It seemed to be an incontrovertible victory and a moment of unity for Prince William County school employees and educators.

After a visible battle over the last few weeks that at times pitted teachers against school board members and administration, the county School Board on Wednesday passed a budget for the next fiscal year on a 5-3 vote. But some teachers are frustrated by a provision included in the new budget that they say soured what should have been a moment of celebration.

The new budget plan broke last week’s impasse by promising what teachers and employees have said they wanted: a so-called “step” salary increase that rewards teachers based on experience. The board directed Superintendent Steven L. Walts to come up with $5 million in additional cuts that will be needed to provide for the salary increase.

But School Board members also increased hours in the contract school day for teachers--teachers will be required to work 7.5 hours instead of 7.

That part of the motion was not discussed after it was read.

Brandie Provenzano, a Battlefield High School teacher, said board members had “blatantly disrespected” teachers by slipping in the extra half-hour. While most teachers stay at school that long, she and others said board members should have discussed the change openly.

“To slide something under the table like that says ‘We’re working against you,’ ” Provenzano said.

Some teachers said they saw the half-hour extension as a backhanded move given the recent “work to the rule” protests.

When the vote was taken, a chamber full of teachers was nearly silent.

School Board member Betty D. Covington (Potomac) had voted against the budget last week but decided to support it Wednesday because of the promised “step” increase. She has said fair compensation for teachers was a top priority.

After the vote, Covington said board members had been told that the 7-hour contract day was the lowest in the region and that most school systems required 7.5 hours. “They all work hard and they’re already doing it,” she said of teachers.

School Board members Lisa E. Bell (Neabsco), Gilbert A. Trenum, Jr. (Brentsville) and Alyson A. Satterwhite (Gainesville) voted against the budget, saying generally that the board should be more directly involved in determining the cuts and expressing concern about increasing the size of classes.

The board also asked that any additional funds that might come to the school district be directed toward reducing class sizes and putting dollars toward building and improving school infrastructure.

Prince William has the largest class sizes in the state and is looking to make $3 million in cuts to middle school and high school classes. Those cuts would increase class sizes marginally but put the county close to state maximums.

The budget is contingent on local, state and federal dollars staying consistent with projections. Teachers plan to rally at the Board of County Supervisors meeting Thursday to ask for the highest possible real-estate tax rate to help fill budget holes.

Per state law, supervisors cannot set a real-estate tax rate higher than the advertised rate, $1.215 per $100 assessed value.

Supervisors are expected to adopt the county’s overall budget, including spending for schools, at the end of April.