On the Brooklyn block that is Dasani’s dominion, shoppers can buy a $3 malt liquor in an airless deli where food stamps are traded for cigarettes. Or they can cross the street for a $740 bottle of chardonnay at an industrial wine shop accented with modern art.

It is a sign outside that locale, Gnarly Vines, that catches Dasani’s notice one spring afternoon: “Wine Tasting Tonight 5-8.”

Dasani is hardly conversant in the subject of libations, but this much she knows: A little drink will take off her mother’s edge. Without further ado, Chanel heads into the wine shop on Myrtle Avenue, trailed by four of her eight children. They are lugging two greasy boxes of pizza and a jumbo pack of diapers from Target.

The cashier pauses. The sommelier smiles.

“Wanna try a little rosé?” she asks brightly, pouring from a 2012 bottle of Mas de Gourgonnier. “I would describe it as definitely fruit forward at the beginning.”

Chanel polishes it.

“But really crisp, dry, refreshing ——”

“Not refreshing,” Chanel says. “I just think dry.”

“No, it’s very dry,” says the sommelier, a peppy blonde in wire-rim glasses. “It’s high acid, a little citrusy.”

Chanel sticks out her tongue. She finds the woman’s choice of words unappetizing. To the side of the wine display is a large, silver vase that recalls the family urn, prompting Chanel’s son Khaliq to ask if it contains the ashes of a dead person.

“Oh my gosh, for cremation?” the sommelier asks, shaking her head. “We just use it for spitting in.”

“For spitting?” Chanel says with horror.

“Yeah, it’s got rejected wine in it,” the sommelier says.

Chanel scoffs. She might not like the wine, but she sees no reason to spit it out. She moves on to a Tuscan sangiovese.

Ignoring the spectacle, Dasani scans the room, frowning at a sign on the wall: Liqueur. “They got liquor spelled wrong,” she yelps victoriously.

Actually, the sommelier interjects, that is the French word for the delicate, liquid spirits derived from fruits such as pomegranates and raspberries. “But you’re very right,” she offers sweetly. “That is not how you spell liquor.”

“Not the hood liquor,” Chanel says.

Dasani’s neighborhood is one of the most unequal pockets of New York City, the most unequal metropolis in America. ■ Fort Greene occupies less than one square mile. On the map, its boundaries form the shape of a pitcher tilting at the northwestern edge of Brooklyn.

Just north of Fort Greene Park are the projects and, among them, the homeless shelter where Dasani lives.

Just south of the park are some of Brooklyn’s finest townhouses and cultural gems, including the Brooklyn Academy of Music, where theatergoers were lining up to see “Julius Caesar” on the day that Dasani led her mother to the wine shop.

If one thing distinguishes Dasani’s New York from that of her antecedents, it is a striking proximity to the wealth that eludes her.

She routinely walks past a boho-chic boutique on Lafayette Avenue where calfskin boots command $845. Heading north, she passes French bulldogs on leashes and infants riding like elevated genies in Uppababy strollers with shock-absorbing wheels. Three blocks away is an ice cream parlor where $6 buys two salted-caramel scoops.

Like most children, Dasani is oblivious to the precise cost of such extravagances. She only knows that they are beyond her reach.

Nor can this 11-year-old girl be expected to grasp the subtle gradations of Fort Greene’s elite, whose creative class feels pushed out of a neighborhood it once considered more gritty than tony.

Dasani sees the chasms of Fort Greene more plainly, reasoning that wealth belongs to “the whites” because “they save their money and don’t spend it on drinking and smoking.”

Such perceptions are fed by the contrasts of this neighborhood, where the top 5 percent of residents earn 76 times as much as the bottom quintile. Dasani spots addicts gathering outside a food pantry a block from $2 million brownstones. She notes that few people in the projects use the Citi Bikes stationed nearby. The celebrated bike sharing program, unveiled this year, requires a credit or debit card for a $101 security deposit.

Dasani also knows that not everyone in the projects is poor. Her Uncle Waverly, who lives in the Walt Whitman Houses across from her shelter, the Auburn Family Residence, works as a supervisor for the parks department and has a Lexus S.U.V. When he drives past Dasani and her siblings, he pretends not to know them.

