When Abraham Lincoln School in Garfield reopens in September, students will cram into a building constructed 50 years after the 16th president was assassinated and is showing its age: A sagging roof, water damage from leaks in the mortar, no air- conditioning.

It gets no better in some schools in Paterson, where the local teachers union has reported mold, leaky ceilings and rodents.

But they do have running drinking water, which is more than can be said of at least half the schools in Jersey City.

Those schools are examples among dozens throughout New Jersey’s 31 so-called Schools Development Authority (SDA) districts that will fully reopen this school year in “deplorable conditions,” as the Education Law Center put it in legal filings.

Hot, overcrowded, poorly ventilated classrooms have become a way of life for students and teachers in these districts that have been so down-at-the-heels that the Supreme Court ruled decades ago that the state is responsible for school repairs and replacement so students can get a “thorough and efficient” education.

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