In and out of classrooms, sleeping in shelters, shielded by parents, homeless children can seem invisible to society at large.

A national study released Monday finds that one in 50 children in America is homeless. They're sharing housing because of economic hardship, living in motels, cars, abandoned buildings, parks, camping grounds or shelters, or waiting for foster care placement.

"That is something that I don't think most people intuitively believe to be true," said Ellen Bassuk, an associate professor of psychiatry at Harvard Medical School and president of the National Center on Family Homelessness.

The national center last did such a report 10 years ago, and numbers of children without a permanent place to sleep are growing.

In Sacramento County, where debates over homeless issues have hit a pinnacle in recent months, school districts counted more than 6,000 children without stable housing during the last school year, a number that has been rising steadily since 2002.

The national center's study, "America's Youngest Outcasts," shows that California had 292,624 homeless children, the 10th largest population in the nation, during the time of its count, the 2005- 2006 school year. The group counted 1.5 million homeless kids across the country, about 200,000 more than the figure it reported a decade before.

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