The D.C. Council’s education committee on Monday unanimously approved a bill that aims to provide the city’s public schools with additional money to help low-income students and others at risk of academic failure.

The bill leaves the dollar-figure of the infusion up to Mayor Vincent C. Gray (D), but there are signs that the investment could be significant: More than 30,000 D.C. students fit the bill’s definition of “at risk,” and a study that Gray’s administration commissioned found that serving at-risk youths could cost as much as $120 million per year, according to the bill’s fiscal impact statement.

“The bill acknowledges what common sense already tells us, which is that certain students require additional resources to support their education because of issues of poverty and other barriers,” said Committee Chairman David A. Catania (I-At Large), who introduced a version of the bill in June as one of seven measures meant to accelerate the city’s school improvement efforts.

The bill, co-sponsored by 10 of Catania’s 12 colleagues, now heads to the full council for approval. It has won praise from many school advocates, and it has the support of the Gray administration, according to Deputy Mayor for Education Abigail Smith, who said her staff worked with the committee to revise the bill.

“We’re supportive of where it’s landed,” Smith said. But she added that it’s too soon to say how much Gray will propose spending on at-risk students — and on schools overall — next year.

Consultants, working for Smith’s office, are wrapping up a year-long study on school funding and plan to release final recommendations in December. The draft recommendations, released in October, suggested boosting overall school funding by $180 million. It included $88 million in new funds for at-risk students, but “at risk” was defined more narrowly than it is in the bill.

The city’s schools — both traditional public and public charters — receive $9,306 for each student they enroll, plus additional funds for students with disabilities and those learning English as a second language. But advocates have long argued that the District — like many other jurisdictions, including Fairfax County — should also provide schools with extra resources to educate poor children, who often come to class with profound challenges and tend to lag behind their more-affluent peers.

The current version of Catania’s bill defines at-risk students as those who are homeless, in foster care or who qualify for food stamps or the welfare program known as Temporary Assistance for Needy Families. The category also includes high school students who are a year or more older than they should be for their grade level.

Schools would receive extra dollars based on the number of at-risk students they enroll. Charter schools would be able to use the money however they wish.

The traditional school system would be required to funnel 90 percent of the at-risk funds to individual schools, and principals would be required — with the help of parents and other members of the school community — to write a plan showing how that money would be used to lift the achievement of poor children.

The bill initially proposed requiring the school system to turn over the majority of all its funds to principals to spend at their discretion. That drew opposition from Chancellor Kaya Henderson, who argued it would be impossible to ensure equity of offerings across the city. Henderson’s spokeswoman declined to comment Monday.

The bill caps the amount that the central office can take away from any individual school to 5 percent of that school’s budget, an attempt to create continuity for the schools’ academic programs. The bill also would create a new grant program to support vocational education.