I received several types of answers to the question about division by zero.

One group of answers dealt with dividing a pie or a set of candy bars among n people.  It does not make sense to divide something among zero people.  One student wrote that if you divide a pie by 8 you have 8 pieces, but "in order to divide [a pie] by zero you would have to have an entire pie while not having any slices of pie."  This type of answer is good for dividing a positive real number by a positive integer only.  I would use it with elementary school students, but not with someone who expects an answer that works with any kind of number.

One student claimed that a [positive] number divided by 0 would be infinity, and infinity is not a number.  Although it was not stated, this relies on the fact that the limit of (say) 2/x as x approaches 0 (from above) is infinity, which is true but generally not known to high school students.

Some students used the equivalence of a/b=c with a=bc, as I did in my answer, and put b=0, but did not distinguish between the cases a=0 and a not equal to zero.

The best answer is that a/b=c means a=bc, so a/0=c means a=0c=0.  If a is not zero, there is no c that makes this statement true, and a/0 cannot equal any number.  If a is zero, then every c makes the statement true.  In that case we do not allow a/0 because we want division to produce a single answer.