A Queens principal canceled an eighth-grade math class and had students watch “The Karate Kid” for 50 minutes so their teacher could tutor the principal’s son instead, investigators found.

PS/MS 105 Principal Laurie Shapiro told special school investigators that her son, a Nassau Community College student, had initially sought help from the math teacher during a free period.

But when the teacher told her he needed “a little more time” for the tutorial — although his fourth-period math-class kids were arriving — Shapiro escorted the students to an auditorium where other classes were already watching the movie.

Officials couldn’t confirm whether it was the original — starring Ralph Macchio and Noriyuki “Pat” Morita — or the 2010 remake with Jaden Smith.

The other classes were allowed to watch a movie rather than learn because their teachers were attending a training workshop elsewhere, according to an investigative report concluded in June 2011.

Shapiro was fined $2,000 yesterday by the Conflict of Interest Board for catering to her college-aged son rather than to her students.

She did not respond to an e-mail seeking comment.

Shapiro earns $143,426 in her 14th year as principal, and has had no prior transgressions, according to the Department of Education.

A second school leader, PS 382 Principal Avon Connell-Cowell, was also fined for putting her family — rather than students — first.

Connell-Cowell, whose misdeeds were first documented by The Post, had a teacher baby-sit her nephew in the Bronx school building nearly a dozen times when, in fact, the instructor was supposed to be leading a class.

The 3-year-old had been left in classrooms with kindergartners and first-graders for several weeks at a time, staffers had alleged to The Post in 2010.

He was not a registered student at the school.

Connell-Cowell was also fined for supervising and evaluating her sister — who was hired to work as a family worker in the Fordham Heights building in late 2009.

The two miscues cost the principal a $4,500 fine.

Connell-Cowell earns $124,501 in her third year as principal. She has been reprimanded in the past for verbal abuse, according to the DOE.