(CNN) -- "I think we're going to have a pretty good Christmas," Cindy Hill joked Friday, just minutes after a Missouri lottery official announced that Hill and her family had won half of the record $587.5 million Powerball jackpot.
"We're still stunned by what's happened. It's surreal," Hill said. "Every once in a while you look at each other and say, 'Did we really win that money?'" said the Dearborn, Missouri, resident.
Seated at a table at Dearborn's North Platte R-1 High School, Hill, her husband, Mark, their three grown sons, Jason, Cody and Jarod, and their adopted 6-year-old daughter, Jaiden, joyfully answered questions from the media.
Hill said she purchased the ticket at the Trex Mart around 4:45 p.m. Wednesday, then left it in her car overnight. The next day, after she took Jaiden to school, she stopped by to check the numbers.
"I didn't have my glasses. I was thinking, 'Is that the right numbers? Is that the right numbers?' And I was shaking, I called my husband and said, 'I think I'm having a heart attack,'" she said.
Her oldest son also had trouble believing she had the right numbers.
"I got a text from my mom that said 'call me ASAP,' and she's kind of the girl who cried wolf," Jarod, 31, said. "So, I got that text. I was like, 'Oh, geez.' I finally got a hold of her. She said, 'I won the Lotto.' I didn't believe her for actually a couple of hours because I just thought she was pranking me and then taking it too far."
"God blessed us," Hill said. "But we were blessed before we ever won this."
Life has changed quite a bit for the Hills in 2012. Mark Hill, a maintenance worker, said he got a new job in February, after he was unemployed for a while.
Jason, 28, said he hopes this newest, biggest life change won't cause chaos for his family.
"I hope we stay grounded. I hope we stay the great people we were yesterday and the day before," he said.
Even though the Hills can now afford to live anywhere in the world, one thing that probably won't change is their zip code.
"We want our daughter to be raised here as well," Cindy said. "We'll stay in this area."
The Hills weren't the only winners in Missouri: the state lottery gave Trex Mart $50,000 for selling the winning ticket.
Lottery officials have not yet confirmed the identity of the other Powerball winner, who bought a ticket in Arizona.
The question of who won the Arizona jackpot -- sold at a convenience store in Fountain Hills -- took an interesting twist Thursday when a man walked into an Exxon gas station in Upper Marlboro, Maryland, to casually check a stash of lottery tickets.
"I got it!" acting manager Negassi Ghebre said the man shouted after checking the tickets against the winning numbers.
"Then he showed us the numbers, and the numbers were right, they matched," he told CNN.
Before that development Thursday, the manager of the Four Sons Foods Store in Fountain Hills, Arizona, said he hoped he had been the one manning the register when the winning ticket was sold.
"Unbelievable," manager Bob Chebat said. "Everyone comes in here buying tickets, joking they'll take care of you if they win. But chances are so slim that it becomes standard that no one does win. I just don't know what to say. I'm shocked. I hope I was the guy who sold the winning ticket."
Back in Missouri, clerk Kristi Williams, at the Dearborn Trex Mart where that state's winning ticket was sold, asked every customer the same question Thursday: 'Have you checked your ticket?' " she told CNN affiliate KCTV of Kansas City.
The Arizona store will receive $25,000 for selling the winning ticket. The payout to sellers varies state to state as it is determined by each state's lottery officials.
The prize for the lottery -- held in 42 states, the U.S. Virgin Islands and the District of Columbia -- swelled to the largest in Powerball history after the jackpot rolled over 16 times without a winner.
It still doesn't match the U.S. record payout of $656 million, set in March by a Mega Millions jackpot. Three winners split that pot.
California added its name Thursday to the states participating in Powerball, with the California Lottery Commission voting unanimously to adopt the mega-jackpot lottery game. Powerball tickets will go on sale in California on April 8.
Lottery officials previously urged winners to take their time coming forward.
Winners should sign the ticket, put it in a safe place and seek legal and financial advice before redeeming it, Missouri Lottery Director May Scheve Reardon said.
In Dearborn, resident Bill Matney said he hopes the winning ticket holders don't "get deluged by a lot of people wanting part of their winnings."
"And that they put it to a good use like charity," he told KCTV. "I mean, who can spend that much money?"
The Hills said they plan on setting up a scholarship fund, and donating to other charities, specifically mentioning adoption advocacy and the Shriners as pet causes.
And when it comes to this Christmas, while Jaiden Hill wants a pony, despite the family's windfall, her mother said, "The pony's not going to be for a while."
CNN's Shawn Nottingham and Kyung Lah contributed to this report.