Nearly 80 percent of school staff and child care workers in the United States have received at least one dose of the coronavirus vaccine, the Centers for Disease Control and Prevention said on Tuesday.

The announcement comes as the Biden administration has made an ambitious push to reopen schools and return to in-person instruction by the president’s 100th day in office. That goal has been tempered by dangerous virus variants, protests from teachers’ unions, and the fears and frustrations of students and parents.

The push to reopen schools has gathered momentum as evidence mounted that proper safety measures limited virus transmission in schools and coronavirus cases fell sharply from their January peak. Education officials and experts have cited the urgency of getting students back in classrooms before the academic year ends.

About eight million teachers, school staff and child care workers received their first vaccine dose by the end of March, according to the C.D.C., with about two million receiving their shot through the Federal Retail Pharmacy Program.

President Biden announced the program in March, urging nationwide access to vaccines for school employees and child care workers. But a hodgepodge of eligibility guidelines followed, as some states chose not to deviate from their rollout plans. By the end of March, however, K-12 educators in all states had become eligible to receive the vaccine.

While the acceleration of vaccinations among educators and staff has reduced the resistance from teachers’ unions to reopening classrooms, school systems with powerful unions, especially on the West Coast, have been slower to revert to in-person instruction.

Union resistance has led a bipartisan group of governors in several states to prod, and sometimes force, school districts to open. The result has been a major increase in the number of students who now have the option of attending school in-person, or will soon.

According to a school reopening tracker created by the American Enterprise Institute, 7 percent of the more than 8,000 districts being tracked were fully remote on March 22, the lowest percentage since the tracker was started in November. Forty-one percent of districts were offering full-time in-person instruction, the highest percentage in that time. Those findings have been echoed by other surveys.

In February, the C.D.C. issued guidelines that said K-12 schools could reopen safely as long as they followed basic health protocols like masking or distancing.

More recently, it said that elementary students and some middle and high schoolers could be spaced three feet apart in classrooms, instead of six feet, as long as everyone was wearing a mask. Unions had used the six-foot guidance to oppose bringing children back for normal schedules.

“Our push to ensure that teachers, school staff, and child care workers were vaccinated during March has paid off and paved the way for safer in-person learning,” Dr. Rochelle Walensky, the center’s director, said in a statement released on Tuesday.

Mr. Biden touted the C.D.C.’s newly released benchmark while visiting a vaccination site in Alexandra, Va., on Tuesday.

“That is great progress protecting our educators and our essential workers,” Mr. Biden said of the new estimate. “And because our vaccine program is in overdrive, we are making it easier to get a vaccination shot.”

The American Federation of Teachers, the nation’s second-largest teacher’s union, on Tuesday released a survey that reported over 80 percent of association members had been vaccinated or had made a vaccine appointment. About 85 percent of members said their school was “operating on at least a part-time basis,” according to the survey.

Randi Weingarten, the federation’s president, said in a statement on Tuesday that “A.F.T. members have embraced vaccines as vital to getting back in the classroom.”

“They want to return, the road map to reopening is robust, and if we instill trust and meet fear with facts we can finally end this national nightmare,” Ms. Weingarten said.

Around the United States, businesses, schools and politicians are considering “vaccine passports” — digital proof of vaccination against the coronavirus — as a path to reviving the economy and getting Americans back to work and play.

New York has rolled out “Excelsior Pass,” billed by the state as “a free, fast and secure way to present digital proof of Covid-19 vaccination” in case reopening sports and entertainment venues require proof of attendees’ status.

Walmart is offering electronic verification apps to patients vaccinated in its stores so they “can easily access their vaccine status as needed,” the company said.

But the idea is raising charged legal and ethical questions: Can businesses require employees or customers to provide proof of vaccination against the coronavirus when the vaccine is ostensibly voluntary?

Can schools require that students prove they have been injected with what is still officially an experimental prophylaxis the same way they require long-approved vaccines for measles and polio? And finally, can governments mandate vaccinations — or stand in the way of businesses or educational institutions that demand proof?

Legal experts say the answer to all of these questions is generally yes, though in a society so divided, politicians are girding for a fight. Government entities like school boards and the Army can require vaccinations for entry, service and travel — practices that flow from a 1905 Supreme Court ruling that said states could require residents to be vaccinated against smallpox or pay a fine.

Backers of digital vaccination cards are pressing the Biden administration to become involved, at least by setting standards for privacy and for verifying the accuracy of the records.

The White House is clearly skittish.

