Amid great destruction, with at least two dozen people dead — including nine children — the residents here began to assess the severity of their calamity Tuesday after their third major tornado in 14 years, a staggering run of weather misfortune.

Yet there was good news in the aftermath of the historic twister that hit Monday just as school was about to let out: The death toll reported by the state Medical Examiner’s Office ratcheted down from 51 to 24. Officials discovered that they may have double-counted fatalities.

That number was expected to creep upward again, and Oklahoma Gov. Mary Fallin said some bodies may have been taken directly to funeral homes. She said 237 people had been injured “so far as we know.”

Hope of finding survivors trapped in the ruins of the city faded as the day wore on, although officials had not despaired. John D. Doak, the state’s insurance commissioner, said late Tuesday afternoon that the hunt for survivors is “still a very active search.” He said he drove through the area and saw search teams with dogs. “I think they’re doing second and third passes through homes, which is absolutely the right thing to do,” he said.

In the heart of the devastation stood the remnants of Plaza Towers Elementary School. Moore Mayor Glenn Lewis said he was told that seven students were killed there when a cinder-block wall collapsed on them during the tornado. Scores of children and their teachers survived by crowding into a girls’ restroom, with the teachers lying on top of children as 200-mph winds removed the roof as though it were made of cellophane.

Addison Roberts, 7, climbed out of the Plaza Towers debris unscathed, and Tuesday night sat eating dinner with her family in front of her destroyed home. She complained about the quality of the cheese on her turkey sandwich.

She was rock solid through all the turmoil, said her grandfather Jack Eldred. When her father came to pick her up after the tornado, “she was patting him on the back, saying, ‘It’s okay, Dad,’ ” he said.

“He was crying,” Addison said.

The city of 55,000, about 11 miles south on Interstate 35 from downtown Oklahoma City, is coping with the infrastructure and communication problems common after natural disasters: power failures, gas leaks, lack of water, poor cellphone service. An area of about four square miles was sealed to outsiders as first responders continued to search for victims amid heaps of wreckage.

One of the first things workers did Tuesday was put up street signs.

“You can’t tell where you’re at. The whole city looks like a debris field,” Lewis said Tuesday.

Said Oklahoma City Mayor Mick Cornett, describing his thoughts while touring the damaged areas Tuesday: “No one possibly could have survived this. And yet, we know they did. We know people crawled out of that rubble. We’re talking levels of debris four feet high as far as the eye can see.”

Sue Ogrocki, an Associated Press photographer who raced to the scene Monday, saw first responders pull 12 children and two adults out from under collapsed walls, then hand them to parents, teachers and neighbors who formed a line.

“I was amazed at how people maintained their composure. I was amazed that the firemen who were digging with their hands could get those kids out. I mean, they’re professional. And they were in a hurry to get the kids out, but they weren’t panicking, they were doing their job and they were doing it quickly and very well,” Ogrocki said.

One woman experienced what seemed like a miracle while on television: Barbara Garcia was telling a CBS News crew about her dog, a miniature schnauzer, who was ripped from her arms by the tornado as she huddled in a bathroom. As she told the story, a reporter noticed the snout of the dog, ragged but seemingly unharmed, poking out from where Garcia’s house had been.

“Oh! Oh!” Garcia said. Then, “I thought God answered just one prayer, ‘Let me be okay.’ He answered both of them.”

The city of Moore has faced tornadoes before. It was hit by an EF5 twister — the most powerful on the Enhanced Fujita scale — on May 3, 1999, with 41 reported deaths. Another strong tornado struck on May 8, 2003, but by then many residents had re­inforced rooms and shelters, and there were no fatalities.

Lewis, the mayor, began to tear up while speaking at a news conference Tuesday, saying: “I was the actual mayor here on May 3, 1999, so this is not my first rodeo with this. But it doesn’t get any easier, especially with the loss of life.”

President Obama issued a disaster declaration and dispatched Federal Emergency Management Agency Administrator W. Craig Fugate to Oklahoma to help with recovery efforts.

“There are empty spaces where there used to be living rooms and bedrooms and classrooms, and in time we’re going to need to refill those spaces with love and laughter and community,” Obama said.

The twister materialized Monday afternoon in what had been a blue sky only hours earlier. The National Weather Service had been warning for days that the conditions were going to be ripe for super-cell thunderstorms. Then, at 2:40 p.m. Central time, the Weather Service issued a tornado alert even though the funnel had not yet descended from the clouds.

