CHICAGO -- The head of the teachers' union here said on Thursday that she was hopeful that a deal could be reached to end the teachers' strike in time for the city's 350,000 public school children to return to class on Monday.

When asked whether a deal could be brokered in time for a resumption of school next week, Karen Lewis, president of the Chicago Teachers Union, said: "I'm praying, praying, praying. I'm on my knees for that. Please, yes, I'm hoping for Monday."

Despite the apparent progress, teachers were out picketing again on Thursday morning, and the union has not called off a large protest rally scheduled for Saturday. The strike began on Monday, after school had been in session for one week.

Ms. Lewis said that even if the union and the Chicago Board of Education were able to reach a deal Thursday, that she would then need to get approval from the union's other leaders, which might not occur until sometime Friday.

On Wednesday night, union and public school officials left negotiations with smiles on their faces, saying progress had been made in what have been very tense contract talks.

"I'm smiling," Ms. Lewis said on Wednesday night. "I'm very happy. It's a lot better than it was this morning."

Ms. Lewis added, "We made a lot of progress today. We spent a lot of time on evaluation. We still have a lot of work to do."

David Vitale, president of the Chicago Board of Education, also struck an upbeat tone as he left the negotiating session Wednesday night.

"I really think we shared a lot of back-and-forth and what really needs to get done to solve those most difficult issues," Mr. Vitale said.

The strike, now in its fourth day, has turned life upside down for hundreds of thousands of families.

On Wednesday, students could be found in contingency programs at schools, in churches and in costly day care centers. Some slept late, stayed home alone, then wandered their neighborhoods as if there were one more chapter of summer.

Others found themselves headed to their parents' jobs at laundromats, restaurants, libraries and offices. A Chicago alderman, Roberto Maldonado, arrived at City Hall on Wednesday with his 11-year-old son, Rene, in tow. Elsewhere, relatives -- grandparents, especially, it seemed -- were suddenly being pressed into baby-sitting duty.

So far, many Chicago families have expressed a degree of patience with their new, topsy-turvy circumstances. Some parents -- their children beside them -- have even joined the teachers' picket lines.

But, for some families, particularly those without extra money for day care and without job flexibility, the strike was creating serious financial strains. In Chicago public schools, 87 percent of students come from low-income families. More than 80 percent of public school students are African-American or Latino.

"I'm just worried about paying the bills now," said Sandra Gonzalez, 28 and a single mother, who said she had recently begun cleaning apartments after people moved out, but feared she could not work as much as she needed to now with her three children out of school. "I can understand how the teachers are feeling frustrated," she said. "But I'm also counting my hours these days, and I'm definitely on the edge to cover my bills."

For students with nowhere to go, school officials have opened 147 schools for half-day programs and for meals, staffed with nonunion workers. But fewer than 26,000 children attended such programs on Tuesday, far fewer than the 350,000 who found themselves without classes. School officials said they would increase the hours of those programs on Thursday, but some parents said they worried about sending their children to unfamiliar schools with supervision they felt uncertain of.

The strike arrived after months of violence in Chicago -- homicides are up 30 percent over last year -- and in some neighborhoods, families said they worried that a lack of school might bring still more danger. As of Sept. 2, 1,706 shootings had taken place here since the year's start, a 10 percent increase over the same period in 2011, and much of the violence has been attributed to young gang members. As the strike began, the Chicago police said they were adding to their presence on the streets, and there has not appeared to be a particular increase in violence.

On Wednesday morning in Englewood, a struggling neighborhood on the city's South Side, groups of teenagers stood on street corners and outside convenience stores, as children rode bikes down sidewalks and played games in the park. "I should be in school," said Johvelle Danner, 14, a freshman playing basketball by himself.

"I don't want to be out here doing nothing," he said. "It's dangerous."

First Published: September 13, 2012, 5:00 p.m.