The food she offers is supplied by the federal government to the state, which distributes it each summer through various sites.
Poe's program is supervised by the Archdiocese of Philadelphia, which feeds children of all backgrounds in the suburbs and the city, according to Anne Ayella, assistant director of nutritional development services for the archdiocese.
Other summer feeding sites are run by the Philadelphia Department of Parks and Recreation and the Philadelphia Housing Authority. The School District of Philadelphia feeds some students who are in class during summer.
However great the need is in summer, though, not everyone gets to eat.
"Far too many kids" are missing out on the nutrition they need to be healthy, said Laura Wall, executive director of the Greater Philadelphia Coalition Against Hunger. Their families, who are feeling "a great financial strain, then turn to local food pantries for help."
In July 2013, for every 100 Pennsylvania students who ate free or reduced-price lunch in school, 19 participated in summer meal programs, according to data from the Food Research and Action Center, an antihunger advocacy group.
In Philadelphia, 160,000 low-income students in public, charter, and Catholic schools qualified last year for free or reduced-price lunch, according to the coalition's latest available figures.
But on an average day, about half of the students were not taking part in summer meals.
Experts are at a loss to explain what's happening to the children who aren't participating in summer meals programs, or how they are getting by.
In Darby Township, it's clear "there's a lot of need," said Carol Conway, 58, a disabled U.S. Army veteran who volunteers with Poe. "Around 99 percent of the kids are low-income, and three-quarters come from single-parent families."
Told to be quiet the other day, two dozen chattering, exuberant children at the library hushed and seated themselves in three seconds, because they knew what was coming.
"Some parents don't have enough, and kids are here for food," said James Samura, 13.
For Lorie Wade, 57, who cares for her three grandchildren during the summer, Poe's program is a neighborhood necessity. "It's hard to get them nutrition in the summer, and I'm so thankful for this."
On Tuesday, the children ate lunches of chicken nuggets, fruit, juice, cookies, and nonfat milk.
Afterward, Conway declared them "calm and happy."
"I love them all," she added. "I love them all so much. This is our future, right here. And we have to take care of it."