Taxis honk their horns, buses roar down Broadway, and, on 46th Street, the whir of a cement mixer adds to the urban symphony as crowds line up outside the Richard Rodgers Theatre for the Wednesday matinee of “Hamilton: An American Musical.”

It’s crowded, noisy and chaotic.

And then Bay Shore High School arrives.

“Here they come,” calls out one of the security guards outside the theater, as the first of 11 Hampton Jitney buses makes a slow turn off Eighth Avenue, around 1 p.m. Over the next half-hour, 487 students and 65 chaperones are disgorged onto the already teeming streets, to attend the March 30 afternoon performance of “Hamilton.”

Those already lined up for the show — the hottest ticket on Broadway in years — watch the unfolding scene. “This must be the field trip of a lifetime,” says Ray Olszewski of Columbia, South Carolina, who has brought has 15-year-old daughter Maggie here to see “Hamilton.”

The presence of most of Bay Shore High School’s junior class here is the culmination of a yearlong effort by both the school and the community to give students not only an opportunity to see a Broadway show, but to learn the lessons of American history that “Hamilton” famously and hip-hop-ingly teaches.

The woman behind it all looks slightly stunned as the students are ushered into the theater. “Right now, I’m just glad we managed to get all the buses crosstown,” laughs Susan Barbash, the head of the Bay Shore Schools Arts Education Fund. It was Barbash’s inspiration, after seeing “Hamilton” during its pre-Broadway run in February, 2015 to organize this juggernaut. She bought the tickets for the March 30 performance last summer, and led the effort that raised $85,000 to pay for the trip.

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“I’m excited that all the students were able to attend,” Barbash said. “Not just the honors kids, not just the drama kids.”

Kids like Briona Copes, 17, a junior. “I’m actually really very excited,” she said, in the lobby of the theater.

“The anticipation for this is remarkable,” said Zander Pacella, 17, one of the Bay Shore seniors who was able to get a ticket. Pacella, who is involved with theater at the high school, knows about “Hamilton” and its charismatic creator, Lin-Manuel Miranda. “His writing is very different than anything that’s been done in musical theater,” he said. “I think students will really like this.”

One disappointment: A few days before the show, it was announced that Miranda was on vacation and that understudy Javier Muñoz would play Hamilton — something he did for one of the performances President Barack Obama attended, so you know he’s no slouch in the role (he also appreciated Bay Shore’s presence, as the actor “liked” a number of tweets posted by the school in the days leading up to the March 30 show).

The Bay Shore contingent made up nearly half of the 1,321 seats in the theater: Among those in attendance was Barbash’s mother, Lillian. In 1995, she and her late husband Maurice helped organize a similar trip for both the junior and senior classes of Bay Shore High to see the Broadway show “Having Our Say.” She pronounced herself “delighted” at what was transpiring in 2016 thanks to her daughter’s efforts, and added: “What we did 20 years ago was nothing like this.”

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That’s because the “Hamilton” project involved a great deal of integration into the social studies, English and arts curriculum: As part of their American history studies this year, Bay Shore students have read excerpts from Ron Chernow’s 2004 biography of Alexander Hamilton that forms the basis of the show. They’ve studied the life of the orphaned Caribbean immigrant who became one of the key figures in the American Revolution and the founding of the republic — before his untimely death in a duel with lifelong nemesis Aaron Burr.

So when, at the very start of the show, Burr (Leslie Odom Jr.) raps about Hamilton — “How does a bastard, orphan, son of a whore and a Scotsman, dropped in the middle of a forgotten spot in the Caribbean by Providence, impoverished, in squalor, grow up to be a hero and a scholar?” — the Bay Shore students know the answer.

And yet, even though they were familiar with Hamilton’s rags-to-riches story, and its tragic conclusion, the show’s magic seemed to overwhelm them by the end.

“It was amazing,” said Chloe Golde, a 16-year-old junior. “I cried.”

“I wasn’t expecting it to be as good as it was,” said junior Dejon Moore, also 16.

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Afterward, six members of the cast — including Muñoz — came out for what on Broadway is called a “talk back” — an opportunity for the actors to speak to the audience. The performers answered questions that had been submitted in advance by the 13-member student committee (that included Golde and Moore). One question was: “What kind of student were you in high school?”

“A theater nerd,” said Jonathan Groff, who plays King George III.

“I got into trouble a lot,” admitted Okieriete Onaodowan, who plays both James Madison and the obscure (but real) tailor-soldier-spy Hercules Mulligan. But, said Onaodowan, when he realized “they always need dudes in plays,” he discovered theater.

“I was a good student, I think,” said Daveed Diggs (Marquis de Lafayette and Thomas Jefferson), whose very appearance prompted squeals from many of the girls in attendance. “I found it hard to learn things the way people wanted me to learn.”

In a sense that was the whole point of Bay Shore’s “year of Hamilton.” This was an exciting, new way to learn about an old story: In class the next few days, the students would discuss the show and debate the question of whether Hamilton was the most important founding father.

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“I already thought he was,” said Abby Cervera, 16, a junior. “Seeing the show just drove the point home.”

And so at the very end of “Hamilton,” as the lives of these distant but now vivid historical figures are recounted, and Odom plaintively sings, “But when you’re gone, who remembers your name? Who keeps your flame? Who tells your story?,” the Bay Shore students again know the answer.

They will.