Russian ordinal numbers behave like adjectives. Also, thankfully, if you have a long number only the last word is affected when the gender and/or case change:
The floor numbering uses the system common in the U.S., i.e. the floor on the ground level is "the 1st floor". This is what you are going to see on the elevator buttons—so we try to stick to this "literal" translation.
A typical structure of a university::
университе́т
↳факульте́т ("department"), отделе́ние ("subdivision")
. ↳ ка́федра ("branch")
If a "department" (a.k.a. "a faculty") is really large, it may have several "отделе́ния" inside, which are then subdived further into "ка́федры".
A university can also have an "институ́т" ("institute") inside. Or a number of them. An institute may have departments of its own.
The grading system in Russia uses numbers 2 to 5:
In speech we usually call them «дво́йка», «тро́йка», «четвёрка» and «пятёрка». «Едини́ца»(1) is virtually never assigned (maybe only in the case of particularly mighty failure, combining poor performance with misdemeanor).
Universities—officially—only use the words («неуд.», «уд.»/«удовл.», «хор.», «отл.» when abbreviated). And yet, the numbers are also widely used in conversation.
A school lesson is 45 minutes long, followed by a short break («переме́на»).
A class at a university consists of two 45-minute-long periods, often with a 5-minute break in between. This is why people usually call it «па́ра» ("a pair, a couple"). In the Russian Far East «ле́нта»("a ribbon") is a more popular term—but do not try your luck using this term anywhere else!
Summer break and shorter breaks during the academic year are «кани́кулы». This is a plural-only noun.
Finally, a word (or two) about grades/school years. For the sake of convenience, this course assumes that первый класс is the exact equivalent of first grade or year one, etc, which may or may not be the case depending on where you're from. For the record, Russian schools run from первый класс when you are six or seven years old to одиннадцатый класс when you are seventeen, although the last two years are not compulsory.