Out of 300 seeds that were planted, 80% sprouted. How many of these seeds sprouted?

1. TRANSLATE the problem information

• Given information:
  • Total seeds planted: 300
  • Percentage that sprouted: 80%
  • Need to find: How many seeds sprouted

• What this tells us: We need to find 80% of 300

2. TRANSLATE the mathematical operation

• "80% of 300" means multiply: \(80\% \times 300\)
• Convert percentage to workable form: \(80\% = \frac{80}{100} = 0.8\)

3. SIMPLIFY to find the answer

• Calculate: \(0.8 \times 300 = 240\)
• Check: Does this make sense? 80% is close to 100%, so 240 should be close to 300 ✓

Answer: \(240\)

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Students misinterpret "80% of 300" and think they need to divide instead of multiply.

They might calculate \(300 \div 80 = 3.75\), reasoning that they're finding "how many groups of 80 fit into 300." This completely misses that percentages represent multiplication, not division. This leads to confusion and guessing since 3.75 doesn't make sense as a number of seeds.

Second Most Common Error:

Conceptual confusion about percentages: Students add the percentage number to the total instead of taking a percentage of the total.

They calculate \(300 + 80 = 380\), thinking that "80% sprouted" means adding 80 to the original number. This shows they don't understand that percentages represent parts of a whole, not additions to the whole. This leads to an unrealistic answer since more seeds can't sprout than were planted.

The Bottom Line:

The key challenge is understanding that "80% of" always means multiplication, and recognizing that the result should be less than the original total when the percentage is less than 100%.