I have looked around at some of the questions regarding letters of recommendation and can't seem to find one specific to my situation. I am currently applying to graduate school in math, and some of the schools I am applying to require 3 letters of recommendation, while others ask for more. Is it considered rude to ask a professor for letters to the schools which ask for more recommendations and not for others? I don't want it to seem as if he was my `fourth choice' so to say. If not, what is the best way to phrase this to the writer? Thanks!
There is no need to explain to the LOR writers that their letters will only be used for programs that require more than three letters. Ask them for a LOR as you normally would. Provide them with the info they need to write the letter: a list or the programs they need to send their letters to, your transcript, your resume, what you hope the writer will emphasize in their letter, etc. as usual. You do not need to tell them the other programs for which their letters will not be needed, nor do you need to elaborate on where they stand on your "ranking system."
Also, it is perfectly okay to have someone as the "fourth choice", as you put it. When you need four letters inevitably some potential writers will know you better than the others. The fact that someone doesn't know you the best is in no way a judgment of your (or your professor's) ability, and I'm sure your letter writers will understand this.