A factory worker needs to pack at least 240 boxes during a 5-hour work period. What is the minimum number...

1. TRANSLATE the problem information

• Given information:
  • Must pack at least 240 boxes
  • Work period is 5 hours
  • Need to find minimum boxes per hour

• What this tells us: We need to find the rate that will allow exactly 240 boxes in 5 hours (the minimum to meet "at least 240")

2. TRANSLATE the calculation needed

• To find rate: divide total quantity by time
• Set up: \(240\) boxes \(\div\) \(5\) hours = ? boxes per hour

3. Calculate the minimum rate

• \(240 \div 5 = 48\) boxes per hour

4. APPLY CONSTRAINTS to confirm the answer

• Since we need "at least 240," packing exactly \(48\) boxes per hour for \(5\) hours gives us exactly \(240\) boxes
• This is the minimum rate that meets the requirement

Answer: C) 48

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Misinterpreting "at least 240" and "minimum rate"

Students may think: "If I need at least 240, I should pick a rate higher than what I calculated to be safe." They calculate \(240 \div 5 = 48\) correctly, but then think they need to choose a higher number to ensure they definitely get "at least 240."

This may lead them to select Choice D (60).

Second Most Common Error:

Poor TRANSLATE reasoning: Setting up the division incorrectly

Students may confuse which number goes where and calculate \(5 \div 240\) instead of \(240 \div 5\). While this gives approximately \(0.02\), it doesn't match any answer choice, which leads to confusion and guessing.

The Bottom Line:

This problem tests whether students can correctly translate rate word problems into mathematical operations and understand that "minimum rate" means the exact rate needed, not something higher.