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A national teachers’ union says its members can strike to ensure schools reopen safely.

The second-largest teachers’ union in the United States announced on Tuesday that it would support its 1.7 million members if they choose to strike in districts and states that move to reopen classrooms without adequate health and safety measures.

The union, the American Federation of Teachers, said strikes should be a “last resort.” But the resolution approved by the organization’s executive council gives educators and their union representatives additional muscle in negotiations over what would constitute adequate protection for teachers and school employees.

The union is pushing for schools to wait to reopen classrooms until coronavirus transmission rates in a community fall below 1 percent and average daily test positivity rates stay below 5 percent — something that very few places have achieved. A recent New York Times analysis found that only two of the nation’s 10 largest school districts could reopen under the latter threshold.

The union also wants effective contact tracing in place in regions that reopen schools, mask requirements for students and teachers, updated ventilation systems in school buildings and procedures to maintain six feet of distance between individuals.

“We will fight on all fronts for the safety of our students and their educators,” the union’s president, Randi Weingarten, said in a speech at the organization’s annual convention, which is being held online this week. She said that if the federal government can support the cruise industry and hedge funds during the coronavirus crisis, “they sure as hell can help working families, and can help educators ensure our kids get the education they need.”

Some online activists have been pushing for even stricter guidelines than those recommended by the A.F.T., with some educators demanding that schools stay shuttered until there are no new cases in a region for 14 days.

Education leaders have said they need hundreds of billions of dollars to implement measures that would allow schools to reopen safely. On Monday, Senate Republicans introduced a stimulus package that fell far short of what Democrats and organized labor have proposed. The legislation would provide $70 billion for K-12 education, but condition two-thirds of that money on schools reopening at least partially in person, a priority for President Trump, who sees it as key to reviving the nation’s economy by allowing parents to work.

The A.F.T.’s authorization vote leaves it up to local chapters to make the decision on whether to plan a strike. The Florida Education Association has already sued Gov. Ron DeSantis and other officials to prevent school buildings from reopening in that state, where virus cases are surging. On Tuesday, Florida again broke its daily record for deaths, reporting 186 fatalities. It also reported 9,230 cases.

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Republicans use their relief proposal to fund a F.B.I. building Trump has championed, drawing charges of self-dealing.

Credit…Erin Schaff/The New York Times

Senate Republicans, under pressure from the White House to embrace an obsession of President Trump’s, have included in their latest emergency pandemic aid proposal $1.75 billion for the construction of a new F.B.I. headquarters in downtown Washington, D.C.

The proposal drew outrage from Democrats, who charged that it was an attempt by Mr. Trump to use the economic stabilization package — meant to help struggling Americans weather a pandemic and a recession — to enrich himself.

They have long charged that Mr. Trump intervened to make sure the F.B.I. scuttled plans to erect a new headquarters in suburban Washington and instead chose to refurbish its existing building, in order to make sure that the site was not redeveloped with a project that would compete with his company’s luxury hotel across the street. The Justice Department’s top investigator last year launched an inquiry into the decision.

“They managed to have enough money for $2 billion for the F.B.I. headquarters that benefits Trump hotel, and they say they have no money for food assistance?” Senator Chuck Schumer, Democrat of New York and the minority leader, said on Monday. “What the heck is going on?”

Some leading Senate Republicans, who included the F.B.I. building money in the $1 trillion recovery package they rolled out on Monday, appeared not to know themselves.

Senator Mitch McConnell of Kentucky, the majority leader, at first said he did not believe the funding had been included in the measure, and then told reporters to ask the administration “why they insisted on that provision.”

Asked about how the construction of a new F.B.I. building related to the pandemic, Senator Richard C. Shelby of Alabama, the chairman of the Appropriations Committee, said, “Good question,” and stressed that it was “an administration proposal.”

The line item is just one of a long list of differences between Republicans and Democrats who are staring down a Friday deadline to strike a compromise on a new round of federal virus aid before enhanced jobless benefits expire.

