A noun is said to be number transparent when the verb doesn't agree with it even when it functions as the subject in constructions like, A number of people were there. In this case, the head of the subject is singular number, but nevertheless, were agrees with plural people. What I just realized recently is that there's a big difference between a number and the number. In the COCA, [a number of * are/is] turns up 353 instances of are and only 19 of is, for a ratio of 18.6:1. In contrast, [the number of * are/is] results in only 16 instances of are and 291 of is, for a ratio of 1:18.2, almost exactly inverse.
Other determiners have other patterns. The are to is ratios are: