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So this happens sometimes at the movies: a film comes along and does things you’ve seen a hundred times before. You know you’re being worked over emotionally, with cinematic tricks and techniques that have been around forever. But the story soars anyway, and you walk out genuinely moved and entirely satisfied.

Such is the case with Gifted, the story of Mary, a seven-year-old math prodigy caught in a custody battle that will determine the trajectory of her life. Chris “Captain America” Evans plays Mary’s uncle and guardian, Frank, a former philosophy professor turned boat mechanic. Mary’s mother (Frank’s sister), a math prodigy herself, committed suicide just after Mary was born. The trauma sent Frank spiraling out of academia and into the bars and harbors of coastal Florida. (He’s the “damaged hot guy,” as one tavern admirer says.) Frank and Mary live in a trailer park, where Frank tries to provide his niece with a poor-but-normal, nongenius life.

This is going to be tricky, because Mary is a “one-in-a-billion” prodigy. When school officials flag her talent, her domineering grandmother (Lindsay Duncan) swoops down from Harvard, intent on taking custody and forcing Mary into the kind of suffocating childhood that killed her mom. It’s Little Man Tate dipped in Kramer vs. Kramer, but goddamn if it doesn’t work like magic.

It’s all about the performances. Evans is excellent, displaying depths unplumbed in his comic-book movies. Mckenna Grace, just ten years old, gives one of those impossibly good childhood performances that pop up with curious regularity. Octavia Spencer contributes powerful grace notes as Frank’s landlord, who loves the little girl deeply.

But the real revelation here is Jenny Slate as Mary’s grade school teacher and Frank’s inevitable love interest. As we saw in her feature debut, Obvious Child, Slate is an enormously compelling performer with astonishing range. Gifted maps some very complex emotional territory, and Slate’s empathetic performance is critical. Her eyes speak some language of the heart that’s a million years old.

The film occasionally wanders into contrivance, especially toward the end, but I was so deeply hooked by then that I was willing to forgive just about anything. Director Marc Webb (500 Days of Summer) is a born filmmaker. His movies have a natural narrative grace, and he’s a strong visual stylist, too. Gifted has a sunset that’s a sixty-second testament to the art of the moving picture. That thing needs to be in a gallery somewhere, on infinite loop. Gifted isn’t a particularly original film, but it’s heartfelt and accomplisheda very good story, very well told.

This article appeared in print with the headline “One in a Billion.”