A bologna sandwich: That’s what students of Shelby County Schools in Memphis, Tenn., received for lunch if they forgot to bring the $2 or so to pay for their food.

Nothing: That’s what some impoverished students (80 percent qualify for free lunch) would rather sit with in the cafeteria than be revealed as the “poor kid” to their classmates.

“We see kids every day that don’t go through the lunch line because they don’t want to be identified as that kid who gets a free meal. That stigma is huge,” Tony Geraci, the executive director of Shelby County Schools’ nutrition program, tells The Commercial Appeal.

But come this school year, that will all change. The school system will be serving three meals to every single student in the district — breakfast, lunch and dinner — all for free, regardless of how wealthy their family may be.

It’s due to a federal program that’s changing the way cash reimbursements for school lunches are distributed. Rather than judging individual families in relation to the poverty line, the government is now looking at the economic well-being of entire cities. Known as the “community eligibility provision,” the program kicks in once 40 percent of the school district’s population is considered low-income (largely based on signups for food stamps). Reimbursements in Memphis will now doled out based on how many meals are served in a cafeteria rather than how many poor kids attend a school, creating an incentive to serve additional meals.

Nutritious meals had been (and continue to be) correlated with academic performance. One 2002 study undertaken by a Harvard Medical School professor found that students “at nutritional risk” missed more days of school and expressed more anxiety and aggression — areas that all showed improvement six months later when a free breakfast program was implemented. It may sound simplistic, but a plate of chicken or lasagna could the difference between kids who pay attention to their teacher and the ones who focus on their empty stomach, a divide that largely falls on economic lines.

America’s subsidized school lunch programs date back to World War II, when many young men were rejected from the draft due to the lingering physical consequences of childhood malnutrition. The National School Lunch Act, passed in 1946 as a “measure of national security,” got a major update in 1998 when Congress agreed to start paying for snacks for youngsters in certain after-school extracurriculars. Launched experimentally in 2010, the latest expansion goes even farther, ensuring there’s food on every child’s plate at every meal. It’s part of First Lady Michelle Obama’s signature “Let’s Move!” campaign to end childhood obesity.

Supporters say the latest plan is essential to preventing hunger in classrooms in Memphis and across the country — Chicago, Boston, Baltimore, parts of New York City and elsewhere. Not only does “community eligibility” eliminate stigma for children who’d otherwise qualify for free or reduced lunch, it also ensures that other students — the ones who didn’t file their annual paperwork, others who may be just above the poverty cutoff or some of the growing number of homeless youth — don’t fall through the gap. For several kids, not eating a healthy meal at school means not eating at all.

“Kids won’t be going home and saying, ‘I’m hungry,’ and their mother just says, ‘I don’t have anything for you to eat,’ and not enough money to go to the market maybe,” one student in Baltimore, Adria Johnson, told the local news station when her district qualified. All together, nearly 6.4 million students across 13,800 districts are now being fed by the expanded criteria. In Memphis alone, parents will save $1.8 million they previously forked over for lunch.

“Stigma really overshadows a lot of the great things we do,” Geraci says. “For once, we’ll be able to have a program where we can say, now it’s time to learn, now it’s time to eat, now it’s time to play. That’s huge for this district.”