Mark Meadows, the White House chief of staff, and Steven Mnuchin, the Treasury secretary, planned to go to Capitol Hill on Tuesday to begin negotiating with Democrats, who are pushing a $3 trillion aid bill. Speaker Nancy Pelosi is scheduled to hold another meeting with the two men and Mr. Schumer in her Capitol Hill suite at 4 p.m. Tuesday, the third such meeting in the last two weeks.

Another Yankees-Phillies game is postponed over stadium worries.

Credit…Brad Mills/USA Today Sports, via Reuters

The Yankees’ game against the Philadelphia Phillies on Tuesday has been postponed, according to a person familiar with the matter who was not authorized to speak publicly before the official announcement.

The teams’ game on Monday night was also postponed following news of an outbreak within the Miami Marlins, who had played three games at the Phillies’ Citizens Bank Park over the weekend. Phillies’ players and staff members received additional testing on Monday but the results of those tests has not yet been announced. The visiting clubhouse at the ballpark was also being disinfected.

On Monday, the Marlins’ scheduled games against the Baltimore Orioles for that day and Tuesday were also postponed. The Marlins have at least 18 confirmed positive cases among their players and coaches, according to another person familiar with the matter who was not authorized to discuss the results.

The Yankees, who arrived in Philadelphia on Monday, have been sequestered in their hotel and were not allowed to go to Citizens Bank Park on Monday. To stay active, some worked out indoors.

But after Tuesday’s postponement, the Yankees plan to leave town. They were expected to return to New York on Tuesday afternoon and work out at Yankee Stadium. The last time they played was on Sunday in Washington, defeating the Nationals, 3-2.

Hajj during the pandemic: Sterilized pebbles, bottled holy water and no kissing the sacred stone.

Credit…Saudi Ministry Of Media, via Reuters

In any other year, Muslims undertaking the hajj, the annual pilgrimage to the holy city of Mecca that observant Muslims are obligated to perform at least once, would drink from a holy well. They would kiss the Kaaba’s sacred black stone as they thronged the Grand Mosque. Before they left Mecca, they would collect pebbles to ritually stone the devil.

During the virus edition of the hajj that begins on Wednesday, the black stone is off limits. Authorities in Saudi Arabia are issuing bottled water from the Zamzam well instead of letting pilgrims drink from cups at the source. Also in the pilgrim packages: sterilized pebbles to hurl at the devil, personal prayer rugs and other items intended to prevent an outbreak from marring the hajj.

But the chief public health measure the Saudi government has taken is to limit attendance, shrinking one of the world’s most famous crowds to a select few. About 2.5 million Muslims from around the world performed the hajj last year; this year, Saudi Arabia said it would allow just 1,000 pilgrims, all of them from within the kingdom, though it has not released the final number.

Across the Middle East, celebrations for Eid al-Adha, the festival of sacrifice that marks the end of the hajj this weekend, will likewise be paler this year.

In Oman and Bahrain, where the unchecked spread of the virus among low-paid foreign laborers living in crowded conditions has contributed to two of the world’s worst outbreaks, officials have urged residents to forego the large celebrations that usually mark Eid, and Oman has reinstituted a domestic travel ban and curfew. In Egypt, new cases have fallen as the country resumes normal life, but a live broadcast will replace communal Eid prayers.

In the United Arab Emirates, where it is common for residents to buy sheep or other livestock to sacrifice and donate during Eid, the authorities were encouraging people to use apps to reduce crowding at slaughterhouses and markets.

Countries across the region are reopening despite lingering hot spots. While Persian Gulf countries including Oman and Bahrain continue to struggle with large outbreaks, smaller ones in Yemen and Syria — where years of war have decimated health care systems and mired the population in deepening poverty — are rapidly metastasizing.

Trump shares a video containing misinformation about hydroxychloroquine. Social media platforms respond.

Credit…Doug Mills/The New York Times

Mr. Trump shared on his Twitter account Monday night a viral video containing a series of false or misleading medical claims about the coronavirus, as social media companies scrambled to halt the video’s rapid spread.

Facebook and YouTube removed versions of the video, and Twitter later removed the post shared by the president. At least one version, which was shared on Facebook by the right-wing Breitbart news site, had garnered over 13 million views before it was removed. Other versions of the video, including shorter, edited clips, were still online Monday night.

