LOS ANGELES (Reuters) - As Los Angeles teacher Diana Castillo picketed in the rain alongside her husband, brother and daughter, who all work for or attend district schools, she didn’t bring up the paychecks her family would be missing.

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Instead Castillo, when asked what drove her to walk out of her classroom at Harbor City Elementary School to join the city’s first teacher strike in 30 years, talked about the colleague whose job was eliminated while she was on maternity leave, and the classes that keep growing in size.

“My husband and I are both Los Angeles Unified School District (LAUSD) teachers and we’re both dedicated to this,” said Castillo, who wore a plastic poncho and red cap in a rare California rainstorm, a laminated sign around her neck listing the recent cutbacks at Harbor City Elementary.

“This is bigger than a paycheck.”

Castillo’s brother also teaches for the district and her two daughters attend one of its high schools.

As some 30,000 teachers spent a third day on picket lines at schools across the nation’s second-largest school district on Wednesday, a union leader expressed optimism that stalled negotiations could be restarted with help from Mayor Eric Garcetti.

Among demands for smaller class sizes and more support staff at 1,200 schools, United Teachers Los Angeles has also asked for a 6.5 percent pay raise. The LAUSD has offered 6 percent.

On the picket lines, teachers largely dismiss the pay issue. What’s at stake is class sizes so large some students don’t have desks, outdated equipment, and nurses or counselors who only work one day a week, they say.

The average number of students per class in the district was 26, the LAUSD said in a position paper that cited data from October 2018. But 35 percent of classes have 30-40 students and six percent had 40 pupils or more, it said.

The average class size in an urban U.S. primary school is between 22 and 28 students, according to the federal National Center for Education Statistics.

“The classrooms are falling apart. They look sad,” said Elizabeth DiMartino, 37, who teaches preschool for children with special needs at an elementary school in the San Fernando Valley neighborhood of Los Angeles. “We spend so much of our own money just to make the classrooms look presentable.”

DiMartino said she previously taught in Maryland, where the school provided not only full-time nurses but instructors in art and music.

“The biggest thing is this sense that these things are bonuses. If you have a nurse, if you have art, PE, music -- those are necessities, those are basic things,” she said.

The union is demanding $800 million toward new staff, versus the district’s offer of $130 million. Schools Superintendent Austin Beutner has said the district simply can’t afford all of the resources the teachers are asking for.