But without money to buy furniture, the family shared a queen-size bed and ate meals sitting on the floor, the plates atop crates. Much of the rest of the apartment was bare.

“We didn’t have anything, but we were so happy to have our own space,” Ms. Farquharson said. “We made it work.”

Desiring a positive family environment for her children, she decided to contact the Children’s Aid Society, one of eight organizations supported by The New York Times Neediest Cases Fund. It gave the family $1,800 to buy bunk beds for the children, as well as a kitchen table, dressers, a lamp and a television stand.

“It made it home,” Ms. Farquharson said.

Her own childhood has informed her hands-on mothering, she said. As a teenager and self-proclaimed “wild child,” Ms. Farquharson often fought peers in the streets, and when at 16 she had her eldest child, Quanelle, the city’s Administration for Children’s Services threatened to take her son away, she said. Her mother was granted custody.

Years later and in a committed relationship with Mr. Jones, she hoped to have more children, but doctors said she would not be able to have any more because of a blockage in one of her fallopian tubes. Still, the couple kept trying.

And in 2008, doctors told her that she had defied the odds. At first she did not believe she was pregnant, but later that year she gave birth to Lasaun, and four years after that she had Savaun. She considered the birth of her children — “my two miracles, walking” — a chance to raise the family she dreamed of as a child.