A certain park has an area of 11,863,808 square yards. What is the area, in square miles, of this park?...

1. TRANSLATE the problem information

• Given information:
  • Park area: 11,863,808 square yards
  • Linear conversion: \(\mathrm{1\text{ mile} = 1,760\text{ yards}}\)
• What we need: Area in square miles

2. INFER the area conversion relationship

• Key insight: Since we're converting area (square units), we need to square the linear conversion factor
• If \(\mathrm{1\text{ mile} = 1,760\text{ yards}}\), then \(\mathrm{1\text{ square mile} = (1,760\text{ yards})^2}\)
• This gives us: \(\mathrm{1\text{ square mile} = 1,760^2\text{ square yards}}\)

3. SIMPLIFY to find square yards per square mile

• Calculate: \(\mathrm{1,760^2 = 3,097,600\text{ square yards per square mile}}\) (use calculator)

4. SIMPLIFY the unit conversion

• Divide the given area by our conversion factor:
• \(\mathrm{11,863,808\text{ square yards} \div 3,097,600\text{ square yards per square mile}}\)
• \(\mathrm{= 3.83\text{ square miles}}\) (use calculator)

Answer: B. 3.83

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak INFER skill: Students forget that area conversion requires squaring the linear conversion factor

Students might think: "1 mile = 1,760 yards, so I just divide by 1,760"
This gives them: \(\mathrm{11,863,808 \div 1,760 = 6,740.8}\)

This may lead them to select Choice D (6,740.8)

Second Most Common Error:

Poor SIMPLIFY execution: Arithmetic errors in calculating \(\mathrm{1,760^2}\) or the final division

Students may incorrectly calculate \(\mathrm{1,760^2}\) or make division errors, leading to answers that don't match any choice exactly. This causes them to get stuck and guess.

The Bottom Line:

The key challenge is recognizing that area conversions require squaring the linear conversion factor. Many students apply linear conversion logic to area problems, missing this crucial step.