To solve the problem, we need to determine the total number of nuts the squirrel collects. The squirrel collects 12 nuts per hour for 12 hours each day and does this for 12 days.
- Calculating the total number of nuts collected:
- Per hour: 12 nuts
- Per day (for 12 hours): \( 12 \text{ nuts/hour} \times 12 \text{ hours} = 144 \text{ nuts/day} \)
- For 12 days: \( 144 \text{ nuts/day} \times 12 \text{ days} = 1,728 \text{ nuts} \)
Now let's analyze the students' expressions:
Student A:
- Provided:
- With Exponents: \( 12^3 \)
- Without Exponents: \( 12 \times 3 \)
- Result: 36 nuts
Student B:
- Provided:
- With Exponents: \( 12^3 \)
- Without Exponents: \( 12 \times 12 \times 12 \)
- Result: 1,728 nuts
Evaluation of Students' Work:
-
Student A:
- Mistake:
- The expression \( 12^3 \) correctly represents \( 12 \times 12 \times 12 \), but the missing multiplication factors leads to incorrect interpretation.
- The expression \( 12 \times 3 \) is also incorrect since it does not account for hours and the number of days; it incorrectly simplifies the problem to just multiplying the number of nuts by the number of hours (which in this case, would result in 36).
- Final Result: 36 nuts (incorrect)
- Mistake:
-
Student B:
- Correctly interpreted the problem by writing \( 12^3 \) as \( 12 \times 12 \times 12 \) to represent the repeated addition of 12 nuts through the total hours and days.
- Final Result: 1,728 nuts (correct)
Conclusion:
Student B is correct. The incorrect calculation by Student A primarily arises from a misunderstanding of how the total nuts were to be computed systematically through multiplication of the correct dimensions (hours and days) which Student B accurately captured.
The correct mathematical expressions to represent the situation would focus on multiplying the collection rate by time, capturing all dimensions accurately.
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