After starting a school sports day 30-meter dash Wednesday in Coventry, William told head teacher Gill Naylor, "I think George will be running faster than me very soon."
The prince, 32, gave out medals at the finishing line, jokingly telling the winner, "Love the shoes, seriously fast!" Posing for a group picture with the racers, he tried to put the kids at ease, teasing, "Look excited, be happy!" And when they raised their arms and gave a smile, William said, "That's better!"
Naylor told PEOPLE, "He was lovely with the children, really friendly and charming."
In honor of the little prince's first birthday next week, Earlsdon Primary School created a special, slightly larger replica of the medals the children received for their races.
William also accepted a plaque custom-made by an artistic teacher and decorated with "GEORGE" spelled out in Scrabble letters.
The gifts came after he gave an update on his son to two of the hundreds of fans lining the routes around the War Memorial Park. Sisters Mavis Jarvis, 74, and Mary Jarvis, 72, from Leicester quizzed him about George.
"We asked him straight away about the baby and he said it's his birthday next week," Mavis told reporters. "He said George is charging around and opens doors. He said he's lovely. We told William, 'You're lovely too.' "
As he mingled with the crowds, William pondered his own childhood memories. Speaking to 90-year-old Freda Jones, who had witnessed the opening of the park in 1927 when she was just 3, he said, "I often think back and wonder what was my earliest recognition and how young I was when I did it."
William patiently held Jones's hand as she showed him a poignant black-and-white picture of her father, Arthur Russell, a regimental sergeant major in the Royal Warwickshire regiment, with Field Marshall Sir Douglas Haig, who opened the park.
"He told me it was a great piece of history," Jones told PEOPLE.
The duke, who took the train to Coventry while wife Kate stayed at home with George, also laid a wreath at the park's war memorial and joined children from Howse Primary School planting poppy seeds near the children's play area.
Imogen Hastings, 11, told PEOPLE: "He was saying he wanted to play in the playground as he really liked it. He wanted to go in the water and said he'd come in his trunks next time."
William was also serenaded by a class of Stivichall Primary School children, who had composed a special song. He grinned as they chanted:
"W.I.L.L. Duke of Cambridge.
"Shake his hand, he's the man.
"He said it might not get to number one, but it was a really good song," one student, Matthew Askew, 11, told PEOPLE. "We told him we are doing a Shakespeare production and changed the song for him."
In something of a theme on these recent walkabouts, William was given (and made sure to wear immediately) an elasticated "loom band."
"I gave it to him and he said he's got about 200 at home," said Tamara, 11, from nearby Whitley Abbey Primary School.
"As someone who has always enjoyed sport, and now as a new father, I appreciate the importance of allowing our children the freedom to experience outdoor space," he wrote.
"And not just children – adults benefit just as much, for a stroll, to walk the dog, to exercise or just to get some fresh air. Outdoor space is more than a nice-to-have for every community – it is an inalienable part of living well."