The video featured what appeared to be a group of doctors in white coats, standing in front of the Supreme Court building in Washington, D.C., in what appeared to be a news conference. The doctors made a series of misleading claims, including that hydroxychloroquine could be taken as a preventive measure.

The use of the drug to treat or prevent coronavirus has been widely disputed by the medical establishment. The Food and Drug Administration revoked its emergency authorization in June after deeming it “unlikely to be effective” while carrying potential risks, and the National Institutes of Health halted clinical trials of the drug in June. But Mr. Trump repeatedly boosted the drug in the early months of the crisis, and said in May (not in June, as an earlier post said) that he was taking it himself.

It was the most recent example of misinformation that has spread about the coronavirus, at times being shared by Mr. Trump and others in the White House. A YouTube spokesman said in a statement that the video had been removed for “violating Covid-19 misinformation policies.”

On Tuesday, Twitter put limits on the account of Donald Trump Jr., the president’s oldest son, after he also shared the widely circulated video. Twitter said he was required to delete the tweet with misinformation, and the platform said it would also limit his account’s functionality for 12 hours.

“The tweet you referenced was in violation of our Covid-19 misinformation policy,” a Twitter spokesman, Ian Plunkett, said. “We are taking action in line with our policy here.”

GLOBAL ROUNDUP

The Venice Film Festival will return, with masks and without blockbusters.

Credit…Arthur Mola/Invision, via Associated Press

The Venice Film Festival announced the lineup on Tuesday for its 77th edition, setting out precautions including temperature checks and new outdoor screening sites for one of the first large international festivals held since the pandemic began.

The festival will run from Sept. 2 to Sept 12, with a reduced schedule. Between 55 and 60 films will be screened, as opposed to last year’s 80.

“The show must go on and the world must go on,” said Roberto Cicutto, the president of La Biennale di Venezia, which runs the festival, in a phone interview, adding that it was important “to watch and to discuss movies together, to live this art the way we used to live it.”

Films in contention for the festival’s top prize, the Golden Lion, include Chloé Zhao’s “Nomadland,” starring and produced by Frances McDormand; Mona Fastvold’s “The World to Come,” starring Vanessa Kirby and Casey Affleck; and “Pieces of a Woman,” directed by Kornel Mundruczo and starring Shia LaBeouf.

Screening in the festival’s nonfiction section will be “Salvatore Ferragamo: The Shoemaker of Dreams,” a documentary directed by Luca Guadagnino, as well as “City Hall” from Frederick Wiseman, a look at Boston’s administrative center.

Though Shanghai’s international film festival went ahead in July, the pandemic has forced the cancellation or postponement of most of the gatherings that traditionally structure the year for filmmakers in Hollywood and elsewhere in the West, including Cannes and the Tribeca Film Festival.

Here are other developments from around the globe:

  • Spain’s prime minister said that Britain had made “an error” by imposing a quarantine on everyone arriving from his country, a decision that blindsided British vacationers and dealt another blow to Spain’s tourism industry. Prime Minister Pedro Sánchez, in an interview with the news outlet Telecinco on Monday, said that Britain should have taken into account the regional divergences in Spain’s coronavirus cases and not issued a blanket order.

  • Data released by the United Nations World Tourism Organization on Tuesday showed that leisure travel fell by 98 percent during the first five months of the year, compared with 2019. The group said that globally 300 million fewer people traveled, representing a loss of $320 billion for the tourism industry.

  • Vietnam suspended domestic flights into and out of the tourist destination of Danang for 15 days after discovering at least 14 coronavirus cases, according to Reuters. International travel was halted months ago, but domestic tourists still traveled to Danang, a coastal city. About 80,000 people, mostly tourists, were ordered to evacuate on Monday after the discovery of the country’s first local transmissions in 100 days.

  • China recorded 68 new virus infections on Monday, its National Health Commission said on Tuesday, including six in Liaoning Province and 57 in the northwestern region of Xinjiang, where a flare-up since mid-July has shown little sign of abating. As China battles the surge, the authorities in the northeastern port city of Dalian, in Liaoning, have said they will test all 6 million residents after an outbreak. Samples have been collected from about 1.68 million Dalian residents as of Sunday night, the official Xinhua news agency reported.

