To find out how many nuts the squirrel collected, we need to calculate the total number of nuts collected in a structured way.
The squirrel collects 12 nuts per hour for 12 hours a day for 12 days. We can represent this mathematically as follows:
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Calculate the total number of nuts per day:
- The number of nuts collected in one day: \( 12 \text{ nuts/hour} \times 12 \text{ hours} = 144 \text{ nuts/day} \).
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Calculate the total number of nuts over 12 days:
- Total nuts collected in 12 days: \( 144 \text{ nuts/day} \times 12 \text{ days} = 1,728 \text{ nuts} \).
Now, we can express this calculation in two ways: with and without exponents.
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Without exponents:
- \( 12 \text{ nuts/hour} \times 12 \text{ hours} \times 12 \text{ days} = 144 \text{ nuts} \times 12 = 1,728 \text{ nuts} \)
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With exponents:
- We can group the factors:
- \( 12^2 \) (for hours per day) and \( 12^2 \) (for days) = \( 12^3 \)
- Total would be \( 12^3 \cdot 12 = 1,728 \text{ nuts} \).
Comparison of Students' Answers:
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Student A's Answers:
- Total: 123 nuts (incorrect)
- Expression: 12 ⋅ 3 (incorrect)
- Calculated nuts: 36 nuts (incorrect)
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Student B's Answers:
- Total: 123 nuts (incorrect)
- Expression: 12 ⋅ 12 ⋅ 12 (correct, representing the daily collection of nuts)
- Calculated nuts: 1,728 nuts (correct)
Explanation:
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Student A:
- The total number of nuts (123) and the expression (12 ⋅ 3) are completely incorrect. The expression does not accurately represent the calculations based on the problem description. The factor 3 does not relate to any part of the problem (which involves 12 hours and 12 days).
- His final answer (36 nuts) also does not reflect the calculations at all.
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Student B:
- The total number of nuts collected is 1,728 nuts, which is correct according to our calculations.
- The expression he provided (12 ⋅ 12 ⋅ 12) correctly assumes the collection of nuts over the appropriate hours and days, but he mistakenly wrote 123 in his total, which is incorrect.
Conclusion:
Student B has the correct final total of 1,728 nuts, although he miswrote the total as 123 at the end. Both students misunderstood or miscalculated their final numbers, but Student B provided a correct multiplication expression related to the problem, while Student A's entire setup was incorrect. The overall correction for both is to emphasize proper multiplication and account for all the parameters in the problem correctly.