Los Angeles teachers will walk picket lines for a fifth day Friday after the union and school district officials returned to the bargaining table with hopes of ending the massive strike in the nation’s second-largest school district. Contract negotiations resumed Thursday for the first time in nearly a week with no word on whether either side provided a new offer. Union officials tempered expectations. “We should be aware that we’ve been at this for 21 months and there are some very fundamental issues that there are key differences on. So an agreement is not going to take shape overnight,” said Alex Caputo-Pearl, president of United Teachers Los Angeles. “But today there’s been good and hard work on that.” Caputo-Pearl said negotiations likely would continue Friday and possibly through the weekend. Mayor Eric Garcetti had urged both sides to resume talks at City Hall. The mayor does not have authority over the Los Angeles Unified School District but he has sought to help both sides reach an agreement. Teachers planned a huge rally at downtown’s Grand Park on Friday — the first day with no rain in the forecast since the strike began. Clashes over pay, class sizes and support-staff levels in the district with 640,000 students led to its first strike in 30 years and prompted the staffing of classrooms with substitute teachers and administrators. Parents and children have joined the protests despite heavy rain that has drenched the city. Overall attendance fell to 83,900 students on Thursday. With state funding dependent on attendance, student absences cost the district about $97 million over four days, the district said. At the same time, it doesn’t have to spend about $10 million a day on teacher pay. The union representing principals urged LA Unified to close schools until the strike is over. If the district can’t close the campuses, Associated Administrators of Los Angeles asked for additional resources for principals who have helped keep schools running while teachers walk picket lines. In response, Beutner acknowledged the administrator’s sacrifices but said LAUSD schools must remain open to provide a safe place for students. All 1,240 K-12 schools in the district were open — a departure from successful strikes in other states that emboldened the LA union to act. The union rejected the district’s latest offer to hire nearly 1,200 teachers, counselors, nurses and librarians and to reduce class sizes by two students. It also included a previously proposed 6 percent raise over the first two years of a three-year contract. The union wants a 6.5 percent hike at the start of a two-year contract. District officials have said teacher demands could bankrupt the school system. Superintendent Austin Beutner has urged the teachers to join him in pushing for more funding from the state, which provides 90 percent of the district’s money.