D.C. Council members David A. Catania and Marion Barry are pushing to spend more than $40 million of the city’s projected — and unexpected — additional revenue on public education, funds that would be distributed to schools as extra dollars for poor children.

Under the lawmakers’ proposal, the traditional school system and each charter school would receive $744 for every student who qualifies for free or reduced-price lunch, a common measure of poverty.

Catania (I-At Large) and Barry (D-Ward 8) estimate the spending would result in an additional $25.5 million for the city’s traditional schools and $17.5 million for charter schools. They plan to introduce a budget amendment Wednesday, when the council is scheduled to take its final vote on the fiscal 2014 spending plan, according to a letter they sent to Mayor Vincent C. Gray (D) on Tuesday afternoon.

That vote will come days after city officials forecast a jackpot for the District — an estimated $92 million in extra revenue that was not anticipated. The council has authority to spend $50 million of the surplus; to spend the rest, the council will have to pass a supplemental budget.

Catania, chairman of the council’s Education Committee, proposed increasing funds for poor children in a package of legislation introduced this month. Hearings on those bills begin next week.

“This unexpected windfall that we’ve received that comes at the tail end of the appropriations process is an opportunity to correct an error in the existing budget,” he said, criticizing Gray for a spending plan that cut local spending for traditional schools by $1.8 million.

Catania, often mentioned as a potential 2014 mayoral candidate, and Gray, who has not said whether he will run for reelection, have both sought to drive public conversation on education policy.

Gray has his own spending priorities for the extra revenue.

The mayor is seeking to allocate $10.2 million to charter schools to use as they wish and $12.7 million to the traditional school system to upgrade technology and library resources.

He also is seeking $6 million in senior grants, $7 million in arts funding and $11 million to expand day care for infants and toddlers.

“The mayor said what he would like to do with the funds,” said Gray spokesman Pedro Ribeiro, adding that a school-funding study is underway and that administration officials believe it makes sense to wait for its results before making big changes.

Council Chairman Phil Mendelson (D) is expected to present his own proposal Wednesday for spending up to $50 million of the extra revenue. Mendelson had not released details about his plan as of Tuesday afternoon.