Kate Middleton Gets 'Broody' on Outing with Baby — and Prince William Has Something to Say About It!

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Jane Barlow - WPA Pool/Getty Kate Middleton

Kate Middleton and Prince William's first stop in Scotland may have stirred up some maternal instincts!

The couple kicked off their visit to Scotland on Wednesday by visiting St. John's Primary School, where young students are learning about empathy by observing an infant — A.K.A. their "tiny teacher," Saul!

"Can you get my wife out of here before she gets broody?" Prince William, 39, joked about Kate, 40.

It seems William was right to worry — before the end of their visit, Kate was holding 10-month-old Saul in her lap as they looked through a book.

RELATED: Kate Middleton and Prince William Are in Scotland! Why Their Royal Titles Change When They're in the Country

The Duchess of Cambridge with P3 pupils during a visit to St. John's Primary School, Port Glasgow
The Duchess of Cambridge with P3 pupils during a visit to St. John's Primary School, Port Glasgow

Alamy Stock Photo Prince William and Kate Middleton

While the couple is parents of three — Prince George, 8, Princess Charlotte, 7, and Prince Louis, 4 — Kate has hinted that she is sometimes tempted to have another little one — especially when she's on outings with children. Kate has made early childhood development one of the key causes in her royal work and constantly being around babies has become an occupational hazard!

On the first day of her solo royal tour in Denmark in February, Kate met with parents and their babies during a visit to the University of Copenhagen.

"It makes me very broody," Kate shared. "William always worries about me meeting under one-year-olds. I come home saying, 'Let's have another one.' "

The Duchess of Cambridge with P3 pupils during a visit to St. John's Primary School, Port Glasgow
The Duchess of Cambridge with P3 pupils during a visit to St. John's Primary School, Port Glasgow

Alamy Stock Photo Kate Middleton

Prince William also joked about the prospect of Kate wanting another baby in January during the couple's visit to Lancashire.

While taking photos with some families, the couple met Trudi and Alastair Barrie and their daughter, Anastasia. Kate held the baby girl as they posed for a photo, causing onlookers to coo and prompting Prince William to joke, "Don't give my wife any more ideas!"

As Kate handed the baby back to her parents, William quipped, "Don't take her with you."

Kate's jewelry choices may also hint that their family is complete with their three children — as she has several necklaces featuring the trio's initials.

Prince William speaks to Olivia Wilson, two, during a visit to the Wheatley Group in Glasgow, to hear about the challenges of homelessness in Scotland
Prince William speaks to Olivia Wilson, two, during a visit to the Wheatley Group in Glasgow, to hear about the challenges of homelessness in Scotland

Andrew Milligan/WPA Pool/Shutterstock Prince William

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During the school visit, the Duke and Duchess of Cambridge (who are known as the Earl and Countess of Strathearn when in Scotland) joined the children in sitting on the floor to watch baby Saul crawl around. The Roots of Empathy classroom program sees infants taken to visit elementary schools on a regular basis in order to allow the school children to observe the infants' development and emotions.

"Do you think lots of schools should have a project like this?" Kate asked the students. When they replied in agreement, she added, "We do too."