Three of the 24 schools that the city tried to close and reopen this summer could undergo “turnaround” after all.

Under the aggressive form of the federally prescribed school overhaul process that the department tried to carry out, all teachers at the struggling schools were required to reapply for their jobs. The city set no quota for rehiring, but the requirement that no more than 50 percent be rehired in order for the schools to qualify for federal funding was widely known.

An arbitrator ruled in June that the city’s version of turnaround ran afoul of its contract with the teachers union.

But three of the schools — some of the smallest proposed for turnaround — turned over more than 50 percent of their teachers last year anyway, so they meet the federal requirements for funding. The schools are Bread and Roses Integrated Arts High School, J.H.S. 22 in the Bronx, and M.S. 126 in Brooklyn.

Now, the city has asked for turnaround funding for them and for 15 other schools that it is shutting down through its regular closure process. Under that process, used for years, one school phases out while others phase in in the same space.

According to materials that the State Education Department presented to the Board of Regents in Albany this week, the State Education Department is currently reviewing the city’s application for the federal funds, known as School Improvement Grants. If the application passes muster, the city would get about $25 million for the 18 schools and, where applicable, their replacements.

Last year, the city received $60 million to fund 11 school closures it had planned before finding out about the grants. The funds went to 16 new schools, two of them charter schools, that opened in space vacated as the 11 low-performing schools shrank, the department said at the time.

SED’s briefing papers to the Regents also give a hint at what happened after the arbitrator’s decision torpedoed the city’s more aggressive turnaround plans this summer. They say that the department formally withdrew its application for the School Improvement Grants in September — more than two months after the arbitrator’s ruling and more than a month after a judge threw out the city’s request to have the ruling overturned.

Now, the city must submit documents that show how it plans to improve the schools. Those documents are due by the end of this month, according to the briefing papers.

The 18 schools that would receive SIG funds if the city’s application is approved are below.

In first year of phase-out:

Washington Irving High School, Manhattan, first year of phase-out
Samuel Gompers Career and Technical Education High School, Bronx, first year of phase-out
Jane Addams High School for Academic Careers, Bronx, first year of phase-out
Grace Dodge Career and Technical Education High School, Bronx, first year of phase-out
I.S. 296 — The Anna Gonzalez Community School, Brooklyn, first year of phase-out

In second year of phase-out:

Norman Thomas High School, Manhattan
IS 195, Manhattan
School for Community Research and Learning, Bronx
Bronx Academy High School, Bronx
John F Kennedy High School, Bronx
Christopher Columbus High School, Bronx
Monroe Academy for Business and Law, Bronx
Paul Robeson High School, Brooklyn
Beach Channel High School, Queens
Jamaica High School, Queens

Still open:

Bread and Roses Integrated Arts High School, Manhattan
J.H.S. 22, Bronx
M.S. 126, Brooklyn