Ginoveva De Leon, center, shares a snack with her children Selena, 6, left, and Oliver, 2, at their apartment in Arlington. When school is closed, De Leon must often scramble to find day care. (Allison Shelley/For The Washington Post)

When Ginoveva De Leon picked up her 6-year-old daughter from Barrett Elementary School last week, the teachers waved goodbye and told her, “See you Tuesday!”

She was confused: Next Tuesday? It was only Wednesday.

That was the moment she learned that the Arlington County school would be closed Thursday and Friday for parent conferences. And on Monday, school would still be closed for the Columbus Day holiday.

Five days with no school.

“My head was in the clouds,” said the 27-year-old mother, who works five days a week at McDonald’s. “I was thinking, ‘Oh my goodness, what am I going to do?’ ”

Days off from school create a perennial scramble for working parents. Even when parents plan in advance and have their school calendars synced with their Outlook accounts or their refrigerator calendars, any disruption to complicated family schedules poses a logistical and financial challenge.

And the school year comes with a lot of disruptions.

Public schools are closed an average of 29 days each school year, according to an analysis of academic calendars for the country’s two dozen largest school districts released Tuesday by the Center for American Progress, a D.C.-based liberal think tank.

The figure includes federal and state holidays, professional development and seasonal breaks. It does not include summer, snow days or sick days.

The number of scheduled days off from school amounts to nearly twice the number of vacation days that the typical private- ­sector employee has on hand. For low-wage workers, who are less likely to have paid holidays and flexible work schedules, all 29 days pose the same riddle: How to pay bills and take care of their kids?

“Schools make it really hard for parents to balance their commitments to their children and their jobs,” the report said.

In the past, stay-at-home mothers cared for their children around the edges of school. But today, 67 percent of mothers are working, and the percentage of single parents has more than tripled since 1960.

This generation of parents is working harder to make ends meet and often raising children without the help of extended family nearby.

When De Leon does not go to work, she does not get paid. So days off from school alter the fundamental calculation her family budget is built on.

De Leon makes $9.25 an hour at McDonald’s, where she has worked since 2008, cooking or ringing up orders. After taxes, she usually takes home $50 or less a day.

Payday is every other Tuesday. On Wednesday, she pays the babysitter, a relative who charges $20 a day to take care of her 2-year-old son, Oliver.

The balance goes toward bills and food. But when she has to pay for two children in child care, her salary almost completely disappears.

“On holidays and vacations, it doesn’t work,” she said.

So she called her manager and said she could not come in on Thursday.

Kate Sinkins, a divorced mother in Arlington, said that by the time she realized that her daughter’s school would be closed two days last week, instead of one, taking time off from work did not seem like an option. A government lawyer, she did not have much vacation time and worried about appearing unprofessional by taking off or bringing her child to work.

She called six babysitters before she found someone who could watch her daughter for half a day. Her neighbor agreed to help for the other half.

“And I’m one of the lucky ones because I can afford a babysitter,” she said.

The report found that New York City and Los Angeles last school year had among the highest number of scheduled days off — 33 and 34, respectively. Los Angeles also had 26 shortened school days throughout the year for professional development.

The reasons that schools close vary and are sometimes surprising: The first day of hunting seasons is a holiday in some school districts. Massachusetts schools closed for Patriots’ Day.

In the Washington region, Fairfax County had 28 days off and Montgomery County had 26 days off. Prince George’s County was closed for 33 days.

Many educators are pushing for extended school years and school days in an effort to close the academic achievement gap between children from wealthy and poor families.

It is very stressful for parents who have to figure this out.

Maryland Gov. Larry Hogan (R) bucked that trend in August when he ordered schools to end classes by June 15 and start after Labor Day, beginning in 2017. Delaying the start of the school year would be good for businesses, he said, particularly in beach communities that rely on tourism. Some parents say they are pleased that a longer summer might mean fewer days off during the school year to meet the 180 school days mandated by law.

Public debates about school schedules are often determined by business needs or transportation concerns, in addition to academic achievement, said Catherine Brown, lead author of the report.

“The missing piece has always been the perspective of the parent,” she said.

The report recommends ­“family-centered schools,” with longer school days and parent conferences facilitated by home visits or Skype.

Misaligned school and work schedules drive down economic productivity, by reducing levels of full-time employment usually among mothers with elementary-school-aged children, the report said.

And while children get out of school hours before most parents’ workdays end, just 45 percent of public elementary schools offer before- or after-care, according to federal data.

Privately run camps and county recreation programs attempt to fill the gap on days when school is closed. But they can cost upward of $65 per child daily. Some have a sliding scale, but they fill up quickly, according to parents.

A community center where De Leon lives also offers children’s programs. But the budget is small, and it serves just a fraction of the children in the rent-controlled housing development.

So outside their apartment window in Buckingham Village, young children could be seen milling around and riding their bicycles last week.

De Leon kept her children inside and spent the day cooking, cleaning and doing laundry on Thursday.

By Friday, 6-year-old Selena was officially bored.

“Every morning she asks, ‘Do we have school today? Do we have school tomorrow?’ ” De Leon said.

That morning, De Leon walked with her children to a nearby food bank, where she filled the stroller with a free chicken, some rice, a bag of apples and three bags of hot-dog buns.

When they came home, Selena tossed a ball into a small hoop mounted on the wall, while her little brother ran back and forth from the bedroom where their father, already back from an early shift at a construction site, was watching television.

After a while, she got out her backpack and sat at the dining table. She helped herself to a pumpkin-shaped cookie and opened a big zip-top bag of books.

She pulled out each book one at a time, moving her finger along the words.

“She puts pickles in the pan,” she read, laughing out loud. “She puts peanuts in the pan.”

At 2:45 p.m., she tied a blanket around her shoulders like a cape and skipped outside with her mother to walk the two blocks to her school for a 3 p.m. conference.

After two days off, she planned to work straight through the next week, she said. She picked up an extra shift on Sunday when her husband could stay with the children. On Saturday and Monday, she would hire a babysitter, even if it meant handing over most of her salary to the sitter.

By Tuesday, things would be back to normal. School would be back in session.