Sign up for a free school lunch and you could win a free trip to Hawaii.

Schools Chancellor Joel Klein and the starting right tackle for the New York Jets, Kareem McKenzie, launched a campaign yesterday to encourage public school children to have their parents fill out federal forms.

They told eighth-graders at J.H.S. 234 in Brooklyn that all children, not just ones who can’t afford school food, should fill out the forms since the federal government reimburses the city for each meal eaten in its school cafeterias.

“We have not done as effective a job as we need to, and it really goes to the bottom line,” Mr. Klein said. “The more money we get from the feds on reimbursements, that frees up money that we would otherwise have to spend city funds on food. This is an effort to put the food bill at the federal doors.”

The chief executive of the office of school support services, Marty Oestreicher, said last year about 800,000 of the city’s 1.1 million pupils filled out the forms.

He said it’s unclear how much the city would benefit if an additional 300,000 students filled out the forms, adding it depends on whether the students deserve free, reduced-price, or full-price meals.

Washington gives New York City $2.32 for each student who eats lunch for free, $2.07 for each student who eats a reduced price lunch, and 29 cents for each student who pays full price.

As part of the new campaign, the Jets donated prizes, including a trip to Hawaii, bicycles, passes to Chelsea Piers, gift certificates to Barnes & Noble, and an autographed football. Children whose forms are processed by October 22 have a chance to win.

As Mr. Klein announced the food initiative, his deputies and employees continued ironing out the kinks of the freshly started school year.

Up in the Bronx, the chancellor’s senior counselor on education policy, Michele Cahill, was at the high school enrollment center at the Bronx High School of Science, chipping in.

A father, George Liggins, brought his son, Malik Rainer, 16, to the center holding a stack of papers. He showed one form from the regional office, saying Malik could transfer from Park West to Bronx Aerospace because of a safety concern. He also carried a letter from Bronx Aerospace saying he couldn’t attend school there.

After inspecting the papers, Ms. Cahill told the father, “Everyone wants to keep their enrollment down. Sometimes they do things that should not be done.”

She assured the family that Malik wouldn’t have to go back to the school where he’d been attacked the year before.

Public Advocate Betsy Gotbaum said after spending two days at the high school enrollment centers, “I’m frustrated and I don’t even have a problem…. I speak English and I’m confused.”

She said next year, students who want to transfer and students who want to enroll for the first time should all go to one center. This year, the new centers are only for first-time students, not for those who are dissatisfied with their school.

Mr. Klein said the centers have enrolled 13,000 or 14,000 students.

“There are still parents who want transfers of their students because they’re still unhappy with the schools their students are in. That is not the function of these enrollment centers,” he said. “I feel for these parents. I wish I had more schools that parents were excited about, but we’re not going to be able to accommodate all of their desires for transfers and that has caused some backup.”

He said parents whose children have already been assigned schools, even if they’re not ideal schools, should send their children to class.

“I’d be the first to say I feel for those parents,” Mr. Klein said. “I wish we had greater options. But we don’t have them available, and that’s the reality.”