The number of school-age children in New York City who live in shelters or “doubled up” in apartments with family or friends has swelled by 70 percent over the past decade — a crisis without precedent in the city’s history.

By day, New York’s 114,085 homeless students live in plain sight: They study on the subway and sprint through playgrounds. At night, these children sometimes sleep in squalid, unsafe rooms, often for just a few months until they move again. School is the only stable place they know.