Breakfast had already been free systemwide, school officials said, and the city’s stand-alone middle schools had a universal free-lunch pilot in place since 2014 that fed an additional 10,000 children who would not necessarily have qualified for free or discounted lunches, officials said.

Among the parade of speakers at Wednesday’s announcement was City Councilman Ben Kallos, who recounted his own experience with the stigma of subsidized school meals.

He grew up on the Upper East Side and, like many of his neighbors, attended Bronx High School of Science. But his mother’s income in his single-parent household was low enough that he qualified for reduced-price lunches — a fact he tried to hide from his peers by not eating.

“I had to choose between friends and food,” Mr. Kallos said. “I hope no child makes the same poor choices I did.”

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