The New York fifth-graders of Mad Hot Ballroom make their teachers cry. If you’re not careful, they’ll make you cry, too.

Students Jatnna, left, and Wilson practice their steps in Mad

This inspiring and almost entirely delightful documentary is about a great idea: teach public school kids to tango, rumba, foxtrot, merengue and swing dance. Grab children at an impressionable age, inner-city kids who could very easily go the wrong way, and turn them into little ladies and gentlemen.

It’s physical exercise, but it’s not PE. It teaches manners, how to interact with the opposite sex and physical grace. They learn “Cuban motion” and the dance “frame.” They learn discipline.

Marilyn Agrelo’s film follows three public schools in New York, from hip Tribeca, gritty Washington Heights and middle-class Bensonhurst, as these 10-, 11- and 12-year-olds – 6,000 of them from throughout the city – learn the moves and prepare for the big annual competition.

The teachers may say it’s not about “winning.” But they give themselves away.

“I want that trophy,” says Yomaira Reynoso, a charming but determined instructor at P.S. 115 in Washington Heights.

Agrelo’s film is at its best showing the mismatched couples. Girls, more confident at this age, often towering over the boys, sigh at the graceful moves of their dance-artist teaching assistants. The boys just blush and look at the floor and whisper about those aliens they have to hold hands with and lead in a foxtrot.

Over the course of a school year, the kids get better. The wallflowers come down off the walls. The poor English speakers learn the language through dancing.

And the kids learn a little boy-girl psychology. They bicker over who is more inept at this. They complain about the opposite sex. The mysteries of their gender counterparts are revealed in a pre-adolescent, non-threatening, non-dating environment. You start to see how any school could benefit from this.

New York City fifth-graders eye the trophies before the start of a ballroom dancing competition in the documentary, Mad

Agrelo wisely lets the kids and the teachers tell their own story. The editing seamlessly blends scenes and songs danced-to at the various classes.

But she focuses too much on the big city-wide dance-off. She introduces a villain school, from more affluent Queens, late in the game. But even those kids, habitual winners of the top prizes, are learning and benefiting from the drills of their no-nonsense teacher.

The kids are adorable, and so is the movie. You may not cha cha your way out of the theater. But you will want to drop in on that next PTA meeting to see what it takes for your child’s school to toss in a little ballroom in between bouts of dodgeball.