Question

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.
Two students provided these answers.

This table presents the data collected by students A and B on the number of nuts gathered by a squirrel over a specific period of time.
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.

(2 points)

Answer 1

To determine which student is correct, we need to correctly calculate the total number of nuts collected by the squirrel.

The squirrel collects:
- 12 nuts per hour
- for 12 hours
- over 12 days

We can calculate the total number of nuts collected using the following expression:

**Without exponents:**
The total number of nuts = (nuts per hour) × (hours per day) × (days)
= 12 nuts/hour × 12 hours/day × 12 days

Now let's perform the calculation:
- First, calculate the number of nuts collected in one day:
\(12 \text{ nuts/hour} \times 12 \text{ hours} = 144 \text{ nuts/day}\)

- Next, calculate the total over 12 days:
\(144 \text{ nuts/day} \times 12 \text{ days} = 1,728 \text{ nuts}\)

Now, let's also express this using exponents:
- The total can be expressed as:
\(12^3\), where \(12^3 = 12 \times 12 \times 12\).

So, both the expression with exponents and the one without yield the same result, which is 1,728 nuts.

Now, reviewing the students' answers:
- **Student A**:
- Wrote the total as \(12 \times 3\), which gives \(36\). This is incorrect because they did not take into account the full multiplication over all three variables (nuts per hour, hours per day, and days).

- **Student B**:
- Wrote the total as \(12 \times 12 \times 12\), which is \(12^3 = 1,728\). This is correct, as it accurately reflects the calculation based on the squirrel’s collection.

**Conclusion**: Student B is correct, and Student A made an error in their calculation by incorrectly interpreting the quantities to be multiplied together. Instead of calculating the total correctly, they multiplied 12 and 3 only, ignoring the necessary multiplications for hours and days.