“The government is not now nor will we be supporting a system that requires Americans to carry a credential,” Jen Psaki, the White House press secretary, said on Tuesday.

Republican critics say vaccine passports raise the specter of centralized databases of vaccinated people, which they view as a government intrusion on privacy.

“A vaccine passport — a unified, centralized system for providing or denying access to everyday activities like shopping and dining — would be a nightmare for civil liberties and privacy,” Justin Amash, a former Republican congressman who is now a libertarian, wrote on Twitter last week.

But, in fact, every state already has a database, or an “immunization registry.” And under “data use agreements,” the states are required to share their registries with the C.D.C., though the agency de-identifies the information and not all states have agreed to provide it.

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Three weeks after suspending its vaccination campaign, Nepal has started administering shots again thanks to a gift of doses from China.

Nepal, a poor Himalayan nation, had been depending on vaccines manufactured in neighboring India, but last month India began cutting vaccine exports as the country experienced a surge in coronavirus cases. Nepal’s vaccination effort ground to a halt, even as infections began to rise again.

Last week, Nepal’s other giant neighbor, China, stepped in with a donation of 800,000 doses of the vaccine developed by Sinopharm, a state-owned company.

The vaccines will be administered to essential workers, Nepali students preparing to travel to China to study and those living in districts along the Nepal-China border, health officials said. Taranath Pokhrel, a senior official in Nepal’s health department, said that the Chinese government asked Nepal to give priority to the students and to people involved in cross-border trade, presumably to reduce the risk of infected people crossing into China.

Thousands of Nepali students study at Chinese universities under Chinese government scholarships. China, to increase the appeal of its vaccines, has said that foreigners who are inoculated with Chinese-made vaccines may face fewer bureaucratic hurdles entering the country.

Nepal, a nation of 30 million people, has vaccinated more than 1.7 million and slowly begun reopening to visitors, including to a few hundred climbers attempting to scale Mount Everest. The country reported very few infections in January, but new cases have surpassed 300 in recent days, part of a worrying resurgence in new cases across South Asia. India, which shares a porous border with Nepal, recorded more than 115,000 new infections on Wednesday, by far its highest daily total since the pandemic began.

The future of Nepal’s vaccination campaign remains uncertain because the Chinese donation falls short of the two million vaccine doses Nepal was due to receive under an agreement with the Indian manufacturer, the Serum Institute of India. Nepal officials said that they had paid the company 80 percent of the contract price but received only half of the doses. Serum’s chief executive said this week that he hoped to restart exports by June if new infections in India subsided.

“Our entire diplomatic channels are mobilized to get vaccines, but none has assured us of providing vaccines when we tried to procure them,” Dr. Pokhrel said.

In other news from around the world:

• In Japan, officials in Osaka canceled public Olympic torch relay events scheduled for next week and declared a medical emergency as a surge in coronavirus cases strains the hospital system. The prefecture’s 8.8 million residents were asked not to leave their homes except for essential matters. Olympic organizers said the ceremonial relay would be held at a park without spectators — the latest sign of trouble with the Tokyo Olympics scheduled to open in less than four months.

• The Moderna vaccine is now being administered in Britain, with a 24-year-old woman in Wales who is a caregiver for her grandmother the first person in the country to receive that vaccine on Wednesday. The Pfizer and AstraZeneca shots are already being used in the country. Vaccinations in Britain have slumped this month, reaching their lowest level since the inoculation campaign started. In a Twitter post, Prime Minister Boris Johnson urged people to “get your jab as soon as you are contacted.”

• Regulators in South Korea granted final approval to the Johnson & Johnson vaccine, making it the third vaccine authorized for use in the country amid growing concerns about the pace of its inoculation campaign. Officials reported 668 new coronavirus cases on Wednesday, the highest tally in three months, with most of the cases found in Seoul and other major cities.

• Germany’s troubled vaccine rollout may face another hurdle after a shipment of up to 880,000 Moderna vaccines that had been promised for the end April was canceled, the news site Business Insider reported. Separately on Wednesday, state and federal health ministers were meeting to discuss how to handle cases of people who have received a first dose of the AstraZeneca vaccine after that shot use was discouraged for use in people under 60.

Chancellor Angela Merkel of Germany has called for a short and strict nationwide lockdown to bring down the number of new coronavirus infections in the country, according to her spokeswoman, but will meet with local officials next week to discuss potential regulations.

