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The pair appeared cheerful as they walked towards the school, where they met with pupils ahead of a talk with experts on early childhood education.
After a few minutes of private chat, the two donned their masks and headed into a classroom at Connor Downs Academy in Hayle.
They were greeted by silence among pupils. "They're scared to death," Dr Biden joked of the children as Kate remarked it was "the quietest class" she had ever visited.
America's First Lady said "these kids are so smart" as she sat with pupils who appeared to be learning maths.
Dr Biden is herself a teacher, albeit of rather older students at a community college in the US. Asked by reporters about the significance of early years education, she replied: "It's very important.
"It's the foundation of everything. So I can tell you as a teacher at the upper levels, if they don't have a good foundation they fall so far behind.
"So this is amazing to see what these children are doing, and how far advanced they are at four and five years old!"
At one point, Dr Biden and Kate sat next to one another as pupils read from the book Greta and the Giant.
"Do you know this book?" Kate asked Dr Biden of the Greta Thunberg-inspired story.
“I know Greta of course,” the First Lady said.
The pair were also shown how the children care for rescue rabbits kept at the school. Dr Biden carried a bowl of carrots when they went outside to see the bunnies.
Head teacher Janice Eddy told reporters ahead of the visit that the animals help children to learn about empathy. The school also has an outdoor classroom and a pond, she said.
Connor Downs Academy is a "trauma-informed school", meaning it is able to support children who have experienced trauma in their lives.
Ms Eddy said the school is "very much about nurturing the child as a person" and "supporting their positive relationships with one another with adults with society and also supporting their mental health."
The children had been taught about the White House and were "quite aware of who's coming", Ms Eddy said. "And obviously incredibly excited in the way that a four or five year old can be. Perhaps not completely understanding."
After meeting with pupils, the First Lady and the Duchess co-chaired a round-table discussion with experts in early years education from both the UK and US, with some appearing by video link.