  • Kenya’s president, Uhuru Kenyatta, closed all bars and banned the sale of alcoholic drinks in restaurants for 30 days to try to curb the spread of the virus. In a speech Monday, Mr. Kenyatta said recent reopening measures had given “some Kenyans false comfort that this is not a serious health risk to them and their families.”

A concert in the Hamptons is being criticized for a lack of social distancing.

Credit…Kevin Mazur/Getty Images

A charity concert Saturday night in the Hamptons that featured performances from the chief executive of Goldman Sachs and the D.J. duo the Chainsmokers drew outrage and a state investigation after video footage showed attendees appearing to ignore health precautions.

The concert, called Safe & Sound, was supposed to involve guests sitting outside near their vehicles in spaced-out areas to watch the performances, including one from the chief executive of Goldman Sachs, David M. Solomon, also known as D.J. D-Sol.

Tickets cost up to $25,000, according to Billboard.

The event generated angry social media posts and on Monday, criticism from state officials. In a letter to the supervisor of Southampton, where the concert was held, New York’s health commissioner, Howard A. Zucker, wrote that he was “greatly disturbed” by reports of thousands of people standing close and “generally not adhering to social-distancing guidance.”

“I am at a loss as to how the Town of Southampton could have issued a permit for such an event, how they believed it was legal and not an obvious public health threat,” Dr. Zucker wrote.

The town supervisor, Jay Schneiderman, who was also listed as an opener for the concert, did not immediately respond to requests for comment on Monday night. The event organizers did not answer questions about whether they knew that people were breaking the rules.

Several people who went to the concert told Buzzfeed News that they felt safe and that people were social distancing.

Elsewhere in the New York area:

  • New York, grappling with how to prevent another large outbreak, will now require travelers from Puerto Rico, Washington D.C. and 34 states to quarantine for 14 days, Gov. Andrew M. Cuomo said Tuesday. The new states added to the list are Illinois, Kentucky and Minnesota.

35 lifeguards were infected in an outbreak at the Jersey Shore.

Credit…Hannah Yoon for The New York Times

Long Beach Island, a popular summertime destination along the Jersey Shore, is now a different kind of hot spot.

Thirty-five lifeguards from two boroughs on the barrier island — Surf City and Harvey Cedars — recently tested positive, the island’s health department announced on Monday.

Public health officials said that half of the lifeguards had mild symptoms and the rest had none. None were hospitalized, the officials said.

The outbreak was traced to two gatherings on July 12 and July 14, according to the Long Beach Island Health Department, which said it dispatched nurses to investigate cases and issue quarantine orders.

“Based on our investigation so far, the workplace was not the source of transmission and practices likely prevented additional cases,” the Health Department said in a news release. “The youth and young adults should recognize they are not immune to this virus.”

During his briefing on Monday, Gov. Phil Murphy of New Jersey mentioned the outbreak on Long Beach Island and said he was troubled by reports of large gatherings of young people.

“This is among us, folks,” Mr. Murphy said. “Any of us who thinks we can just put our feet up and relax and let this take its course is not paying attention, particularly congregating inside, in close proximity, poor ventilation, without face coverings. You’re looking for trouble. You’re absolutely looking for trouble, no matter how old you are.”

Germany, an early model for containing the virus, is confronting a surge. Its top health experts urge masks.

Credit…Matthias Schrader/Associated Press

The German federal agency in charge of disease control sounded an alarm on Tuesday over a rising number of cases across the nation.

Lothar Wieler, the leader of the agency, the Robert Koch Institute, urged Germans for the first time to wear masks outdoors if a distance of 1.5 meters, or about 5 feet, cannot be maintained.

Germany reported 633 new cases on Monday, and four deaths. Though Germany’s daily death count has been in the single digits for most of this month, there have been more than 3,000 new cases over the past week.

“The new developments in Germany make me very worried,” Mr. Wieler said, adding, “The rise has to do with the fact that we have become negligent.”

When the virus began spreading in March, Germany imposed one of the strictest lockdowns in Europe. It was seen as a model for other countries. Since it began reopening, there have been flare-ups that have spurred local lockdowns, including one in June.

