As their first or second weeks of classes ended Friday, at least 250 students and staff on the campuses of six Pennsylvania universities had tested positive for the coronavirus.

Temple University reported 10 cases on Monday, the first day of classes; by Friday, the tally had reached 58, all but six of them on-campus students. Some students and faculty protested the reopening on Monday; most classes are being held remotely or using a hybrid model. About 9,000 students are circulating on campus, a third of the usual number.

By Friday, Villanova University had reported 13 cases, St. Joseph’s University had confirmed 12, and Pennsylvania State University had reported 31.

Both Penn State and Temple did more than 5,000 tests in the first week, according to the schools.

“The percentage remains quite low” of people who tested positive, said Temple spokesperson Ray Betzner. The Philadelphia Public Health Department is “actively working with the university to respond to this increase,” a city spokesperson said Friday.

Bloomsburg University, which began classes on Aug. 17 and earlier this week reverted to almost all remote instruction due to an outbreak, has logged 118 cases among students and one employee. The University of Pittsburgh, which began classes Monday, reported 22 cases by Friday.

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They were among the thousands of college students nationwide who have been sickened since returning to campuses that are trying to enforce protocols like social distancing even as students move into dorms, attend classes, and throw parties.

Officials in Newark, Del., tried to address the issue earlier this week by passing an emergency ordinance restricting private gatherings to 12 people indoors and 20 people outdoors, hoping to put a damper on parties among the University of Delaware students who are returning to off-campus housing, the Wilmington News Journal reported.

But one professor at Kutztown University encouraged students to gather at a local bar and infect each other — then apologized on Friday.

“I think the sooner you guys get it, the better. None of you are going to die from this, and we need to have everyone immune,” business professor Victor J. Massad told students on Monday in a video teleconference obtained by The Inquirer. “And so the sooner that people are immune, the better.”

The comments drew criticism, including from the school’s teachers’ union. The Berks County university had reported only one student, who lives on campus, infected with the virus by Friday.

“This is clearly not the position of the university, and rest assured, the issue has been addressed,” a Kutztown University spokesperson said in an email, adding the school could not release more details because it was a personnel matter.

In an email to The Inquirer, Massad apologized and encouraged all students to follow the university’s coronavirus protocols.

“I was being rhetorical and flippant when I made the comments, I am embarrassed and ashamed of myself to have made them,” Massad said. “It was a complete lapse of professional judgment on my part.”

Statewide, the number of newly confirmed cases reported Friday was the highest one-day total in two weeks. The average number of cases reported daily has been in the 600s all week, part of a general downward trend since late July, according to an Inquirer analysis.

The 835 cases reported Friday were not due to any dump of backlogged test results, which sometimes inflates daily case counts, a spokesperson for the state Department of Health told The Inquirer, saying, “This is another reminder to wear a mask, practice social distancing, and wash your hands frequently.”

The state also reported 20 deaths. Philadelphia announced 152 new cases and no deaths. New Jersey reported 372 cases and nine deaths.

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The governors of both states announced funding for child-care centers using federal stimulus relief money as an unconventional school year begins and the facilities try to recover from the shutdown.

Gov. Tom Wolf announced $117 million for centers, family and group child-care homes, and programs for schoolchildren. It was the last of three installments that totaled $220 million.

Most of the commonwealth’s licensed facilities will receive some money, Wolf said. Earlier this summer, at least 200 of the state’s 7,000 licensed centers said they planned to permanently close.

In New Jersey, $250 million will be distributed to help working families and child-care centers, Gov. Phil Murphy said. Families with eligible income levels can receive child-care subsidies or a child-care support program; applications will open in early September.

Child-care centers will be able to get $75 per month for each subsidy-eligible child through the end of the year, and all centers that have reopened by the start of October can receive money for coronavirus-related costs, according to the Murphy administration.

“Now more than ever, working families need access to child care to balance the many demands they are facing during the ongoing pandemic,” Murphy said in a statement. “With these investments, we are ensuring that high quality child care is accessible and affordable for families across the state.”

Staff writers Erin McCarthy and Laura McCrystal contributed to this article.