In State X, Mr. Camp's eighth-grade class consisting of 26 students was surveyed and 34.6% of the students reported that...

1. TRANSLATE the problem information

• Given information:
  • Mr. Camp's class: 26 students
  • \(34.6\%\) of his students have at least two siblings
  • His class represents all eighth-grade classes in the state
  • State has 1,800 eighth-grade classes, each averaging 26 students
  • Need: students with fewer than two siblings

2. INFER the key insight

• If \(34.6\%\) have at least two siblings, then the remaining percentage must have fewer than two siblings
• Since the class is representative, whatever proportion we find applies to all classes statewide

3. SIMPLIFY to find the complementary percentage

• Percentage with fewer than two siblings = \(100\% - 34.6\% = 65.4\%\)

4. SIMPLIFY to find students per class

• Students with fewer than two siblings per class = \(65.4\%\) of 26
• \(0.654 \times 26 = 17.004 \approx 17\) students per class

5. SIMPLIFY to find the total across all classes

• Total students with fewer than two siblings = \(17 \times 1,800 = 30,600\)

Answer: C. 30,600

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Students may misread "fewer than two siblings" as "at least two siblings" and use \(34.6\%\) instead of \(65.4\%\).

They calculate: \(34.6\%\) of \(26 = 9\) students per class, then \(9 \times 1,800 = 16,200\) students statewide.

This leads them to select Choice A (16,200).

Second Most Common Error:

Incomplete INFER reasoning: Students understand they need to find the complement but get confused about what the representative sampling means.

They might calculate the percentage correctly (\(65.4\%\)) but then apply it to some other number, like the total number of students statewide (\(26 \times 1,800 = 46,800\)), getting \(65.4\%\) of \(46,800 \approx 30,600\). While this happens to give the correct answer, the reasoning path shows they missed the key insight about applying the per-class ratio directly.

The Bottom Line:

This problem tests whether students can work with complementary percentages and understand how representative sampling scales up proportionally. The key breakthrough is recognizing that if the sample is truly representative, you can find the pattern in the sample and multiply it by the number of groups.