It sounds like a dream for some working parents: school for 12 hours a day, starting bright and early at 7 a.m. and ending after dinner, at 7 p.m., all completely free.

One elementary school, Brooklyn Charter School, is experimenting with the idea as a way to tackle two problems at once. The first is a sharp decline in students in urban schools. Families are leaving city public schools around the country, including in New York City, which has led some districts to consider merging schools or even closing them.

The second is the logistical nightmare many parents face as they try to juggle jobs and child care.

Millions of families scramble to fill the gap between school dismissal, around 3 p.m., and the end of the work day, several hours later. Many never escape long waiting lists for after-school programs. Others simply cannot afford to sign up. Lower-income parents often have the hardest time finding high-quality care.

These obstacles — along with high rents and costs of living — are driving families away from the city. Brooklyn Charter School is in Bedford-Stuyvesant, a rapidly changing neighborhood where Black families have departed in droves. The school, where Black students make up three-fourths of enrollment, lost nearly 30 percent of its students during the coronavirus pandemic, shrinking from more than 230 children to fewer than 165.

“We thought, ‘We have to do something radical,’” the principal, Joanne Hunt, said. “School hours aren’t made for working people.”

So far, the idea of staying open 12 hours a day seems to be working. About 80 students have signed up for the longer hours, and the school’s enrollment is now close to 200. It is a sign that in an expensive city, the most important school amenity for some parents might not be a state-of-the-art science lab or a media studio, but affordable child care.

“We love it,” Ayanna Souza said as she picked up her 10-year-old daughter, Jada Lee, on a recent evening. “Before this,” she said, “I was struggling.”

While many of the students in the program do not stay at school for the full 12 hours, staff members acknowledge that it can be a long time for children to be away from home — which may be hard on them and on their families. But long days are a common experience in a city where many parents work long hours to get by, and where commutes can tack on hours to the workday.

Research shows that after-school programs, especially high-quality ones, can help improve a child’s attendance, academics and other measures of well-being, including mental health.

But as the city grapples with budget constraints, hopes have dimmed that the number of after-school seats can be expanded, and some programs have even been cut. Charters often receive funding and grants from outside groups, which can allow them to offer programs that some district schools cannot afford.

Brooklyn Charter used to open its doors at 7:30 a.m. Now, a few dozen students arrive half an hour earlier. They read books and tell stories in an auditorium under the watchful eye of a social worker.

From 8:30 to 4 p.m., school goes on as normal. On a recent Tuesday, there were blocks of math practice, mock English exams and a book fair. When the formal school day ended, the fun began for the seven dozen students who stay late under the care of counselors.

First up: a meal. Angela Alegria, who works in the school’s kitchen, pulled fries out the oven to go with fish sandwiches. The chicken tenders and mozzarella sticks are the favorite, though, according to a group of 6-year-old friends, Aaron, Ashton and Mia.

After dinner that evening, a boisterous comedy session began. Students drum-rolled on tables as their friends took the stage — a large crate in the center of the cafeteria — to crack jokes. One young girl stole the show, asking, “Why did the cow go to the theater?”

She paused, before bringing down the house: “Because he wanted to watch a moooooovie.”

Then the students split up for a series of activities.

Room 320 broke into booms and bangs as older students practiced the drums. An instructor quizzed them about quarter notes and helped them identify low- and high-pitched sounds.

“Hands in places!” the instructor said, later asking one boy who was tipping his instrument back and forth, “How do we hold our drum, sir?”

Across the hall, kindergartners counted on their fingers to complete their math homework. “I did it!” one student yelled out after solving a particularly tough problem.

And in another room, first graders grabbed card stock and markers to design robots to look like Sonic the Hedgehog and Disney princesses. When it was time for the groups to rotate sessions, one girl shouted out something unthinkable.

“Homework time,” she said. “Yay!”

In New York, fewer than half of public schools offer free, city-funded services after school. In addition to boosting academic achievement, these can help keep students out of trouble: Most juvenile crime occurs in the hours around dismissal. But most of those programs end at 6 p.m., if not earlier.

The dearth of choices is gaining political attention. The State Senate recently said it wants to explore options for universal after-school programming. One Democratic lawmaker and potential mayoral candidate, Zellnor Myrie, has argued that such an initiative could be a “game changer” for families.

At Brooklyn Charter, many families just wanted better child care. “There was a huge need in our community,” said Roger Redhead, who runs the program.

Throughout the evening, parents trickled in after work. Princess Williams, whose son Adonis often stays for about two hours after dismissal, said the program had made her family’s life much easier. “It’s just beautiful,” she said.

By 6:30 p.m., only about five students were left.

They entertained themselves with intense tic-tac-toe matches at a cafeteria table. Some wanted to stay even later and keep playing when their family members arrived.

The parents reminded their children: You’ll see your friends again — in 12 hours!