Riding the heels of an announcement that New York City will move more quickly to make free preschool available to all 3-year-olds, Mayor Bill de Blasio on Friday visited a “3-K for All” classroom to encourage parents to sign up for the program.

Applications open Monday for 3-K sites in the four districts that currently offer the program. Those are District 7 in the South Bronx and District 23 in Brooklyn, which opened last year; and District 4 in Manhattan and District 27 in Queens, which are new this year.

This week, the mayor announced the city would expand 3-K ahead of schedule in four additional school districts. The $46 million expansion will begin in April, when applications open for District 5 in Harlem Manhattan and District 16 in Bedford Stuyvesant, Brooklyn.

The program builds on the mayor’s signature education achievement, free pre-K for all 4-year-olds. De Blasio has called early childhood education a game changer for families, who save money on childcare, and an educational boost for students who might otherwise stay at home.

We’ve really devoted ourselves in the next four years to creating a city that becomes more and more fair for everyone,” de Blasio said Friday, when he visited a bustling 3-K classroom at P.S./I.S. 323 in Brownsville. “This is one of the most basic ways we can do that – that every 3-year-old get the same strong start, and that it is universal, and it is free.”

During the mayor’s visit, 3-K teacher Carine Bruny said her students would be “pros” by the time it came to start kindergarten. As they stacked blocks and cooked imaginary meals in the classroom kitchen Friday, they were also learning how to work together, Bruny said.

Throughout the day, she encourages her young students to share what they’ve done and how they feel.

“They are expanding their language skills from one-word responses — or no response at all — to sentences,” she said.

While the city was able to launch the program for 4-year-olds, dubbed Pre-K for All, at lightning speed, it will take longer to extend free preschool to younger students. Constrained by space and funding, the city has started offering 3-K in mostly high-needs districts — though de Blasio says he hopes to make it available across the city.

The programs are open to families regardless of where they live, but some give priority to those who live in the district.

By next year, city officials expect to serve 5,000 3-K students. They hope to make it available across the city by 2021, with spots for more than 60,000 3-year-olds.

But, with an estimated price tag of more than $1 billion, that will require an influx of about $700 million from outside sources at a time when the city faces budget threats from both Washington, D.C. and Albany.