On Thursday, the Jets announced that they had acquired Brett Favre from Green Bay. Friday, they’ll get to work on determining what kind of quarterback Favre will be in New York.

That work will be done by head coach Eric Mangini and, especially, by offensive coordinator Brian Schottenheimer, whose job for the next month is to devise an offense that will best utilize Favre’s skills. Schottenheimer needs to modify his offensive approach to put Favre in the best position to help the Jets win games, but without rewriting the playbook to such an extent that it nullifies the work the Jets’ other offensive players have already done this off-season.

That’s no easy task, especially because Favre is a very different quarterback from Chad Pennington, who played eight seasons for the Jets but was released just hours after the Favre trade became official. Whereas Pennington’s greatest weakness has always been his lack of arm strength, Favre has a cannon for an arm. In Schottenheimer’s two seasons as offensive coordinator, he called plays designed to hide Pennington’s weak arm. Now he needs to call plays that will exploit Favre’s strong arm.

But he can’t take that too far. After all, the Jets want the Brett Favre of 2007, the one who led the Packers to the NFC Championship game by completing a career-high 66.5% of his passes while throwing for 28 touchdowns and just 15 interceptions. They don’t want the Brett Favre of 2005 (61.3% completions, 20 touchdowns, and 29 interceptions) or 2006 (56% completions, 18 touchdowns, and 18 interceptions).

To ensure that the Jets get Favre at the top of his game, Schottenheimer needs to rein in Favre’s wild streak. He has been celebrated throughout his NFL career for having the courage to take chances — but when he was throwing all those interceptions in 2005 and 2006, he went from courageous to reckless. The best approach for Schottenheimer may be to use a short passing attack similar to the one he called the last two seasons with Pennington at the helm — only with the knowledge that Favre’s strong arm will allow him to get the ball in the receivers’ hands more quickly than Pennington could.

A common misconception about Favre is that he has played his entire career in various versions of the West Coast offense, and that he needs that offense to be successful. The truth is, Packers coach Mike McCarthy turned Favre’s game around in the last two years using a different approach.

McCarthy’s first NFL job was with the Kansas City Chiefs, where he spent six seasons as an assistant to Marty Schottenheimer, Brian’s father. The elder Schottenheimer always ran a very straightforward, vanilla offense, and McCarthy learned from that emphasis on simplicity. It was by simplifying the offense in Green Bay that McCarthy helped Favre find the fountain of youth, and Schottenheimer can do the same with the Jets.

With training camp already underway, Favre will have to get accustomed to the way the Jets do things in a hurry. But although these circumstances are less than ideal, old quarterbacks can learn new tricks. Last season, Vinny Testaverde signed with the Carolina Panthers on a Wednesday and started a game four days later, completing 20 of 33 passes and leading the team to victory. If Testaverde could do that, Favre can be completely prepared to play for the Jets in a month.

Favre’s most important task for the coming month is to work on his timing with the Jets receivers, especially starters Laveranues Coles and Jerricho Cotchery. Although Coles and Cotchery had a personal rapport with Pennington that will be hard to duplicate, they have to be thrilled that, in Favre, they now have a quarterback who can stretch the field with the deep ball and zip bullet passes to them along the sidelines.

In fact, Coles and Cotchery are quite similar to Favre’s top receivers in Green Bay last season, Donald Driver and Greg Jennings. All four are small receivers who run precise pass routes; Coles is like Driver in his ability to go over the middle, while Cotchery is like Jennings in having the speed necessary to stretch the field. Favre doesn’t have a big adjustment to make there.

The best-case scenario for the Jets is that Favre’s career has a final act in New York reminiscent of Joe Montana’s two seasons with the Kansas City Chiefs. In 1993, Montana was traded to the Chiefs after 13 years with the San Francisco 49ers, and in his first year in Kansas City, he made the Pro Bowl and led the Chiefs to the AFC Championship.

The worst-case scenario is that Favre’s career ends the way Joe Namath’s did. Namath stuck around with the Jets long after his physical skills had diminished, and he ultimately ended his career with one last unsuccessful season in 1977 with the Los Angeles Rams.

No one wants to see Favre go out like that. The Jets have the next month to work out an approach that ensures he doesn’t.