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.

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.

(6th grade words)

Answer 1

Let's break down the problem.

The squirrel collects 12 nuts an hour, for 12 hours, over 12 days.

To find the total number of nuts, we can write the expression in two ways:

1. Without Exponents: We can calculate it step by step:
   • First, find out how many nuts are collected in one day:
     • That's 12 nuts/hour × 12 hours/day = 144 nuts/day.
   • Then, find out how many nuts are collected in 12 days:
     • That's 144 nuts/day × 12 days = 1,728 nuts.

So, the total number of nuts collected can be represented as: \[ 12 \text{ nuts/hour} \times 12 \text{ hours/day} \times 12 \text{ days} = 1,728 \text{ nuts} \]

2. With Exponents: We can use exponents to express this as:
   • \( 12^3 \) (which means 12 × 12 × 12) because we're multiplying 12 three times.

Now, looking at the students' answers:

• Student A wrote:

  • Expression: \( 12 \times 3 \)
  • Total: 36 nuts

• Student B wrote:

  • Expression: \( 12 \times 12 \times 12 \) or \( 12^3 \)
  • Total: 1,728 nuts

Who is correct?

• Student B is correct because he accurately calculated the total number of nuts collected by the squirrel.

What did Student A do incorrectly?

• Student A made a mistake by only multiplying 12 by 3 (which gives 36) instead of recognizing the three separate factors of 12 (12 nuts, 12 hours, and 12 days). This is why his total is much lower than the correct amount. He didn't consider the hours and the days correctly in his calculation.