At around 11 a.m. on a recent Thursday, half of the children at an early childhood center in Queens fidgeted in their seats as they waited for their classmates to clean the remaining toys from the floor. Then they could all go outside.

The Saratoga Early Childhood Education Center, which offers universal prekindergarten during the school year, looks like any other provider except for one crucial difference: It’s housed at one of the largest family shelters in the city. This fall the center’s pre-K program will grow from half-day to full-day, as part of the mayor’s pre-K expansion plan.

In its effort to add thousands of pre-K seats this fall, the city has tapped non-traditional providers, including libraries, yeshivas, and shelters. A group called Homes for the Homeless receives EarlyLearn grants to fund the pre-K programs at Saratoga Family Inn and at another shelter in the Bronx, both of which are expanding to full-day this fall.

When Saratoga started offering universal pre-K in 2012, the enrollment specialist, Sade Dickson, had to help parents get past the stigma attached to offering a school for all kids in a homeless shelter.

“I say, ‘Come and see for yourself,’” Dickson said, adding that she stopped people with small children in the park or at community meetings. “A lot of them come and are impressed with the curriculum and see that the kids are happy.”

The school at Saratoga is bright and cheery, with a large outdoor space filled with trees. Still, one must pass a guard booth and front desk and walk along a windowed corridor with yellow painted brick to get to the education center.

And while the educational standards match those of any other universal pre-K site, the teacher here, Jodi Daniels, said the program lags in parent engagement and daily attendance. Families in shelters come and go, which means class size fluctuates throughout the year.

“A month later you could have five new kids,” Daniels said.

Daniels, whose son just finished kindergarten, which included pages and pages of Common Core worksheets, knows where her pre-K kids need to be before kindergarten.

“It’s imperative that they have pre-kindergarten,” she said. “Otherwise, in kindergarten they will be absolutely lost.”

Students learn not just their ABCs in pre-K, but social skills as well, which are particularly important for kids from the shelter who are sometimes behind their peers in socializing. When the outside kids, as Daniels calls them, come into school with stories about trips to Coney Island or Disney World, they share those stories with the inside kids.

“It sparks their imagination,” Daniels said. “So they know there is more outside of the nearby airport and the McDonald’s down the street.”