Dasani charts the patterns of Fort Greene Park by skin color. The basketball courts are closest to the projects, drawing black children to that northwestern corner. On the rare occasion when Dasani ventures to the opposite quadrant, she sees white women sunbathing in bikinis or playing tennis near a water fountain outfitted for dogs.

She never finds those women at the nearby Bravo Supermarket for Values, where thieves are photographed in Polaroids that fill the store’s “Wall of Shame.” Wearing naked expressions, they are forced to pose with their stolen items — things like Goya beans and Kraft cheese. A woman named Mary holds a can of tuna in a photograph titled “Catch of the Day.”

Dasani is more likely to encounter shoppers of another stratum at the local Target, where they can save on items that for her family represent a splurge.

Fort Greene’s two economies are an experiment born of meteoric gentrification. In the last decade, the neighborhood has been remade, with the portion of white residents jumping by 80 percent as real estate prices more than doubled despite the recession.

Just the word “gentrification” is remarkably divisive. It derives from the Middle English word “gentrise,” which means “of noble descent.” The word has become shorthand for an urban neighborhood where muggings are down and espresso is roasted — a place that has been “discovered,” as though no one had been living there.

Dasani’s Fort Greene reaches deep into the last century. Her grandmother Joanie grew up in the Raymond V. Ingersoll Houses, next to the Walt Whitman Houses. Both projects opened in 1944, an era of New Deal reforms that gave rise to white flight and urban decay. Fort Greene, like other black areas, was redlined, allowing banks to disinvest and property values to plummet.

The neighborhood’s prospects started to change in 1978, after the city declared part of Fort Greene a historic district. By the time Dasani was born there in 2001, a billionaire was preparing to run for mayor. A year after taking office, Michael R. Bloomberg announced an ambitious redevelopment plan for Downtown Brooklyn.

Fort Greene’s transformation came swiftly. Through aggressive rezoning and generous subsidies, the city drew developers who, in the span of three years, built 19 luxury buildings in the surrounding area that catered — across racial lines — to the educated elite.

Dasani and her siblings routinely pass the Toren, a glistening, 38-story glass tower on Myrtle Avenue offering a 24-hour concierge, gymnasium, pool and movie theater. In June, a condominium there sold for $1.4 million.

Just blocks away stand the Ingersoll and Whitman projects, which engulf Dasani’s shelter and, like Auburn, have fallen into disrepair.

It is the juxtaposition of these neglected time capsules to Fort Greene’s luxury towers that seems to mock the neighborhood’s effort at ascension. For the arriviste investor, the projects present a rude visual interruption, an inconvenient thing to walk around, but never through.

For Dasani, these faded buildings hold a legacy so intricate and rich it could fill volumes were it ever told.

The homeless shelter where she lives is the very building where Grandma Joanie had been born, back when it was Cumberland Hospital. Just across the way is the fifth-story apartment where Joanie grew up, helping her own mother raise seven other children in the clasp of poverty.

Three generations later, little has changed. Even as the fortunes of this neighborhood rose, Dasani’s matrilineal line, from her great-grandmother to her mother, has followed a trajectory of teenage pregnancy, addiction and violence.

Fort Greene is now a marker. For one set of people, arriving signals triumph. For another, remaining means defeat.

Dasani will do better, she tells herself. “People don’t go nowhere in Brooklyn,” she says. Chanel promises they will move this spring, after the tax refunds arrive.

Yet as Dasani walks through her grandmother’s streets, it is not with the sense of imminent departure so much as melancholic return.

Chanel was 8 when she found her mother’s crack pipe in a jewelry box. She held it up to the light and showed it to her brother. ■ We gonna toss it, he said. ■ They opened the window and watched as the brown glass vial soared through the air, crashing onto the sidewalk.

It was the mid-1980s, and crack had swept the streets of Brownsville, Brooklyn, where Chanel’s mother, Joanie, now lived. Chanel visited on weekends. The rest of the time, she stayed with her godmother, Sherry, who had been the common-law wife of Chanel’s father. Chanel’s mother was his lover.

