A class is given this question on a test about exponents: A squirrel collects 12 nuts an hour for 12 hours on 12 days. Write an expression with and without exponents to find how many nuts the squirrel collected.

Question

Two students provided these answers.

Student A Student B
123
123

12⋅3
12⋅12⋅12

36 nuts 1,728 nuts
Which student is correct? Explain what the incorrect student did incorrectly.

Answer 1

To find the total number of nuts collected by the squirrel, we can break down the problem as follows:

1. The squirrel collects 12 nuts per hour.
2. It collects nuts for 12 hours each day.
3. This happens for 12 days.

We can calculate the total nuts collected by multiplying these values together:

Total nuts = (Nuts per hour) × (Hours per day) × (Days)
Total nuts = 12 nuts/hour × 12 hours/day × 12 days

Without Exponents:

The expression without exponents is: $$12\times 12\times 12$$

With Exponents:

The expression with exponents can be written as: $${12}^3$$

Now let's analyze the answers of the students:

• Student A: 123

  • They wrote an expression "12 ⋅ 3," which is incorrect since it does not account for the hours and days properly. The correct multiplication should include all three instances of 12, not just multiplying by 3. Student A's answer of 36 nuts is also incorrect based on the wrong expression.

• Student B: 123

  • They provided the expression "12 ⋅ 12 ⋅ 12," which is correct and matches the calculation we did. The answer "1,728 nuts" is also correct because: $$12\times 12=144144\times 12=1,728$$

Conclusion:

Student B is correct. Student A miscalculated by simplifying the expression incorrectly and didn't include all the contributions of the nuts being collected per hour and per day. Instead of recognizing that the squirrel collects nuts for a combination of hours across days, Student A mistakenly reduces the calculation to an incorrect multiplication.