PATERSON, NJ – Paterson Public Schools ranked among New Jersey’s “underachievers” in terms of providing breakfast to students who live below poverty levels, according to a study released by an advocacy group on Tuesday.

Although 20,879 Paterson students were eligible for the free breakfasts, just 5,691 of them were getting the meals as of March 2012, according to the report by Advocates for Children of New Jersey. The city school district would be eligible for almost $5 million in federal funding to pay for the breakfasts if every eligible child were getting the food, the report said.

Local education officials are well aware of the problem. This year, Paterson Public Schools launched a pilot program at Schools 8 and 9 under which students would be provided breakfast in their classrooms after the start of the school day.

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“As you know the district is moving ahead with a pilot “Breakfast After the Bell” program for this very reason,’’ said spokeswoman Terry Corallo. “We are aware that our ‘before school’ breakfast participation numbers are low because many children simply do not show up to take advantage of the current program. By serving breakfast in the classroom, we will reach many more children and provide them with a nutritional start to their educational day.”

The district plans to expand the program to other schools in coming months, according to Corallo.

The Advocates for Children report said the “Breakfast After the Bell” program had helped boost participation in the federal nutrition program in many districts around the state. The report said the number of children in New Jersey participating in the program had increased by 21 percent from October 2010 to March 2012.

Community Charter School of Paterson was ranked tops in the state with 90 percent of its eligible students getting breakfasts through the program. Meanwhile, Passaic and Garfield were listed among the high-poverty areas that had made significant progress in boosting the number of students getting the subsidized breakfasts.

Under the program, children in a family of four that earns less than $30,000 are eligible for free breakfasts, while students in families with incomes between $30,000 and $42,000 are eligible for reduced price meals.

Paterson School Board member Jonathan Hodges said he wanted to know how many of the eligible children in the district were getting breakfast from their families before school and how many “are coming to school hungry.’’