Outline for a Deal on Chicago Teachers" Contract Schoolteachers gathered outside the Inter-American Magnet School in Chicago before canvassing the neighborhood to raise support for their strike negotiations. CHICAGO - Five days into the teachers" strike that has halted classes for 350,000 public school students across this city, leaders on both sides of a contract fight said Friday afternoon that they had an outline in place for an agreement that could clear the way for schools to reopen Monday. Robert Bloch, the attorney for the teachers" union, said that both sides were still working out the details but that union officials were "hopeful" that they could present a complete agreement to the union's house of delegates on Sunday. "This has been one of the most difficult labor contracts negotiated in decades," he said when asked why negotiations had taken so long. Emerging from the negotiating room shortly after Mr. Bloch, David J. Vitale, president of the Chicago Board of Education, said, "The heavy lifting is over and the framework is in place." Later, he added that parents "should be prepared to have their kids in school by Monday." The two sides broke up for the day but plan to reconvene Saturday morning in Mr. Bloch's office to work out the remaining details. Talks between striking teachers and public schools officials had extended into the early morning hours here on Friday as the union and the leadership of the city's schools sought to reach a tentative deal in time for consideration by the union's roughly 700-member House of Delegates, which was scheduled to meet Friday afternoon. While that timetable was pushed back to Sunday, both sides expressed optimism that the delegates would vote to lift the strike on Sunday, in time for school to reopen by Monday morning. Eventually the union's full 26,000 membership will vote on whether to ratify the contract, but the strike vote will come first. Earlier in the week, Chicago Public Schools officials had deemed talks close to resolution while union officials declared the sides "miles apart." As recently as Wednesday evening, the sides had sparred publicly over whether formal talks were really taking place at all. Given four days of picketing outside largely empty schools, months of negotiations and a roller coaster of sharp and sometimes shifting talk from those involved in the negotiations, few here seemed quick to predict whether the first teacher's strike here in 25 years would in fact finally be resolved.. It was unclear precisely what had turned the mood of talks inside a Michigan Avenue hotel from sour on Wednesday afternoon to hopeful by Thursday morning, but schools officials said they presented a new offer that included several changes in areas the union had been concerned about. Among the proposed changes, according to schools officials: teachers" raises would average 16 percent over four years at a cost of $320 million, as had already been offered, but would be distributed differently; health insurance rates would not rise for teachers with families, as had been planned, if the union agreed to take part in a wellness program; and an appeals process would be created for teacher evaluations, which have been a significant area of disagreement. Since last November, this city's 26,000 public schoolteachers have been negotiating over the terms of the four-year contract, but the battle has played out more broadly, over the direction and philosophy of the school system, even as it struggled to solve gaping budget deficits. Mayor Rahm Emanuel has called for a longer school day, more control for principals in picking teachers, thorough evaluations for teachers, and expansion of the city's charter schools. The teachers have said they felt under siege, and pitted against a larger national education trend that they say fails to consider Chicago's realities, like the fact that 87 percent of public school students here come from low-income homes. In many ways, teachers here have said they see their fight here as a larger one, taking place not only over education but also over the role of labor at a time when states like Indiana, Ohio and Wisconsin have fought battles with Republican leaders over collective bargaining rights and the power of unions. In fact, the Chicago Teachers Union announced on Thursday that it would hold a "Wisconsin-style" rally over the weekend, and that it expected wide attendance by supporters from other states. "The teachers" union here saw this as a local struggle within a larger national battle of what a lot of teachers call the privatization of schools," said Robert Bruno, a professor of labor relations at the University of Illinois. They didn't see this as just localized. The issues that are being pushed here are being pushed in many urban and suburban school districts. Around the city, families said they were hopeful that the strike was nearly over. Many had expressed tolerance for the circumstances and the child care juggling act they found themselves in, in some cases, only a week into a new academic year, but patience seemed likely to run thin in the coming weeks. In 1987, the last time teachers here went on strike, an agreement took 19 days. A relatively quick end to the fight here would also quiet an awkward issue for President Obama in his hometown in the heart of a presidential campaign season. Mr. Obama's aides said he had not chosen a side in the strike, which pitted his former chief of staff, Mr. Emanuel, against a crucial bloc of his political support, the unions. Steven Greenhouse contributed reporting from New York.