I have used this activity with students from grades 8 through 12. I have no doubt it can be used with younger students as well. I have found that this activity works equally well with the older students as it does with the younger ones. This is an activity that you can do to fill time at the end of a class if you finish early. It is fun and allows you to review key words/concepts in a unit.
With large classes you might want to divide the class into groups of 3-4. In smaller classes, you might think of pairing the students up.
Explain to the students the rules. Make it clear that the only correct answer is the one you have listed as the common denominator on your sheet. This will prevent arguments when there are several possible common denominators for a given list.
If you have access to an overhead projector, you could place the lists of words on a transparency. You then reveal one word at a time and give time to the students to guess what the common denominatorcould be. If there is no guess within a few seconds, reveal the next word, and so on. Alternatively, you can also write the words on a blackboard or on another surface.
The team that guesses first gets points, as many points are there are unrevealed clues left +1. If their guess is wrong, take away as many points as there are clues unrevealed +1. This incites the students to guess as soon as they can, but at the same time to avoid wild guesses. Tell the group before you reveal the first word in a series how many words their are in that list. They will then know how many points they stand to gain or loose.
The team with the largest total at the end wins - even if it is in the minus range!
There are no limitations to the "common denominators" of a list of word you prepare. It could be that they all begin or end with the same latter, that they all are found in a given prayer, that they are all objects that have the same color, that they are all people who are males or females... You could also have phrases or complete sentences as clues rather than individual words. You can be as whimsical as you wish, giving a list of 5-letter words, with "words of 5 letter" being the only common denominator. If one of these is thrown in once in a while, it keeps the students on their toes and gives an added challenge to those students who like to solve puzzles.