But on Tuesday, Mr. Wieler said he wondered if this latest uptick was a harbinger of something more.

“We don’t know if this is the beginning of a second wave, but of course it could be,” he said. But he added, “I am still optimistic that we can prevent this.”

‘Not sparing anyone’: A Texas funeral home sees the toll of the virus all around.

Credit…Tamir Kalifa for The New York Times

Johnny Salinas Jr., the owner of Salinas Funeral Home typically handles five funerals a week. But on a recent day, with the virus tearing through his community, he saw that many grieving families in a single day.

A sixth family was waiting, too. His own.

Mr. Salinas changed from a polo shirt into a crisp black suit and left his office for the chapel next door. The light blue coffin of his great-uncle, who died of Covid-19, sat at the front of the room, adorned with white flower arrangements and a wooden crucifix.

“The virus is not sparing anyone,” Mr. Salinas said. “Not even my family.”

In the Rio Grande Valley of Texas, funeral homes — like hospitals — are overloaded and struggling to carry out basic services and keep up with the expanding crisis. Local funeral homes, officials said, have not experienced such demand in decades.

About one in 60 residents of Hidalgo County is known to have had the virus, and about one of every 2,000 people has died from the virus, a New York Times database shows. Hidalgo County now has one of the highest per capita death rates in the state.

At the start of July, fewer than 50 deaths in Hidalgo County had been attributed to the virus, according to the database. By Saturday, there had been more than 450.

“It’s like a bad dream,” said Linda Ceballos, a co-director of Ceballos Funeral Home in McAllen. “You want to wake up, but you can’t.”

The death toll is forcing funeral directors to bypass traditional services like velorios, viewings that sometimes last for days and are filled with prayers, hugs and sorrowful Spanish-language songs. Instead, many funeral homes are shortening viewing times and limiting attendance. Some have ordered large refrigerator trucks to store bodies until they can get to them.

Transit workers were New York City’s pandemic lifeline. These three paid a price.

Credit…Jonah Markowitz for The New York Times

When the virus engulfed New York, it pummeled the transit work force: So far, 131 transit workers have died from the virus and more than 4,000 have tested positive, making the Metropolitan Transportation Authority one of the hardest-hit government agencies in New York.

For many, the pandemic has left an indelible mark. Pan Chan, a bus driver, moved out of his family’s home for months to shield his wife and children. Sally Lutchman, a train conductor, worried that she might have infected her husband, who was hospitalized with Covid-19 for months. Cesar Torres Jr., a second-generation bus operator, watched his father die.

Now, as riders trickle back, these workers are facing the prospect of a second wave, even as they are coping with the trauma from the peak of the outbreak.

Advertising industry cuts could be permanent.

Credit…Chipotle

The advertising industry may see permanent cuts after marketing budgets have dwindled during the pandemic. Agencies will likely be smaller, and work could start going to part-time contractors.

The tightening industry has already led to simpler and more practical ad campaigns, and more clients have asked that their ads be made by and feature a more diverse group of people, while also demanding more evidence that the ads are effective. Agencies have also experimented with digital tools to help brands stay relevant, such as a “tension map” that analyzes online conversations around the country.

“There’s a big correction — a lot of these teams have gotten too big and too bloated,” said Gaston Legorburu, founder of the Florida-based ad agency Glue IQ. “They’re now having the realization that they can do twice as much with half as many people.”

In 2020 and 2021, agencies will shed 52,000 jobs, and half of these will not return, predicted Jay Pattisall, an analyst with the research firm Forrester.

The pandemic takes an extra toll on families with special needs.

Missing social contacts and altered routines can be particularly intense for children with developmental challenges. Disturbed sleep and eating habits, too, can make life more challenging for the children and their families. Here are some strategies to cope better.

Reporting was contributed by Davey Alba, Julia Calderone, Sheera Frenkel, Dana Goldstein, Raphael Minder, Claire Moses, Amanda Rosa, Edgar Sandoval, Anna Schaverien, Kaly Soto, Eleanor Stanford, Daniel Victor, Neil Vigdor, James Wagner, Vivian Yee, Elaine Yu and Mihir Zaveri.