The twister came down at 2:56 p.m., west of Moore. At first it was a thin funnel, like a finger trying to take the temperature of the soil. But it widened, becoming barrel-shaped. Weather Service survey teams said the tornado reached EF5 status, and at one point was 1.3 miles wide. It plowed toward the east for 17 miles before abruptly breaking apart.

“This was the storm of storms,” said Cornett, the Oklahoma City mayor.

“The monster returned,” began the front-page story in the Oklahoman newspaper.

This had not been a bad tornado year until Monday. In fact, it had been remarkably quiet, with 274 twisters reported nationwide as of that day, much lower than the average of 491 through May 20. This had been a welcome break from a string of years in which violent thunderstorms — spawning tornadoes, hail and powerful straight-line winds, and possibly ramped up by climate change — had caused record amounts of damage in addition to many fatalities.

The record year for insured losses was 2011, when massive, long-track tornadoes struck Tuscaloosa, Ala., and Joplin, Mo., and insurance companies paid $26 billion in claims. Although that easily set the standard, 2008, 2009, 2010 and 2012 were also far above the norm in insured losses. In fact, those are the five years in U.S. history with the highest insured losses from storms, said Robert Hartwig, president of the Insurance Information Institute, a trade association for the insurance industry.

“From our perspective, when we look at long-term trends, it does appear that the weather is getting worse,” he said.

Is that from anthropogenic global warming? Hartwig said it’s not the industry’s job to say.

“We do see an increase in variability, volatility and the cost associated with natural disaster events, not only in the United States but around the globe. It’s not for the insurance industry to determine whether climate change is the cause of any weather event,” Hartwig said. “Whether it’s global warming, per se, that’s going to be left to the scientific community to ascertain.”

He said that the 1999 twister that hit Moore caused $1 billion in losses, and that Monday’s tornado could be comparable. “It’s going to be hundreds of millions of dollars, no question,” he said. “Could it surpass the billion-dollar threshold? Yes, it could.”

Peter Hoeppe, director of geophysical risks for Munich RE, a huge reinsurance company, said that the key for places such as Oklahoma is to ensure that people have quick access to a safe room, ideally underground.

“If you have a tornado with a power of E4 or E5, there is no structure that can withstand them, at least not a structure that is economically sensible to build,” Hoeppe said.

Tim Samaras, a storm researcher whose work is supported by the National Geographic Society, and who was chasing a different tornado in Oklahoma on Monday, said the practice of taking shelter in hallways is insufficient when a school is directly hit.

“The only way you’re going to solve that problem is to build tornado-proof rooms in these schools that can hold 500 to 700 children. Unfortunately, it comes down to cost. There is no part in a school building that can withstand an EF4 or EF5 tornado. None,” Samaras said.

Officials in Moore acknowledged that the two schools hit by the tornado, Plaza Towers and Briarwood, lacked safety rooms. Lewis said the schools that were rebuilt after the 1999 twister had safety features, but not Plaza Towers, an older school. Pam Lewis, a fourth-grade teacher and the mayor’s wife, said, “It would be very rare to find schools with safety rooms, because it’s so expensive.”

Law enforcement officials blocked entry into the worst-hit neighborhoods. Outside one barricade at Fourth and Wilson streets, Robin Wood camped out with 25 cases of water bought by her church, the Community Church of Lawton. Over the day, a tent city arose, stocked with food, clothes, toys and water. Residents kept bringing donations as rescue workers crossed the barricades for something to drink.

“People bring more and more, and people keep taking and taking,” said Wood, 37. The stay-at-home mom hadn’t slept in more than 32 hours, and other volunteers kept telling her to rest, but she continued to bound out of the chair to unload new deliveries.

Residents faced the prospect of looters taking advantage of the situation. Gloria Teague, 52, said she and her husband and sons-in-law had not planned to return to their damaged home on Kings Manor Street, but they were looking for a lost dog. When they showed up, one son-in-law surprised two men who were looting the house. One of the looters dropped an armful of possessions and the other let go of a bucket full of bullets.

“We lost everything, and you’re coming to take what’s left?” Teague asked incredulously. Police made two arrests at the scene, and an officer who would not give his name said the entire neighborhood would be closed at night, and even the residents would be asked to leave.

Achenbach reported from Washington. Mark Berman, Lenny Bernstein, Brady Dennis, Jason Samenow and Debbi Wilgoren in Washington contributed to this report.