The amount of Hanna's bill for a food order was $50. Hanna gave a tip of 20% of the amount...

1. TRANSLATE the problem information

• Given information:
  • Hanna's bill = \(\$50\)
  • Tip rate = \(20\%\) of the bill amount
  • Need to find: the dollar amount of the tip

• What this tells us: We need to calculate \(20\%\) of \(\$50\)

2. TRANSLATE the percentage calculation

• "20% of $50" means: \(20\% \times \$50\)
• Convert percentage to workable form: \(20\% = \frac{20}{100} = 0.2\)

3. SIMPLIFY the calculation

• Calculate: \(0.2 \times \$50 = \$10\)
• Alternative approach: \(\frac{20}{100} \times 50 = \frac{1000}{100} = 10\)

Answer: $10

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Students misinterpret "20% of $50" as simply "\(20 \times \$50\)"

Instead of recognizing that "20%" means "20 out of 100," they treat it as the whole number 20. This leads them to calculate \(20 \times 50 = 1000\), giving an unreasonably large tip amount. This leads to confusion and guessing since $1000 seems obviously wrong.

Second Most Common Error:

Incomplete TRANSLATE reasoning: Students calculate the total amount (bill + tip) instead of just the tip

They correctly find that 20% of $50 = $10, but then add this to the original bill: \(\$50 + \$10 = \$60\). This happens because they focus on the total amount Hanna paid rather than isolating just the tip portion as requested.

The Bottom Line:

This problem tests whether students can distinguish between calculating a percentage OF something versus multiplying BY that number, and whether they can identify exactly what quantity the question is asking for.