The Fairfax County school system is applying for a U.S. Department of Education grant worth up to $40 million in the hopes it would help the county overhaul schools attended by its poorest students.

The grant, part of an Obama administration initiative called “Race to the Top,” provides about $400 million over four years to individual school systems. “We’re going for this grant because we need every dollar in these tight times,” said Kim Dockery, a Fairfax County assistant superintendent who is on the grant proposal team.

Dockery said the core of the grant would be spent on schools where more than 40 percent of the students receive free or reduced lunches, a measure of poverty in Fairfax.

She said that although Fairfax County is one of the most affluent in the nation, nearly 42,000 students live below the poverty line and as many as 2,500 are homeless.

County officials said the federal funds would also be used to upgrade database systems that teachers use to track student progress. Dockery also said the money would help pay for teacher training and professional development.

Fairfax County assistant superintendent Dan Parris gave a presentation about the proposal Wednesday night to members of the county council of parent-teacher associations. How the money would be spent would largely come from input from members of the community, Parris said.

“This is a key opportunity to change,” Parris told the group of local advocates and parents. “And if we’re going to make lasting changes, we’re going to need everybody’s voice in the process.”

The competitive grants were previously only open to state education departments. To date, 18 states and the District have been awarded grants.

In August, the White House announced that the 2012 awards would be available to school systems nationwide.

Nearly 900 school systems and local education agencies across the country notified the U.S. Department of Education of their intention to apply. In Northern Virginia, Fairfax County may find itself competing with the Arlington school system. Arlington County notified the Education Department of its intention to apply, but Arlington officials said they are still considering whether they will submit their application.

This year, the Education Department will award between 10 and 25 grants. The amount of money a school system will receive will depend upon its size and student population. Because Fairfax County is one of the largest school systems in the country, with enrollment surging beyond 180,000 students for the first time this year, it is eligible for a grant worth between $30 million and $40 million. Arlington County, with about 22,000 students, may apply for a $5 million grant.

The Race to the Top application deadline is Oct. 30, and the winners will be announced before the new year.