Noun. The guy who doesn't shut up about what he got on that quiz, or sets out after an exam to compare grades with others, usually because he knows he did extremely well. motivations include the desire to brag, or the desire to make others feel bad about their own grades.
Them: What did you get on #14? I put C, so I know for sure I got ONE wrong. This is going to bring my exam average down to a 97%.
You: Fuck off, grade grubbers. No one cares
Someone who feels the need to have a better score than anyone else in the known (and perhaps unknown) universe. If someone gets a higher score, the grade grubber seeks an immediate answer to the question of why s/he does not have the highest, bestest, prettiest score, most colorful star, or brightest happy face sticker, and thus proceeds to not shut up about it for 12 days until the next grade issue arises.