CHICAGO — With the possibility looming for a strike beginning on Monday across Chicago’s public schools, contract talks for city teachers were expected to stretch into the weekend, as hundreds of thousands of families began grappling with the prospect that school, only a few days old for many students, may come to an abrupt halt.

A strike in this, the nation’s third-largest public school system, last occurred a quarter-century ago, and seemingly all involved — union members, city leaders and, perhaps most of all, Chicago parents — said they hoped such an outcome could still be avoided. At points on Friday, those on both sides of the contract negotiations expressed tempered optimism about progress in the closed-door discussions. Still, the two sides were wrestling with an array of matters regarding wages, teacher evaluations and future jobs for laid-off teachers.

“I want the kids of the city of Chicago to stay in the classroom,” Mayor Rahm Emanuel said in an interview on Friday evening. “And the adults should stay in the negotiating room. And that’s where everybody belongs.”

A strike would leave some 350,000 students without classes, sports or college test preparation, and many parents without child care. Chicago Public Schools officials have announced a contingency plan, which would include half-days of supervised activities and meals at 144 schools around the city, but some parents said they were uncertain about their options and anxious about what Monday may bring.