The battle lines have been drawn in the Fairfax County School Board's fight to win voter approval of a $57.2 million bond referendum to build nine new facilities, including five new schools, and renovate nine existing schools.

On one side: The flourishing western section of the county, with its rapidly developing subdivisions and bulging classrooms.

On the other side: The older, eastern section of the county, its school-aged population now grown and many of its classrooms empty.

In the middle is the school board, trying to explain why it is asking voters to approve bonds for new schools almost as rapidly as it is shutting down old ones.

"It's going to be tough," admitted school board Chairman Ann P. Kahn. "We have to convince people in the county that they can't look at this in a parochial manner. When the eastern sections were growing, the entire county voted money for their schools. Now, the western end needs those same considerations."

The bond issue will be on all Fairfax County ballots in the Nov. 3 general election, and is one of four bond issues county voters will be asked to consider. The others include two jail issues and a proposal for secondary road improvements. A yes vote on the school bond issues means approval; a no vote means rejection. A simple majority is required for passage.

Over the past decade, the track record for approval of school bond issues has been checkered: three wins, four losses. And many school officials believe the board has more obstacles than usual to overcome this time around.

Approximately three-fourths of the $57.2 million would go to build five new schools and make major additions to four existing ones -- all in western Fairfax.

Of the five new schools, two -- an elementary and an intermediate -- would be built in the new Franklin subdivision near Chantilly, taking about one-fourth of the total bond package. In addition, the bonds would be used to build elementary schools in the Newington Forest and Cherry Run areas and an intermediate school near Braddock Park. All the new buildings would open by the fall of 1984, according to preliminary projections.

Among other projects proposed for western Fairfax are major additions to four elementary schools: Fairview, Clearview, Lake Anne and Clifton.

In an attempt to woo voters in the older sections of the county, the board has included plans for renovating nine buildings, most of which are inside the Beltway. About $14.5 million would be used for those renovations at seven elementary schools and two high schools. Those schools are Marshall and Woodson high schools and Beech Tree, Braddock, Clermont, Graham Road, Hollin Meadows, Mount Eagle and Westlawn elementary schools.

However, some school officials say the promises of renovations may not be enough to attract the many voters in the older areas of Fairfax, especially those who harbor bitter feelings toward the school board because of recent school closings in those neighborhoods.

"We're doing little more than throwing them a few crumbs," one school official conceded.

In the last two years the board has closed nine schools in the easternmost sections of the county, all because of declining enrollments. Most of the closings occurred against a background of court battles, heated board meetings and outraged parents.

Five of those nine schools have been turned into administrative centers for various school system departments and another is scheduled for conversion to an administrative center, replacing an existing office center.

"That alone could bring the bond down," said school board member Gerald Fill, who represents the Mount Vernon District, where two schools have been closed. "People see tremendous growth in administrative space in an era of unprecedented declining enrollment -- and that translates into big bureaucracy."

Board Chairman Kahn said other factors also could influence the outcome of the bond issue, particularly statewide races that may attract an electorate that is less interested than usual is bond issues.

"There are going to be a lot of people turning out who are informed about the gubernatorial candidates, but who aren't informed about the school referendum," said Kahn. "And that is going to hurt us."

If the Nov. 3 effort fails, Superintendent Linton Deck said the school board will attempt to set another referendum, probably next spring.

In addition to the school construction and renovation, the bond sales would finance construction of a secondary center for physically handicapped students, an elementary center for emotionally disturbed students, a vocational job training center and a storage building for refrigerated food items.

Meanwhile, the board is attempting to overcome opposition by emphasizing what it believes are the stronger selling points of the referendum.

For one thing, school officials say, passage of the bond issue won't mean an increase in county taxes, because the schools will be retiring old bonds and because of the expanding tax base in the county.

But school officials are even quicker to point out what they call critical overcrowding problems in some areas of the county.

"We're going to be having classrooms in the corridors if this doesn't pass," said Fill.

School officials cite a long list of potentially unpopular options they could use if the bond issue isn't approved: double shifts at some schools, massive boundary changes, major busing changes and year-round classes.

Superintendent Deck, in a memorandum to the school board last week, dismissed most of the proposals as long-term solutions to classroom overcrowding and said various options should be used only on a temporary basis.

Deck also contended that some of the temporary solutions could be expensive. For example, Deck said in his memo, portable buildings could be used to relieve some overcrowding. But, he warned, without permanent facilities, 179 portables would be needed by the 1985-86 school year, nearly four times the 45 portables now in use. At a cost of $25,000 each, the board would have to spend more than $3.3 million over the next five years to provide the portables.

Double shifts of classes are the only other option that would accommodate projected enrollment increases in the fast-growing areas, according to the Deck memo.

Although student enrollment countywide has dropped 9 percent in the last decade to 123,785 students this year, that drop has not been consistent throughout the county.

For instance, Herndon High School is 800 students over capacity, said Kahn. And in Chantilly, 4,000 new homes are expected to be built in the next few years, according to projections compiled by Alton C. Hlavin, assistant superintendent for facilities services.

At the same time, the board may be forced to close several more schools in the older sections of the county because of enrollment drops, according to Hlavin.

The enrollment imbalances, Deck said, have created a difficult problem for the school system.

"The dilemma is not declining enrollments," said Deck. "The problem is population mobility. If we had the technology to put buildings on skates and move them to the western part of the county, we could resolve the problem."