For a snowstorm in a certain town, the minimum rate of snowfall recorded was 0.6 inches per hour, and the...

1. TRANSLATE the problem information

• Given information:
  • Minimum recorded snowfall rate: 0.6 inches per hour
  • Maximum recorded snowfall rate: 1.8 inches per hour
  • \(\mathrm{s}\) = any snowfall rate recorded during this storm

• What this tells us: We need to find what values \(\mathrm{s}\) can take

2. INFER what constrains the variable s

• Key insight: Since \(\mathrm{s}\) represents a recorded value from this specific storm, it cannot be less than the minimum recorded (0.6) or greater than the maximum recorded (1.8)

• Strategy: \(\mathrm{s}\) must satisfy both conditions: \(\mathrm{s \geq 0.6}\) AND \(\mathrm{s \leq 1.8}\)

3. TRANSLATE this constraint into inequality notation

• Combined constraint: \(\mathrm{0.6 \leq s \leq 1.8}\)

• This means \(\mathrm{s}\) can equal 0.6, equal 1.8, or be any value between them

4. APPLY CONSTRAINTS to eliminate wrong choices

• Choice A (\(\mathrm{s \geq 2.4}\)): Impossible - no values above 1.8 were recorded
• Choice B (\(\mathrm{s \geq 1.8}\)): Too restrictive - ignores values from 0.6 to 1.8
• Choice C (\(\mathrm{0 \leq s \leq 0.6}\)): Too restrictive - ignores values from 0.6 to 1.8
• Choice D (\(\mathrm{0.6 \leq s \leq 1.8}\)): Correct - matches our constraint exactly

Answer: D. \(\mathrm{0.6 \leq s \leq 1.8}\)

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Students misinterpret what the variable \(\mathrm{s}\) represents, thinking it means 'any possible snowfall rate' rather than 'any recorded rate from this specific storm.'

This leads them to consider theoretical possibilities beyond the recorded range, potentially selecting Choice A (\(\mathrm{s \geq 2.4}\)) if they mistakenly think \(\mathrm{s}\) could be any large value, or getting confused about which bounds actually apply.

Second Most Common Error:

Poor INFER reasoning: Students understand that \(\mathrm{s}\) is constrained but incorrectly think the constraint should exclude the minimum or maximum values themselves, not recognizing that recorded values can equal the endpoints.

This might lead them to look for strict inequalities (\(\mathrm{\lt}\) or \(\mathrm{\gt}\)) rather than inclusive ones (\(\mathrm{\leq}\) or \(\mathrm{\geq}\)), causing confusion when all choices use inclusive notation and leading to guessing.

The Bottom Line:

This problem tests whether students can correctly translate real-world constraints into mathematical inequalities. The key insight is recognizing that a variable representing 'recorded values' must be bounded by the actual recorded minimum and maximum.