Errors don't usually come pre-marked for you, so I have a variety of situations for you to look at. All of these are different in some way from the standard algorithm. Some of them are alternate algorithms--correct ways of solving problems that are different from the usual way. Some of them are error patterns. Some of the students don't make errors in every problem that they solve, but in a consistent subset of problems they will always make a particular error. These fictional students are all as consistent as I can make them--I have tried to do away with all of the careless mistakes. For each student, figure out what they are doing; figure out whether it is consistently correct or is consistently an errors, and try to explain why this way of solving is correct or not correct.
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