Two school districts outside Indianapolis canceled classes Thursday after officials said threats were made against their schools, but many other districts across the country say they received threats that were less than credible, and classes will go on as planned.

Danville Community School Corporation canceled classes following alleged threats from two students who've been arrested. The nearby Plainfield Community School Corporation just west of Indianapolis also canceled classes, saying in a message on its website that a threat was "directed to the high school."

Meanwhile, the Miami-Dade County Public Schools and Houston Independent School District announced on their websites that "less-than-credible" threats were received late Wednesday evening, and that schools would be open on Thursday. Officials from Broward County Public Schools in South Florida said they also received a threat. In a tweet sent Thursday, the district announced that all schools would be open Thursday morning.

Also, the Dallas Independent School District announced on its website that schools were opening Thursday after an emailed threat sent to several school district staff and teachers at Pinkston High School and Martinez Elementary School was deemed non-credible. The emails were sent Wednesday night.

In Indiana, Danville Police Chief William Wright says a 14-year-old freshman and a 17-year-old senior were arrested early Thursday after the boys allegedly made threats against Danville schools in separate incidents. He says a classmate overheard the freshman at Danville Community High School saying he was going to "shoot the place up." Wright says the senior was arrested after posting a threat on Facebook after hearing about the freshman's arrest.

Miami and Dallas school officials said federal, state and local law enforcement agencies were notified, and extra security was deployed to schools Thursday.

In Houston, officials said law enforcement officers were making sweeps of school district buildings to ensure student safety. They encouraged parents and students to be vigilant and report any suspicious activity to police.

On Tuesday morning, the Los Angeles school district closed schools after receiving an email threatening a large-scale attack. New York City schools also received a similar threat but officials there concluded it was a hoax.

It's rare for a major U.S. city to close all its schools because of a threat and it reflected the lingering unease in Southern California following the attack that killed 14 people at a holiday luncheon two weeks ago in San Bernardino.

The Associated Press contributed to this report.