A block of ice in a laboratory is melting at a constant rate. The block loses 72 grams of mass...

1. TRANSLATE the problem information

• Given information:
  • Block loses 72 grams of mass in 6 hours
  • Melting happens at constant rate
  • Need to find rate in grams per hour

• What this tells us: We have a total change (72 grams) over a time period (6 hours), and need the rate per single hour.

2. INFER the approach

• This is a rate problem - we need to find "change per unit time"
• Since rate = total change ÷ time, we need to divide the total mass lost by the total time
• The key insight: "per hour" means we're looking for how much melts in exactly 1 hour

3. SIMPLIFY by performing the calculation

• Set up the division: \(\mathrm{72\ grams} \div \mathrm{6\ hours}\)
• Calculate: \(72 \div 6 = 12\)
• Units: grams per hour

Answer: B. 12

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Students misunderstand what "rate in grams per hour" means and think they need to add or subtract the given numbers instead of finding a per-unit rate.

Some students see "72 grams" and "6 hours" and think they should add them together (\(72 + 6 = 78\)), leading them to select Choice D (78). Others might subtract (\(72 - 6 = 66\)) and select Choice C (66).

Second Most Common Error:

Poor SIMPLIFY execution: Students correctly identify this as a division problem but make calculation errors or confuse which number goes where.

They might incorrectly calculate \(6 \div 1 = 6\) (thinking 6 hours divided by 1 hour) or make other arithmetic mistakes, leading them to select Choice A (6).

The Bottom Line:

This problem tests whether students understand that finding a rate requires division and can correctly identify what needs to be divided by what. The word "per" is the key signal that division is needed.