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When doing group work so that everyone participates I have all students write down what the group is accomplishing. For example, when doing a worksheet solving equations, all students will need to help each other complete the problems.
Once time is up I have four cards from a standard deck (the kings). All members pull a card. The student who pulls the King of Hearts* is the one whose paper I collect for the group grade.
You can do this for larger groups (use more cards), homework review, test corrections, etc.
*look at the picture of this card and you will see why this is the card that matters! | 
