Penguin ExhibitType of penguinMaleFemaleTotalChinstrap4159100Emperor82735Gentoo4954103Macaroni424082Total140180320The number of penguins in a zoo exhi...

1. TRANSLATE the problem requirements

• Given information:
  • Total female penguins: 180 (from table)
  • Need: Female population closest to 1/3 of total females
• What this tells us: I need to calculate \(\frac{1}{3} \times 180\), then compare each type's female count

2. SIMPLIFY to find the target value

• Calculate 1/3 of 180:
  \(\frac{1}{3} \times 180 = 180 \div 3 = 60\) penguins
• Target value: 60 female penguins

3. TRANSLATE data from the table

• Female populations by penguin type:
  • Chinstrap: 59 females
  • Emperor: 27 females
  • Gentoo: 54 females
  • Macaroni: 40 females

4. INFER what "closest to" means mathematically

• "Closest to 60" means smallest absolute difference from 60
• I need to calculate \(|\mathrm{value} - 60|\) and find the minimum

5. SIMPLIFY to calculate all differences

• \(|59 - 60| = 1\)
• \(|27 - 60| = 33\)
• \(|54 - 60| = 6\)
• \(|40 - 60| = 20\)

The smallest difference is 1, corresponding to Chinstrap penguins.

Answer: A (Chinstrap)

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE reasoning: Students misinterpret "1/3 of the total female penguin population" and use the wrong total. They might calculate \(\frac{1}{3}\) of 320 (total penguins) instead of \(\frac{1}{3}\) of 180 (female penguins), getting \(\frac{1}{3} \times 320 \approx 107\). When comparing to this incorrect target, none of the female populations are particularly close, leading to confusion and guessing.

Second Most Common Error:

Poor SIMPLIFY execution: Students correctly identify that they need \(\frac{1}{3} \times 180 = 60\), but make calculation errors when finding differences. They might calculate some differences correctly but miss others, or make sign errors. For example, calculating \(|54 - 60|\) as 14 instead of 6, which could make them think Gentoo isn't the second-closest option.

The Bottom Line:

This problem tests students' ability to extract the right numbers from a data table and work systematically through fraction calculations. The key insight is recognizing that "total female penguin population" specifically refers to the 180 in the female column, not the overall total of 320 penguins.