CHICAGO —Teachers in the nation’s third-largest school district prepared to go on strike for the second time since 2012, as contract talks between the Chicago Teachers Union and financially troubled Chicago Public Schools headed into Monday evening with no sign of an agreement.

The CTU has directed its roughly 28,000 members to report to picket lines Tuesday morning unless they hear otherwise from union negotiators. All 652 schools will be open during normal school hours for the district’s 400,000 students, CPS said.

The two sides held negotiations throughout the weekend. On Monday afternoon, teachers picked up strike placards and painted banners.

Earlier in the day, parents and other supporters rallied across from Mayor Rahm Emanuel’s home, and another pro-educators rally was planned for Monday evening.

Teachers have been without a contract since June 2015. The union wants no cuts to salary or benefits and an additional $200 million – or $500 per student – in spending to ensure adequate staffing and “to accommodate the needs of our children,” CTU President Karen Lewis said.

CPS has said it is working within the framework of a January offer, which included pay increases and a cap on privately operated charter schools but would require teachers to contribute more to their pension costs. The union turned it down in February.

About two-dozen people with Parents 4 Teachers rallied in the leafy Ravenswood neighborhood on the city’s North Side.

Several children, off school because of Columbus Day, also were there; one held a placard that read, “Parents, Teachers, Students – United.”

Organizer Erica Hade has several children in the public school system and lives across the street from a school. She said she sees teachers arriving for work at 6 a.m. and leaving 12 hours later.

“How can parents not be supportive of teachers?” she said.

One theme struck by several at the rally was the perception that Emanuel focuses inordinately on wooing businesses to Chicago. At one point, protesters chanted, “Mayor Emanuel, we’re no fools. If there’s money for developers, there’s money for schools.”

People went door to door handing out cards that listed issues they saw as critical, such as enforceable class-size limits, a moratorium on charter-schools expansion and no cuts to teachers’ pay

During the last major strike in 2012, teachers were out for seven school days.

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