How many yards are equivalent to 1,116 inches? (1 yard = 36 inches)

1. TRANSLATE the problem information

• Given information:
  • 1,116 inches to convert
  • \(1 \text{ yard} = 36 \text{ inches}\)
• Find: How many yards equal 1,116 inches

2. INFER the conversion strategy

• Since we're converting from a smaller unit (inches) to a larger unit (yards), we need to divide
• Strategy: Total inches ÷ inches per yard = number of yards
• Set up: \(1,116 \div 36\)

3. SIMPLIFY the calculation

• Calculate \(1,116 \div 36 = 31\)
• Check our work: \(31 \times 36 = 1,116\) ✓

Answer: 31

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak INFER skill: Students sometimes multiply instead of divide, thinking 'bigger number times conversion factor'

They might calculate \(1,116 \times 36 = 40,176\), which gives an unreasonably large answer (over 40,000 yards). This leads to confusion and often causes them to abandon their systematic approach and guess.

Second Most Common Error:

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

For example, they might miscalculate \(1,116 \div 36\) and get 30 or 32 instead of 31. Since this is a calculation-heavy problem, small errors in long division or estimation can lead to selecting an incorrect answer.

The Bottom Line:

The key insight is recognizing the direction of conversion - when going from smaller to larger units, you divide. Students who remember this principle and execute the arithmetic carefully will succeed.