A case on a chemical-weapons prosecution had raised worries about whether the federal government would infringe on states' rights over education.
The justices rule 5-4 that a state may not set an IQ score of 70 or below as the rigid cutoff that would permit it to execute a person with an intellectual disability in a capital case.
The justices declined an appeal of a guidance counselor fired over his self-publication of a purported relationship-advice book for women that contained sexually explicit passages.
The state's highest court upheld the discipline of teachers whose picketing during collective bargaining created "a hazardous situation" for students arriving at school.
The state high court in Massachusetts held that the inclusion of "under God" in the pledge does not violate the state equal-protection rights of atheist and humanist students.
The justices will soon decide whether to take up a case about a public school district's use of a church for its graduation ceremonies.
In a case being watched by school boards, the U.S. Supreme Court upheld prayers before a town's meetings in New York state, despite the prayers' predominantly Christian and sometimes proselytizing nature.
In two cases with implications for students and schools, the U.S. Supreme Court weighed privacy expectations in the age of digital smartphones.
The justices step back into the complex area of when speech by teachers and other government workers is protected by the First Amendment.
The U.S. Supreme Court on Tuesday upheld a Michigan ballot initiative that bars race-based preferences in admissions at the state's universities.