A printer produces posters at a constant rate of 42 posters per minute. At what rate, in posters per hour,...

1. TRANSLATE the problem information

• Given information:
  • Rate: 42 posters per minute
  • Need to find: Rate in posters per hour

2. INFER the conversion strategy

• This is a unit conversion problem from minutes to hours
• Since we're converting from a smaller time unit (minutes) to a larger time unit (hours), we need to multiply
• Key relationship: 1 hour = 60 minutes

3. Set up and calculate the conversion

• Rate in posters per hour = \(\mathrm{(42\text{ posters/minute}) \times (60\text{ minutes}/1\text{ hour})}\)
• Calculate: \(\mathrm{42 \times 60 = 2520}\)

Answer: 2520 posters per hour

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak INFER skill: Students divide instead of multiply, thinking they need to make the number smaller when converting to "hours."

They reason: "Hours are bigger than minutes, so the answer should be smaller than 42." This leads them to calculate \(\mathrm{42 \div 60 = 0.7}\), getting confused when this doesn't make sense in context. This leads to confusion and guessing.

Second Most Common Error:

Arithmetic errors: Students correctly identify the need to multiply by 60 but make calculation mistakes.

Common mistakes include getting 252 (forgetting a zero), 420 (mixing up the multiplication), or other computational errors. This may lead them to select an incorrect answer or doubt their approach.

The Bottom Line:

Success depends on recognizing the conversion direction - when converting from smaller units to larger time periods, the rate (per unit time) increases because you're counting over a longer time span.