The function \(\mathrm{G(m) = 3.28084m}\) gives the length in feet that corresponds to a length of m meters. If a...

1. TRANSLATE the problem information

• Given information:
  • \(\mathrm{G(m) = 3.28084m}\) converts meters to feet
  • A length increased by 1.5 meters
  • Need to find the increase in feet
• What this tells us: We need to determine how a 1.5-meter increase translates to feet using this conversion function

2. INFER the mathematical approach

• Key insight: Since \(\mathrm{G(m) = 3.28084m}\) is a linear function, increases in the input (meters) are scaled by the coefficient (3.28084) to give increases in the output (feet)
• Strategy: Multiply the increase in meters by the conversion factor

3. SIMPLIFY the calculation

• Increase in feet = \(\mathrm{3.28084 \times 1.5}\)
• Calculate: \(\mathrm{3.28084 \times 1.5 = 4.92126}\) (use calculator)
• Round to match answer precision: 4.92 feet

Answer: C) 4.92

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak INFER skill: Students may not recognize that they need to multiply the increase by the conversion factor. Instead, they might think they need to calculate \(\mathrm{G(1.5) = 3.28084 \times 1.5 = 4.92}\) and then subtract something, or they might get confused about what operation to perform.

This conceptual confusion about how linear functions work with increases often leads to guessing among the answer choices.

Second Most Common Error:

Poor TRANSLATE reasoning: Students might misinterpret the problem as asking for the total length in feet after adding 1.5 meters, rather than asking specifically for the increase amount. This leads them to set up incorrect calculations and potentially select the wrong approach entirely.

This may lead them to select Choice A (1.50) if they think the increase in feet equals the increase in meters.

The Bottom Line:

This problem tests whether students understand that linear functions preserve proportional relationships - when the input changes by a certain amount, the output changes by that same amount multiplied by the function's coefficient.