One after another, sick Brooklyn Technical High School teachers called union chapter leader Nate Bonheimer last week, to tell him they’d tested positive for COVID-19.

By Friday, five of them had shared the devastating news. But after being notified about each one, the city Department of Education still ordered the 6,000-student school’s 350 staffers to show up for work last week, saying the building had been cleaned.

“The DOE did not close the school for any of the cases,” said Bonheimer, who worries that inaction exposed others to the dreaded infection.

The city failed to follow a March 9 directive by the state Education Department that “requires an initial 24-hour closure, in order to begin an investigation to determine the contacts that the individual may have had within the school environment.”

DOE did not attempt to identify close contacts, Bonheimer said. “They did not alert the people who needed to know the most to protect themselves, their families and everyone else they came into contact with.”

One infected teacher was so torn by the secrecy he took it upon himself to personally let all his students know his condition.

Around the city, teachers and administrators are outraged that Mayor Bill de Blasio and Schools Chancellor Richard Carranza resisted a drum beat to close the public schools in the name of safety.

Some renamed the coronavirus “Carranzavirus.”

“You say equity and excellence, but every other school district closed before you did. You had these kids like petri dishes spreading this to their families,” an administrator fumed.

Some DOE employees believe de Blasio and Carranza deliberately kept the lid on the COVID-19 cases popping up, putting kids and families at risk.

“The blood is on their hands,” one said

DOE staffers think the two city leaders tried to cover up the cases because they wanted to keep the 1.1-million-student system running despite increasing pressure to shut it down. Finally, with Gov. Andrew Cuomo about to do it, the mayor relented and closed the schools for students on March 16. They will remain shut until at least April 20, after the spring break.

An expert agreed the failure to notify health officials was dangerous.

“The chancellor was not properly following state policy,” said Aaron Carroll, a health sciences researcher and pediatrician at Indiana University School of Medicine.

The information freeze started March 10, when Carranza, in an email obtained by The Post, told administrators not to alert city health officials about COVID-19 cases among students or staff.

“At the moment, there is no reason for any school to call [the Health Department] to report potential or confirmed cases,” Carranza wrote, repeating the statement later in the same email.

Carranza said DOH would get test results from labs, and school personnel should help “by keeping their phones clear.”

Health department spokesman Patrick Gallahue said Friday the agency “was in agreement with DOE on the directive.”

At several campuses and DOE offices citywide, multiple staffers have tested positive but affected buildings remained open while workers, students and parents were kept in the dark, whistleblowers said.

At the Grand Street campus in Williamsburg, which houses three high schools, a teacher returned from a trip to China over the February break. Despite reports of the outbreak, the teacher did not self-quarantine, but returned to teach kids in all three schools Feb. 26 through Feb. 29, a staffer said.

The teacher then became sick and stopped working. The school was not closed, and employees were not notified, insiders said.

Up to four other staffers have since become sick, they said.

The teacher did not return a message, but a relative said Friday, “He’s very ill, and so is his entire staff,” before declining to comment further.

Last Thursday — after Grand Street teachers worked three days in a row in the building — the principals sent a joint letter saying that “members of our school community” had self-reported positive COVID-19 tests. It did not say how many members or give other details.

“Unfortunately, the DOE suspended keeping track of positive cases,” a teachers’ union official told a staffer on Tuesday. The DOE would not comment on the Grand Street or other cases.

At the Jamaica High School campus, which houses three schools, Carlos Borrero, principal of the High School for Community Leadership, blasted a robocall to parents the Sunday before schools closed for students, reporting the school had “one confirmed” case and another “preliminary positive” case identified over the prior two days — while students attended. One was a teacher, Borrero said.

Asked about the announcement last week, the DOE would not give details.

“The city is no longer confirming information about individual cases due to the volume, but we support any school that wants to notify their community of a self-confirmed case,” said DOE spokeswoman Miranda Barbot.

At the Grace Dodge High School campus in the Bronx, a teacher self-reported a positive COVID-19 test on Thursday, March 12, staffers said. The DOE did not close the school the next day, when kids still attended before de Blasio announced that all schools would close for students starting March 16.

Teachers received a form letter from Carranza confirming a staffer had tested positive, saying the building was “disinfected.” The school was not closed while teachers worked last week.

“We asked when students and parents would get notification, and they still haven’t gotten it,” a teacher said. The DOE had no comment.

At the Bronx’s Alfred E. Smith campus which houses three high schools, teachers reported for three days of training on remote-teaching to begin next week.

“Ten minutes before the end of the last day, the union rep walked through the hall and said, ‘You’re free to leave,’” a teacher said. She asked why.

As custodians arrived in Hazmat suits, the union rep replied, “There’s coronavirus in the building.”