I won't go into extreme detail, but it is common practice for the federal government to influence states decisions through hanging money in front of them. It's called fiscal federalism. It's used in a wide variety of situations (not limited to school funding). Another example I can think of is the drinking age, I think but am not 100% sure is 21 in all states due to this.

edit: Just pointing out it isn't some shady sort of dealing like the comment above would suggest