EAST MILLINOCKET, Maine — A small portion of a Florida woman’s $370.9 million Powerball winnings will fix Schenck High School’s roof by September 2014 if residents accept her $1.8 million donation, officials said Tuesday.

The Board of Selectmen voted 5-0 on Monday night to set a special town meeting at Schenck for 6 p.m. Tuesday, Sept. 24, where residents will vote whether to accept the financial gift from the family of town native Gloria MacKenzie, said town Administrative Assistant Shirley Tapley.

If voters approve accepting the gift, the funds will pay for roof repair, plus possibly the replacement of the gymnasium floor or improvement of the school’s accessibility for disabled residents, Superintendent Quenten Clark said.

A contractor will likely be picked to oversee the work sometime early next year. Construction will then begin in summer 2014, he said.

“With any luck at all by next [school] year we will have a new roof,” Clark said Tuesday.

The MacKenzie family’s generosity might not end there, said Clint Linscott, the board’s chairman.

“I have been led to believe there may be more gifts towards protecting the future of the building,” he said. “I think we should definitely support it [the $1.8 million gift] and be very appreciative of it.”

Rumored since MacKenzie came forward with the winning $590.5 million Powerball ticket on June 5, collecting a lump sum of $370.9 million that totaled $278 million after taxes, she sent word of her intent through family members who visited Clark’s office on July 23. Family members have declined to comment since the ticket was cashed.

Residents found the news thrilling. They have wrestled with the problem of the school’s leaky roof all year. The school board had recommended that voters support a $1.87 million proposal to fix the roof and make some other repairs at a referendum that has been delayed until the school system’s proposed budget is passed. Selectmen had opposed it, but wanted voters to decide.

Schenck, which also houses kindergarten to fourth-grade students in the Opal Myrick Elementary School wing, will still get about $636,000 in state aid for the roof job, Clark said Tuesday.

The school building, which has portions that date back to the Eisenhower administration, also has an aging boiler system and a declining population. As of September, 381 students are enrolled in the schools, compared to 420 from a year ago, Clark said.

Schenck’s population peaked during its approximately 55-year-history with 600 high school students. This year, Opal Myrick’s kindergarten hosts 21 pupils. It had 33 a year ago, Clark said.

“We were pretty packed in so it [the declining student population] does fit the space better. But the business is about children, so in the end the decline in enrollment is never a good thing,” he said.

School officials have discussed consolidating with Millinocket or other towns, but the only ongoing effort toward that end, Clark said, are discussions among the towns’ athletic directors about consolidating fall sports teams.

The aging boiler and air systems and the declining population will likely be the next things school officials and architects will have to tackle as they mold the future of the school building, Clark said.

“Enrollment is an issue. Designing a school system for the enrollment that you have is something that needs looking at in the future,” Clark said. “Unless something dramatic happens in the area you are going to see the enrollments and populations continue to decline for another few years.”

“You can have a good small school,” Clark added, “and you have to design an entity for that.”