A special camera is used for underwater ocean research. When the camera is at a depth of 58 fathoms, what...

1. TRANSLATE the problem information

• Given information:
  • Camera depth: \(58\text{ fathoms}\)
  • Conversion: \(1\text{ fathom} = 6\text{ feet}\)
  • Need to find: depth in feet

2. INFER the conversion strategy

• This is a unit conversion problem
• Since we want to convert FROM fathoms TO feet, we multiply by the conversion factor
• Set up: \(58\text{ fathoms} \times \frac{6\text{ feet}}{1\text{ fathom}}\)

3. SIMPLIFY the calculation

• The fathom units cancel out: \(58 \times 6\text{ feet} = 348\text{ feet}\)

Answer: \(348\)

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak INFER skill: Students divide instead of multiply, thinking "if 1 fathom equals 6 feet, then to find how many fathoms are in feet, I should divide."

They calculate \(58 \div 6 = 9.67\text{ feet}\), which doesn't make sense since fathoms are larger units than feet, so the depth in feet should be a bigger number than the depth in fathoms.

This leads to confusion and potentially guessing among answer choices.

Second Most Common Error:

Poor SIMPLIFY execution: Students correctly set up \(58 \times 6\) but make arithmetic mistakes.

Common calculation errors include \(58 \times 6 = 288\) or \(58 \times 6 = 368\), leading them to select incorrect answer choices if available.

The Bottom Line:

Unit conversion problems require clear thinking about whether to multiply or divide. Remember: when converting from a larger unit to a smaller unit, you multiply by the conversion factor to get a larger number.