A hiking trail is 528 feet long. What is the length of the trail in yards? (1 yard = 3...

1. TRANSLATE the problem information

• Given information:
  • Trail length: 528 feet
  • Conversion factor: \(\mathrm{1\ yard = 3\ feet}\)
• Need to find: Length in yards

2. INFER the correct operation

• Since \(\mathrm{1\ yard = 3\ feet}\), this means 3 feet make 1 yard
• To convert from feet (smaller unit) to yards (larger unit), divide by 3
• Operation needed: \(\mathrm{528 ÷ 3}\)

3. SIMPLIFY the calculation

• \(\mathrm{528 ÷ 3 = 176}\)

Answer: A (176)

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak INFER skill: Students confuse which operation to use for unit conversion. They might think "\(\mathrm{1\ yard = 3\ feet}\)" means they should multiply \(\mathrm{528 × 3}\) to get the answer.

This logical error leads them to calculate \(\mathrm{528 × 3 = 1,584}\), causing them to select Choice D (1,584).

Second Most Common Error:

Poor TRANSLATE reasoning: Students misinterpret the conversion process and treat it like a simple addition problem, thinking they need to add the conversion factor to the given measurement.

This leads them to calculate \(\mathrm{528 + 3 = 531}\), causing them to select Choice B (531).

The Bottom Line:

Unit conversion problems require understanding the relationship between units and applying the correct operation. Remember: when converting to a larger unit, divide by the conversion factor; when converting to a smaller unit, multiply by the conversion factor.