The bills, which were approved 23-15 and 24-14 by the Senate in a rare Saturday session, reflect a deal announced late Friday by legislative leaders and Gov.
The agreement, which does not include state school funding for the state fiscal year that begins in one-and-a-half months, was criticized by superintendents and backed by teacher unions.
Many districts, facing pressure from teachers and mixed reaction among parents, are starting with remote-only instruction due to COVID-19.
Schools' funding is based on their number of students.
Districts also would have to administer a benchmark assessment to K-8 students twice, including once in the first nine weeks.