Many teenagers need space away from their parents to be with friends and to gain their independence. But space is one thing that teenagers in a homeless shelter — who must share single rooms with their families and who must be with a parent at all times — do not have.

That’s why the nonprofit Homeless Children’s Playtime Project is leading an effort to build a teen center at D.C. General, the former hospital that serves as the city’s largest shelter.

The group is preparing to renovate the hospital’s old waiting room — a dusty, forgotten space that has been cordoned off for years — into a bright, light-filled space where teens and tweens can use computers, do homework and spend time together.

“We’re really thrilled to have an opportunity to transform it and send the message to teens that you’re welcome here; this is a safe space,” said Jamila Larson, the Playtime Project’s founder and executive director. “Many of the teens we know, they say the hardest part of living in a shelter is hiding it from their friends” at school, Larson said. “I think it’s going to help teens to find belonging and safety.”

As housing costs in the District have risen in recent years, the number of homeless children and families has spiked, mirroring a rise in child homelessness nationwide. There are now more than 1,200 homeless children in the city, according to the Department of Human Services, including more than 400 at D.C. General.

This is the plan for the preteen side, for kids 8-12 years old, at D.C. General shelter. (Courtesy of Gabe Peyton)

It’s not known how many of those children are teens and tweens; the city doesn’t keep track.

The climbing numbers of homeless children in the District, and the conditions in which they are forced to live, drew little public notice until last year’s disappearance of 8-year-old Relisha Rudd, who lived at D.C. General. Relisha has been missing for about 18 months and is presumed dead.

The ensuing outrage helped the Playtime Project win its long campaign to build a shelter playground. There had been little political will to build a playground at the shelter, widely seen as a shameful place to house families; then-Mayor Vincent C. Gray had been promising to close D.C. General, not fix it up. But Larson argued that children needed — and deserved — a place to run and play in the meantime.

The playground opened a year ago, and on a recent weekday night it was crowded with shrieking, laughing kids.

D.C. General has a room for infants, also courtesy of the Playtime Project, a tiny D.C. nonprofit group that works to carve out kid-centric places in shelters that can otherwise feel overwhelming and scary.

But older children, who have outgrown slides and swings, have had no such dedicated place. “They’re obviously children, too, but they have very different needs,” Larson said.

Destyni Tyree, 16, has lived at D.C. General since February, and she doesn’t complain about it. “It’s fine,” she said, and then her eyes light up as she talks about graduating from high school a year early and applying to college.

But she acknowledged that it can be tough. “I love my mom and my sister dearly, but sometimes I need to get away from them,” she said.

Destyni sometimes chats with other girls in the bathroom while they do their makeup and hair. But otherwise there’s nowhere else to hang out: The hallways are ­off-limits, as are other families’ rooms.

“I think it will give the kids a new outlet,” said her mother, DeQuetta Tyree.

Larson’s group has held evening programs for teens several nights a week for the past three years. But they meet in a shared activity room and are often displaced when others need it.

The new space will give teens a stable place that’s all theirs. Gabe Peyton, a local builder and designer who is volunteering his time to lead the project, showed teens drawings of the renovated space this week.

Wooden cubbies stacked six feet high will separate the large room into a space for teenagers on one side and tweens 8 to 12 on the other. Stained structural columns will become green “reading trees” with bookshelves around their bases; old waiting-room chairs will be replaced by tables and computers; and there will be a snack area.

“Oh, that looks good!” said one young woman with long braids.

The Playtime Project won a $30,000 grant from Lowe’s to buy furnishings and building materials. Peyton and a team of more than 80 volunteers are planning to work over several weekends in October, knocking out several walls to let in more light, painting, and installing new ceiling tiles and windows.

A ribbon-cutting is planned for Oct. 21.

“I like to work with really good people, and everyone was just so kind,” said Peyton, who is donating more than 100 hours of work. “I saw the space and thought we could do something really cool with it.”

Larson said that the administration of Mayor Muriel E. Bowser (D) has embraced the project and helped make it happen quickly, a welcome change after the long fight to build the playground. Larson said that the teen center — as well as a new laundromat in the shelter and flowers planted outside in what has long been a patch of dirt — is evidence that the administration is trying to improve conditions there even as there are plans to close it by 2017.

“We’re really grateful for the Playtime Project,” said Dora Taylor, spokeswoman for the Department of Human Services. “Of course we’re happy to try to make it easier for them to do their work.”