School districts throughout New York will see more state aid this year than last, but wealthier districts were rewarded a little more Tuesday.

The state Legislature agreed to a tentative budget that would return much of the money taken from school districts to balance the budget in previous years. Wealthiest schools lost the most when the funds were taken, and thus are getting the most back.

That meant the big winners were school districts like Ballston Spa, which is getting a 10 percent increase, and Corinth, which is set to receive a 16.6 percent increase, in combined general and building aid. Ballston Spa and Corinth are considered districts with average need, according to the state.

Also online • State legislators rush to pass budget by deadline.

School aid changes Schenectady: 5.1 percent, $5.1 million Duanesburg: 8.7 percent, $582,000 Scotia-Glenville: 8.1 percent, $1.4 million Schalmont: 6.9 percent, $849,000 Mohonasen: 6.6 percent, $1.3 million Niskayuna: 4.5 percent, $850,000 North Colonie: 8.1 percent, $1.5 million Guilderland: 5.2 percent, $1.1 million Albany: 7 percent, $6 million South Colonie: 8.5 percent, $1.7 million Gloversville: 3.2 percent, $1.3 million Johnstown: 3 percent, $562,000 Northville: 4.4 percent, $161,000 Mayfield: -3.8 percent, -$350,000 Broadalbin-Perth: 5.4 percent, $877,000 Wheelerville: 4.3 percent, $67,000 Oppenheim-Ephratah-St. Johnsville: 1.8 percent, $244,000 Amsterdam: 1.9 percent, $753,000 Fonda-Fultonville: 6.6 percent, $946,000 Canajoharie: 5.5 percent, $668,000 Fort Plain: 1.9 percent, $225,000 Burnt Hills: 2.7 percent, $540,000 Corinth: 16.6 percent, $1.7 million Galway: 8.5 percent, $643,000 Shenendehowa: 3.5 percent, $1.5 million Mechanicville: 6.2 percent, $597,000 Ballston Spa: 10.2 percent, $2.6 million S. Glens Falls: 8 percent, $1.9 million Schuylerville: 7.1 percent, $1 million Saratoga Springs: 6.2 percent, $1.8 million Stillwater: 3.5 percent, $363,000 Waterford: 9 percent, $588,000 Middleburgh: 4.5 percent, $464,000 Cobleskil-Richmonville: 5.9 percent, $1.1 million Schoharie: 13.2 percent, $1.3 million Sharon Springs: 4.3 percent, $220,000 Full list of school aid projections

Schenectady, which is considered a high-need district, is slated to get a 5.1 percent increase. Most of the suburbs surrounding Schenectady will see much higher increases.

The stark difference between wealthy and poor districts made some superintendents uncomfortable. Saratoga Springs City School District Superintendent Michael Piccirillo said the state budget clearly favored his district.

“I’m advocating for my school district, but I’m also advocating for all school districts. Whatever works for all of us, that’s what I want,” he said. “I don’t want to see any school district become financially insolvent.”

Schenectady City School District Superintendent Laurence Spring said the varying aid percentages are discriminatory, though he added he did not think any one individual intentionally sought to discriminate against poor, urban schools where minority students are in the majority. But, he said, that was the result.

“We didn’t even get the average” aid increase, he said. “That’s not only a statement of ‘We’re OK with you urban school districts.’ It’s ‘We’re going to increase the gap.’ ”

One of the state legislators who represents Schenectady agreed. Assemblyman Phil Steck, D-Colonie, said he was dismayed by the final decision, a product of negotiations between the Assembly and Senate.

“It’s not what we had hoped for, for Schenectady,” Steck said.

The Assembly had proposed an increase in foundation aid, which is given out based on a formula that takes into account each district’s level of poverty, high-needs students and other factors. Few districts receive the total amount of foundation aid the formula calls for, and districts receive widely varying percentages of their total formula-based aid.

Schenectady receives 55 percent of the aid the formula says it needs. By comparison, according to a 2012 study, Ballston Spa received 82 percent and Corinth received 94 percent of the aid required by the formula.

Steck said increasing foundation aid would make sense because the formula was created to settle a court case. The formula set out exactly how much money was needed for each district to provide a sound, basic education.

“The governor has a theory that money doesn’t matter with schools,” Steck said, “but the fact is, the courts said otherwise.”

The Senate wanted to eliminate the Gap Elimination Adjustment, rather than adding to foundation aid. The GEA is the amount of aid subtracted from each district to balance the state’s budget in prior years. The state had promised to pay it back.

Steck said that wouldn’t have helped poorer school districts like Schenectady because wealthier districts were hit harder when they lost aid to balance the state budget.

“To be fair, they took more money from the wealthier districts. So when you restore it, you give more money back to the wealthier districts,” Steck said.

The Legislature came to a compromise that eliminated much of the GEA while also funding some increases in foundation aid. That’s why wealthier districts ended up with much higher percentage increases in aid.

Assemblyman Angelo Santabarbara, D-Rotterdam, said he was relieved Gov. Andrew Cuomo did not insist state aid increases be linked to his education reforms. Santabarbara said he did not want aid “held hostage to any conditions from the governor,” but added he’s still not satisfied by the increases.

“But we can’t stop now,” he said. “I will continue the fight for public education with legislation to finally end the GEA this year and ensure fair distribution of aid to our upstate schools.”

Spring has spent his two years as Schenectady’s superintendent trying to persuade legislators that his district’s aid is unfairly low. While Schenectady gets 55 percent of the aid called for in the formula, Saratoga Springs receives 109 percent of its foundation aid, according to the formula, while Schoharie receives 110 percent.

Saratoga Springs will see a 6.2 percent increase in aid, while Schoharie will receive a 13.2 percent increase.

“Honestly, we were hoping for an increase in the 8 percent range,” Spring said. “We thought that would be a show of good faith. The state would acknowledge that they can’t make all that up in one year, but we’re going to catch up.”

Getting less than the average indicated to him that state officials were “forgetting” about Schenectady’s funding dilemma, he said.

Schenectady had hoped for a $6 million increase and had tentatively built its budget on that premise. That means the district will have to cut about $900,000 from its proposed budget.