CHICAGO -- The number of students staying home sick with the flu is multiplying nationwide and normally quiet school nurses' offices suddenly look like big city emergency rooms, packed with students too ill to finish the day.

The federal government has urged schools to close because of the swine flu only as a last resort. But schools are closing by the dozens as officials say they are being hit so hard and so fast by the H1N1 virus that they feel shutting down for a few days is the only feasible option.

"There was nothing else we could do," said Michael Frechette, the superintendent of Connecticut's Middletown Public Schools where a middle school closed for the rest of the week after 120 students stayed home sick Monday and another 25 were sent home by noon. "The only way to stop that transmittal was to keep the kids home for the rest of the week."

At least 351 schools were closed last week alone -- affecting 126,000 students in 19 states, according to the U.S. Education Department. So far this school year, about 600 schools have temporarily shut their doors.

The number of closures this year appears on target to surpass the roughly 700 schools closed last spring when the swine flu outbreak first hit.

"This is scary," said Kathryn Marchuk, a nurse whose son attends St. Charles East High School outside Chicago, which closed for three days last week after about 800 of its 2,200 students called in absent. "So many people are sick. It's just everywhere."

Many school officials said they were afraid the virus would spread faster if they stayed open.

"Students are in such close proximity (to each other) and they're in two or three classrooms a day at two or three different desks," said Donna Lovell, director of pupil personnel for Berea Community Schools in Kentucky, which closed for four days last week after 20 percent of its students called in sick. "It's an incubator situation."

Whether it is all effective is debatable, with some experts saying that closing schools merely spreads the number of cases over a longer time.

But school officials like Frechette disagree, saying students who get sick this week while they're at home cannot infect nearly as many people as they were if they were walking the hallways of schools.

"Nobody's at school so they're not infecting each other," he said. Besides, he said, "kids are dying (and) it's just four days."

With such a surge of sick students, many schools are also scrambling to come up with ways to keep kids on top of their studies.

The U.S. Education Department recommended districts and schools provide ill students with remote learning opportunities such take-home assignments or posting homework and class lessons on the Internet.

Though some schools are doing that -- including Keigwin Middle School in Middletown, Conn., where assignments are posted on its Web site and students are asked to read 20 minutes a day -- others say assigning sick students homework is a wasted effort.

"If you want to make a kid really hate school ... the most effective thing you could do is to make them do their homework and school work when they have a fever and are not feeling well," said Nancy Kalish, an education writer who co-authored a book, "The Case Against Homework."

Jim Blaney, a spokesman for the district that includes St. Charles East High, said that although parents or healthy students could come to the school to pick up books, the days the school was closed were not the time to push ahead with lesson plans.

"We wanted the kids to get healthy, stay home, rest," he said.

Though there is no way to know how many children actually had swine flu, the deaths so far of roughly 1,000 people in the U.S. -- some of them children, including a 14-year-old in Ohio and another in Illinois this month -- have cast a shadow on school districts.

"We're a small community where everybody pretty much knows everybody," said Jon Hussman, a principal in Culdesac, Idaho, a town of fewer than 500 residents. "(And) when you have the possibility of death in that community, that's something you want to avoid."

The way Steve Bianchetta sees it, there is no incubator like a high school, a view that helps explain why the central Illinois superintendent closed Watseka High School for two days last week after a third of the school's 330 students were absent.

"They're not as hygienic as the younger kids," he said. "They hold hands, they drink out of each other's sodas."

Some officials say another reason for shutting down was that sick kids were still showing up.

Closing school "took the pressure off," said Katy DeSalvo, whose daughter, Amy, a 17-year-old senior at St. Charles East had been home sick and worried that missing school would hurt her grades. "She wants to go to Duke (and) all the kids, particularly the higher-achieving kids, want to go back. And they'd infect everybody."

Some districts closed even for small numbers of sick students. In Traverse City, Mich., the school district closed every one of the 18 schools even though the number of absentees at some was not close to 20 percent.

"It was in the best interest to do so," said Jayne Mohr, the associate superintendent for the 10,000-student district. "You could see it spreading, making its way across the 300-square mile district."

Not everyone believes shutting down is the best option.

Some children, especially in low-income districts, depend on schools for free lunch and parents can't always take off work to stay at home. Plus, shutting school doesn't always keep kids from spreading the virus.

"If kids were isolated in their homes it may help," said Julie Pryde, administrator in Illinois' Champaign-Urbana Public Health District. But "kids congregate at malls, at each other's homes, they go to movies -- and that is not helpful."

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Associated Press writers David N. Goodman in Detroit, Jessie L. Bonner in Boise, Idaho, and Maria Sudekum Fisher in Kansas City, Mo., contributed to this report.