Praise be to Allah.
Allaah has blessed this ummah with many great blessings, among which is the fact that Allaah has bestowed upon this ummah unique privileges which He did not bestow upon the previous nations. These unique privileges include the fact that they may pray in any place so long as that place is taahir (pure, clean) and not naajis (unclean) and is not a place where it is forbidden to pray. It says in a hadeeth whose authenticity is agreed upon, which was narrated from Jaabir ibn ‘Abd-Allaah, that the Messenger of Allaah (peace and blessings of Allaah be upon him) said: “I have been given five things that were not given to any of the Prophets before me. I have been granted victory by means of awe, (by His frightening my enemies) for a distance of one month’s journey; the earth has been made a mosque (place of worship) for me and a means of purification, therefore anyone of my ummah can pray whenever the time for prayer is due; the spoils of war have been made permissible for me; and each Prophet was sent only to his own people, but I have been sent to all of mankind; and I have been granted (the power of) intercession.”
(Narrated by al-Bukhaari, 419; Muslim, 810).
Undoubtedly this is a great blessing which makes things easier for the Muslims. So you may pray anywhere in the school, so long as it is a clean place.
Please see also Question No. 9455.
With regard to the places where it is forbidden to pray, such as graveyards and washrooms, it was narrated in a saheeh report that the Prophet (peace and blessings of Allaah be upon him) said: “All of the earth is a mosque, apart from graveyards and washrooms.” (Narrated by al-Tirmidhi, al-Salaah, 291; classed as saheeh by al-Albaani in Saheeh Sunan al-Tirmidhi, 262).
It was also narrated that it is forbidden to pray in the places where camels sit, and other places where there is evidence (daleel) to say that it is forbidden to pray in them.
Undoubtedly the matter of prayer is one of the matters which cannot be taken lightly. So you must strive to pray before the time of that prayer is over. May Allaah help you to obey Him. And Allaah knows best. May Allaah bless our Prophet Muhammad.