A small plane “broke up in flight” over Syosset on Tuesday afternoon — shortly after the pilot sent a mayday — killing all three aboard and forcing people on the ground to dive for cover, authorities said.

Witnesses said they heard buzzing then a loud boom just before the single-engine Beechcraft Bonanza plummeted to earth at about 3:39 p.m. near two public schools in a residential area off Cold Spring Road.

Authorities said no injuries were reported on the ground.

Part of the plane landed in a field across from Berry Hill Elementary, and members of a lacrosse team heard odd noises as they practiced outside near Syosset High.

“Five seconds later, you saw like huge chunks of the plane falling out of the sky,” said Emilee Meltzer, 16, a lacrosse player and sophomore at the school. “It was just falling apart.”

Students screamed and sprinted for cover. Some team members cried afterward, Meltzer said.

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Two men and a woman aboard the plane died, about three hours into their scheduled journey from Myrtle Beach, South Carolina, to Plainville, Connecticut, federal investigators said. Their names were not released.

The six-seat aircraft was 43 years old and registered to David C. Berube of Bristol, Connecticut, who is licensed to fly and land multi-engine planes and certified to navigate by instruments, according to the Federal Aviation Administration. It was not clear if he was piloting the Beechcraft on Tuesday.

Attempts to reach family members were unsuccessful.

Authorities said the pilot had sent a mayday to Republic Airport in Farmingdale, and information from FlightAware, an airplane tracking service, shows the plane was cruising at an altitude of 7,000 feet before it suddenly disappeared from radar.

The plane broke apart in midflight, an uncommon occurrence, Robert Gretz, a senior investigator with the National Transportation Safety Board, told reporters at the scene Tuesday night. The debris field extends over a two-mile radius, making the investigation even more challenging, he said.

“I’m not sure if it’s an explosion or some kind of loss of control or an overstress of the airplane,” he said. “At this point, we don’t know. It could be anything.”

But shortly before the disaster, the pilot reported that part of his cockpit instrument panel was not working, Gretz said.

Flying without instruments would be “challenging” in bad weather, he said, but investigators will look at whether the plane was temporarily in a pocket of turbulent weather or flying above the clouds. At the time, a drizzle was falling on and off over the Long Island.

“You do need your instrumentation to fly through bad weather,” Gretz said. “The best analogy I can give is driving through fog ... You need your lights, you need your instruments.”

Gretz said investigators will also look at the plane’s age and maintenance records, stresses on the plane’s frame and the pilot’s health and background: “Basically, we are looking at the pilot, the machine and the environment.”

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Nassau police have cordoned off a large area, and officers planned to search late into the night for more wreckage and other evidence.

Around the neighborhood, pieces of the plane, large and small, could be seen in fields, woods and residential yards — from a seat on a road to bits caught in trees, said acting Police Commissioner Thomas Krumpter.

“It did break up pretty significantly,” he said. “In the other plane crashes we’ve dealt with in Nassau County over the years, we’ve never seen a debris field like this. There was at least one house that I saw that got hit by debris. It was a piece of the fuselage that hit the roof of the house and fell off.”

Syosset High junior Zachary Comroe, 17, said he was walking home from baseball practice when a plane overhead sounded louder than usual.

“I was thinking, what was it doing flying on a day like this, a rainy, fogged-up day?” he said. “After a couple of seconds of watching it fly, I actually heard the engine stall.”

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Comroe said he then heard a boom, adding: “From there it kind of started spinning out. As soon as that happened, pieces started falling off.”

In-flight breakup is “extremely rare,” said Phil Derner, founder of NYCAviation.com, an aviation news and blogging website.

Aviation has become so safe these days because so many common causes of crashes have been addressed, he said, so when a plane crashes nowadays, it’s often due to “oddball reasons.”

The NTSB said it was the seventh small plane crash this year on Long Island. Investigators plan to issue a preliminary report within a week and a fuller report in six months.

Cold Spring Road was closed in both directions between Townsend and Chelsea drives to preserve the crash scene.

Ethan Seidner, 11, of Syosset said he saw parts of the wings and the destroyed body of the plane in a field behind Shelter Rock Church on Cold Spring Road.

Before the crash, he and his family heard an explosion and saw debris rain down, “falling very slowly, kind of floating down.”

“The plane was making a grinding noise and then a popping sound,” said another witness, Terry Corrigan, 53, who lives nearby on Willets Drive.

The Syosset Central School District had held students and staff at South Woods Middle School, Berry Hill and Syosset High at the urging of police and released everyone shortly after 5 p.m.

The Syosset school district released a statement saying “As of 5:10 p.m., we were informed by Nassau police that we may dismiss all students and staff from the three buildings that retained them. Transportation is available for all students and we will dismiss them to parents, as well.”