It's Thursday morning at Roanoke's William Fleming High School, and 18 freshmen are working in small groups to complete a math quiz.

If past trends are any indication, almost half of these students won't graduate from high school. But their principal, Susan Lawyer Willis, hopes these students, who are part of a math-intensive pilot program, will buck the trend.

They'll have to.

With a strict federal deadline creeping up and tough new graduation requirements imposed by Virginia education officials, city school leaders are under the gun to improve the city's stubbornly low graduation rate.

The 2005-06 school year's graduation rate was 57 percent, the fifth worst in the state, after Cumberland County, Petersburg, Richmond and Bristol. For 2004-05, the rate stood at 58 percent and at 63 percent the year before that.

"There's no doubt about it, we're not satisfied about it," said Richard Layman, the Roanoke school system's chief academic officer.

Under the federal No Child Left Behind Act of 2001, school districts must post a 100 percent graduation rate by 2014. That means that every student in fifth grade this year will have to graduate from high school.

Also, starting this year the Virginia Department of Education is giving students less discretion in choosing their high school classes, something that could hurt graduation rates.

Where before students had to receive one credit in both reading and writing and four credits in a subject of their choice in order to graduate, they now will have to receive credits in reading, writing, math, history, science and one subject of their choice.

"Our diploma requirements become a little bit more rigorous this year," said Charles Pyle, a spokesman for the state Department of Education.

The earlier requirements were a temporary measure to give students flexibility as schools adjusted to a 2004 rule mandating that students pass Standards of Learning tests to graduate, he said.

But the tougher requirements could cause some students to become disenchanted and drop out of school, Layman said.

"Any time you take away electives, it's going to have an impact on some children," he said. "If you are a marginal student to begin with, that might have an impact on your decision as to whether to stay or not."

Only regular high school diplomas or advanced diplomas can count toward the graduation rate, according to the rules set by No Child Left Behind. That means that some students who cap their high school careers with other certificates, such as a General Educational Development diploma, or students with disabilities who receive a special diploma or a modified standard diploma, are not counted as having graduated, something local and state education officials have tried to change.

It doesn't help that the statistics Virginia school districts rely on are merely estimates that only track cohorts of students to report their graduation rates.

For instance, the city's 1,112 freshmen in 2002 had dwindled to 608 seniors last year.

Where did those students go?

The school system has identified 201 members of the potential class of 2006 as dropouts, leaving hundreds who didn't drop out but who didn't make it to 12th grade. They may have repeated ninth grade and be on track to graduate a year later, they may have moved out of the district or they may have moved from one school to another within the district, further muddying the counts.

"It just makes our job really difficult giving you clear accurate numbers which don't double-count, triple-count the same individual," Layman said.

To remedy that, state education officials plan to introduce a new tracking system in 2008 that will keep tabs on individual students as they proceed through their school careers.

Willis says she's already doing that at William Fleming. All of the students in the grant-funded math class, which will give them two credits of algebra this year rather than one, were handpicked because they failed their eighth-grade math SOL test by just a few points.

"The goal to increase the graduation rate is to get them hooked and successful, have them experience success that first year," she said.

But efforts to keep students in school have to start much earlier, Layman said, citing studies that show that poor academic performance can often predict whether or not a student drops out.

So administrators are targeting elementary and middle school students, helping them perform better long before they even think about dropping out.

"We all -- schools, parents, caregivers and the community -- need to do a better job of stressing the importance both to the individual and to the community of taking advantage of the excellent education opportunities we offer," said school board Chairman David Carson.

The city's low graduation rate has divided political leaders, with candidates during this year's city council election disagreeing over the best way to help the schools.

David Trinkle, a former school board member who won his race for council in May, said he would be willing to give the school system additional funding to boost graduation rates if school leaders can prove the money would be well spent.

Trinkle, who made education a major theme of his campaign, expressed confidence in school administrators and urged residents to be patient while the schools adapt to a new administration and to Superintendent Marvin Thompson, who is in his second year.

"The school board, over the last couple of years, has implemented a system of changes including new administration and new programming, and we have to give it time to see the effect," he said.

But Trinkle's fellow city councilman, Brian Wishneff, has run out of patience.

"I don't think we're ever going to see progress," he said. "It's just a disaster."

Wishneff, who was not up for election this year, blamed top administrators for the graduation rates. He has called for Thompson to be replaced.

In the long run, keeping students in school is good for the city's bottom line. Dropouts are more likely to earn less and to need more costly city and state services, Layman said, adding that low graduation rates can also blunt a locality's economic development efforts.

"There's a direct impact economically to our community and to our city of children that leave school before they graduate," he said.

But it's not easy to persuade a teenager to stick around, especially if that teenager is dealing with pressures outside school.

"When you have an at-risk population, that makes your job that much more difficult," Layman said.

It's hard to say at this point how successful the school system's long-term strategy will be. Test results have been mixed in the past three years, with math scores dipping while scores in English and science have improved slightly.

Still, this year's senior class is almost half as large as the freshman class four years ago.

But administrators say they're hopeful they'll see more students walk across the stage in a few years.

Karizimine Fitzgerald, a ninth-grader in Fleming's math intensive pilot program, is determined to be one of them.

"I want to finish high school, go to college and be a nurse," she said.

Her classmate, Sam Cotton, vowed to stick it out as well.

Their math teacher, Suzie Fore, who is cramming two years' worth of algebra into a single year, is convinced her charges won't quit school.

"They'll make it. That's not an option," she said.