“Throughout everything, Lyla was thoughtful, kind, always thinking of others, and an amazing friend,” Alkon said in an email Saturday. “The outpouring of grief among her friends, peers and classmates from Brookline and beyond upon learning of her and her family’s tragic passing, is a tribute to how many lives she and her family touched in a loving, profound way.”

She said Lyla and Matthew Goldstein were deeply proud of their daughters and the adults they were becoming.

Valerie, an alum of Newton South High School, graduated from Syracuse University in May and was working as a fifth-grade instructor in Rocky Mount, N.C., as part of Teach for America, according to her LinkedIn profile.

Violet Goldstein was a student at the Rhode Island School of Design, according to a college spokesperson. Violet’s college roommate, Finleigh Lewis, said she was “a beautiful source of light” who radiated kindness and genuine care for every person she met.

“They were both outstanding,” Alkon said of Valerie and Violet during a phone interview later Saturday afternoon. “As was Lyla, as was Matt, really all of them were outstanding.”

A relative of the Goldsteins declined to comment when reached by phone on Saturday. Other family members could not immediately be reached.

The family lived at 29 Margaret Road in Newton, according to city records, where flowers were left on the front steps Friday. City officials said the Goldsteins were active in community events.

Alkon said Lyla was a “dedicated Girl Scout troop leader” when her daughters were in the scouts. A former three-sport athlete at Brookline High School, Lyla Goldstein continued playing basketball throughout her adult life, Alkon said. She was also listed as a board member of the Newton Girls Basketball Association.

Newton City Councilor Bill Humphrey, whose district includes the Goldsteins’ neighborhood, recalled chatting with Lyla and Matthew Goldstein when he’d be out knocking on doors.

“I remember that Valerie would write in to the City Council about her passion for a more sustainable world and a just society as soon as she was old enough to vote, and she asked me to help her with a class project on local environmental policy,” Humphrey said in a statement on social media. “I know many leaders, activists, and educators found both sisters to be memorable and engaging over the years. All four of you will be missed by our community and beyond.”

Goldstein was an eighth-grade math and health teacher at the Edith C. Baker School in Brookline, according to Justin Brown, the president of the Brookline Educators Union. He led the math league and the school’s Gender and Sexuality Alliance.

Brookline Superintendent Linus J. Guillory Jr. said in a Friday statement that Goldstein was “an exceptional educator” and “beloved” member of the school community.

He also inspired his colleagues. A woman who said she worked across the hall from Goldstein said in a social media post that he “took care of everyone around him – his family, his coworkers, his students, etc.”

“He could find the upside to every situation,” she wrote.

The Goldsteins had been expected to arrive at a holiday gathering on Wednesday, but family members contacted authorities when the four did not answer phone calls and messages, officials said. Wakefield police responded to the home at 2962 Province Lake Road and found the four adults dead inside late Wednesday afternoon.

New Hampshire investigators identified the home’s gas heating system as the source of the carbon monoxide leak, officials said. New Hampshire State Fire Marshal Sean Toomey said Friday that investigators believe there was “some sort of malfunction” with the system that prevented carbon monoxide gas from exiting outside the home.

“We’re still looking into all the details of that failure at this point,” he said.

Town records from Wakefield, N.H., show that the Goldsteins purchased the five-bedroom lakeside home in 2017. The property, which was built in 1984, is located on Balch Lake.

Several pictures on Matthew Goldstein’s Instagram page showed the family swimming and kayaking on Balch Lake. A video he posted Dec. 22 showed one of his daughters splitting wood outside the house. After the news of their deaths, the post has received a flood of condolences in the comments.

Toomey said “there were no carbon monoxide alarms” in the home. He urged New Hampshire residents to make sure they have working carbon monoxide detectors and check with their relatives and neighbors to make sure they do as well.

“Carbon monoxide is a silent killer,” he told reporters. “It’s colorless, odorless, and it will mimic flu-like symptoms, headaches, nausea. Especially at this time of year, with all the regular illnesses going on, it can be mistaken for something else, and that stresses the importance of having the working carbon monoxide alarms in your homes at this point.”

The office of the state’s chief medical examiner determined Goldstein’s cause of death was carbon monoxide poisoning, and the manner of his death is pending. The cause and manner of deaths of Lyla, Valerie, and Violet also remain pending, officials said. No further information was released Saturday.

Toomey said the state typically sees two or three deaths from carbon monoxide poisoning in a given year, but the number rose above 10 in 2024, including the Goldsteins. He expressed sympathy for the family and their relatives and friends, as well as the first responders who found the family in the home on Christmas Day.

“This has been a terribly tragic year for both fire deaths and carbon monoxide deaths,” he said. “I think it wears on all of us. … To lose a whole family of four right in the peak of the holiday season, it hits home even more.”

Tonya Alanez of the Globe staff contributed to this report.

Nick Stoico can be reached at nick.stoico@globe.com.