Students in 22 city schools will miss a seventh straight day of class on Wednesday while the Department of Education continues to restore buildings damaged and disrupted by Hurricane Sandy.

And thousands of other students will have to make their way to school on their own because the department does not have enough buses to move all of the students who need transportation.

After calling local private bus companies and petitioning the state and federal emergency relief organizations, the city has rounded up more than 100 additional buses to join the 7,400 that ran on Monday, officials said this evening. But still, buses will serve students at fewer than half of the 43 schools that are so severely damaged that they must be moved. Those schools, which together enroll about 20,000 students, are opening for the first time on Wednesday.

A major problem, Chief Academic Officer Shael Polakow-Suransky said this evening, is that the department’s transportation hub, located in Long Island City, still does not have power. The department can only add new routes, not make the ones it already operates more efficient, while the computer system that programs the city’s 7,700 school bus routes is down, he said.

“We don’t have access to any of that,” he said. “Everything we are doing at this point is by hand.”

Families are finding out today whether their children will have a ride to school. Students and parents at schools without busing will be given Metrocards — but only after they make their way to their closed schools first. The department will reimburse families for the trip.

For high school students, who do not typically get bused, the department will provide Metrocards, and students who live on the Rockaways, where public transportation still has not been restored, will be able to take school buses to their relocated schools. But because of the bus shortage, they will have to wait until 10 a.m. to board buses that have already run one route.

High school students who live in the Rockaways but attend schools that survived the storm unscathed might have an even harder time leaving the peninsula: Polakow-Suransky said he did not know whether the department planned to bus them at all.

In buildings that will begin co-locations on Wednesday, principals and teachers from the host and relocated schools worked together today to plan how space and supplies will be shared. Where possible, teachers brought materials from their damaged schools to the new sites, and Polakow-Suransky said the department had given each school extra funds for supplies.

That planning process will get underway tomorrow for 13 Queens schools — with 6,000 students — that still do not have power and must be relocated. Polakow-Suransky said it was “unlikely” that most of the schools would have their power restored before Thursday, when students are expected to report to new locations.

The other nine schools, enrolling 7,000 students, that will not reopen to students until at least Thursday are located on three high school campuses that have been used as shelters since the storm.

One of the campuses that cannot reopen tomorrow is John Jay High School in Brooklyn, where Mayor Bloomberg said during a news conference that about a dozen evacuees had come down with “what we believe to be a stomach virus.” The department expects that its four schools will be able to open on Thursday, after a vigorous cleaning. But one of the schools, Millennium Brooklyn High School, is choosing not to wait: Its website instructs students to report Wednesday to nearby P.S. 321.

Two other buildings that have served as shelters will not be ready to reopen to students on Wednesday because the city is reducing the number of evacuees staying in them. At Franklin Delano Roosevelt High School in Brooklyn, there are still 800 evacuees, and George Washington Campus in Manhattan received a new influx of people needing housing today, Polakow-Suransky said.

Students at five other campuses that have been used as shelters will return on Wednesday, most to buildings that still house some evacuees. Manhattan’s High School of Graphic Communication Arts, where teachers decried conditions in the building last week, has been closed as a shelter site.

And among the schools in operation tomorrow, 35 still will not have heat. Department officials said they are providing warm meals and urging students to bundle up against the cold, which has become bitter this week.

Polakow-Suransky said the schools that are closed for an additional day will have to make the time up in the future, posing a scheduling challenge that grows as the days without classes stack up. But he said the department was trying whenever possible to urge students to learn outside of school.

And with a potentially damaging northeaster bearing down on the city, he emphasized that the department’s recovery has proceded swiftly given the magnitude of destruction after Sandy. On Sunday, more than 200 schools were without power and 65 schools were expected to have to relocated.

“Obviously the reason that we’re moving heaven and earth and why we’re pushing so hard to get these schools open is we want to have students in school,” Polakow-Suransky said.