In an action to recover damages for personal injuries, etc., the defendant Herricks Union Free School District appeals, as limited by its brief, from so much of an order of the Supreme Court, Nassau County (Alpert, J.), dated March 11, 2003, as, upon reargument, denied its motion for summary judgment dismissing the complaint and cross claim insofar as asserted against it, and the plaintiffs separately appeal, as limited by their brief, from so much of the same order as, upon reargument, granted that branch of the cross motion of the defendant Irving Pergament, as administrator of the estate of Moshe Pergament, which was for summary judgment dismissing the complaint insofar as asserted against him.
Ordered that the order is modified, on the law, by (1) deleting *608the provision thereof denying the motion of the defendant Her-ricks Union Free School District for summary judgment dismissing the complaint and cross claim insofar as asserted against it and substituting therefor a provision granting the motion, and (2) deleting the provision thereof granting that branch of the cross motion of the defendant Irving Pergament, as administrator of the estate of Moshe Pergament, which was for summary judgment dismissing the fifth cause of action, and substituting therefor a provision denying that branch of the cross motion; as so modified, the order is affirmed insofar as appealed from, with one bill of costs payable by the plaintiffs to the defendant Her-ricks Union Free School District, the complaint is dismissed insofar as asserted against the defendant Herricks Union Free School District, and the action against the remaining defendants is severed.
In 1993 the then-infant plaintiff, Paul Siegell (hereinafter the plaintiff), and the now-deceased defendant, Moshe Pergament, were students at Herricks High School. During a “frisbee relay race” in physical education class, the plaintiff allegedly sustained personal injuries when Pergament ran into or pushed him from behind while they were going for the same frisbee. The plaintiff and his mother commenced this action against, among others, the Herricks Union Free School District (hereinafter the District) and Moshe Pergament. They asserted causes of action alleging negligent supervision against the District and alleging negligence and battery against Pergament. During the pendency of the action, Moshe Pergament died and was replaced as a defendant by his father, the defendant Irving Pergament, as administrator of his estate. After discovery, inter alia, the District moved and Irving Pergament cross-moved, for summary judgment. The Supreme Court denied the District’s motion and granted the cross motion. We modify by granting the District’s motion and denying that branch of the cross motion which was to dismiss the fifth cause of action alleging battery against Moshe Pergament.
The Supreme Court should have granted the District’s motion for summary judgment dismissing the complaint and cross claim insofar as asserted against it. “Schools are under a duty to adequately supervise students in their charge and they will be held liable for foreseeable injuries proximately related to the absence of adequate supervision” (Mirand v City of New York, 84 NY2d 44, 49 [1994]; see Capotosto v Roman Catholic Diocese of Rockville Ctr., 2 AD3d 384 [2003]). In addition, the plaintiff must prove that a school’s negligence in supervising its students was a proximate cause of his or her injuries (see Mirand v City *609of New York, supra at 50; Capotosto v Roman Catholic Diocese of Rockville Ctr., supra). “Where an accident occurs in so short a span of time that even the most intense supervision could not have prevented it, any lack of supervision is not the proximate cause of the injury and summary judgment in favor of the School defendants is warranted” (Convey v City of Rye School Dist., 271 AD2d 154, 160 [2000]; see Capotosto v Roman Catholic Diocese of Rockville Ctr., supra at 385-386; Lopez v Freeport Union Free School Dist., 288 AD2d 355, 356 [2001]).
In this case, the plaintiffs injuries were caused by a “spontaneous and unforeseeable act committed by a fellow . . . student” (Sangineto v Mamaroneck Union Free School Dist., 282 AD2d 596 [2001]; see Capotosto v Roman Catholic Diocese of Rockville Ctr., supra; Wuest v Board of Educ. of Middle Country Cent. School Dist., 298 AD2d 578 [2002]; Shabot v East Ramapo School Dist., 269 AD2d 587 [2000]). Further, Moshe Pergament’s prior disciplinary problems were insufficient to place the District on notice that he would intentionally run into or push the plaintiff into a wall during a frisbee relay race (see Calabrese v Baldwin Union Free School Dist., 294 AD2d 388 [2002]; O’Neal v Archdioceses of N.Y., 286 AD2d 757 [2001]; Kennedy v Seaford Union Free School Dist. No. 6, 250 AD2d 574 [1998]; Moores v City of Newburgh School Dist., 237 AD2d 265 [1997]). Therefore, the District was entitled to summary judgment dismissing the complaint and cross claim insofar as asserted against it (see Tanon v Eppler, 5 AD3d 667 [2004]; Calabrese v Baldwin Union Free School Dist., supra).
The Supreme Court should have denied that branch of Irving Pergament’s cross motion which was for summary judgment dismissing the fifth cause of action alleging battery against Moshe Pergament. “ ‘The elements of a cause of action [to recover damages] for battery are bodily contact, made with intent, and offensive in nature’ ” (Tillman v Nordon, 4 AD3d 467 [2004], quoting Zgraggen v Wilsey, 200 AD2d 818, 819 [1994]). In this case, a triable issue of fact exists as to whether Moshe Pergament intentionally ran into or pushed the plaintiff, causing his injuries.
The plaintiffs’ remaining contentions are without merit. Florio, J.P., Townes, Cozier and Mastro, JJ., concur.