Prekindergarten student Devonte Berry, 4, leads his class in an alphabet song at Aiton Elementary School in Washington, D.C., in 2015. (Erin Schaff for The Washington Post)

New York City Mayor Bill de Blasio announced Monday that his administration will soon launch an effort to provide free, full-day prekindergarten programs for all 3-year-olds in the city by 2021.

The plan, which starts in the fall, calls for expanding Pre-K for All, a de Blasio program that is free for families and through which the city more than tripled the number of 4-year-olds in high-quality full-day prekindergarten.

The administration projects that by the end of fiscal 2021, the city will spend $177 million on the project, but more than triple that amount will have to come from the state and federal government.

Given that the Trump administration has not made universal prekindergarten a priority and has proposed cutting the U.S. Education Department budget by some 14 percent, it is not clear whether or how much the city can expect to get from the federal government. De Blasio acknowledged in an announcement speech Monday that the funding is not settled. “This is going to be a game-changer, but it’s also going to be hard to do,” he said.

De Blasio said in a statement:

“The research is clear — investment in early-childhood education reaps benefits for students, families and communities for years to come. Using the successful model we developed for Pre-K for All, we are doubling down with free, full-day, high-quality 3-K for All for our three-year-olds. This extra year of education will provide our children with a level of academic and social development that they cannot get later on, while at the same time, alleviating some of the strain New York City’s working families face today.”

The program will launch in two districts in the fall, one in Brooklyn’s Brownsville section and the other in the South Bronx — at a cost of $16 million for the first year, the administration said. It will expand to other districts in future years.

Universal prekindergarten was a priority of the second term of the Obama administration, although there was relatively little federal education funding for investment. Few places in the country offer free preschool for 3- and 4-year-olds; one of those that does is Washington, D.C. Most preschool programs are aimed at 4-year-olds.

According to the Education Commission of the States in a January 2017 report:

In the 2016-17 budget year, 30 states increased funding levels for pre-K programs. Overall, state funding has increased by $480 million or 6.8 percent since 2015-16. Additionally, since Education Commission of the States began producing this report five years ago, states have increased funding to pre-K programs by 47 percent …

In 2016-17, six states (Idaho, Montana, New Hampshire, South Dakota, North Dakota and Wyoming) did not provide state funding for pre-K programs. Most of these states have attempted to secure funding for pre-K programs, but the proposals continue to be denied.