The D.C. school board yesterday approved a plan to furlough all school employes without pay for up to five days between June and Sept. 30 to help cover part of the $6.4 million deficit in the current year's budget.

The board said the furloughs of the approximately 9,000 school employes would be done on a sliding-scale basis so that officials at the top of the pay scale, such as Acting School Superintendent James T. Guines, will be furloughed more days than those employes who are paid less. But no employes will be furloughed more than five days.

The furlough for teachers, who work 10 months of the year, will take place in September, according to R. Calvin Lockridge, chairman of the board's finance committee. It will be up to the superintendent's staff to designate on which days and furloughs will occur. Lockridge said the furlolugh will probably take place during the first week of September before school starts, but after the teachers have come back on the payroll from their summer vacation. He said the teachers may have to forfeit their salary for two of the four days they normally receive pay at the beginning of the year for preparation and planning.

Year-round school employes will be furloughed sometime between June 1 and Sept. 30, Lockridge said. During the furlough days, the entire school system will be shut down. The furloughs will save the system between $800,000 and $1 million each day of a total of $4 million to $5 million, Lockridge said.

The furloughs are an attempt to eliminate the $6.4 million deficit in the budget for the year ending Sept. 30. The school system is facing a projected $22 million deficit for the 1981-1982 school year. The school board has not taken any action on how to deal with that problem, pending final congressional action on the city budget for the year starting Oct. 1. Guines last week proposed a series of cutbacks for the next school year, ranging from cutting as many as 800 teachers to eliminating the entire adult education and prekindergarten programs.

Lockridge's finance committee had originally recommended having the furlough in June, but that move was opposed by Washington Teachers Union president William H. Simons, who said the teachers would prefer that the furlough come at the begining of the next school year.