A year after the first lockdown was successful in tamping down cases, the country’s 16 governors are finding it harder than ever to agree on a unified plan to stem new infections. And with only months left in office, Ms. Merkel has found it increasingly difficult to rally support for a national lockdown as fatigue from prolonged restrictions looms large even as cases rise.

The governors and Ms. Merkel are scheduled to meet on Monday to hammer out new regulations.

While Armin Laschet, the governor of the country’s most populous state and a potential successor to Ms. Merkel, has made similar calls for a two- to three-week hard lockdown to bring down infections, other governors are pushing back. The governor of one small state even began a pilot program on Tuesday to reopen theaters, gyms and restaurant patios.

“A common nationwide approach would also be important here,” Ulrike Demmer, the deputy government spokeswoman, said during a daily news conference, referring to the confusing and often contradictory rules set by state governors. Ms. Demmer also pointed to the rising number of coronavirus patients in intensive care wards as a cause for concern.

According to Ms. Demmer, the goal is to get the infection rate below 100 new cases per 100,000 before the authorities should consider easing restrictions.

On Tuesday, the German health authorities recorded an average of 110 infections per 100,000 people over the previous 7 days, but warned that because fewer people were tested over the Easter holiday weekend, the number was likely to be much higher.

According to a New York Times database, Germany is averaging 15,562 new infections daily and since the pandemic began. More than 77,000 have died with the disease in the country since the pandemic began.

A 28-year-old man has died in the Philippines after the police forced him to do 300 squats as punishment after he was caught violating coronavirus lockdown rules.

The man, Darren Manaog Peñaredondo, was detained on Thursday in General Trias city, a Manila suburb, over a curfew violation. Officials have struggled to contain infections in the southeast Asian nation and have increasingly resorted to harsh tactics to enforce restrictions, rights groups say.

He was released the following day, but first was forced to complete 300 squats, his relatives said.

It is not the first time that the authorities have been accused of using aggressive tactics against civilians during the pandemic. President Rodrigo Duterte told the police last year not to be afraid to shoot anyone who “causes commotion,” after 20 people protesting restrictions were arrested. Last year, a former soldier suffering from mental health issues was gunned down by the police as he tried to cross a coronavirus checkpoint.

Mr. Peñaredondo’s partner, Reichelyn Balce, said that when he returned home on Friday after being detained, he had shown signs of fatigue.

“He told me that he fell when doing the exercises,” she said. “He struggled to walk when he got home. When he went to relieve himself, he turned blue and convulsed.”

She said that Mr. Peñaredondo was revived but he later died.

Two police officers who imposed the harsh punishment have been suspended pending the results of an investigation into their actions, said Brig. Gen. Ildebrandi Usana, a national police spokesman.

The local police had initially denied the events, but two men who were detained with Mr. Peñaredondo signed a sworn statement about the ordeal.

Cristina Palabay, who leads a local rights group called Karapatan, said that the police punishment amounted to “a form of torture that is cruel and inhuman” and signaled that the local police had adopted a “strongman approach.”

Ms. Palabay’s group aids families of the thousands of citizens killed in the president’s aggressive war on drugs.

The country’s Commission on Human Rights was critical of what it called an “overreach of the enforcement of quarantine rules and regulations,” according to the body’s spokeswoman, Jacqueline Ann de Guia.

Ms. de Guia said that curfew violations called for community service or a fine, rather than harsh physical punishment.

Kenna Tanner and her team can list the cases from memory: There was the woman who got tired and did not feel like finishing her hike; the campers, in shorts during a blizzard; the base jumper, misjudging his leap from a treacherous granite cliff face; the ill-equipped snowmobiler, buried up to his neck in an avalanche.

All of them were pulled by Ms. Tanner and the Tip Top Search and Rescue crew from the rugged Wind River mountain range — the Winds, as the range is known locally — in the past year in a sprawling, remote pocket of western Wyoming. And all of them, their rescuers said, were wildly unprepared for the brutal backcountry in which they were traveling.

“It is super frustrating,” said Ms. Tanner, Tip Top’s director. “We just wish that people respected the risk.”

In the throes of a pandemic that has made the indoors inherently dangerous, tens of thousands more Americans than usual have flocked outdoors, fleeing crowded cities for national parks and the public lands around them. But as these hordes of inexperienced adventurers explore the treacherous terrain of the backcountry, many inevitably call for help. It has strained the patchwork, volunteer-based search-and-rescue system in America’s West.

Where places like Canada or Switzerland have professional, full-time teams that manage everything from lost tourists to fatal mountaineering accidents, most operations in the United States are handled by a loose network of volunteer organizations like Tip Top, which are overseen by local sheriffs.

