Prince Harry chatted with a math class and competed in an obstacle course Saturday at a Harlem children's organization on Day 2 of his first official visit to the United States.

Harry visited a ninth-grade classroom at the Harlem's Children Zone, a community organization that offers families social and educational services, where 14 students were working on math in preparation for a Regents Exam.

"Who's the best pupil?" he asked the class and joked, "I was always the worst!"

Later, the 24-year-old prince competed in an obstacle course with the Prince Seesio of Lesotho, who co-founded Harry's Lesotho-based charity that aids the African country's impoverished children.

He lost the race but threw his arms in the air and yelled, "Yeah!" to the cheering kids.

The prince was to participate later Saturday in a polo match on Governors Island in New York Harbor, facing off against Argentine polo player and heartthrob Nacho Figueras.

It's fun with a serious purpose, however. The Veuve Cliquot Manhattan Polo Classic will benefit the U.S. arm of Harry's Lesotho-based charity, Sentebale, which aids the African country's impoverished children.

Harry — famed for his youthful, at times embarrassing, escapades — began his trip Friday with a prayerful stop at the site of the Sept. 11 terror attack. At the World Trade Center, he spent about 15 minutes quietly speaking to a half-dozen relatives of 9/11 victims.

Among them was Chip Callori, whose brother, Joseph Amatuccio, was killed. "It's a very kind gesture on his part — for him to realize that this is a sad but important part of our history," said Callori.

On a chain-link fence overlooking the Sept. 11 memorial under construction at ground zero, Harry attached a wreath of peonies and white and yellow roses. Standing alone, he bowed his head in silence for a few minutes.

A handwritten note on the wreath read: "In respectful memory of those who lost their lives on Sept. 11, 2001, and in admiration of the courage shown by the people of this great city on that day." It was signed, "Harry."

Harry walked along the southern perimeter of the 16-acre site, stopping to pore over rebuilding plans two officials showed him. He peppered officials with questions about the construction.

Officials of the Port Authority of New York and New Jersey have projected finishing dates for the memorial, a skyscraper and a transit hub between 2011 and 2014 but have no completion dates for four other office towers.

As he left the site, he said, "It's just fantastic to see what's going on and hopefully everyone will be happy with the results — I'm sure they will be."

At the firehouse across the street that houses Engine 10 and Ladder 10, which lost five members on Sept. 11, the prince shook hands with firefighters, then stepped in to admire their equipment as they talked and laughed.

Back on the street, Harry suddenly broke away from his security detail and turned the corner to see the side of the firehouse, which is graced by a bronze memorial to 343 firefighters killed at ground zero.

A few feet away, hundreds of people behind police barricades strained for a glimpse of smiling, red-haired Harry. His fun-loving, outgoing nature erupted as he strolled over to shake hands and chat.

The younger son of Prince Charles and the late Princess Diana is third in line to the British throne, after his father and older brother, William.

Early Friday afternoon, Harry formally named the British Memorial Garden in Hanover Square downtown to honor the 67 British victims of the terrorist attack. He helped plant a so-called "Elizabeth" magnolia tree as part of a New York program to plant 1 million trees in the city.

His father, Prince Charles, and stepmother, Camilla, dedicated the center stone of the garden in 2005 during their New York visit.

Later in the afternoon, Harry visited Manhattan's Veterans Affairs Medical Center, where he was greeted with loud applause and toured a clinic that treats veterans with post-traumatic stress disorder and its prosthetics facilities.

He shook hands with Paul Yarbrough, a double amputee with two prosthetic arms, and jokingly pretended his grip was too tight, crying out in pain. He then watched the 42-year-old Gulf War veteran pick up a bottle of orange Snapple and drink it.

Joining the prince there was a 21-year-old British soldier who lost both legs when he stepped on an anti-tank mine in Afghanistan last year, while Harry was commanding troops nearby.

Dubbed "the party prince," Harry is a much-watched member of the royal family, regularly making newspaper headlines with his romantic escapades and brushes with scandal. Several years ago, he apologized for wearing a Nazi swastika armband to a friend's costume party.