Amari Whitfield, 5, left, and his sister, Amera Bakker, 8, play with donated Leapfrog toys while their mother, Tara Whitfield, looks over their shoulders in their new apartment on March 7 in Washington. (Bill O'Leary/Washington Post)

Ivy Duke could have dropped her donation in one of three yellow bins behind the National Center for Children and Families in Bethesda. Instead, she tucked the used toy inside a Lord & Taylor shopping bag, handed it to an employee inside the building and then, just in case, e-mailed the executive director to make sure she knew what had been left.

This wasn’t any toy. It was a LeapFrog Leapster game system that her son, Ian, a boy who had endured five open-heart surgeries by the age of 4, had played with for years and now wanted to go to the right home.

“He said it should go to a family where there is more than one kid,” Duke said. “It should be a family where a lot of kids can appreciate it.”

Every year, millions of items worth billions of dollars are donated across the nation: clothes, books, bikes, tools, tchotchkes, junk. On any given day at the children and families center, two dozen people might bring bags filled with the unwanted contents of their closets or garages. Most donors never know what happens to their stuff.

In this case, a treasured plaything did not take the anonymous route. It connected two Washington area families who likely would have never crossed paths.

One lives in a Montgomery County neighborhood where pillars adorn spacious homes. The other lives in a three-bedroom apartment in a Southeast Washington complex surrounded by an iron fence.

Before their move to Anacostia in November, it had been four years since Tara Whitfield and her two children, Amari, 5, and Amera, 8, had a space to call their own. A housing voucher enabled them to leave the New Beginning Temporary Family Shelter. Before that, they were at the D.C. General Hospital homeless shelter.

“It was scary,” Whitfield said. “But we got through it.”

Her family ended up in the shelter after her mother died, Whitfield said, leaving her without a home and the support system she had always relied on. The single mother said it has been a challenge to find a job that fits her children’s schedule — at a recent interview she was asked to work nights — and that she has had to explain to her children why she doesn’t have a car or why they had to start school with only one uniform.

When the two ask for toys they see advertised on TV, she said, “You don’t know what that does to me.”

The educational game system couldn’t have arrived at a better time for the family. Christmas was around the corner, and a donated tree sat in the corner of their apartment waiting for presents to be placed underneath it. The children’s wish list was clear about what they wanted: “Games.” But Whitfield knew she couldn’t afford any.

Sheryl Brissett Chapman, the center’s executive director, said that when she read Duke’s e-mail, she decided this donation should be treated differently. It was put aside, and employees at the nonprofit, which oversees 18 programs, including New Beginning, were asked to find the right fit.

Just days before Christmas, Whitfield’s case manager from the shelter arrived at her door. With him, he carried the contents of that Lord and Taylor bag: not one, but two hand-held Leapsters, along with 16 game cartridges. Bought new, the set would have cost more than $500. The children opened the game sets on Christmas morning.

“Normally, they have to share everything so once they got these gifts, their faces just lit up,” Whitfield said. “Amari stayed up playing with it the whole night.”

Amari, who wants to be a firefighter so badly he has been known to chase trucks down the street, zipped through the living room one afternoon, a blur of energy. Then he grabbed the game console, popped in a “Go Diego Go!” game and curled up on the couch next to his mother, all focus.

“I think it’s awesome,” Amari said of the game system. Of the boy who gave it, he said, “We should be thankful that he picked the right family.”

Whitfield said she considered letting her children think that Santa brought the Leapsters, but when she learned of their origin, she thought it was important to tell them about the boy who owned the games first. She said she has also encouraged her children to donate the clothes and toys they outgrow.

Kareem Davis, the program director for New Beginning, said the Leapsters did more than give two children something to open on Christmas. “The impact it had on this family is, ‘Someone does care about me,’ ” Davis said.

Ivy Duke said she chose the center because she had once volunteered to rake leaves there and knew that the agency worked directly with families.

In the e-mail she sent to Chapman, Duke joked that Ian was “spoiled” and explained his rocky start to life. His heart condition was diagnosed during her 20-week sonogram, and he was only 3 days old when he had his first surgery.

Ian, now 10, talks about his heart condition in the past tense. He doesn’t let it stop him from playing baseball or basketball or, on a recent afternoon, Ultimate Frisbee. Even so, he’s aware of his limitations.

“I can’t do tackle football. I can’t do roller coasters,” he said. At a friend’s birthday party, he noticed a sign warning people with heart conditions against playing laser tag, so he asked an attendant’s permission. “They said I could do it, and I survived — yay,” he said. “I’m so glad I didn’t ask how fast the go-carts went because the go-carts were so much fun.”

Ian, who recently won fourth place in a school chess tournament and during an art class produced an impressive self-portrait that now hangs over his family’s fireplace, said he is glad that two children have his game. It was a favorite toy of his from the age of 5 to 8, but he has moved onto an Xbox and his father’s iPhone. “I just wanted someone to have it because I enjoyed it,” he said, “and I wanted someone else to enjoy it.”

He also received an unexpected gift in return. Amari and Amera each made him a thank-you card.

Amari’s features two glitter-traced hands with the words, “These hands appreciate these gifts.”

Amera, a third-grader who loves art and reading, went through three versions before she settled on the one she sent. It reads: “The world will be a better place if everyone had a heart like yours.”