Stranger things had happened in Brownsville, and now that Chanel’s father was dead, the two women made peace, despite their differences. Joanie relied on welfare to support her habit. Sherry ran a day care center and shunned drugs.

“It was like two different people trying to raise one kid,” Chanel says.

At Sherry’s rowhouse in East New York, Brooklyn, Chanel minded her chores and did her homework.

At Joanie’s, the child watched dance parties meld into a predawn haze.

Worried that Joanie would unduly influence Chanel, Sherry sent the 10-year-old girl to live with a relative in Pittsburgh and attend Catholic school. But Chanel longed for her birth mother and began to act out. Within a few years, she returned to New York and moved in with Joanie. They soon wound up in a shelter in Queens, where both were exposed to tuberculosis.

Over the next few years, they drifted apart.

Joanie turned her life around after President Bill Clinton signed legislation in 1996 to end “welfare as we know it,” placing time limits and work restrictions on recipients of government aid. She got clean and joined a welfare-to-work program, landing a $22,000-a-year job cleaning subway cars for the Metropolitan Transportation Authority. “This is the happiest day of my life,” she told Chanel.

By then, Chanel had dropped out of high school and was addicted to crack. She had joined a sect of the violent Bloods gang, tattooing her street name, Lady Red, in curly letters across her right arm. She was a regular in the crack dens of Bedford-Stuyvesant.

Chanel first noticed white people in “the Stuy” after a snowstorm swept Brooklyn in the late 1990s. Out of nowhere, two cross-country skiers appeared along Franklin Avenue like “a pair of aliens.” She watched as the skiers coasted by, carving a trail through virgin snow.

She sensed that Brooklyn was on the cusp of change. But she could not have imagined that just five blocks from that spot, people would one day line up to buy blood orange and hibiscus doughnuts at an artisanal shop called Dough.

The first commercial signs of Brooklyn’s transition were simpler. In 2001, Chanel spotted a new brand of bottled water — Dasani — on the shelves of her corner store. She was pregnant again, but unlike the miscarriages of her teens, this baby was surviving. Chanel needed a name.

For a 23-year-old Brooklyn native who had spent summers cooling in the gush of hydrants, the name “Dasani” held a certain appeal. It sounded as special as Chanel’s name had sounded to her own mother, when she saw the perfume advertised in a magazine. It grasped at something better.

Dasani was born on May 26 at Brooklyn Hospital Center in Fort Greene. The doll-faced infant weighed only 5 pounds 6 ounces. She was strikingly alert and had, the nurse noted, a “vigorous cry.” Three days later, Chanel left her with Joanie and took off.

Even as a baby, Dasani was awake to the world. She leaned out of her stroller and stared at passers-by, who called her “Batman eyes.” She was tiny, but never frail, and began walking at only 8 months.

Chanel would surface from time to time, but Dasani latched on to Joanie. A year later, Chanel had a second daughter by the same man, naming her Avianna, inspired by the more expensive brand of Evian water.

Joanie had hit her limit, so Chanel turned to the city’s shelter system. With both babies, she reported to the Department of Homeless Services intake office in the Bronx. They were sent to 30 Hamilton Place, a family shelter in Harlem.

Down the hall, a single father had moved in with his own two children. He called himself Supreme. He had sad, knowing eyes that made him look older than his 26 years. He never talked about the past.

Supreme was born to heroin addicts in the Cypress Hills projects of East New York. By age 7, he knew how to shop with his mother’s food stamps and cook grits for his four younger siblings. When the pantry was empty, he made sugar sandwiches.

He was 9 when he came upon the lifeless body of his baby sister. She had been left near the entrance of the projects, wrapped in a blanket. Supreme stroked her head and kept saying her name, Precious. “She didn’t wake up,” he says.

Investigators for Child Protective Services thought the 2-year-old girl had swallowed sleeping pills, though the medical examiner concluded that she had died of sudden infant death syndrome. The father had left Precious alone when she died. When her mother found her, Supreme recalled, she panicked, leaving the girl’s body outside as she ran for help.

