I'm grading an exam that has some unusual directions. 10% of the exam is multiple choice, and I grade that unusually also, but the issue I'm facing has to do with the other 90%. I give my students freedom to choose among a number of questions to fill out that 90%. There are 10-point, 20-point, 30-point, and 40-point questions. They can skip one whole section, but they need to do at least one question from each of the other three sections. The easiest way to do it is to do one 20-point, one 30-point, and one 40-point, but there are lots of permutations to get to 90 points while doing something from each of three sections.
I've had students answer 100 points of questions. If one of their questions is a 10-pointer, then I just don't grade that one. If not, then I'll count a 20-pointer at half value (i.e. if they would have gotten an 18 out of 20, then it's 9 out of 10). I've also had students just not answer enough questions, in which case they end up with a lower score than they might have had. But for the first time (this is the third time I've used this model -- really the fourth and fifth times, if you count each section as a separate time) I've got a problem with a student answering the wrong point total where I can't think of a good solution.
This student answered three questions besides the multiple choice. She did two 40-point questions and a 10-point question. That does lead to the right point total, but it wasn't from three sections. The questions were taken from two of the four sections instead of the required three. So how do I handle this? I could simply grade the questions she did and ignore it, but that sends a message that the exam rules aren't really important. I do think some point loss is required. It's not clear how many points to penalize her, though. It isn't as if there's a question amount over the total that she's done, since she's done the right number of points. But I could claim that two 40-pointers is impossible within the rules I stipulated and then count the 40-pointer as a 30-pointer, something akin to what I do if they do too many points worth total without any 10-pointers to ignore. That 40-pointer should have been two 20-pointers or a 30-pointer and a 10-pointer. Those are the only ways for her to have followed the directions that get as close as possible to the questions she actually answered. The more generous option of those two,, then, would count one of the 40-pointers (the second one, to be precise, since that's the one that took it over the top) as a 30-pointer and insist that she should have done a 30-pointer instead and then a missing 10-pointer.
The result would be penalizing her 10 points, a whole letter grade, for not answering the right combination of questions. Does that seem too harsh? Does it seem easy enough to explain to her when justifying why I penalized her this amount? I'm not entirely satisfied with this way to handle it, but I'm also at a loss for how I might better handle this case.