a small but growing number are offering a third option

Hello,

This is a sentence from NYTimes's article 'Admission to College, With Catch: Year's Wait' by Lisa W. Foderaro: 'Now, as colleges are increasingly swamped with applications, a small but growing number are offering a third option: guaranteed admission if the student attends another institution for a year or two and earns a prescribed grade-point average.'

Don't we have to use 'is' after 'a small but growing number'?

Thank you in advance.

*I'm not a teacher*

I'd like to have a try.
It seems to me the sentence should be read as "a small but growing number [of colleges] are offering ...." and in this case we have to use a plural verb. However, if the sentence was "The number of colleges that....is growing", a sigular verb would be the way to go.

Hello,

It is Hall of Shame time for me. I completely forgot about a very good book I have 'Test of English as a Foreign Language Preparation Guide' by Michael A. Pyle, M.A. and Mary Ellen Munoz, M.A. published by Cliffs Notes.
Here is a rule:
a number of + plural noun+plural verb
the number of + plural noun+singular verb