When the doors swing open in Fairfax County schools Tuesday, many of them will stay open longer.

For the students entering seventh through 12th grades, the ideals and the ordeals of class will last half an hour longer each day, as intermediate schools and high schools in Fairfax expand to a seven-period day.

By adding the half-hour and shaving the average class from 50 to 47 minutes, the School Board hopes to allow students more opportunities to take classes they otherwise wouldn't be able to squeeze into their schedules, such as art, music, theater or computer science.

While the addition of the seventh period is the most dramatic change in store for the county's 128,000 public school students, it is by no means the only one. Among the others, three new elementary schools will open, lunch prices will go up by a dime or more, class sizes will generally be larger and teachers will inaugurate a more comprehensive -- and controversial -- sex education program.

With 171 schools, 17 special education centers and 15,200 employees, Fairfax is the largest school district in the area and in the state as well as the 10th largest in the nation.

For Superintendent Robert R. Spillane and the School Board, the most vexing issue dominating this year's public policy agenda will be money.

A casual look at the spreadsheets wouldn't convince anyone that the Fairfax school system is in need. With an operating budget of $875.8 million this year and per-pupil spending of $6,736, Fairfax is certainly among the wealthiest divisions in the state.

But Gov. L. Douglas Wilder has decided to cut state aid to local school districts to help make up an estimated $1.4 billion shortfall in Virginia's budget. Although Wilder has not detailed a plan, Spillane said he expects to lose $7 million to $8 million this year and about $15 million next year.

The school district can absorb this year's cut with a $7 million reserve set aside during the summer, but crafting a budget for the next year could be far trickier. Not only will state aid be cut, but the Fairfax Board of Supervisors has voted to limit its contributions, meaning the school district is looking at a 3.4 percent increase for 1991-92 -- the lowest in decades.

School officials are already talking about a $47.8 million shortfall between projected revenue and what they say is required to simply hold ground. Critics said the school district can make ends meet by trimming administrative fat.

Spillane said it is premature to worry, believing the community will not sit still for damaging budget cuts. "It's one thing to set projections," he said. "We'd all like to hold down the cost of education. We'd all like to keep the tax rates down. The reality is, in good times and bad times you still have to educate the youngsters."

One possible victim of the funding battles may be the restructuring of the elementary school day. The School Board has voted to end early Monday closings beginning in September 1991 to give students 2 1/2 hours more in school each week and to make day-care accommodations easier for working parents, but now the board will have to find a way to pay the $9 million cost.

Teacher union leaders who have opposed the change see the price tag as ammunition, and some board members who supported the restructuring have already begun to back off.

Spillane remains optimistic that the idea can be phased in over three to five years, meaning Monday hours will be extended as scheduled, but new teachers needed to handle the increased workload will be hired only incrementally.

"We're going to have to bite that bullet," he said. "There's definitely going to be some unhappiness about that, but we're always saying we should do what's educationally best for the children."

Quite likely, the budget difficulties will also give longtime opponents of Spillane's teacher merit pay program another chance to try to kill the landmark system -- on fiscal grounds because they have failed on policy grounds.

The program awards 9 percent bonuses to those teachers who have been rated excellent in a rigorous evaluation and will cost about $9.6 million this year. However, a strong majority of the 10-member School Board, including Chairman Kohann H. Whitney (Centreville), still supports the program and at the moment there appear to be no more than three votes to kill it.

"Everything will be on the table and that may include merit pay," said Joanne T. Field (Dranesville), the board's budget committee chairwoman. "But it's not something that could be gotten rid of overnight."

Money also will be an issue during the November election. School officials and PTA leaders will lobby voters to approve a $169.3 million bond referendum to pay for construction of several new schools and renovations of older ones.

Meanwhile, three new schools will open Tuesday. Poplar Tree and Centre Ridge elementary schools, both in Centreville, will open their doors to students for the first time, and students assigned to the new Willow Springs Elementary School will move from last year's temporary housing into the new building.

At the same time, the 375 students from Bren Mar Park Elementary School near Alexandria will be split up for the year while asbestos is removed from that building. Younger students will attend Belvedere Elementary while older ones will be shipped to Poe Intermediate; the school is scheduled to reopen in September 1991.

Among other changes this fall:School officials will continue to look for ways to boost minority achievement. With the population changing dramatically in the eastern half of the county and minority test scores still lagging, Spillane is under increasing pressure to develop strategies to ensure that Fairfax educates all students. Lunch prices will go up 10 cents in elementary and intermediate schools and 15 cents in high schools. All 1,300 school buses will be outfitted with an elaborate and expensive two-way radio system so that buses can be recalled during snowstorms and drivers can call for help in emergencies. The new family life education program will be introduced to more grades across the county. The most controversial aspect includes a ninth-grade unit that deals with homosexuality for the first time in Fairfax public schools. High school principals will experiment with different ways to combat absenteeism. Several schools may adopt an innovative system modeled last semester at West Potomac and Edison high schools that does not allow parents to excuse students from missed classes.