There are 320 marbles in a container. Of these marbles, 10% are red. How many marbles in the container are...

1. TRANSLATE the problem information

• Given information:
  • Total marbles: 320
  • Red marbles: 10% of the total
  • Question asks: How many red marbles?

• This tells us we need to find 10% of 320

2. TRANSLATE percentage to mathematical operation

• "10% of 320" means: \(320 \times \frac{10}{100}\)
• We can also write this as: \(320 \times 0.10\)

3. SIMPLIFY the calculation

• \(320 \times \frac{10}{100} = 320 \times 0.10 = 32\)

Answer: A. 32

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Students correctly calculate \(10\% \text{ of } 320 = 32\), but then misread the question and think they need to find how many marbles are NOT red.

They calculate \(320 - 32 = 288\) and select Choice B (288).

Second Most Common Error:

Poor TRANSLATE reasoning: Students don't understand what "10% of" means mathematically, so they just look at the numbers given (320 and 10) and try different operations.

They might add: \(320 + 32 = 352\) and select Choice D (352), or they might just select the total number given and choose Choice C (320).

The Bottom Line:

This problem tests whether students can translate a basic percentage statement into the correct mathematical operation. The key insight is recognizing that "10% of 320" means multiplication: \(320 \times 0.10\).