The changes, which Mr. Steiner, his deputy John King and Merryl H. Tisch, the chancellor of the State Board of Regents, described in an interview on Monday, are subject to approval by the State Legislature. Ms. Tisch said they needed lawmakers to approve a package of education legislation within the next 10 days, so that the state could meet the June 1 application deadline for the federal competition known as Race to the Top.

New York did not win one of the first Race to the Top grants. Last week, the State Senate voted to more than double the number of charter schools in the state, another move aimed at winning Race to the Top money. The Assembly has not voted on that issue, though pro-charter advocates have been furiously lobbying and running advertisements.

Testing data would be used for only a fraction of the teachers in the state, because many teachers instruct in subjects or grades that do not have an annual exam. Mr. Steiner and Ms. Tisch have criticized the state exams, saying they may have become too easy and predictable in the last several years. But Mr. Steiner said that they were “not useless,” and that the department was taking steps to improve them, including changes this year that broadened the material covered by the tests.

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Lawmakers are likely to approve the changes if they are backed by the teachers’ unions. But Mr. Steiner said it remained unclear if the state was out of “choppy waters.”

The unions — the New York State United Teachers and the United Federation of Teachers , the city’s union — did not gain any clear benefit from the deal, other than shielding themselves from criticism that they were hurting the state’s chances in Race to the Top. And union leaders who backed the plan could face significant backlash from members, particularly at a time when many districts are planning for layoffs.

“The concept of this has never been unacceptable,” said Richard Iannuzzi, the president of the state union. “But doing it unilaterally or making evaluations solely dependent on students’ test scores were not options.”

New York City began evaluating teachers based on test scores three years ago. But in 2008, the Legislature banned the use of student test scores in teacher evaluations, a move that was backed by the union.

That law expires this year, and just after Mayor Michael R. Bloomberg won re-election last fall, he announced that the city would begin to tie test scores to decisions on which teachers earn tenure, a move that angered the union.

Officials at the New York City Department of Education privately had hoped for more changes in the evaluation system, like giving even more weight to student test scores. The city would now have to try to win those changes during contract negotiations with the union, which are at an impasse.