During spring migration, a dragonfly traveled a minimum of 1,510 miles and a maximum of 4,130 miles between stopover locations....

1. TRANSLATE the problem information

• Given information:
  • Minimum distance: 1,510 miles
  • Maximum distance: 4,130 miles
  • \(\mathrm{d}\) = a possible distance the dragonfly traveled

2. TRANSLATE each constraint into inequality form

• "Minimum of 1,510 miles" means: \(\mathrm{d \geq 1,510}\)
• "Maximum of 4,130 miles" means: \(\mathrm{d \leq 4,130}\)

3. INFER how to combine the constraints

• Since the dragonfly's distance must satisfy BOTH conditions at the same time, I need a compound inequality
• The distance must be at least 1,510 AND at most 4,130
• This gives us: \(\mathrm{1,510 \leq d \leq 4,130}\)

Answer: B. \(\mathrm{1,510 \leq d \leq 4,130}\)

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Confusing the direction of inequality symbols with minimum/maximum language.

Students often think "minimum of 1,510" means \(\mathrm{d \leq 1,510}\), mixing up that minimum means the value must be AT LEAST that amount (so \(\mathrm{d \geq 1,510}\)). This fundamental translation error leads them to flip the inequality directions.

This may lead them to select Choice A (\(\mathrm{d \leq 1,510}\)) thinking it represents the minimum constraint.

Second Most Common Error:

Poor INFER reasoning: Not recognizing that both constraints must be satisfied simultaneously.

Students might correctly translate each piece individually but fail to combine them into a compound inequality. They might focus on just one constraint (usually the first one mentioned) and ignore the other.

This may lead them to select Choice A (\(\mathrm{d \leq 1,510}\)) by only considering the first number mentioned, or cause confusion leading to guessing.

The Bottom Line:

This problem tests whether students can accurately translate everyday language about ranges into mathematical notation. The key insight is remembering that "minimum" sets a lower bound (\(\mathrm{\geq}\)) while "maximum" sets an upper bound (\(\mathrm{\leq}\)), and both constraints work together to define a valid range.