Later that day, the agency’s workers removed Supreme and his siblings from the home. For the next three years, Supreme bounced from foster care to group homes. He soon dropped out of school and left for North Carolina to join the crack trade. By 17, Supreme had a felony drug conviction and was serving time at a maximum-security prison in Walpole, Mass.

It was there that he discovered the Five Percent Nation, a growing movement whose followers believe they are the chosen “5 percent” of humanity. The Five Percenters were shaping urban culture and music, while spreading the word that the black man is God.

That message — that God was within him — filled Supreme with a sense of power over his destiny, one that until now had been steered by outsiders.

Supreme left prison in 1997 with a high school equivalency diploma. He married and moved to Washington, finding work as a barber. Six years later, his wife — pregnant with their third child — had a heart attack and fell down a flight of stairs to her death.

Chanel took pity on this solemn widower, who came to the shelter a few months after his wife’s passing. Dasani and Avianna were the exact same ages as his children. He seemed different from the other men. He was always reading, and had a way with words.

“I fell in love with his brains,” Chanel says.

Two incomplete families soon became one.

Chanel embraced the Five Percent, wrapping her head in a scarf and vowing to stay off drugs. They married at the city clerk’s office on Feb. 4, 2004.

For Chanel, it was a moment of triumph. Women in her family almost never married.

“We were the product of split-up families,” she says. “We always wanted a big family. One family. One full family.”

In an instant, everything changed.

Chanel and Supreme were summoned to the Administration for Children’s Services office in Bedford-Stuyvesant — the same brick building where Supreme had been escorted as a child.

Standing there, in the lobby, the memory came rushing back. Supreme was 9 again, losing his sister, then his parents, then his other siblings, all in the course of a day.

Soon his own children became accustomed to knocks at the door as the agency’s caseworkers, responding to a handful of complaints about possible neglect, began to monitor the family. They inspected the children from head to toe, searching for signs of abuse.

Dasani learned to spot a social worker on the street by the person’s bag (large enough to hold files). She became expert at the complex psychic task of managing strangers — of reading facial expressions and interpreting intonations, of knowing when to say the right thing or to avoid the wrong one.

“They can use that in a court of law against the parent,” she says, back in the voice of “Criminal Minds.”

She pauses.

“I love my parents. They’re tough, but I should not be taken away from them.”

Dasani remained tethered to Grandma Joanie, who had proudly kept her job as a sanitation worker. She now lived in a cozy apartment in Bedford-Stuyvesant. On weekends, Joanie would fix the children B.L.T. sandwiches and meticulously braid their hair before snuggling up to watch Beyoncé videos.

Dasani was Joanie’s favorite. With this child, Joanie could finally be a mother. With Joanie, Dasani could be a child.

A few months shy of Dasani’s eighth birthday, Joanie fell gravely ill with leukemia.

On March 7, 2008, she died in the same hospital where Dasani had been born. She was 55.

“Why she had to go away so quickly?” Dasani asks.

At the funeral, mourners gasped as the tiny girl flung herself on the open coffin. Dasani kicked and wailed as Chanel tore her away.

Joanie was cremated and her ashes placed in a black and silver urn that remained with Dasani’s family, accompanying them like a talisman.

Her death brought a rebirth. Chanel inherited $49,000 of Joanie’s pension savings.

At the time, the family had been renting a small apartment in East New York through a city program offering time-limited subsidies to the homeless.

That month, the family’s subsidy expired.

Chanel’s inheritance saved them from homelessness. Months later, the city began a new rent subsidy program called Advantage. With its help, Chanel leased a duplex on Staten Island, and in summer 2008, boarded the Staten Island Ferry with Supreme and the children. It was their first time on a boat. They raced to the back and leaned into the salty mist.

Staten Island was quiet and green. In their new apartment on North Burgher Avenue, the children rolled around on the wall-to-wall carpet. There they lay, pressed together, that first night.

It was their first real home. The children’s euphoria steadily rose with that of their parents.

“When they’re happy, I’m happy,” Dasani says. “When they’re sad, I’m sad. It’s like I have a connection, like I’m stuck to them like glue.”

Chanel and Supreme talked giddily of starting a youth center that would teach the Five Percent ethos known as the “Five P’s”: proper planning prevents poor performance.

