A number of should be used with a plural verb. Think of it this way: A number of equates to the word they.
- A number of fans buy tickets at the game. (They buy tickets.)
- A number of dogs in our neighborhood actually like the mailman. (They like the mailmam.)
On the other hand, when using the number of, use a singular verb. The number of equates to the word it.
- The number of snowstorms this year was more than expected. (It was more than expected.)
- The number of dogs in our neighborhood has grown over the past several years. (It has grown.)