Kate Middletonis keeping her children top of mind.

The new Princess of Wales, 40,stepped out in SandringhamThursday with her husbandPrince Williamto tour tributes left inQueen 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, andPrince Louis, 4 — are adjusting toLambrook School, where they enrolled asfirst-time pupilsjust last week.

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 anorientation daywith their parents at their new school in Windsor on September 7.

kate middleton

On September 8, their first day of the term, Buckingham Palace announced that their great-grandmother “peacefully” died at age 96 at her belovedBalmoral Castlein Scotland, after her doctors said they were “concerned” for her health.

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

Prince George, Princess Charlotte and Prince Louis, accompanied by their parents the Duke and Duchess of Cambridge, arrive for a settling in afternoon at Lambrook School, near Ascot in Berkshire

Prince Williamtraveled north to be with his family while mom Katestayed behind in Windsorto be there for their kids.

For more on the Royals, listen below to our daily podcast PEOPLE Every Day.

The senior royals have since stepped out for ceremonial events leading up to the Queen’sstate funeralon Monday, opening up in Sandringham about what that somber day might be like.

Prince William and Kate Middleton.Chris Jackson/Getty Images

Prince William, Prince of Wales and Catherine, Princess of Wales view floral tributes at Sandringham

“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.”

Catherine, Princess of Wales and Prince William, Prince of Wales view floral tributes at Sandringham

Prince William, Prince of Wales and Catherine, Princess of Wales view floral tributes at Sandringham

Can’t get enough ofPEOPLE’s Royals coverage?Sign up for our free Royals newsletterto get the latest updates onKate Middleton,Meghan Markleand more!

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

source: people.com