“Hallo, this is Andrew Lloyd Webber,” the megahit composer’s voice says over the National Theatre’s sound system at the beginning of the musical “School of Rock.” Apparently everyone asks him whether the kids we will see onstage play their instruments live. “The answer,” Lloyd Webber assures us, “is an emphatic ‘Yes, they do.’ ”

That’s your reason to catch the show that wraps up a three-year Broadway run Sunday and that has a touring company at the National for the next week. It’s the 2003 Jack Black movie nicely expanded with new Lloyd Webber songs that remind us what a pop-rock creature he has always been. The show’s refrain, “Stick It to the Man,” gives the kids a striding, rebellious anthem to boing up and down to, and as they deliver buzzy guitar solos and bass lines thick as sequoias, these youngsters are irresistible.

That’s not to say that “School of Rock” has been converted into a musical for the ages. The comedy is too cartoonish, and the fingerprints of the merrily demented Jack Black are still all over the main role. Merritt David Janes has the rolled-out-of-bed look and the raspy pipes, but his Dewey — the slacker who bluffs his way into a substitute teacher position at a swanky elementary prep school — is so laid back and offhand that sometimes you miss the cool bond this dude is forming with the kids.

It’s a neat plot that’s kind of true: There are real Schools of Rock, thrusting electronic instruments into small hands to learn power chords and crunchy beats. The convergence of kid and adult, rock and by-the-book worlds makes this a perfect project for Lloyd Webber, who was a classically oriented, pop-smitten musical sensation himself as a child. His solid batch of new songs (alongside a handful of the movie’s tunes such as the terrific title anthem) includes the comic power ballad “I’m Too Hot for You,” sung by the band that kicks Dewey out for being an out-of-control soloist.

You also get a gloss of Mozart’s “Queen of the Night” from “The Magic Flute,” because for laughs, that’s how Lloyd Webber rolls. As a prep school survivor, he surely had fun concocting the prim, jerkily cadenced “Faculty Quadrille” for the addled teachers.

Still, it’s genuinely catchy numbers such as “You’re in the Band” that zip right up your spine with exuberant melody (and singable lyrics by Glenn Slater) as Dewey figures out which kids can play what. Leanne Parks plucks a bass that looks as tall as she is, and she sports a mean rock sneer. Mystic Inscho nimbly works his way up and down the guitar fretboard. Cameron Trueblood keeps a rock-steady beat on drums. Theo Mitchell-Penner plies the keyboard with Rick Wakeman flair.

Grier Burke earns her spot as lead singer, brassy Sami Bray nails her part as the class boss and band manager, and the entire gang is affecting as they sing “If Only You Would Listen” to their overcontrolling parents. There’s even a good power ballad for the strait-laced principal, sung with earthy feeling by Lexie Dorsett Sharp, and the comparatively simple show is staged without a lot of technical fuss by Laurence Connor. Really, you’re in this for the kids. The kids are alright.

School of Rock, music, Andrew Lloyd Webber; lyrics, Glenn Slater; book, Julian Fellowes. Directed by Laurence Connor. Scenic and costume design, Anna Louizos; lights, Natasha Katz; choreography, JoAnn M. Hunter; music director, Martyn Axe; sound design, Mick Potter. Through Jan. 27 at the National Theatre, 1321 Pennsylvania Ave. NW. $54-$204. 800-514-3849. thenationaldc.com.