IRBID, Jordan — A mother and young girl from Syria shuffled into the principal’s office at the towering Qadasiya school on Wednesday, hoping to find a way for the child to attend class with other kids who speak, look and study like her. Let her stay, a Ministry of Education official said, and you can fill out the paperwork afterward.

The Jordanian government last week relieved pressure on already packed public schools by moving hundreds of Syrian children into special afternoon shifts at three schools in this northern Jordanian city, as the government buckles under the weight of Syrian refugees.

A major influx of refugees in recent weeks — about 500 cross into Jordan each night — has severely strained already overstretched Jordanian infrastructure and has put pressure on the kingdom’s finances as it faces some of the most significant protests in its history, which were sparked by simmering discontent over the worsening economic situation here. As it did when Iraqis fled violence in their country, the government has pledged to provide free education, health care and other services to the Syrians.

Five hundred Syrians have enrolled so far at Qadasiya, and many more pour in each day, said Rania al-Reyahna, the principal. The ministry’s plan has opened up space in schools in the north where class sizes had reached upwards of 50 or 60 students.