Supreme landed a job at Heavenly Cuts, a barbershop a few blocks away. Chanel bought a used, cherry-red Dodge Durango and a rolling kitchen island at Home Depot. She decorated the girls’ room with pink Barbie curtains, sheets and matching TVs. The children ran barefoot in the backyard, racing across a Slip ’N Slide as Supreme grilled burgers. Joanie’s urn occupied a place of honor in the living room.

This was, without question, the high point of their collective life.

It would take years for Chanel to understand why things so quickly fell apart. It was not obvious, in that blinding moment, that money could be useful only if they knew how to spend it. To think it would bring salvation was as quixotic as expecting a set of keys to drive a car.

Money was not going to heal a father who had never been a child. When customers took a seat in Supreme’s chair at the barbershop, they saw a pair of hands expertly at work. They did not see the boy who, at age 7, had learned that very skill by cutting his brothers’ hair while his parents were strung out on heroin.

What money brought was a quick escape from all that. Over the next two years, Supreme and Chanel bobbed and wove through a fog of addiction. Supreme started doing heroin. Chanel became hooked on painkillers during an extended stay at Staten Island Hospital, where she was being treated for a recurrence of the tuberculosis she contracted in a shelter.

Children’s Services hovered over the family, ensuring that Chanel and Supreme submit to random drug tests. Eventually, Supreme and Chanel stopped working.

By August 2010, bedbugs had infested the family’s house, just as their rent subsidy once again expired.

The city’s shelters were filling with former Advantage recipients — families who had been homeless before taking the rent subsidy, only to become homeless again.

On Aug. 20, Dasani’s family boarded the ferry to Manhattan, where they headed to the Department of Homeless Services’s intake office in the South Bronx.

As Dasani’s family approached the entrance, Chanel spotted two abandoned baby turtles in a cardboard box. She stuffed them in her pockets.

Six days later, the family arrived at Auburn, along with its two forbidden pet turtles and Joanie’s urn.

Children are said to be adaptable. On outward appearances, Dasani and her siblings became inured to the dehumanizing ways of Auburn — the security checks at the entrance, the grimy bathrooms, the long waits for rancid food.

Yet nothing prepared them for what happened on Sept. 7, 2011, a year after they arrived.

Chanel and the children had been “logged out” of Auburn, the official description of what happens when residents who have been absent for more than 48 hours are sent to the Bronx intake office to fill out forms and answer questions. The entire family must make this onerous trip, even on school days.

That evening, tired and hungry, they returned to their room. It looked ransacked. Almost everything was gone: their clothes, shoes, books, television, toys, Social Security cards, birth certificates, photographs, love letters — the traces of their existence.

Joanie’s urn had also vanished.

Chanel raced down to the security guards, Dasani chasing after her.

“Where are my mother’s ashes?” she screamed. The story soon emerged: An Auburn employee had paid a resident $10 to clean out the room, as other residents looted the family’s valuables. Everything else was tossed in the garbage.

Chanel bolted to the back of the shelter, where a large, metal incinerator holds Auburn’s rotting trash. She waded in, the garbage reaching her waist. She searched frantically. This could not be Joanie’s final resting place, she kept telling herself.

She cursed. She wept aloud.

Finally, she stopped. The truth was setting in. Fifty-seven years after Joanie had been born, here in this very building, her remains were dumped in the garbage.

Upstairs, the room felt cursed.

Joanie had always protected the children, in life and in death. Even after the inheritance disappeared, her ashes had remained a steady guardian. But now Joanie was gone. In her absence, a devastating chain of events unfolded.

Chanel paced the room that evening, desperate and broke. Supreme was gone after another fight. She expected no help from Auburn. Still, she had gone to the trouble of filing a complaint, writing in hurried print, “I don’t know what to do my kid start school tomorrow and I have nothing.”

The next day, Chanel left the children alone in the room, defying the shelter’s rules, and hit the streets in search of cash. A man approached her on Myrtle Avenue asking where he could buy drugs. He did not look like an undercover officer, so she steered him to the projects. She was arrested and later pleaded guilty to drug possession charges, though Chanel maintains she was innocent.

