Noah’s Ark is a great puzzle that I always do with my 6th graders.
Mr. Noah wants his Ark to sail along on an even keel. The ark is divided down the middle, and on each deck the animals on the left exactly balance those on the right — all but the third deck. Can you figure out how many seals are needed in place of the question mark so that they (and the bear) will exactly balance the six zebras?
I posed this question to my geometry kids: Given any positive integer, exactly how many factors does it have? How do figure this out without having to list all its factors?
Former NCTM President Michael Shaughnessy — my former teacher from Portland — calls this problem Factor Craze and discusses it on his monthly Problem to Ponder (now in archive).