with the wrong unit can be wrong by many powers of ten.
Sources for this lesson
Pause and explain
How many cm² are in 1 m²?
Worked example
A map uses 1:25000. What real distance is represented by 8 cm?
Show the worked solution
- 8×25000 = 200000 cm.
- Divide by 100 to get 2000 m, or 2 km.
Answer 2 km.
Try a topic test
Choose Easy, Normal or Difficult. Save your answers and open worked review after finishing.
Test this topic →From guided practice to a new situation
Write your answer and reasoning first. Use a hint only if you are stuck. The model solution is for self-checking; your written work is not automatically marked.
Add 1.4 m and 35 cm, giving the result in metres.
Give me a hint
Convert centimetres before adding.
Compare my reasoning
- 35 cm = 0.35 m.
- 1.4 + 0.35 = 1.75 m.
1.75 m.
Look for these in your work
- Use one unit
- Label the result
Convert 0.6 m² to cm² and 0.002 m³ to cm³.
Give me a hint
Use the squared and cubed factors.
Compare my reasoning
- 0.6×10000 = 6000 cm².
- 0.002×1000000 = 2000 cm³.
6000 cm² and 2000 cm³.
Look for these in your work
- Match dimensions
- Check powers of ten
A 1:500 drawing shows a 3.2 cm side. Find the real side in metres; then the perimeter of a square with that side.
Give me a hint
Find a real length before using the perimeter rule.
Compare my reasoning
- 3.2×500 = 1600 cm = 16 m.
- Square perimeter = 4×16 = 64 m.
Side 16 m; perimeter 64 m.
Look for these in your work
- Define the required length
- Use the scale in common units
Common mistakes
- Square and cube the conversion factor for area and volume.
- A scale ratio needs common units.
What can you explain now?
How many cm² are in 1 m²?
Compare with the explanation
10000 cm².
A 100 cm by 100 cm square has area 100×100 cm².
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Make it stick
How many cm² are in 1 m²?
If you needed the solution, close it and solve the problem again from a blank page. A correct answer is stronger when you can explain the reason for each step.