An inspector begins a day of work with a large sample of shirts that need to be checked for defects....

1. TRANSLATE the problem information

• Given information:
  • Inspector starts with large sample of shirts needing inspection
  • Inspector works at constant rate throughout morning
  • Need to model number of shirts REMAINING over time

• What this tells us: We're looking at how a quantity (remaining shirts) changes as time passes

2. INFER what "constant rate" means mathematically

• Constant rate means the same amount of work gets done each unit of time
• In mathematical modeling, constant rate of change = linear model
• This eliminates exponential models (C and D), which have changing rates

3. INFER the direction of change

• As the inspector works, shirts get checked and removed from the "remaining" pile
• More time worked = fewer shirts remaining
• This means our y-value (remaining shirts) decreases as our x-value (time) increases
• Decreasing relationship = negative slope

4. Confirm the model type

• Linear model ✓ (due to constant rate)
• Negative slope ✓ (remaining quantity decreases over time)

Answer: B. A linear model with a negative slope

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Students focus on "work being done" rather than "shirts remaining"

They think: "More work gets done as time passes, so the relationship should be positive!" This leads them to miss that we're modeling the REMAINING shirts, not the completed work.

This may lead them to select Choice A (positive slope).

Second Most Common Error:

Conceptual confusion about exponential vs linear models: Students don't clearly understand what makes a model exponential versus linear

They might think: "This involves time and a decreasing quantity, that sounds like decay!" without recognizing that the constant rate is the key indicator of a linear relationship.

This may lead them to select Choice D (exponential decay model).

The Bottom Line:

Success requires carefully identifying what quantity is being modeled (remaining shirts, not completed work) and recognizing that constant rate always indicates a linear model, regardless of whether the quantity increases or decreases.