A rectangular sheet measures 12 inches by 9 inches. A smaller rectangular section measuring 4 inches by 2 inches is...

1. TRANSLATE the problem information

• Given information:
  • Original sheet: 12 inches by 9 inches
  • Cut-out section: 4 inches by 2 inches
  • Need to find: area of remaining portion

2. INFER the solution strategy

• "Remaining portion" means what's left after cutting out the smaller section
• Strategy: Calculate original area, calculate removed area, then subtract
• Remaining area = Original area - Removed area

3. Calculate the original area

• Area of rectangle = \(\mathrm{length} \times \mathrm{width}\)
• Original area = \(12 \times 9 = 108\) square inches

4. Calculate the removed area

• Removed area = \(4 \times 2 = 8\) square inches

5. Find the remaining area

• Remaining area = \(108 - 8 = 100\) square inches

Answer: A. 100

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak INFER skill: Students calculate the original area correctly (108 square inches) but forget that they need to subtract the cut-out area. They think the problem is just asking for the area of the original sheet.

This may lead them to select Choice C (108).

Second Most Common Error Path:

Poor INFER reasoning: Students misunderstand what "cut out" means and think they should add the two areas together instead of subtracting.

They calculate: \(108 + 8 = 116\) square inches

This may lead them to select Choice D (116).

The Bottom Line:

This problem tests whether students can correctly interpret "remaining portion" as a subtraction operation rather than just a single area calculation. The word "remaining" is the key signal that something has been taken away.