The number of raccoons in a 131-square-mile area is estimated to be 2,358. What is the estimated population density, in...

1. TRANSLATE the problem information

• Given information:
  • 2,358 raccoons in a 131-square-mile area
  • Need to find "raccoons per square mile"

• The phrase "per square mile" tells us we need a rate calculation

2. INFER the mathematical approach

• "Raccoons per square mile" means we need to find how many raccoons exist in each square mile on average
• This requires dividing total raccoons by total area
• Set up: Population density = Total raccoons ÷ Total area

3. Calculate the population density

• Population density = \(\mathrm{2,358\;raccoons \div 131\;square\;miles}\)
• Population density = \(\mathrm{18}\) raccoons per square mile

Answer: A. 18

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Students may not recognize that "per square mile" requires division. They might think the answer is simply one of the given numbers from the problem.

This may lead them to select Choice B (131) thinking that square miles is the answer, or get confused and guess among the given values.

Second Most Common Error:

Weak INFER reasoning: Students might set up the division incorrectly, calculating \(\mathrm{131 \div 2,358}\) instead of \(\mathrm{2,358 \div 131}\), or attempt to add/subtract the given numbers.

This leads to either a very small decimal (wrong direction division) or values that don't match any answer choice, causing them to get stuck and guess.

The Bottom Line:

This problem tests whether students understand that "per" indicates a rate calculation requiring division, and whether they can identify which quantity should be divided by which.