BALTIMORE — On the first day of the coronavirus school closure at Sinclair Lane Elementary School, Janet Bailey, the cafeteria manager, showed up to the school’s kitchen like any other day, ready to do her job. She began fixing the favorites of the 250 or so children who relied on her to feed them daily — chicken patties, a fruit and vegetable, and flavored milk.

On the second day, Ms. Bailey realized that she had answered a calling. By the time the building in northeast Baltimore had opened at 10 a.m., there was a line. Among the first was a man who said he only had a half a loaf of bread in the refrigerator.

“I just packed him up, no questions asked,” said Ms. Bailey, one of dozens of food service workers who signed up to staff meal sites around the city. “I didn’t know his situation, if he had four kids at home or not, like he said. But I know he was hungry. We are supposed to be here to meet the needs of the community. How could I say no?”

After the coronavirus shut down America’s education system, districts fortified their school meals programs to ensure that their most needy students would stay fed. One month in, school leaders realize the federal programs set up to subsidize the meals of tens of millions of students cannot meet the demands of an emergency that has turned their cafeterias into food banks and community kitchens.