Critics have raised concerns about the costs to districts - as much as $300 million, according to lawmakers - and the schools' ability to transition to the requirements that could be in place by 2017.
The standards are a voluntary initiative, so far adopted by 45 states, that establishes proficiency requirements for kindergarten through 12th grade in the three core areas. Tests in composition, civics, and government would be added later.
The proposed regulations still need approval from the state's Independent Regulatory Review Commission, a panel of members appointed by lawmakers and the governor. The plan also faces consideration in the House and Senate.
If approved, the standards would take effect with high school graduates in 2017 (current ninth graders), and require them to demonstrate proficiency in Algebra I, Biology I, and language arts on the Keystone Exams or a state-approved assessment alternative.
A spokesman for the Pennsylvania State Education Association, the union representing a majority of public school teachers, said it was pleased with the revisions.
"The new language allowing superintendents to waive the use of the Keystone Exams as a graduation requirement is a step in the right direction," spokesman Wythe Keever said. "The PSEA opposes high-stakes graduation exams."
The changes did not alleviate the fears of critics such as Lawrence Feinberg, a Haverford Township school board member, who said the plan creates unattainable goals for many lower-income students.
"It floors me districts like Philadelphia don't have resources to meet state standards - and now you will deprive students of a high school diploma," Feinberg said.
State Sen. Mike Folmer (R., Lebanon), chairman of the Education Committee, said he had reservations about the cost to districts.
Samuel Lee, superintendent of the Bristol Township schools in Bucks County, said the principles behind core standards "have great merit."
But Lee said he was worried about a lack of time to prepare for what appear to be rigorous tests.
"The content and the core material that we've been working with for 12 years now may not be aligned with the assessments we'll have to attend to next year," he said. "We may not have time to appropriately transition."
Contact Amy Worden at 717-783-2584 or email@example.com, or follow@inkyamy on Twitter.
Inquirer staff writers Angela Couloumbis and Ben Finley contributed to this article.