A portion of pay increases for Fairfax teachers, reserve funds for school construction and school hiring, new carpeting for schools and part of a new energy conservation program are among the primary targets marked by the Fairfax County School Board for potential budget cuts.

In the past two weeks, the school board has been identifying specific areas for potential budget reductions at the request of the county board of supervisors. The supervisors asked that the school board, as well as all other county departments and agencies, develop lists of potential cuts totaling 2.5, 5 and 7 percent of the total amount these departments have requested from the county for funding. The supervisors say they want the lists to help them judge which areas of the county budget can be cut if necessary.

The school board's possible cuts, totaling $5.9 million, equal 3.5 percent of the $167 million that the schools have asked the county to contribute to its $264 million operating budget for school year 1978-79. The board has asked the supervisors if this list of potential cuts will be sufficient. The supervisors could require a list of more extensive cuts.

The school board has told the supervisors, however, that they cannot guarantee the areas they have identified will be the ones ultimately cut if the supervisors insist on reducing the county's $167 million share of school support.

The school board chose several of these potential cuts from a list of 18 areas that included funds for textbooks, field trips, metric education and instructional supplies. After heated and emotional debate on what areas should be cut at a special meeting last week, most school board members agreed cutting additional areas would adversely affect the schools' educational program.

The supervisors hold the purse strings to the school budget, but the school board controls what individual items in the school budget are cut or increased. The supervisors had indicated they wanted the school board to make cuts that would not affect personnel or programs such as band and string music education, junior varsity soccer, art and other extracurricular programs.

"If we have to make more cuts, there is no guarantee we will be able to avoid looking at instructional programs and personnel cuts as a result," said Superintendent S. John Davis.

Other areas the school board has marked for potential reductions include a $1.4 million expense to meet state accreditation standards. The state has granted a two-year postponement of a requirement to lower the size of classes in grades four through six which would have forced the county to provide 138 more teachers and aides. Despite the postponement, the school board has been considering enforcing the requirement, but if the supervisors cut the budget, the schools will take advantage of the two-year delay.

The board also has looked at cutting the county's $76,000 share for the salaries and benefits for the staff of the Educational Employe Retirement Fund and another county contribution of $78,000 for general public education that can be made up in increased state aid.

Supt. Davis' proposed 7.1 per cent cost of living pay increase for all school employes would be reduced to 5.5 per cent - the same proposed by County Executive Leonard Whorton for all county employes - if the supervisors reduce the school budget and the school board makes the cuts indicated in its potential list.

Another $1 million would be cut eliminating a school construction reserve fund that the school board had set aside to got to ward building one of several new elementary schools needed in the county. About $387,000 would be cut by eliminating a special reserve fund used to hire new teachers in September when school enrollment is more than anticipated.

Some $78,000 would be cut by not replacing worn carpeting or providing new carpeting in some elementary schools, and $277,000 would be cut from a $440,000 energy conservation pilot program to reduce energy bills inthe schools.