Nelson baked 78 muffins. In each pan, he baked 6 muffins. Students were asked to write an equation that tells how to find $$ p $$, the number of pans of muffins he baked. One student answered that it was $$ 78-6=p $$. What error did this student make and what would you suggest? The student to provide related calculations and additional reasoning to support your answer.

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To solve the problem, we need to determine how many pans of muffins Nelson baked, given that he baked a total of 78 muffins and each pan holds 6 muffins.

### Step 1: Identify the known conditions
- Total muffins baked: $$ 78 $$
- Muffins per pan: $$ 6 $$

### Step 2: Formulate the correct equation
The student proposed the equation $$ 78 - 6 = p $$. This equation is incorrect because it suggests that you subtract the number of muffins in one pan from the total muffins to find the number of pans, which does not make sense in this context.

### Step 3: Correct reasoning
To find the number of pans $$ p $$, we should divide the total number of muffins by the number of muffins per pan. The correct equation should be:

$$
p = \frac{78}{6}
$$

### Step 4: Perform the calculation
Now, let's calculate the number of pans:

$$
p = \frac{78}{6}
$$

Calculating this gives:

$$
p = 13
$$

### Conclusion
Nelson baked $$ 13 $$ pans of muffins.

### Suggestion for the student
I would suggest that the student should think about the relationship between the total number of muffins and the number of muffins per pan. Instead of subtracting, they should consider how many groups of 6 muffins can be made from 78 muffins, which leads to division rather than subtraction.

Thus, the correct approach is to use division to find the number of pans, as shown in the equation $$ p = \frac{78}{6} $$.
The student's equation $$ 78 - 6 = p $$ is incorrect because it subtracts the number of muffins per pan from the total muffins instead of dividing. The correct equation should be $$ p = \frac{78}{6} $$, which equals 13 pans.

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