Boston’s public school system needs to spend $61 million more to educate the city’s children next school year, in part because enrollment is expected to be the highest in nearly a decade, according to a proposed budget presented to the School Committee on Wednesday.

The district expects nearly 1,200 more students next school year, mostly in prekindergarten and elementary school, as well as special education, pushing enrollment to an estimated 58,271.

More children mean more classrooms. Books and blocks must be bought, as well as desks, chairs, computers, and whiteboards. But, more importantly, more children mean more staff. The district’s proposed $934.4 million budget is a 7 percent increase over the current year, John McDonough, the school system’s chief financial officer, said before the School Committee meeting.

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“We’re in higher demand; more families are choosing Boston public schools,” said McDonough. “While it’s good news for the district, it creates additional costs.”

In part because of rising health care costs, employee raises, and transportation costs, the district had forecast a $76 million budget gap. But money from the city’s general budget will help plug most of that, providing $58.2 million.

The remaining shortfall was bridged by eliminating vacant positions, saving unspent grant money, changing school start times by 15 minutes, and renegotiating some contracts.

Transportation costs were lower than projected after negotiating a new contract. The current 10-year, $464 million contract with First Student Inc., the private provider that ferries Boston students to and from school, expires at the end of this year. Last school year, buses were persistently tardy, arriving well after the first bell sounded.

First Student was one of four companies that bid on the new contract with the district. School administrators would not say who was selected, because the deal is not final.

“We’ve been able to preliminarily identify a bidder who can provide higher-level service at a lower cost [than projected],” said Lee McGuire, a district spokesman.

Next year, the district must pick up the tab associated with “turnaround schools,” because the federal grant that supports them is set to expire. That state designation helped those 11 schools, some of them among the state’s lowest-performing, receive extra resources to extend the school day and hire more experienced teachers.

An additional $30 million infusion of cash from the city as part of the mayor’s Quality Improvement Funds is one reason the district was able to keep those initiatives, officials said.

The money, half of which must be spent on facility improvements, will be spent over three years, allowing the district to extend the school day, work with community partners, and reward effective teachers and school leaders. The money will also support 21 schools that the district deemed in need of additional support in September.

Wednesday’s hearing was just the first step in approving the budget, on which the School Committee will take a final vote in March. The budget is then rolled into the mayor’s budget, which must be approved by the City Council.

“I think we’ll find that when the mayor submits his budget to the City Council and we look at what other departments are seeing, I don’t know that any other will see this kind of increase,” said Samuel R. Tyler, president of Boston Municipal Research Bureau.

“My impression is that the School Department budget is the one that had the biggest challenge.”