Is it.....
my Classmates and me
or
my classmates and I
Depend on how you use it
It depends upon whether you and your classmates are the subject of the sentence (in which case use ".. and I"), or the object of a verb or preposition. That is more complicated grammar than I was taught in third grade.
My classmates and I are going on a field trip to the natural history museum
(The phrase is the subject in there; therefore, you use "I")
The vice principal told my classmates and me to go back to our classroom.
(The phrase is the direct object in this sentence; therefore you use "me")
... just as DrWLS said.