For much of the country’s history, this patchwork system met demand. But that trend has shifted in the past decade — and rapidly, over the past year — as less experienced recreationalists push further into treacherous places.

No one expects the eventual end of the pandemic to stem the flood of newcomers to the Winds, which people grudgingly admit have been discovered. Property values continue to soar in Sublette County, and even this winter, locals say out-of-state plates were more common than Wyoming plates in trailhead parking lots.

“You can’t stop it,” said Chris Hayes, who works at an outdoor retailer in Pinedale and also runs a fishing guide service. “There’s no secret place anymore. They’re all gone.”

Before the pandemic, I found comfort in the routine of my life and the rhythms of my family — what Nora Ephron once called the “peanut-butter-and-jellyness” of days with children. I liked the morning thunderdome of getting the children dressed and fed, dropping them at school and taking the 20-minute walk to the subway.

At this point my commute is the five feet from my bed to my desk, and I am somehow both tired and agitated when I start work each day. My kids never leave the house, except when we go to the same three parks in our neighborhood. Sometimes when I go running outside, I fantasize about just … not stopping, my eyes thirsty for some new horizon.

In other words, I’m so freaking bored.

Here’s how one boredom researcher — yes, there are boredom researchers — has defined the emotion. “‘Feeling unchallenged’ and perceiving one’s ‘activities as meaningless’ is central to boredom,” concluded a study by Wijnand Van Tilburg, an experimental social psychologist at the University of Essex in England.

Even in normal times, boredom is a very common emotion — a study of almost 4,000 American adults found that 63 percent felt bored at least once in a 10-day sampling period. The causes of boredom are multifaceted, but a lack of control over your situation is a common one. He added, “There’s research that shows when you’re limited in your control over the situation — that intensifies boredom.”

Knowing that many of us may not be able to have much control over our movements for at least the next few months, how do we try to alleviate our boredom? First, the researchers I spoke to said it’s important to acknowledge there’s no easy fix for our doldrums — so much of what is happening right now is beyond our control, and the vaccines are just beginning to be tested in children under 12, so we may not be able to make big moves just yet.

This weekend, we saw relatives I adore for an outdoor Easter egg hunt. Just 90 minutes of warm interaction with these beloved adults made me feel so happy and alive that I was smiling for the rest of the day.

As the weather gets warmer and more of my peers are inoculated, I am planning more get-togethers. Whenever I drop back into the doldrums, I will think about all the walks and dinners and hugs on the horizon.

Stress-baking and panic shopping. Vegetable regrowing and crafting. Now we can add another hobby to a year of quarantine trends: backyard maple sugaring.

Among the many indicators that it’s on the rise: a run on at-home evaporators and other syrup-making accouterments. A surge in traffic and subscriptions to syrup-making websites and trade publications. And, of course, lots of documentation on social media. (The Facebook group Backyard Maple Syrup Makers added some 5,000 members, almost doubling the its community, in the past year.)

Tapping maple trees and boiling the sap into syrup — known as sugaring — isn’t a new hobby. What’s unique about this year is the influx of suburban and urban backyard adventurers fueling these maple sugaring highs.

Claire and Thomas Gallagher, for example, tapped a tree behind their home in New Rochelle, N.Y., for the first time three weeks ago.

“It’s such a fun thing to do with the kids, it gets us outside, it’s educational,” Ms. Gallagher, 37, said. And with everyone at home all winter and probably the spring as well, the Gallaghers decided there would never be a better year to try it.

Because sugaring is a sticky business — and boiling sap indoors can mean resin all over the walls — many backyard amateurs turn to small-scale, hobby-size evaporators like the ones sold by Vermont Evaporator Company in Montpelier, Vt.

“When we started our company five years ago, our customers used to look just like us: rural homeowners with five to 10 acres of land,” said Kate Whelley McCabe, the chief executive. “Now we sell to people all over the country and to a growing number of suburban and urban customers.”

The governor of New Hampshire, Chris Sununu, is a dedicated sugarer. His 8-year old son, Leo, is his tree tapping assistant, and his two teenagers, Edie and Calvin, “do the heavy lifting.”

Governor Sununu said that when the tree sap begins to flow, it’s the official signal that spring has arrived. “It’s been a long winter and a long year. The sun is coming up, the days are getting warmer, and when the sap ran this year, we knew we were really coming out of winter with a lot of optimism,” he said in an interview.