word choice - "A classmate and I was" vs "A classmate and I were"

I'm writing a resume right now targeted towards a specific company. My girlfriend (a classmate) and I were (see, I don't know if that's the right word, hence this question!) the first from our school to be awarded a scholarship from this company.

Is it more correct to say:

Awarded such and such scholarship in 2011. A classmate and I were the first students from my college to be awarded this scholarship.

Or:

Awarded such and such scholarship in 2011. A classmate and I was the first students from my college to be awarded this scholarship.

The first seems much more correct when spoken, but the rule I've been taught is to take the other person out and use the words that make sense about just you.

Answer

And links two things (e.g. a classmate and I), and results in a plural subject (A classmate = 1, I = 1, so a classmate and I = 1 + 1 = 2), so were is correct:

Awarded such and such scholarship in 2011. A classmate and I were the first students from my college to be awarded this scholarship.

The rule you refer to applies only to figuring what case of pronoun to use (e.g. I or me), not to whether you should use singular or plural (e.g. was or were). When you use the rule to figure out which of I or me is correct, you should alter the number of the verb (were becomes was) and direct object (students becomes student) when you take out the other person:

A classmate and I were the first students becomes I was the first student (correct).

A classmate and me were the first students becomes Me was the first student (incorrect).

When you add the classmate back into the sentence, you can be assured of the proper pronoun (I, not me).