Virginia and four other states will remain exempt from the key parts of No Child Left Behind for up to four years, freeing them from the most onerous requirements of the main federal education law that left many schools facing sanctions.

Education Secretary Arne Duncan announced Tuesday that the states — the others are Kentucky, Minnesota, New Mexico and North Carolina — were approved for waivers under a fast-track process. The states were eligible for expedited treatment because federal education officials said they were meeting their commitments under their respective waivers.

No Child Left Behind expired in 2007, but Congress failed to rewrite it, despite widespread agreement that the law was unworkable. In 2011, the Obama administration began excusing states from some of its strictest requirements. In exchange, states had to enact reforms and accountability standards favored by the administration, such as using student test scores in teacher evaluations. The Obama administration has issued waivers to 42 states and the District of Columbia, but many of those will expire this year.

The waivers will become moot if a new federal education bill is signed into law. Efforts are underway in the House and Senate to rewrite the George W. Bush-era education law, which has been widely panned as excessively harsh and too stringent. It required, for example, that all students be proficient in reading and math by 2014. And it penalized schools that fell short of the mark, forcing them to submit to federally approved improvement plans.

Without the waiver, most Virginia schools would be labeled as failing.

“For far too long, the creativity and innovation of schools was held back by NCLB, a law that created literally dozens of ways for schools to fail and no way for them to succeed,” Duncan said in a conference call with reporters. “That’s why our department offered flexibility to states from the top-down prescriptive requirements.”

Tuesday was the deadline for states to apply for waivers. Maryland and the District applied to extend their exemptions from the law. The Department of Education said that by late spring or summer, it will issue responses to states that applied for waivers.

Virginia Superintendent of Public Instruction Steve Staples touted the state’s success under the waiver, saying state intervention had managed to boost achievement in many of the worst-performing schools.

“Virginia’s performance under the flexibility waiver shows that states can make progress in narrowing achievement gaps and improving outcomes for students in historically low-performing schools without the overly prescriptive federal requirements that characterize the No Child Left Behind era,” he said.

Virginia’s waiver was first approved in 2012. It requires districts to tie student test scores to teacher evaluations through a metric called student growth percentiles, which aims to measure the impact a teacher has on a student’s academic growth.

But few — if any — districts have used the measure in teacher evaluations, and even the state has called it problematic and riddled with errors. Despite this, Duncan still approved the state for an expedited waiver.

In Virginia’s most recent waiver application, officials said they will move to a different way to measure student growth. The new measure will strictly compare a student’s test scores from one year to the next, dividing test scores into eight levels and calculating how many levels the student has advanced.

Staples said student growth percentiles proved unworkable, which is why the state moved to change how it measured student growth. The new metric is “a truer measure,” he said.

Student growth percentile “just isn’t a very good measure to use,” he said, and school districts informed state officials that the measure was not useful for teacher evaluations.

Although Virginia’s waiver was approved, federal education officials still want the state to rework how it addresses high-poverty schools that appear to be failing English-language learners, students with disabilities, and black and Hispanic students. Schools that receive Title I money for having high poverty levels and perform poorly among those demographic groups are designated “focus schools” and are required to hire coaches to boost student achievement.

The state had proposed that schools be able to shed the label “focus schools” as soon as they rose above the bottom 15 percent of Title I schools, regardless of how students were performing. The state said it wanted to ensure it was focusing resources on the worst-performing schools.

But in a letter released Tuesday, Deborah S. Delisle, assistant U.S. education secretary, said the criteria also should take into account student academic progress before schools are allowed to be free of the label “focus schools.”

“We wanted to be sure that the focus schools are actually making progress,” Delisle said in the conference call with Duncan. Virginia has until June 30 to change the criteria.

The waiver also highlighted expanded pre-kindergarten programs that came about thanks to a federal grant and additional training for teachers of students who are learning to speak English.