D.C. Schools Chancellor Kaya Henderson defended her proposed budget Monday during a four-hour D.C. Council hearing that repeatedly circled back to questions about how the school system plans to spend tens of millions of dollars meant to serve at-risk youth.

Lawmakers also pressed Henderson to explain why she has proposed to delay some school modernization projects and accelerate others, a move that has triggered protest among communities that had been counting on now-delayed renovations.

Henderson acknowledged the frustration and the gaps yet to be filled but said she’s proud of the spending plan, which includes an increase of more than $50 million in city taxpayer funds. It focuses on three priorities: strengthening middle schools, extending the school day at more low-performing elementary schools and boosting students’ satisfaction across the city.

“We’re making big investments to really reinvigorate a school system that has been decimated by a lot of individual decisions,” Henderson said. “We just can’t do everything at the same time.”

The school system received $44 million for at-risk students this year, funds aimed at helping close the city’s enormous achievement gap. The D.C. Council passed a law late last year that allocated the money to schools based on the size of their at-risk population.

The school system did not do that, Henderson said, because officials didn’t have enough time to plan for the shift and didn’t want to undercut investments they have made in prior years, including a promise last year to fund librarians and art and physical education teachers at every elementary school.

“Other school districts who have made this shift do it over two or three years,” she said, pledging to implement the new law more fully next year.

Education Committee Chairman David A. Catania (I-At Large), who wrote the new law on at-risk funding, pointed out that some relatively affluent schools are slated to see an increase in per-pupil funding next year while some high-poverty schools will see a decrease.

Anacostia High, for example, is expected to add nearly 100 students next year, but its budget would shrink. “It seems anathema to what we’re trying to do,” Catania said, adding that he will look for ways to add funds back to Anacostia.

Henderson said the school system expects to make major investments in improving high schools in fiscal 2016 after investing in elementary schools this year and middle schools next year.

She plans to reopen Spingarn High in Northeast as a vocational education hub that would offer courses in transportation, hospitality and information technology to students from the city’s traditional and charter high schools.

More than $60 million has been set aside to reopen Spingarn, but council members Monday expressed skepticism about that investment. Catania and David Grosso (I-At Large) both questioned whether it makes sense to open a new career-education center when so many other schools are desperate for renovation and many city high schools — including Phelps Architecture, Construction and Engineering next door to Spingarn — are half-empty.

“I just think maybe the timing is not right here,” Grosso said.

Council member Marion Barry (D-Ward 8) pressed Henderson to justify her decisions to strip some schools of expected renovation dollars, including Johnson Middle School in Southeast, which lost $11 million in next year’s budget.

Henderson said she needed to balance the budget because of the rising cost of construction projects at some schools and overcrowding at others. Barry called that unacceptable, echoing parents who have complained that renovation decisions are unpredictable and seem politically motivated.

“I disagree vigorously with balancing the budget for other schools on the back of schools in Ward 8,” Barry said, pledging to fight to restore Johnson’s funds.

Council members dwelled only briefly on proposals to overhaul school boundaries and student-assignment proposals, which have been controversial since Mayor Vincent C. Gray’s (D) administration released them early this month.

Catania pointed out that the proposals contemplate costly initiatives, such as several new middle schools, and asked why officials released the proposals without first analyzing the effect they would have on the school system’s budget and future enrollment.

Henderson is not in charge of the overhaul, which Deputy Mayor for Education Abigail Smith is leading. But Henderson said she believed the goal was to “figure out which were the ideas that resonate most with the community” and to enable a more focused analysis of those ideas.

“Doesn’t that seem a bit cart-before-the-horse?” said Catania, who has vowed not to adopt any of the proposals if he is elected in November. “None of these plans have any analysis nor are they sustainable from a financial perspective.”