The D.C. Council approved a package of education bills Tuesday intended to address some of the city’s most vexing issues, including students at risk of dropping out and schools with a shortage of exceptional teachers.

Most of the measures bundled by Chairman Kwame R. Brown into the Raising Expectations for Education Outcomes Act of 2012 are high in aspiration but modest in scope. Brown’s edgiest proposal — that high school students be required to take the SAT or ACT and apply to at least one college or postsecondary institution — was softened after discussions with Mayor Vincent C. Gray (D) and D.C. school officials. Three other provisions are for small pilot programs.

Even so, officials will have to find funds to cover the $2.8 million cost, D.C. Chief Financial Officer Natwar M. Gandhi said.

The bills authorize:

● An early-warning system in selected schools to track how students in grades 4 through 9 are progressing toward high school and college. It would identify those at risk of dropping out and offer more individual help.

● A series of financial incentives for “highly effective” teachers — as identified by the IMPACT evaluation system — to work at low-performing schools. Of the 663 educators deemed highly effective last year, just 71 worked in the 41 schools in wards 7 and 8, while 135 taught in the 10 schools of Ward 3. Inducements include a $10,000 “transfer bonus,” housing assistance and, possibly, income tax credits. The initial effort would involve 20 teachers in four schools.

● That the mayor establish a plan to ensure that all high school students take the SAT or ACT and apply to a college or other postsecondary institution before graduating. Brown had originally pitched this as a requirement. But D.C. school officials expressed misgivings about creating a new hurdle to graduation, and the D.C. Public Charter School Board saw it as a potential drag on its autonomy.

● A pilot program establishing five “community schools” similar to J.C. Nalle Elementary in Southeast Washington. This measure, sponsored by council member Michael A. Brown (I-At Large), would turn the schools into hubs for health services, job training and other social programs.

The bill was amended Tuesday to add a fifth provision: an early childhood measure sponsored by council member Vincent B. Orange (D-At Large). It requires Schools Chancellor Kaya Henderson to ensure that 3- and 4-year-olds are ready for kindergarten and that students entering fourth grade be able to read on grade level and do basic math.

The bill passed with one no vote and one abstention. Council member Phil Mendelson (D-At Large) said that the teacher incentive provisions were too costly and that truancy and low elementary reading scores were far more pressing problems.

“Making kids apply to college isn’t going to change that,” he said.

Council member Tommy Wells (D-Ward 6) said that although he favored the ideas in the bill, he abstained because he thinks the council should not function as a de facto school board, potentially politicizing education matters.

“There’s a lot of mischief that can be had,” said Wells, who was a member of the old D.C. Board of Education.