On Friday, the Obamas had a surprise that was not on the agenda. They were greeted at the Diaoyutai State Guest House by Chinese President Xi Jinping.
Xi said he "cherishes the well-established good working relations and friendship" with the US president, according to a Chinese Foreign Ministry press release.
Xi also said he "has kept in close communication" with the White House through channels, including meetings and phone calls.
"I believe that through concerted efforts China-US relations will keep advancing to the goal of a new type of relationship between major nations," Xi said.
Much of the Friday trip was accompanied by China's First Lady Peng Liyuan, who had originally invited the Obama women on the trip.
Mrs Obama said she was amazed by China's culture when she tried her hand at Chinese calligraphy for the first time on Friday at the Second High School Affiliated to Beijing Normal University, which has a sister-school relationship with the Sidwell Friends School in Washington DC, where Malia and Sasha attend.
"I want to try again, it's beautiful," she said after writing the Chinese character 永 (yong), which means "forever".
Yang Jie, the class teacher, said ancient Chinese calligrapher Wang Xizhi spent decades writing the character.
"Mrs Obama has done very well for a beginner," Yang said.
At the school, Mrs Obama also observed a robotics class and played ping-pong with students, a scene reminding many of the 1971 ping-pong diplomacy visit when the American table tennis team was invited to China, ahead of the later historic ground-breaking trip by President Richard Nixon.
The Obama women were scheduled to visit the Terracotta Warriors Museum and the ancient City Wall in Xi'an in northwest China on Monday. They will then go to Chengdu in southwest China to visit another high school and a panda base before heading back to the US on Wednesday.
Contact the writers at chenweihua@chinadailyusa.com and zhaoshengnan@chinadaily.com.cn.