Children participating next year in a program that will provide child care before and after school will be chosen by lottery this summer, said Karen Severn, Prince William County's director of school-age child care.

There is room for only 30 children at each of seven schools, one in each magisterial district. The process of choosing them will begin next month, when the county will mail applications for the pilot program to about 4,000 families.

Parents who need supervision for their children will have only a short time to respond, Severn said. Applications must be in hand by late July, when members of the School Age Child Care Committee will draw names for each class.

Severn said she expects great demand for the program this year, and she anticipates its rapid growth, based on projections that there will be nearly 5,000 more elementary school-age children in the county by 1995.

"Women are in the work force and they will stay there," Severn said. "We've got to quit dragging our feet. It's here. How do we address that?"

Prince William has lagged behind other jurisdictions in offering school-age child care, which has been available in Fairfax County and elsewhere for more than a decade.

The before- and after-school program, which is to be operated by Minnieland Inc., a private day-care provider based in Prince William, will be available in these elementary schools: Nokesville, Occoquan, Springwoods, Neabsco, Pattie, Marumsco Hills and West Gate. Weekly fees are expected to run $45 to $50 per child for before- and after-school care. Child care before or after school will be $20 less, Severn said. Minnieland also provides a 10 percent discount for each additional child in a family.

Before-school care will start at 6:30 a.m. The after-school program will begin most days at 3:30 p.m., when school is dismissed. It will begin at 1 p.m. on Thursdays, an early dismissal day for all county elementary schools. Parents must collect their children by 6:30 p.m.

Severn said only children attending schools where the program is offered will be eligible to participate. At each school, the committee's lottery will assemble a class of 30, as well as a waiting list. Parents will be notified before the school year starts Sept. 4.

Minnieland, which runs 14 child-care centers in the area, was one of four child-care providers to bid on the county's program. The organization was chosen on the basis of its program proposal; the committee then negotiated a fee structure.

Early mornings will concentrate on helping children get organized for their school day, said Dean Kilby, 60, a former county principal and now a Minnieland supervisor who will direct the program. In the afternoons, children will snack and then have at least an hour outdoors for physical activity. They will come inside for arts and crafts, games, or tutoring if they need it.

"The afternoons will be more a leisurely environment, not an extension of the school day," Severn said. "When we talked with the citizen's advisory group, they said what we really would like to see is time out."

The county is providing up to $10,000 for start-up costs at each center, mostly for equipment or any needed changes in facilities. Restrooms at Nokesville, for instance, must be repaired before the program can begin there.

Finding space for the program in county schools has been the greatest challenge, Severn said. In three schools, the program will have its own classroom. In the remainder, the after-school program will share a gym or multipurpose room with existing activities.

This week, attorneys for the school system and the county were busy putting the finishing touches on the Minnieland contract and sorting out the last remaining insurance and liability clauses.