Investigators believe the argument came to a head Wednesday and got violent when someone threw a pencil at Cedeno, allegedly setting him off, CBS2's Janelle Burrell reported.
The young child was pronounced dead at St. Barnabas Hospital with injuries to the chest, and the other teen was transported to the hospital "in grave condition" with wounds in the arm and torso.
"I'm heartbroken at the loss of one of our students and this tragedy should never have taken place", said Schools Chancellor Carmen Fariña. It escalated today after some back and forth within the classroom, ' Boyce said.
The 18-year-old suspect was taken into custody and is being interviewed after the deadly incident in the Bronx building, which houses the Urban Assembly School for Wildlife Conservation and PS67.
In the wake of the stabbing, the first slaying inside a city school in almost 25 years, authorities have installed two body scanners and two X-ray machines at the Urban Assembly School for Wildlife Conservation.
Cedeno's family claimed they alerted a school guidance counselor about the "extreme bullying", according to Hornback, but it wasn't immediately clear if they notified a counselor at Urban Assembly or staff at another school where he'd also faced bullying.
Cedeno has been charged with murder, attempted murder, manslaughter, attempted manslaughter, assault and criminal possession of a weapon.More news: Siemens Alstom merger creates European giant
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Police say a high school student stabbed two students during history class, killing a 15-year-old and critically injuring a 16-year-old.
Cedeno walked out of the classroom where he stabbed the boys, handed his Schrade switchblade to a counselor in the hallway and walked to the assistant principal's office to wait for police, officials said.
"And less than half of students polled at the school previous year - 47 percent - said they felt safe on campus, well below the city average", the report says.
The school does not have metal detectors, officials said, adding that this knife would have been picked up if there were.
Police say 15 to 20 students witnessed the attack.
"I tried to called the school".
"I knew it was going to happen eventually, but I was in shock", she said. She plans to pull her daughters out of school.
Some students will feel safe because when classes start resume, they will go through metal detectors and be subject to random screenings.