Last night, the Rochester school board unanimously approved a $734 million budget for the coming school year. The budget is about $6 million more than what Superintendent Bolgen Vargas proposed several months ago, and it will fund longer school days in as many as 10 schools this fall.

The budget closes a $50.2 million gap through a combination of attrition — more than 100 teaching positions will not be filled — and by using a plan proposed by Governor Cuomo that offers municipalities and school districts some flexibility for funding pensions. District officials say layoffs will be minimal.

Vargas says the budget builds on earlier priorities by providing city students with more opportunities to participate in arts, music, and sports programs. And it gives students extra time to prepare for the state’s more rigorous curriculum, referred to as the Common Core.

While Vargas got much of what he wanted in the budget, some board members are unhappy. Board member Van White resubmitted a proposal to fund converting School 17, one of the district’s most troubled schools, to a Freedom School.

The Freedom School in Rochester is one of more than 200 nationwide and originated with the support of the Children’s Defense Fund and its founder, Marian Wright Edelman. The schools emphasize literacy and the arts. But other board members are concerned with the costs and how the school would be operated.

Board member Cynthia Elliott said the idea had not been thoroughly thought out and she was concerned that it may cause instability at a time when the board is trying hard to create stability in the district.

Board member Mary Adams said she was concerned that the budget cuts too deeply into social and emotional services city students need.

The city school district’s 2013 to 2014 budget now goes to City Council for a vote next month.