Hi! I am currently a freshman at a highly ranked medium sized university on the West Coast. I am from the East Coast and I realized a few months into my freshman year that going to school so far away from home wasn’t going to work for me. Now, I have written essays and filled out the application. My GPA is pretty high and I am heavily involved in extracurricular activities on campus. My major issue, however, is recs. First off, my school is on the quarter system which makes it really hard to make close relationships with professors so early in the year (we just started our second quarter and all of my courses in the first quarter were large lectures of about 200 students). There is one professor who I have talked to a lot and I think could write a very good letter for me, but that is about it. Would it be appropriate to ask a professor whose class I did very well in but had little contact with for a recommendation? Any advice would be much appreciated. My second problem is the quarter system in general. Does anyone know how this typically works with the midterm report/ eventually transferring credit to a semester school? Thanks 
If you know a TA well enough, you could probably ask him or her to write the recommendation for you with the professor’s approval. Not sure about transferring credit, but I think you can just send your latest grades to the schools for your midterm report (though I am not 100% sure on this either).
Yes, you can ask the prof whose class you did well in to write one of your letters. They do this kind of thing all the time.
Good luck!
Generally, 1 quarter credit unit = 2/3 semester credit unit. For example, quarter system schools like Stanford typically require 180 quarter credit units to graduate, while semester system schools like Cornell typically require 120 credit units to graduate. So if you take 45 quarter credit units at Stanford and transfer to Cornell, they become 30 semester credit units for Cornell purposes. Note that this common credit system is called the credit hour system.
Of course, some schools have other ways of counting credits. At schools where only courses are counted, and all are of equal size, the conversion to credit hours can be approximated by the ratio of the number of courses needed for graduation to 120 (semester) or 180 (quarter). Other types of credit counting systems can be converted to credit hours in a similar fashion.
Be careful of sequences of courses when transferring credit. If, for example, you take a partial sequence of courses at Stanford and then transfer to Cornell to take the rest of the sequence, you may find that the dividing lines between parts of the sequence may not line up, so you may have to take a course that partially repeats the previous course.
You said that you are involved in EC’s on campus, do you have any supervisors that could write up a LOR?