"George?" he'd say.
"Washington!" Sarah would say, followed years later by Lilly, Olivia and lastly, Willa.
"Cleveland!" his daughters would reply for the 22nd president of the United States.
Then would come the 23rd president, Benjamin Harrison, followed by "Grover?" again.
"Grover Cleveland, again!" they'd say, giggling, for the only president to serve two nonconsecutive terms.
As each daughter memorized the names of the presidents, always giggling at the 24th president's name, "I'd say 'Let's do a children's book' " about the presidents, Burns told CNN.
In the meantime, Burns made stunning documentaries about the national parks
, the Civil War, the Roosevelts and baseball that brought history to life on our television screens.
Thomas Jefferson, Abraham Lincoln, Theodore Roosevelt and Franklin Delano Roosevelt all featured prominently in his work, and he's met six presidents: Jimmy Carter, Ronald Reagan, George H.W. Bush, Bill Clinton, George W. Bush and Barack Obama.
"I'm one of those nerds of the history of the United States," Burns said. "I may be American history's biggest fan."
Decades later, Burns' oldest daughter, Sarah, is 33 and a mother herself. At last, Burns' first children's book, "Grover Cleveland, again!" is coming out in July.
Since we know Burns loves both the U.S. presidents and national parks, CNN asked him to help us commemorate the National Park Service turning 100 this year.
Burns picked the presidents who did the most to create and protect the nature and history cared for by the National Park Service.
Yosemite's presidential protector
For the very idea that some or part of our natural resources should be set aside for present and future generations, Burns thanks President Abraham Lincoln (1861-1865).
In the middle of the Civil War, with casualties mounting, President Abraham Lincoln signed legislation to set aside part of what is now Yosemite National Park, even though Lincoln had never seen it.
"The land was set aside not for kings or noblemen but for everybody else," said Burns.
"Americans love their manifest destiny," said Burns, referring to the 19th century belief that justified the United States' expansion across the continent. The congressional bill signed into law by Lincoln says, " 'but save a few places for everybody,' " Burns said.
Creator of the world's first national park
Before any member of Congress proposed creating the nation's first official national park at Yellowstone, the plan had been to set aside the land and give it to a state to protect, as had been done with Yosemite.
There was just one problem: Yellowstone was in three territories -- Wyoming, Idaho and Montana -- and none of them were states yet.
That's why President Ulysses S. Grant (1869 -1877) signed legislation that "created the world's first national park," said Burns.
Grand Canyon's ardent advocate
President Theodore Roosevelt
, who was known as the "conservation president," signed the 1906 Antiquities Act into law.
The act establishes that archeological sites on public lands are important public resources and authorizes the President to designate landmarks, structures and objects of historic or scientific interest as national monuments.
Roosevelt (1901-1909) used his authority to protect about 230 million acres of public land, including five national parks, through Congress, and eight national monuments, under the Antiquities Act.
Congress fought him on turning the Grand Canyon into a national park, so he named it a national monument under the Antiquities Act. (It became a national park in 1919.)
"Roosevelt was given one of greatest legislative gifts ever -- the Antiquities Act, which permitted him to set aside small parcels of public land for their scientific or historic value, " said Burns. "Being a naturalist, he was saving these places for all people for all time."
Launching the National Park Service
President Woodrow Wilson (1913-1921) is better known for helping create the Federal Reserve, signing the 19th Amendment granting women the right to vote (reversing his position), attempting to keep the United States out of World War I and trying to create a United Nations-like League of Nations.
But he also made a contribution to preservation.
On August 25, 1916, Wilson signed the Organic Act, the result of a decadeslong effort that created the National Park Service.
At the time of his signing the legislation, the new bureau took over the protection of the existing 14 national parks, 21 monuments, two reservations and those yet to be established.
In some ways, our modern national park service is based on Franklin D. Roosevelt, Burns said.
"What Roosevelt began to understand is that it's not just about protecting natural wonders or magnificent falls of Yosemite or the Grand Canyon or the diversity of the Everglades," he said. "It's also about social history."
Under Roosevelt (1933-1945), the park service took over the responsibility of the War Department's parks and monuments, the U.S. Forest Service's national monuments (and most monuments going forward) and the national capital parks.
Roosevelt also created the Civilian Conservation Corps, which during the heart of the Depression provided work developing national parks, forests, historic sites and other natural sites.
"As freedom evolves, so does the idea of the park service," said Burns.
Increasing access for the middle class
With the development of the national highway system under President Dwight D. Eisenhower (1953-1961), National Park Service sites were overwhelmed by visitors.
In 1956, National Park Service Director Conrad L. Wirth launched the "Mission 66" program to upgrade facilities and management by the park service's 50th anniversary in 1966. (By 1966, Lyndon Johnson was President.)
That's why many park service sites have visitor centers, hundreds of employee residences and employee training centers.
'We had grown up'
When Ken Burns starts talking about the national parks, he finds much to love about the presidents and the park sites they protected.
There are the bison that still exist because Yellowstone's protections saved them, said Burns, and the Everglades, which is one of the most diverse environments anywhere.
"It's the only place where alligators and crocodiles both exist, and there's such a diversity of plant and bird life," he said.
Burns also appreciates the National Park Service sites that remind us of our difficult and painful past.
Manzanar National Historic Site
, where many Japanese-Americans were interned during World War II, protected in 1992 under President George H.W. Bush is one of those sites.
So is the Little Rock Central High School Historic Site
, which was protected in 1998 under President Bill Clinton, and is still a working high school.
"I know of no country that has copied (that decision) to the extent we have, acknowledging all aspects of our complicated place in history," Burns said.