NEW YORK — In the neighborhood of East New York, elementary school Principal Janet Huger-Johnson, who grew up there, aims to make her school a sanctuary, a place where kids might be able to forget for a moment that they are living through a pandemic.

So Tuesday, the day tens of thousands elementary school students were to be welcomed back across New York City, she donned a pair of colorful sneakers and a polo shirt with East New York Elementary School of Excellence emblazoned on it. It was also personalized with her own slogan: “It’s Huger Time.”

Huger-Johnson tried to broadcast warmth through two masks and watched as lines of students, spaced out along yellow circles that had been spray painted on the sidewalk, took their first steps into the building since mid-March. The hallways were mostly empty, and the freshly polished linoleum glistened. The school was somehow both frozen in time and hurtling toward an uncertain future. Bulletin boards in the hallways were wrapped in cellophane, displaying winter-themed art projects and presentations from Black History Month, which was in February.

“I didn’t want the children to feel all of this,” Huger-Johnson said. “In the middle of that, you’re hopeful that kids are not impacted by just the struggles as we as adults were going through.”

A zealous planner, Huger-Johnson has been working nearly nonstop since schools closed in March to build an online curriculum essentially from scratch, researching best practices and software and pumping up an exhausted teaching corps that has suffered illness and loss. But no amount of planning and orchestration would make this year normal. It could not make up for the fact that 100 families — nearly a quarter of the school’s enrollment — were still awaiting tablet computers from the city’s education department or that two-thirds of her teachers were working remotely because of medical conditions, leaving her building shorthanded. The city lost at least 75 school employees to covid-19 — including a cafeteria worker at East New York Elementary.

And there was nothing she could do about the fact that the city’s infection rate was creeping upward, with outbreaks in Zip codes not far from East New York, inching toward the threshold that would force the city to shut down all schools. For the first time in weeks, the city’s positivity rate had exceeded 3 percent. Mayor Bill de Blasio has said he will shut down schools if the seven-day rolling average exceeds 3 percent.

Speaking from city hall not long after schools opened their doors on Tuesday, de Blasio called it “cause for real concern.”

This year, Huger-Johnson and school leaders across the country are being asked to do more: Keep children safe from school shooters and bullies and the novel coronavirus; tutor those who are below grade level and catch up the legions of students who fell behind in the spring; address continuing trauma wrought by the pandemic and the kids’ existing mental health problems.

At East New York Elementary, this has meant more check-ins on the emotional well-being of students, but also limiting student-to-student contact. The playground is wrapped in yellow caution tape, off-limits to students. A classroom has been set aside as the isolation room — a place where students who develop symptoms at school will be quarantined. Plush toys have been removed from all classrooms because they cannot be easily disinfected. Last week, the stuffed animals were corralled in a classroom and sat forlornly in a line, as if yearning for playmates.

One of the most taxing mandates in many places is that schools provide virtual learning in addition to traditional, in-person classes. And, as economic calamity wreaks havoc on school budgets, many of them are taking on these responsibilities with fewer teachers and fewer resources — all in the midst of a pandemic whose impact on children is still poorly understood.

The virus has created a cascade of logistical challenges for schools, immensely complex organizations even in non-pandemic times. New York City is by far the nation’s largest district, but the challenges it faces are common to school districts large and small, urban and rural.

“Frankly, I don’t know of another institution, public or private, that has so many moving parts with so much public pressure on it from so many angles on it as much as public schools have,” said Michael Casserly, executive director of the Council of the Great City Schools, a coalition of large, urban districts. “I have never seen a situation like this in the 43-plus years I’ve been doing this work, where public school leaders have devoted so much time, effort, creativity and just sheer endurance in trying to solve a set of problems where there’s just no obvious good resolution.”

Few districts are more complex than in New York City, home to children from some of the nation’s wealthiest and poorest Zip codes and one of the most linguistically diverse communities on the planet. It is also massive, with 1,700 public schools that educate more than 1 million students — roughly the population of Vermont. And its school system is under the control of de Blasio, who is frequently sparring with the powerful teachers union.

In an attempt to accommodate all families, de Blasio in July offered them the option of keeping their students home full-time for remote learning or a “blended” option, in which students would return to classrooms part-time and take virtual classes the rest of the time. Teachers, too, would be able to apply for medical accommodations to allow them to work from home if they had an underlying condition that would make them more vulnerable to covid-19. At the last minute, the city also allowed staff members who live with medically vulnerable people to apply for medical accommodation.

The plan created immense staffing needs. At East New York Elementary School of Excellence, Huger-Johnson said, about two-thirds of her teachers qualified to work from home, meaning she had more than enough to teach virtual classes. But she still needs two additional teachers for in-person instruction. Until she can hire them, students who arrive at school are taking virtual classes from their classrooms under the supervision of a substitute teacher.

It’s the same way many high schools are dealing with staffing shortages — middle and high schools are set to reopen for students on Thursday — but it is an arrangement that erases the benefits of in-person instruction.

The union that represents the city’s principals said the system needs at least 1,200 more elementary school teachers.

Despite Huger-Johnson’s efforts, there were some parents who arrived at school frustrated Tuesday morning. Because the school wants to cut down on the number of students wandering hallways, no child is allowed in the building early. One woman fidgeted anxiously and huffed that she needed to be at work. Another showed up with her two sons, only to be turned away because the school said she had signed up for remote learning. And yet another was still weighing whether to send her asthmatic son, who is struggling with reading, back to school.

But there were moments of normal first-day jitters. Eva Gray’s 5-year-old daughter, Grace, clung to her mother’s legs. She had picked out her favorite mask — a blue one with white polka-dots — and a pair of mary jane shoes with cats on them for her first day.

“She said she’s happy,” Gray said. “She wants to come and see kids.”