What area, in square centimeters, is equivalent to an area of 2 square meters? (1text{ meter = 100text{ centimeters}}) 0.02...

1. TRANSLATE the problem information

• Given information:
  • Area to convert: 2 square meters
  • Linear conversion: \(1\text{ meter} = 100\text{ centimeters}\)
  • Need to find: equivalent area in square centimeters

2. INFER the area conversion relationship

• Key insight: When converting area units, we must square the linear conversion factor
• Since \(1\text{ meter} = 100\text{ centimeters}\), then:
  \(1\text{ square meter} = (100\text{ centimeters})^2 = 10,000\text{ square centimeters}\)

3. SIMPLIFY the conversion calculation

• Convert the given area:
  \(2\text{ square meters} \times 10,000\text{ square centimeters/square meter} = 20,000\text{ square centimeters}\)

Answer: D) 20,000

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak INFER skill: Students forget that area conversions require squaring the linear conversion factor. They think: "\(1\text{ meter} = 100\text{ centimeters}\), so \(2\text{ square meters} = 2 \times 100 = 200\text{ square centimeters}\)."

This fundamental misunderstanding of how area units scale leads them to select Choice B (200).

Second Most Common Error:

Conceptual confusion about conversion direction: Some students get confused about whether to multiply or divide, especially when seeing large numbers. They might think the answer should be smaller since they're converting to a "smaller" unit (centimeters vs meters).

This leads to confusion and may cause them to select Choice A (0.02) thinking they need to divide.

The Bottom Line:

This problem tests whether students understand that area measurements scale by the square of linear measurements. The key insight is recognizing that 1 square meter contains 10,000 square centimeters, not just 100.