They cheated the kids.

John Dewey HS students got credit for sham “Project Graduation” classes in a grade-fixing scheme that robbed them of their education, according to a new state audit that also slams the city for shrugging off the findings.

The Brooklyn school’s “make-up” and “credit recovery” courses failed to meet a slew of requirements — letting many students improperly graduate, says the blistering audit sent to the city on Friday and provided to The Post.

“Far too many students received course credit they shouldn’t have and that is unacceptable,” state Education Department Executive Deputy Commissioner Elizabeth Berlin said of the “troubling” findings.

The audit comes three years after The Post first exposed the massive diploma giveaway at Dewey, where hundreds of failing students got bogus credits through a program the kids called “Easy Pass.”

Pressed to investigate teacher complaints, the city Department of Education’s internal probe confirmed that students lacking credits in all subjects were listed on class rosters and given “packets” of work — but got no instruction by certified instructors, as required by state law. One rookie teacher purportedly taught 52 classes in a single ­semester, records show.

The state audit examined a small sampling of credits and courses involved in the scam between 2012 and 2015, and found that 89 percent of courses did not provide required instruction time; teachers were not certified in subjects in 77 percent of those classes; and diplomas were wrongly awarded to 75 percent of students after they took bogus “credit recovery” classes.

Whistleblowing teachers charged that Dewey Principal Kathleen ­Elvin orchestrated the scheme to boost the school’s graduation rate and that Chancellor Carmen Fariña was a “de facto accomplice.”

Former Dewey teacher Michael Klimetz said the state’s belated action does not go far enough.

“New York City public-school principals will continue to manipulate grades, issue unearned diplomas, and rob the schoolchildren . . . of a meaningful and comprehensive education until the parties who conspired to perform grade and credit fraud at JDHS on an industrial scale are punished,” Klimetz said.

The city DOE charged Elvin with misconduct in 2015, but a hearing officer dismissed the charges in 2016 when the department failed to turn over records showing it had rubber-stamped the sham credits. The city never appealed.

Elvin no longer works as a principal, but collects $169,916 a year as an administrator in the DOE’s Office of Safety and Youth Development.

The state’s Berlin admonished Phil Weinberg, Fariña’s deputy chancellor of teaching and learning, for claiming the DOE is already doing enough to ​prevent similar fraud:

“Your response to our audit indicates that NYCDOE does not recognize or appreciate the seriousness of the audit findings,” Berlin wr​otte. “NYCDOE must address the findings of this audit and immediately start work on implementing its recommendations so no more students are cheated out of the education they deserve.”

DOE spokesman Will Mantell said, “There are no new findings in this audit.”