How many feet are equivalent to 34text{ yards}? (1text{ yard} = 3text{ feet})

1. TRANSLATE the problem information

• Given information:
  • \(\mathrm{34~yards}\) need to be converted to feet
  • Conversion factor: \(\mathrm{1~yard = 3~feet}\)
• What we need to find: The number of feet equivalent to \(\mathrm{34~yards}\)

2. INFER the conversion approach

• Since we're converting from larger units (yards) to smaller units (feet), we need more of the smaller units
• This means we multiply: \(\mathrm{34~yards × 3~feet~per~yard}\)
• The conversion factor \(\mathrm{\frac{3~feet}{1~yard}}\) ensures the yards cancel out, leaving only feet

3. SIMPLIFY the calculation

• \(\mathrm{34~yards × \frac{3~feet}{1~yard}}\)
  \(\mathrm{= 34 × 3~feet}\)
  \(\mathrm{= 102~feet}\)

Answer: \(\mathrm{102}\)

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak INFER skill: Students confuse the direction of conversion and divide instead of multiply.

They might think: "There are 3 feet in 1 yard, so 34 yards must be \(\mathrm{34 ÷ 3 = 11.33~feet}\)." This backwards reasoning comes from not recognizing that converting to smaller units requires more of those units, not fewer. This leads to an incorrect answer of approximately \(\mathrm{11}\).

Second Most Common Error:

Poor SIMPLIFY execution: Students set up the problem correctly but make arithmetic errors.

They correctly identify that \(\mathrm{34 × 3}\) is needed, but miscalculate and get \(\mathrm{92, 112}\), or other incorrect products. Simple multiplication errors can derail an otherwise correct approach.

The Bottom Line:

The key insight is recognizing which direction the conversion goes - when converting from larger to smaller units, you get more units, so you multiply. This unit conversion logic is what separates confident problem-solvers from students who guess at whether to multiply or divide.