Enrollment at Wilson High School, the city’s largest comprehensive high school, is projected to grow by nearly 10 percent next year, but its budget is expected to shrink.

In what Schools Chancellor Kaya Henderson has dubbed the “year of the high school,’’ many comprehensive schools are poised to get a major boost in funding to provide a more equitable array of academic and extracurricular offerings.

But the proposed $15.6 million budget for Wilson is down more than $300,000 from the current year’s budget. Per pupil spending would drop to $8,307, from $9,276.

“This cut will leave Wilson with insufficient staff to manage almost 1,900 teenagers,” said Council member Mary Cheh (D-Ward 3) in a letter to Henderson. “It will also endanger the school’s continued success and jeopardize its efforts to bridge the achievement gap.”

In the letter, released Tuesday, she noted that the Ward 3 high school serves students from across the city, including 582 who are considered “at risk,” a new city classification that includes students who are in foster care or homeless, receiving welfare benefits or food stamps, or who are performing at least a year behind in high school.

At-risk students are afforded an extra allocation of funding in next year’s budget. This year, the chancellor had discretion in how those funds were spent. For next year, they must be apportioned strictly according to school’s at-risk populations, as spelled out in the law.

Henderson said in an interview this month that the strict allocation of an at-risk fund meant she had to cut in other areas. Wilson benefited in the past from a minimum level of per-pupil funding that was set to help larger schools. Henderson said the base-line funding was put in place because big schools “were getting short-changed.”

Ballou High School’s per-pupil funding is also down in the proposed budget for next year, from $15,696 to $12,958, because of other cuts. A historic “specialty allocation” — worth $947,100 this year — that Ballou received for years was eliminated. The Ward 8 school is also no longer eligible for a stabilization allocation meant to offset a drop in enrollment, cutting another $894,000 that it received this year. Overall, net funding and enrollment projections are up at Ballou, which completed a major renovation this year.

Other smaller comprehensive high schools are seeing major increases in funding. Per-pupil spending at Coolidge High School in Ward 4, for example, would grow from $13,889 to $16,209 for a projected enrollment of 401 students.

The fiscal 2016 budget includes an extra $13 million for the city’s nine comprehensive high schools to provide staffing to offer at least six Advanced Placement courses and 20 elective courses, such as choir and marching band.

Current offerings differ widely by school, depending on enrollment and budgets, and many students have clamored for more activities and nonacademic courses. Wilson, with its booming enrollment, already has one of the city’s largest selections of Advanced Placement courses and electives.

Parents at the school are concerned about other effects from budget reductions, including growing class sizes, and diminished capacity to bridge the achievement gap and keep students at the crowded school safe.

“People are really concerned about this,” said Kim Bayliss, president of the school’s Parent Teacher Student Organization. “They are so proud of the school and all the gains that have been made. They want that to continue.”