Pennsylvania is taking a second shot at winning up to $400 million from a federal grant program to help reinvent low-performing schools and fund other changes to its education system.

On Tuesday, the state applied for a share of $3.4 billion to be awarded in the second round of the competition, which is called Race to the Top. Thirty-five states and the District of Columbia sought the grants, which will be given out in late August or early September.

The federal government is using the competition to push states toward carrying out measures it says are key to educational progress.

If it gets the grant, Pennsylvania will split $200 million among 122 of its 500 school districts and 69 of its 135 charter schools. The eligible districts and schools have agreed to revamp their educational systems in return for the money. They enroll 38 percent of Pennsylvania's public school students and 57 percent of its low-income students.

In the Philadelphia area, 24 of 63 districts and several dozen charter schools are participants. Philadelphia would get tens of millions; other districts would get from $100,000 to $8 million, depending on their size and poverty. Those with low-performing schools slated for makeovers - called turnaround schools - would get $650 more for each child in one of those schools.

Philadelphia has 76 turnaround schools; it would get more than $32 million in additional funding. All 14 schools in its Renaissance Schools initiative - which will be converted into charter schools, partnered with education management groups, or given special supervision by the district - are also on the turnaround list.

Suburban turnaround schools would get a combined $5.6 million for students in the Chester Upland, Norristown, Southeast Delco, Upper Darby, and William Penn districts.

Participating schools must adopt one of four turnaround plans. Under one, the principal and at least 50 percent of the staff would be replaced and a new curriculum, more learning time, a new teacher-evaluation system, and new student supports put in place. The second would leave the staff in place but make all the other changes. A school could become a charter school or be administered by an outside educational-management organization. The last option is to close the school.

The grant money would also go to revamp how teachers are evaluated, using student scores on state tests to help determine how well educators are performing.

In the first round of grants, awarded March 29, only Delaware and Tennessee got money. Pennsylvania was ranked seventh and New Jersey 18th. No set number of states will receive awards; U.S. Education Secretary Arne Duncan has said 10 to 15 would likely receive awards the second round.

Because of Pennsylvania's strong first-round showing, Jack Jennings, head of the Center on Education Policy, a Washington think tank that tracks education issues, said he thought the state "has a pretty decent chance" of getting the money, part of the economic stimulus bill passed in 2009.

New Jersey, with Gov. Christie's rejection of a compromise merit-pay plan that would have garnered more support from teachers unions, has less chance, Jennings said.