Nationally, reliable numbers are hard to come by, but New York City has the nation’s largest school system and perhaps its most acute housing crisis.

Not all students who are considered homeless live in shelters. Students in temporary housing includes families living in their cars or in hotels, or those “doubled up” with family or friends. An analysis of the state data, conducted by Coalition for the Homeless, found that families living with relatives or friends drove last year’s increase, with about 4,400 more students living in such situations than the year before. The number of students in shelters increased by roughly 1,900.

The upheaval in the home lives of students in temporary housing often follows them into school. Many of them frequently change schools as they bounce from one temporary living situation to another. Many are placed in shelters far from their original school, which means they must either transfer midyear or commute long distances each day. Many students regularly arrive late or miss days of school altogether.

Those stresses harm their academic performance. A report released this summer by the Institute for Children, Poverty, and Homelessness found that homeless students passed the state English tests at about half the rate as their peers who had permanent homes. Homeless students who were designated as English Language Learners generally took longer to become proficient in the language. On average, the report found that one-third of homeless students miss the equivalent of a month of school. Students living in homeless shelters had the highest rates of chronic absenteeism, meaning they missed more than 10 percent of school days.

Liz Cohen, chief of staff at the Institute for Children, Poverty, and Homelessness, said that while most of the city’s homeless policies are aimed at getting people housed, the academic damage can linger long after students find a place to live.