Last year, Ms. Dunn said she got a call from a mother who was injured in a nearby homeless shelter and needed surgery. But when the mother was forced to find another shelter, her four children, all of whom attended P.S. 446, had to figure out a way to travel to the Bronx to apply for a new placement at the city’s sole intake center for homeless families, Ms. Dunn said.

Ms. Dunn sent one of her social workers to the shelter to help arrange a paid taxi ride to bring the injured mother and her children across the city, but the four students still missed several days of school. That was one of many emergency situations that Ms. Dunn said she dealt with that week.

In one Bronx school district, 10,804 students are homeless

School districts that have long served low-income students are absorbing more homeless students each year.

District 10 in the Bronx served the most homeless children of any of the city’s 32 school districts last year. The district includes Kingsbridge International High School, where about 44 percent of students who attended the school over the last four years were homeless at one point.

More homeless students typically means more tardiness or absentees because of the challenges to get to school. Last year, students living in shelter missed an average of about 30 days in the school year.

Some students have to travel through two or more boroughs to reach school from their shelters; only about half of the city’s homeless families lived in a shelter in the same borough where their youngest child attended school last year. This fall, the city started a program to move more families into shelters no farther than five miles from their youngest child’s school.