Kate Middleton Says George, Charlotte and Louis Are Making 'New Friends' at School

Kate Middleton is keeping her children top of mind.

The new Princess of Wales, 40, stepped out in Sandringham Thursday with her husband Prince William to tour tributes left in Queen Elizabeth's honor following the monarch's death last week. There, Princess Kate connected with the crowd gathered at the gates of Sandringham House and spoke about how their three kids — Prince George, 9, Princess Charlotte, 7, and Prince Louis, 4 — are adjusting to Lambrook School, where they enrolled as first-time pupils just last week.

"Kate said the children have settled in nicely with their new school and have new friends," Lydia Bailey, who lives nearby in Heacham, tells PEOPLE.

On the late monarch's legacy, she adds, "William said the Queen's values will continue for time to come."

George, Charlotte and Louis attended an orientation day with their parents at their new school in Windsor on September 7.

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On September 8, their first day of the term, Buckingham Palace announced that their great-grandmother "peacefully" died at age 96 at her beloved Balmoral Castle in Scotland, after her doctors said they were "concerned" for her health.

PA Prince George, Kate Middleton, Prince Louis, Prince William and Princess Charlotte

Prince William traveled north to be with his family while mom Kate stayed behind in Windsor to be there for their kids.

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The senior royals have since stepped out for ceremonial events leading up to the Queen's state funeral on Monday, opening up in Sandringham about what that somber day might be like.

Chris Jackson/Getty Images Prince William and Kate Middleton

"William said he thinks Monday will be hard," Bex Neeve, 44, from the county of Norfolk, tells PEOPLE. "Kate said it's been overwhelming and she and William are very grateful for everyone being here. She was emotional. They seemed like they were here to soak up all the love."

Her mother Sharon Clouting, 64, adds, "You can tell William is his mother's son. He was chatting so easily and very sincere."

Chris Jackson/Getty Images Prince William and Kate Middleton

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Sarah Tomlinson, 51, from the nearby town of Kings Lynn, came with her friend and the friend's baby.

"My friend's baby was the first jubilee baby to be born in Kings Lynn and named after Prince Louis," she says. "William came over and said how dashing he is in his outfit." The couple also "showed a real interest" in the baby and asked if he was sleeping through the night.

Chris Jackson/Getty Images Prince William and Kate Middleton

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"I can't believe how together they are — they seem to be supporting us rather than us supporting them," Tomlinson adds.