Middle schools — the school system’s weakest links when it comes to test scores — will see an influx of cash starting in September under a new school funding program announced by the schools chancellor yesterday.

Chancellor Joel Klein said extra funding would also go to schools with students living in poverty — although only up until third grade, when the system would switch to funding students based on their state test scores.

“We’re sending new funds to students who have the greatest need,” Mr. Klein said at a news conference where he disclosed the details of the new budgeting system. “It’s a landmark day for our school system.”

The new system, commonly known as “weighted student funding,” will use part of the $1 billion won last year in the Campaign for Fiscal Equity lawsuit — which argued that the city’s education system was underfunded — to redistribute wealth among schools.

About a tenth of the $1 billion won in the lawsuit — $110 million — is going toward raising the budgets of 693 schools currently receiving less than the citywide average. More than twice the amount going to the underfunded schools — $230 million — would go toward maintaining the budgets of schools above the average, which the mayor agreed to protect from funding losses.

Principals would have wide discretion in how they spend the new money, which is drawn from the tax levy, Mr. Klein said. He suggested that many would choose to spend the money to hire more teachers — a scenario likely to please the teachers union.

The teachers union president, Randi Weingarten, praised the mayor’s commitment not to take money from well-funded schools, but suggested that class size reduction — which would require hiring more teachers — should be explicitly required.

“Conspicuously absent is any mention of directing money to reduce class sizes,” she said.

The rest of the $1 billion won in the lawsuit will go toward raising teacher salaries, pre-kindergarten programs, charter schools, and other programs.

The weighted student funding plan works by starting with a basic per-student amount — about $3,800 — and building on it for students with certain characteristics. For example, middle-school students are assigned a weight of 1.08, meaning a school that serves students in grades six through eight would receive $3,800 plus an additional $304.

If the middle-school student was also achieving “well below” the standards on tests, the school would receive an additional $1,894, for a total of $5,998, money the school could keep even if the student improves.

The focus on increasing funding for middle schools comes after new evidence has shown that test scores worsen in grades six through eight.

A parent leader, Zakiyah Ansari, said she was thrilled that the extra money would be directed to the middle grades.

“It’s long overdue,” she said. “Middle schools have been underfunded for so many years.”

Apart from the weighted student funding plan, schools will receive an additional $170,000 on average out of savings from the administration’s efforts to trim the school bureaucracy.