A special camera is used for underwater ocean research. The camera is at a depth of 39 fathoms. What is...

1. TRANSLATE the problem information

• Given information:
  • Camera depth: 39 fathoms
  • Conversion rate: \(1 \text{ fathom} = 6 \text{ feet}\)
  • Need to find: depth in feet

2. INFER the conversion strategy

• This is a unit conversion problem
• Since we want to go FROM fathoms TO feet, and we know \(1 \text{ fathom} = 6 \text{ feet}\), we need to multiply by 6
• Set up: \(39 \text{ fathoms} \times \frac{6 \text{ feet}}{1 \text{ fathom}}\)

3. SIMPLIFY the calculation

• \(39 \text{ fathoms} \times \frac{6 \text{ feet}}{1 \text{ fathom}}\)
  \(= 39 \times 6 \text{ feet}\)
  \(= 234 \text{ feet}\)
• The "fathoms" units cancel out, leaving us with feet

Answer: A. 234

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak INFER skill: Students don't understand which operation to use with the conversion factor. They might think "since 1 fathom = 6 feet, and I have 39 fathoms, maybe I divide 39 by 6 to get the feet."

This backwards reasoning leads to \(39 \div 6 = 6.5\), which they might round to 7.
This may lead them to select Choice D (7).

Second Most Common Error:

Poor INFER reasoning: Students recognize they need to combine 39 and 6 somehow, but choose addition instead of multiplication, thinking "I have 39 of something and need to add 6 to convert it."

This gives \(39 + 6 = 45\).
This may lead them to select Choice C (45).

The Bottom Line:

Unit conversion problems require understanding that when you want MORE of a smaller unit (feet) from a larger unit (fathoms), you multiply by the conversion factor. The key insight is recognizing that 39 fathoms should give you MORE than 39 feet, not fewer.