Robert Bell, the legislator who is sponsoring the Virginia bill, said it represented increasingly nuanced parental thinking as home-schooling has evolved into a more mainstream activity, up from 850,000 students nationally in 1999 to 1.5 million in 2007, the latest figure available from the Department of Education. In Virginia, the number has risen from 3,800 students in 1990 to an estimated 32,000 today, Mr. Bell said.

“Twenty years ago, the perception was that home-schoolers wanted to be as separate as can be from public schools,” Mr. Bell said. “This is the next step, to take part in as much as makes sense for their kids. More and more parents are finding home-schooling a good fit, but they are not saying they want to be completely isolated from public schools.”

For those students who want to participate in sports that require large numbers of players, like football, Mr. Bell said, “high school sports are the only game in town.”

Robert F. McDonnell, Virginia’s Republican governor, has said that he supports the bill. It will now go before the State Senate, which is evenly divided politically and where passage is uncertain.

The bill faces opposition from such groups as the Virginia Association of School Superintendents; the Virginia Education Association, which represents 55,000 teachers; and the Virginia High School League, the governing body for public school sports.

“There are thousands of public school students whose parents pay taxes and who attend public schools and don’t meet the eligibility requirements; they don’t get to compete in sports,” said Ken Tilley, executive director of the Virginia High School League.