The equation h - c = 12 relates the temperature in degrees Fahrenheit at the hottest point of the day,...

1. TRANSLATE the equation components

• Given equation: \(\mathrm{h - c = 12}\)
• Variables defined:
  • h = hottest temperature of the day
  • c = coldest temperature of the day
• Question asks: What does 12 represent?

2. INFER the meaning of the equation structure

• In any equation of the form (larger value) - (smaller value) = result
• The result represents the difference between the two values
• Here: \(\mathrm{h - c}\) gives us the difference between hottest and coldest temperatures

3. TRANSLATE the mathematical relationship back to real-world meaning

• Since \(\mathrm{h - c = 12}\)
• The number 12 equals the temperature difference
• Therefore, 12 represents the difference between the hottest and coldest temperatures

Answer: C - The difference in temperature between the hottest and coldest points of the day

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Students focus on individual variables rather than the equation structure.

They see h = hottest temperature and c = coldest temperature, then assume 12 must represent one of these individual temperatures rather than recognizing that 12 equals the result of \(\mathrm{h - c}\) (the difference operation).

This may lead them to select Choice A (The temperature at the hottest point) or Choice B (The temperature at the coldest point).

Second Most Common Error:

Poor INFER reasoning: Students don't connect subtraction with finding differences.

They recognize that 12 is separate from h and c but fail to understand that when you subtract two quantities, the result represents their difference. They might think 12 represents some other temperature measurement.

This may lead them to select Choice D (The average temperature) or causes confusion and guessing.

The Bottom Line:

This problem tests whether students can interpret the components of a linear equation in context. The key insight is recognizing that in \(\mathrm{h - c = 12}\), the constant term (12) represents the result of the operation (subtraction), which gives the difference between the two temperatures.