The Montgomery County Board of Education asked Tuesday for new, lower-cost options for shifting high school start times, opposing a recommendation from Superintendent Joshua P. Starr to shelve the district’s effort to give teens more time to sleep.

Board members unanimously approved a resolution from the board’s vice president, Patricia O’Neill (Bethesda-Chevy Chase), requesting that Starr examine scenarios that would cost no more than $10 million. They asked him to present a report to them in time for the next budget cycle.

O’Neill and others said they agreed with Starr that the proposal he offered in October — a plan that would have moved high school start times nearly an hour later but with a price tag of at least $21.6 million a year — was too expensive. But they said there must be other ways to reach the goal of resetting the 7:25 a.m. opening bell for classes in Montgomery’s 25 high schools.

“I don’t want to give up on this,” O’Neill said, calling for creative alternatives and expressing disappointment that a more cost-efficient proposal was not brought to the board for consideration.

Board members pointed out that neighboring Fairfax County is considering new high school schedules for similar reasons and at far lower estimated costs. In a memorandum, O’Neill said Fairfax had four options, ranging from $2.8 million to $7.7 million.

“I don’t want to end this conversation today and have it just sit there on the shelf for a long time,” she said during a school board discussion of how to proceed on Starr’s original proposal, which would have moved high school opening bells to 8:15 a.m.

O’Neill said it is important for Montgomery to review the options Fairfax considered, as well as other approaches in use elsewhere.

The board’s president, Phil Kauffman (At Large), recalled that when Montgomery considered the idea of changing high school start times years ago, some options had very little cost associated with them. He said that not all options are perfect but that “there are going to be no perfect solutions that are going to meet everybody’s needs.”

Starr said the district would look closer at Fairfax’s proposals and explore the question . “Maybe they figured out a way to do something that can be applied to us that we just hadn’t though of,” he said. “That would be wonderful.”

The board discussion came near the end of a long school board meeting Tuesday. Earlier, several dozen supporters of later high school start times — including a few pajama-clad teens — turned out for a period of public comment, bearing signs such as “Less Sleeping in Class” and “Decrease Teen Depression.”

The plan Starr offered would have changed school schedules for all students, from elementary through high school. In Montgomery, as in many districts, buses make staggered runs, with the same vehicles transporting students of various ages at different times.

Along with the high school shift, Starr proposed that middle schools would open at 7:45 a.m., 10 minutes earlier than their current schedule, and elementary school students would stay 30 minutes later in the afternoons.

The longer elementary school day drew dissent, with some parents saying that young children need time in the afternoons to play, exercise, do homework or participate in other activities. The extra 30 minutes also drove the price of the proposal higher.

Starr’s recommendation to hold off on the idea of changing high school start times was released last week. He said that the cost was prohibitive with the district facing competing budget priorities, and that community reaction was mixed.

“I wish we had been able to find a way to make it cost-effective and palatable to most people, but that is not what we have right here,” Starr said.

Parent advocates assailed his recommendation to put the idea aside, saying it did not have to be so expensive and disputing his characterization of community support. They also argued that the longer elementary school day did not have to be connected with high school schedules.

Montgomery’s recent push to delay the start of the high school day started with an online petition more than 18 months ago by a Garrett Park parent. It quickly garnered more than 10,000 names and led to the creation of a work group to study the issue.

“We’re delighted that they’re going back to the drawing board on this and they’re going to consider more solutions rather than the one solution Dr. Starr put out there,” said Mandi Mader, the parent who started the petition and later served on the work group.

She said parents look forward to working collaboratively with the district to find lower-cost solutions. “This is a great step ahead for our kids’ health and well-being,” she said.