Negotiators swapped proposals and finance officials crunched numbers at St. Paul Public Schools headquarters on Sunday in hopes of avoiding a teachers strike set for Tuesday.

The two sides were meeting again at 11 p.m. and were prepared to meet again Monday if a new two-year deal was not reached, officials say.

Outside, about 100 teachers, parents and students — many wearing the union’s signature red colors — rallied late afternoon, walking in an ever-widening circle, chanting, “Whose schools? Our schools,” and other slogans.

Superintendent Joe Gothard took part in talks for a second consecutive day Sunday, while on the fifth floor, administrators worked on communications strategies covering strike and non-strike scenarios. A webpage has been created for a “kid space” program that would be offered to elementary students beginning Thursday — if the walkout occurs.

“We have it ready to go live if we need it,” district spokeswoman Toya Stewart Downey said.

The St. Paul Federation of Teachers has been working, too, on “safe sites” for students in the event of a strike.

Standing outside Sunday’s rally, union spokesman Patrick Burke noted the superintendent had been very engaged in negotiations: “We are hoping that there is movement toward a settlement,” he said.

The federation left a 15-hour session on Saturday saying a deal was “still not close.”

Sunday’s talks marked the 11th round of mediation and the seventh session in seven days, and it came a day after Mayor Melvin Carter met with the negotiators to offer encouragement to reach a deal.

The union has pitched wide-ranging proposals with a cost of $159 million over two years, according to district estimates.

The district has sought to hold new spending for teachers to $2.07 million per year.

According to negotiations updates from the Saturday session, the union offered counterproposals on class sizes, staffing for English language learner programs and support for special education students — and expressed disappointment at the district’s response.

The district presented a proposal addressing the same issues, as well as adult basic education, wages and benefits, and new approaches to discipline referred to as “restorative practices.”

The wage proposals presented by both sides on Saturday included 1 percent pay increases.