While, given the picture presented the child's solution makes the most sense, there is another close scenario in which the teacher is correct[1]. So its not really "as simple as that."
this is not a plausible scenario at all. if the quantity of work done is not equal at each step the question is impossible to answer which means that the teacher is nor right, just there is a possibility to be right. but then, every answer could be right, just adjust your cutting path according to the answer you would like to be correct.
Yes, the question did not account for unknown specifics. There is also a 3rd answer which in which the answer accounts for the person making the cuts having to answer the phone half way through the job.
Context is everything, this is a question for a 3rd grader not someone who is in Calculus. I think it's safe to assume the student is right given the screenshot.
[1]http://math.stackexchange.com/a/380007