Kindergarten has come a long way, baby — too far, some say.

Way beyond the ABCs, crayons and building blocks, the city Department of Education now wants 4- and 5-year-olds to write “informative/explanatory reports” and demonstrate “algebraic thinking.”

Children who barely know how to write the alphabet or add 2 and 2 are expected to write topic sentences and use diagrams to illustrate math equations.

“For the most part, it’s way over their heads,” a Brooklyn teacher said. “It’s too much for them. They’re babies!”

In a kindergarten class in Red Hook, Brooklyn, three children broke down and sobbed on separate days last week, another teacher told The Post.

When one girl cried, “I can’t do it,” classmates rubbed her back, telling her, “That’s OK.”

“This is causing a lot of anxiety,” the teacher said. “Kindergarten should be happy and playful. It should be art and dancing and singing and learning how to take turns. Instead, it’s frustrating and disheartening.”

The city has adopted national standards called the Common Core, which dramatically raise the bar on what kids in grades K through 12 should know.

The jargon is new, too. Teachers rate each student’s performance as “novice,” “apprentice,” “practitioner” or “expert.”

Kindergartners are introduced to “informational texts” read aloud, such as “Garden Helpers,” a National Geographic tale about useful pests.

After three weeks, kids have to “write a book about what they’ve learned,” with a drawing and sentences explaining the topic.

In math, kids tackle concepts like “tally chart,” “combination,” and “commutative property,” DOE records show.

The big test: “Miguel has two shelves. Miguel has six books . . . How many different ways can Miguel put books on the two shelves? Show and tell how you know.”

An “expert” would draw a diagram with a key, show all five combinations, write number sentences for each equation, and explain his or her conclusions using math terms, the DOE says.

“A child who’s an ‘expert’ is more like a second-grader,” said Cathleen Vecchione, a kindergarten teacher at PS 257 in Williamsburg, Brooklyn.

“At this point, we’re not ready for it,” she said, noting delays caused by Hurricane Sandy.

The class has learned counting by 10s and up to 50 — but not yet gotten to addition.

“Miss Vee” asked her class to write the sentence, “I have a pet.” Kids struggled with putting letters on the line, spacing, and period placement. One wrote, ‘I. hav. a. pet.” Another wrote, “I wet. a pet.”

The “super challenging” demands leave less time for puzzles, coloring and games, she said.

DOE spokeswoman Erin Hughes said, “These are the types of activities and exercises that students need to work on to acquire the skills they need to be ready for middle school, high school, college and careers.”

But kindergarten, she added, should include a “wide range of activities, including free play.”