When Chanel did not return that night, Dasani felt something in the air. There was a knock at the door. Dasani shushed the kids. They pretended to be asleep. Then the door opened as an Auburn supervisor and Homeless Services police told the children to get dressed.

The Administration for Children’s Services had known for months that Chanel was getting high on opiates, but had been trying to keep the family together. After her arrest, a family judge ordered new drug tests for both parents, revealing that Supreme had also been smoking marijuana.

With that, the agency went to court to have the children removed. In a hearing on Sept. 20, the children’s lawyer objected, arguing that to divide them among foster homes “who knows where in the city” would “present a greater imminent risk to the children than remaining where they are.”

The judge struck a compromise: Both parents needed to comply with a drug treatment program. The children were to remain with Supreme, but Chanel temporarily lost custody.

She had suffered all kinds of losses, but nothing compared with this. Who was she if not a mother? She had always tried to be there, rarely missing a school play or a parent-teacher conference. On Sunday afternoons she would braid hair until her fingers turned numb. At bedtime each night, she flipped through the family dictionary to teach her children a new “word of the day.”

Now, Chanel would be living with Sherry, only seeing the children on supervised visits. She broke the news to the children on a park bench.

“Take care of your siblings,” she instructed Dasani.

Dasani was silent.

Supreme ruled by fear. If the children laughed too loud, he only had to yell “Shut up!” and they froze, a silent dread passing among them. He had an old-fashioned approach to child rearing: Break the rules and you get the belt. Chanel’s presence had tempered him.

When she left, Supreme wrote two words on the wall in black marker: “King Me!”

Under the agency’s supervision, both Chanel and Supreme made steady progress in a treatment program that required taking daily doses of methadone, a synthetic drug meant to control addiction.

Nearly a year later, on Aug. 2, 2012, the judge allowed Chanel to return to her family at Auburn under supervision from the Administration for Children’s Services. She came with a promise: They would save enough money to leave.

Chanel spreads the cash across her bed, all $2,800. The children stare in awe. ■ “I don’t know why I feel so happy,” Avianna says.

Chanel quickly stashes it, announcing no intention of spending her long-awaited tax refund, which arrived Feb. 13.

“Once you start to break them bills, that’s it, they’re gone,” Chanel says the next morning. She is walking through the projects, the money bulging from her pocket. She does not know where to put it, so she holds onto it and, more than anything, the feeling of having it.

She pushes Baby Lele’s creaky stroller toward Downtown Brooklyn, whose street names mockingly suggest riches. Gold. Tillary. Bond. She takes an inventory of all the things she could — but won’t — buy: a new stroller, sneakers, a hair-braiding session for the girls.

Chanel knows that unless she finds a way to save her money, and persuades Supreme not to spend his own tax refund, they will never leave Auburn.

And yet, planning has never been their way. “To plan something is to plan to fail,” she says. “My plan is to do some goddamn laundry.”

Tax season brings a sudden reprieve for a family that, with food stamps, has about $75 a day to spend. This amounts to $7.50 per person in a city where three subway trips cost as much. They survive because they live rent-free and have access to three meals a day.

Chanel is reminded of this when she stops to look at listings in the window of a real estate office near her methadone clinic. A one-bedroom in Bay Ridge, Brooklyn, is going for $1,300 a month.

She sees no option but to leave New York. In a show of commitment, Chanel gives $800 of her tax refund to Grandma Sherry in exchange for a used Chevrolet minivan, which is sitting in the driveway with no permit.

Now they must wait for Supreme’s tax refund.

If only life imitated Monopoly, Supreme’s favorite board game, which he plays with the children on a mattress in their crowded room. “I like building up property and collecting rent,” he says.

But becoming a real renter, he finds, is far more challenging than claiming Park Place on a cardboard square.

Auburn no longer has a housing specialist on staff — the last one died four years ago and was never replaced. Supreme has learned to navigate the web on his prepaid Android from Boost Mobile, but the phone is often disconnected. Chanel feels like a fumbling fool on the shelter’s computers.

