A rectangular garden has a length of 15 feet and a width of 6 feet. If a rectangular pathway with...

1. TRANSLATE the problem information

• Given information:
  • Rectangular garden: \(\mathrm{length = 15\ feet}\), \(\mathrm{width = 6\ feet}\)
  • Rectangular pathway area = 18 square feet is removed from the garden
  • Need to find: remaining area of the garden

2. INFER the approach

• When something is "removed from" an area, we need to subtract
• Strategy: Find total garden area first, then subtract the removed pathway area

3. Calculate the total garden area

• Use rectangle area formula: \(\mathrm{Area = length \times width}\)
• Garden area = \(\mathrm{15 \times 6 = 90}\) square feet

4. Subtract the removed pathway area

• Remaining area = Total garden area - Removed pathway area
• Remaining area = \(\mathrm{90 - 18 = 72}\) square feet

Answer: 72 square feet (Choice B)

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak INFER skill: Students misunderstand what "removed from" means and think they should add the areas together instead of subtracting.

They calculate: Garden area + Pathway area = \(\mathrm{90 + 18 = 108}\) square feet

This may lead them to select Choice D (108)

Second Most Common Error:

Incomplete solution: Students correctly calculate the garden area as 90 square feet but then stop, thinking this is the final answer without considering that the pathway area needs to be subtracted.

This may lead them to select Choice C (90)

The Bottom Line:

The key challenge is understanding that "removed from" requires subtraction, not addition. Students must recognize that when area is taken away from a larger area, what remains is always smaller than the original.