The heading for paragraph 7 of Harbrace College Handbook, Chapter 6a states,
When regarded as a unit, collective nouns, as well as noun phrases denoting quantity, take singular verbs.
. . .
The number is singular; a number is plural.
"The number of students was small." [The number is taken as a unit.]
"A number of students were taking tests." [A number refers to individuals.]
Their examples indicate that it's different depending on if the number is taken as a unit or refers to individuals. In your case I think it's individuals and should use the plural.