The District’s traditional public and public charter schools would receive a major infusion of more than $100 million next year, including tens of millions to improve services for at-risk students, under a budget proposal announced Tuesday evening by Mayor Vincent C. Gray (D).

Signaling the continued strength of the charter school movement, the District’s publicly funded but independently run schools would receive close to half that money. It would be divided among schools depending on their enrollment.

D.C. Public Schools officials estimate that the system’s local allocation would grow by $55 million and its overall budget — which includes a fluctuating federal grant — by $33 million to a total of about $851 million.

“It really is allowing us to live out some of our hopes and dreams for DCPS,” Chancellor Kaya Henderson said of the mayor’s proposal, adding that she is in an enviable position compared with many school system leaders across the country who are facing stagnant or decreasing budgets.

The boost would allow the system to plow more money into Henderson’s priorities: strengthening middle schools, bolstering literacy instruction at struggling elementary schools and improving students’ satisfaction with their schools, officials said.

It would also help extend the school day at some schools; add more custodians; add more staff workers who specialize in special education and teaching English as a second language; and assist the opening or reopening of several buildings, including a new application-only middle school east of the Anacostia River.

“I do feel very, very lucky to have the resources that I need to be able to deliver to the citizens of Washington the kind of education that our young people deserve,” Henderson said.

Full details about Gray’s fiscal 2015 budget and its impact on traditional and charter schools will not be available until the mayor sends his spending plan to the D.C. Council early next month.

It’s not clear how much money schools would receive for each enrolled student, for example, or how many extra dollars for a newly defined category of at-risk students.

Gray’s proposal to substantially increase funding is not a surprise, even though the city already ranks among the nation’s most generous spenders on public schools; his administration recently released a report recommending a $180 million boost in funding for public education, an increase enthusiastically supported by D.C. Council Education Committee Chairman, and mayoral hopeful, David A. Catania (I-At Large).

Catania has been pressing for a middle-school improvement plan and last year successfully pushed a measure to require additional funding for at-risk students.

“I’m glad the mayor intends to fund the initiatives that the Committee on Education has been talking about for more than a year,” Catania said.

Henderson and other officials outlined their broad plan for the additional dollars, including a focus on addressing the city’s uneven offerings for sixth-, seventh- and eighth-graders.

For the first time next fall, all middle grade schools — including standalone middle schools and K-8 education campuses — will be required to provide a full year of math and English for all students; at least a semester of social studies and science in the sixth and seventh grades, and year-long courses in those subjects at eighth grade; and at least a semester of physical education. There are also partial-year requirements at each grade for the fine arts, health and foreign language, and every school must offer at least one section of algebra.

Henderson said that schools will receive the funds they need to fulfill those expectations, no matter the enrollment figure. Each middle-grades school will also be guaranteed a guidance counselor, and the schools will each get an extra $100,000 to hire a social worker, a dean of students or another staff member dedicated to social and emotional support for students.

Those schools will also each receive $5,000 to purchase materials for after-school clubs and $28,000 to defray the cost of field trips and other travel. “Students need to go out and experience things. Some of our kids have, and some have not,” said John Davis, the system’s chief of schools.

Overall, officials said, they expect to spend an additional $17 million on middle schools. “We’re going to work to make sure that every middle-grades school . . . offers every student in every part of the city a full and enriching experience,” Henderson said.

The new investment also includes $77 million specifically to serve charter and traditional school students in a newly defined “at risk” category. “These additional funds represent the next phase of school reform in the District,” Gray said in prepared remarks.

“We must take another giant step forward to tackle the unacceptable achievement gap” between the city’s poor and affluent students, he added.

Next year’s budget will take a step toward lengthening the school day for more students, an idea championed by Gray and Henderson. All middle schools and 21 of the city’s lowest-performing elementary schools can opt for extending the day by at least an hour. The move requires approval by each school’s principal and, under the teachers’ union contract, two-thirds of teachers.

Henderson also plans to hire eight additional reading teachers for the city’s lowest-performing middle schools and to ensure that more elementary schools have help from organizations specializing in intensive reading instruction.

Deputy Chancellor Lisa Ruda said that it’s too early to say what fraction of the overall budget will go to schools vs. central office administration but that she does not expect significant cuts at the school level or an increase in central office budgets.

“This is a good year to be a school in D.C.,” she said. No school, no matter how its enrollment shrinks, will see its budget reduced by more than 5 percent compared with this year, a measure passed by the D.C. Council last year and supported by the school system. The council also passed a measure requiring that DCPS funnel 90 percent of funds meant for at-risk students directly to principals, who are supposed to write a plan for using the money. DCPS officials said they believe that their spending plan aligns with the law.

Principals are scheduled to receive their school budget allocations Wednesday, and they must submit completed 2014-15 spending plans by March 18.

Previously, Henderson had said she would give schools $5 million to turn themselves into more attractive and enjoyable places for children.

The system also plans to expand some specialty positions, hiring close to 50 additional special education teachers, an additional 50 special education aides, two dozen teachers and counselors for students with limited English proficiency, and two dozen custodians.

Decisions about which schools need the extra staff were made in conversations with principals and on a school-by-school basis, officials said, although the custodial help will be concentrated in modernized buildings.

The school system also plans to invest more than $600,000 to establish a planning office, which next year will work to plan for the opening of a selective middle school east of the Anacostia. That office will also head up planning to openBrookland Middle School and reopen Spingarn High and Van Ness Elementary.

Finally, Henderson alluded to planning for a strategy to improve outcomes for young African American males, a group whose academic achievement and graduation rates trail the average. Officials could not say how much the system plans to spend on that effort.

“This mayor, year in and year out, has given us what we need to deliver for kids,” she