Reyes also wounded two classmates before killing himself Monday. The dead teacher was identified as Michael Landsberry, a math teacher at Sparks Middle School.
Sparks spokesman Adam Mayberry cited fairness to families and news media in confirming the boy's name, the Reno Gazette-Journal reported.
Police said the incident took place about 7:15 a.m. Monday as school got under way.
The two injured students were recovering at Renown Regional Medical Center. One had exited surgery and the other was "doing well," the newspaper reported.
Witnesses described a chaotic and confusing scene as the shooting unfolded.
"We heard a pop, like a loud pop, and everybody was screaming and the teacher came to investigate," eighth-grade student Kyle Nucum, 13, said. "I thought it was a firecracker at first, but the student was pointing a gun at the teacher after the teacher told him to put it down, and the student fired a shot at the teacher and the teacher fell and everybody ran away.
"And we ran across the field to get somewhere safe and while we were running we heard about four or five more shots and we just got somewhere safe. This lady let us into her house."
Once the scene was secured, students were evacuated to nearby Agnes Risley Elementary School and eventually to Sparks High School where parents were allowed to pick up their children.
Another student, Michelle Hernandez, said she'd seen the suspect earlier that morning at school and indicated he may have been bullied.
"I heard him saying, 'Why you people making fun of me, why you laughing at me,'" Hernandez said.
Police offered no official theories about the student's motivation.