And then there is the problem of Baby Lele. Investigators have repeatedly cited Auburn for providing no on-site child care, which hinders residents from searching for jobs or housing. Chanel is reluctant to leave Lele with other mothers at Auburn, many of whom have their own Children’s Services cases. If anything were to happen, Chanel’s custody could be in jeopardy.

Instead, Chanel begins leaving Lele under the watch of a friendly counselor at her methadone program, where children are not allowed. The counselor stands outside with Lele as Chanel darts in to swallow her orange liquid dose.

When a clinic supervisor discovers the arrangement, Chanel is exposed. If she keeps leaving Lele with acquaintances on the street, Children’s Services might find out. So Chanel stops going, and the clinic alerts the agency that she has fallen out of treatment. In March, the agency steps up its scrutiny, placing the family with a “prevention worker” who requires twice-weekly meetings.

By now, Supreme has learned that his tax refund was seized by the government for child support owed to two other children he had before meeting Chanel.

Dasani knows before her mother says a word.

They will not be leaving.

Dasani has learned to let disappointments pass in silence. Objecting does nothing to change the facts. ■ But she reveals herself through the questions she asks.

“Mommy, if these projects was your only choice, would you take it?” she asks Chanel one day in March as they are out walking. Chanel nods reluctantly.

Dasani lets it go. She knows not to push.

Spring has brought a new set of worries. For the wealthier children in Fort Greene, it is a season to show off new wardrobes. For Dasani’s family, it is a time of scrambling. Appearances are more easily kept when the same coat is all that people see.

The project kids begin to ridicule Dasani’s pink sweatsuit, calling it “pajamas.” On March 19, she agrees to fight a girl from school at nearby Commodore Barry Park. A crowd gathers as they establish the rules: No one can film it or tell a parent. They pull back their hair and Dasani punches her rival as they tumble to the ground. A man walking his dog pulls them apart.

That evening, Chanel inspects the cut on Dasani’s lip.

Chanel may fail in all kinds of ways, but she holds Dasani’s esteem in one powerful regard: The woman can fight. Dasani has grown up hearing her mother’s stories of street-battle glory, and watching her in the throes of countless slug matches with anyone who crosses her, including the owner of a local laundromat.

Chanel dismisses Dasani’s tussles at school as “kitty-cat fighting.” Back in her day, girls cracked one another over the head with bottles. No one wasted time pulling back their hair.

“You gotta keep your hood credit up,” she tells Dasani. “You take the biggest, baddest one down first and the rest of ’em will back up off of you. That’s just how it works.”

The next day, Chanel and Dasani wander up their favorite block of Myrtle Avenue, passing the Red Lantern, a bike repair shop that sells vegan cookies. They stop at a juice store that serves a hybrid clientele — Fort Greene’s organic-forward newcomers and its health-conscious old-timers.

There, Chanel spots an old flame. He wears a long leather jacket and dark shades. She wonders if he is still dealing.

“Whassup, Red?” he says.

Dasani eyes him closely.

“That was her name from back when she was in the hood,” she says, forever cataloging the details of her mother’s past, even as Chanel tries to part with it.

“I’m good now, see?” Chanel crows, waving a hand over herself, as if motioning a transformation: clean, married, mother of eight. She nods proudly at her children.

It is Dasani’s belief that she and her siblings are the cause of her mother’s ruin. It never occurs to her that, for Chanel, the children represent her only accomplishment.

The next day, Chanel escorts Dasani to school. In the hallway, she spots the girl Dasani fought in the park. “You can fight my kid,” she says hotly, taking the girl by surprise. “I’m with that.”

Minutes later, the principal, Paula Holmes, sits Dasani down. “I believe you can change, but you’re not showing me that,” she says.

Dasani returns to class feeling jaunty. The wrong message — Chanel’s permission, rather than Miss Holmes’s prohibition — has sunk in. “I’ma fight you,” she tells another girl. “My mother said she’ll let me fight.”

With that, Dasani is suspended.

Miss Holmes knows it is a risky move, but nothing else has worked. The girl needs to be shocked out of her behavior. The alternative is to fail in school and beyond.

“Get your things and leave,” Miss Holmes tells her.

Dasani will be out of school for a whole week. She cannot speak.

To be suspended is to be truly homeless.