The teacher provided milk and cookies with the students.
The teacher provided milk and cookies for the students.
The teacher provided milk and cookies with the students.
The teacher provided milk and cookies for the students.
When direct object of the verb "provide" is the things provided, we use the preposition "for" to indicate the recipients. When direct object of the verb "provide" is the recipients, we use the preposition "with" to indicate the provisions. We provide [things] for [people], but we supply [people] with [things].