Principals are struggling to string together enough substitutes; the algebra class actually had one, but he was not up to speed on the subject matter. Teachers are grappling with whether to start new lessons or repeat old ones, all while trying to watch for suspicious coughs or lethargic pupils.  “It’s incredibly hard to keep up continuity of instruction,” said Ms. Ophals, noting that attendance had dropped to about 70 percent from the 97 percent it is accustomed to. In one class on Friday, just 7 of the 26 students were present.  Ms. Ophals was ambivalent about whether the school should have been closed. “I’m glad I’m not the one who has to make that decision,” she said.  The Bloomberg administration has been attacked almost daily by the teachers’ unions, elected officials and many parents for not moving quickly enough to close schools with large numbers of students calling in sick.  The mayor has said that shuttering schools for a sickness that generally has proved to be mild is a difficult call that can disrupt educations and leave working parents in a bind, and health experts do not uniformly agree that it makes any difference.  The mayor’s office this week bent to criticism about a lack of transparency by publishing absentee rates for every school at the end of every day on the Internet. But it maintains that there is no set number of absences needed to close a school; it focuses on schools where there are clusters of students who are sick with symptoms like high fever and persistent coughs.  Many students who are calling in sick may not have the flu or may be staying home out of fear. But the teachers’ union has been collecting reports from teachers and nurses, and on Thursday its president, Randi Weingarten, began publicizing what she said were rates of students sent home with flu symptoms at schools that are open. In two of those schools, more than 10 percent of students were sent home sick, according to union figures.  Education officials say they always follow the health department’s recommendations.  On Friday, the Education Department announced it was closing four more schools until next Thursday: P.S. 58 and I.S. 384 in Queens, P.S. 160 in Brooklyn and P.S. 138 in Manhattan. (A private elementary and middle school, the School at Columbia University, also closed on Friday.)  Five schools that have been closed for several days reopened on Friday, although at two of them only about half the students returned.  In schools that are open, there is plenty of debate over whether to start new lessons or spend time reviewing older material. Many teachers are assuming that the students who are out sick will spend time attending after-school sessions once they return, though they are skeptical about whether they are doing any work while at home.  If continuing on means that one student is on the sixth chapter of a novel while another is still working through Chapter 3 next week, so be it, one teacher said.  “You have do the same thing, have them come in the morning, and do whatever it is you planned to do,” said Bruce Adler, a special education teacher at P.S. 120 in Flushing. “You don’t have them sit there. If they come in and don’t do anything new, we’re not doing what’s required of us.”  There are other practical concerns — while the absentee rates do not affect how much money a school receives, state law requires that money be withheld from schools that do not meet for 180 days of instruction, which is likely to happen at schools closed for several days.  While the law includes provisions for extreme weather or blackouts, for example, there is nothing about widespread illness. Jonathan Burman, a spokesman for the State Education Department, said that it planned to ask for legislation allowing exceptions for the flu outbreak.  The state is also working on contingency plans in case some schools are closed for Regents exams, , which are required for high school graduation.  For the students who are coming to school each day, there are a few perks — normally crowded hallways and cafeterias suddenly feel spacious and teachers can spend plenty of one-on-one time with them.  At P.S. 21, the principal announced that to reward students, there would be no homework for the weekend. At Hunter College High School on the Upper East Side, the principal sent a memo to parents explaining there would be no new material covered in class on Friday or Tuesday, and no homework assigned.  With classrooms less cramped, normally rambunctious students seem far more well behaved, making teachers both thankful and worried. They are fielding questions like, “Will I have to stay at home by myself if I get sick?” and moving farther away from students with the sniffles.  At I.S. 227, a classroom was turned into a sick room after it became obvious that the three chairs in the nurse’s office were insufficient. Many children were coming in with wads of tissues and bottles of hand sanitizer, and more than a few were wearing face masks. Teachers have taken to spraying disinfectant in their rooms.  “It’s like a domino effect — every day you wonder how many kids are coming into class and how many are going to be there at the end of the day,” said Judith Glazer, a teacher at I.S. 125. On Wednesday, Ms. Glazer felt fine, but she had a 100.9 fever by Thursday evening and spent Friday at home in bed, frustrated. “I know I wouldn’t be sick if they would have just closed down.”  Jason Grant and Mathew R. Warren contributed reporting.  A version of this article appears in print on , on Page A14 of the New York edition with the headline: Flu Takes Toll At Schools That the City Keeps Open. Order Reprints| Today's Paper|Subscribe
Some teachers forged ahead despite high absenteeism, and some students took over for absent educators as they reviewed for Regents exams.