“Project Almanac” is an agreeable and entertaining teen time-travel thriller that’s equal parts Ray Bradbury and John Hughes, as the five teen leads trample through the delicate space-time continuum in pursuit of riches, repair and romance.

Produced by Michael Bay and directed by Dean Israelite in his feature-length debut, the film’s big conceit is that we’re seeing footage shot by the characters throughout their adventures, a stylistic decision that ultimately distracts from the pleasures of the script and performances.

As the film begins, nerdy hero David Raskin (played with wit by Johnny Weston) has been accepted to MIT but can’t afford the tuition. While his mom talks about selling the family home, David rifles through the papers and gear his long-dead scientist father left in the attic for inspiration. He and his sister Chris (Virginia Gardner, “The Goldbergs”) find an old video camera with footage of David’s seventh birthday party — and it includes a brief glimpse of 17-year-old David.

Further investigation with the help of fellow tech-head Adam (Allen Evangelista, “The Secret Life of the American Teenager”) and the funny, flip Quinn (Sam Lerner, “Suburgatory”) leads to prototypes and blueprints hidden in the basement by David’s father. “I can’t build a time machine in my basement,” David sputters as the situation dawns on him. Alan re-frames the discussion: “Look at the tape. I think you already did.”

“Project Almanac” is delightfully self-aware, like when Quinn, breaking into his own house to test a little cause-and-effect high jinks, asks “Have any of you seen ‘Looper’?” Andrew Deutschman’s and Jason Pagan’s script is less like the time-travel classics it references — there’s also a touch of Shane Carruth’s brilliant “Primer” — and more like the recent “Final Destination” films.

Like that horror-thriller franchise, “Project Almanac” suggests it’s not smart to mess with the way things should be, especially after David starts going back in time again and again, first to win the heart of new-to-the-clique cool girl Jessie (Sofia Black-D’Elia, “Gossip Girl”) and then to correct all the damage his seemingly minor meddling has wreaked on the fragile fabric of reality. Even with all the teen angst and temporal alterations, the film stays fleet, funny and fast, especially as our leads figure out, through trial and error, how they can take advantage of their new abilities in ways large and small.

Israelite’s direction is good enough that you have to wonder how much better the film would have been if someone had let him shoot the film from a tripod. But you believe the cast as friends, and Weston (“Kelly & Cal,” “Chasing Mavericks”) is a great lead, giving a smart and emotionally aware performance that drives all of the film’s figure-eight looping through the past.