WASHINGTON (CNN) -- The official business of the 57th inauguration commenced on Sunday with President Barack Obama and Vice President Joe Biden completing their oaths of office, quietly satisfying the constitutional obligation to be sworn in on Jan. 20.

The presidential and vice presidential swearings-in took place a day before Obama and Biden take their public oaths at the Capitol in front of hundreds of thousands gathered on the National Mall.

Obama's swearing-in took place during a private ceremony in the White House's ornate Blue Room, where he was joined by his wife, Michelle, and his two daughters.

Chief Justice John Roberts administered the oath to Obama. Justice Sonia Sotomayor performed the honors for Biden at his home at the Naval Observatory in Washington.

Biden was sworn in under a painting by American artist N.C. Wyeth of Abraham Lincoln's second inaugural - an event remembered for the 16th president's solemn address.

That was hardly the mood Sunday at Biden's home, where the vice president's extended family and a few Cabinet officials gathered to watch the ceremony.

His son Beau - Delaware's attorney general - was there, as were his other children, Hunter and Ashley, and a smattering of Biden grandchildren.

He placed his hand on a massive Biden family Bible, held by his wife Jill, and repeated the oath.

Both Obama and Biden traveled to Arlington National Cemetery after Biden's swearing-in for a traditional wreath-laying ceremony.

And the president and his family attended services celebrating the Rev. Martin Luther King Jr. at Metropolitan African Methodist Episcopal Church, one of the most historic churches in Washington.

The tone of Obama's inaugural address Monday will be "hopeful," White House senior adviser David Plouffe said Sunday.

"What he's going to do is remind the country that our founding principles and values still can guide us in a changing and modern world," Plouffe said on CNN's "State of the Union."

"He's going to talk about the fact that our political system doesn't require us to resolve all of our disputes or settle all of our differences but it doesn't compel us to act where there shouldn't and is common ground," Plouffe added. "He's going to make that point very clearly."

Plouffe underscored that Obama's State of the Union address, to take place Feb. 12, will present a more specific "blueprint" of the next four years.

The nation's first African-American president will become only the 17th U.S. leader to deliver a second inaugural address, before he joins the traditional parade up Pennsylvania Avenue to the White House.

Organizers expect 800,000 people to attend Monday's public ceremony -- less than half of the estimated 1.8 million onlookers who crammed the National Mall in 2009.

The smaller crowd this time around reflects the reality of second-term presidencies, when the novelty and expectations of a new leader have been replaced with the familiarity and experiences of the first four years.

Inauguration activities kicked off on Saturday with Obama and first lady Michelle Obama and Biden and his wife, Jill Biden, leading volunteers across the country in National Day of Service Activities.

The Obamas joined in a project at Burrville Elementary School in Washington, aiding volunteers who were sprucing up furniture. Cameras at the school caught the president and first lady staining a bookcase.

The president told volunteers that his family would do volunteer projects on holidays. "So I was taught from a young age," he said, that volunteering "is really what America is all about."

The Bidens volunteered at the National Guard Armory in Washington, helping to put together care packages for service members deployed overseas. Biden's office said volunteers at the armory would produce 100,000 packages.

"We still have 68,000 troops in harm's way in some of the most godforsaken territory in the world," Biden said, adding that the military members can find comfort "knowing that we back home just remember, we know what's going on."

Chelsea Clinton, honorary chairwoman of the Day of Service, said at a kickoff event on the National Mall that Saturday was the 19th anniversary of the day her father, former President Bill Clinton, signed the bill that designated a National Day of Service to coincide with Martin Luther King Jr. Day, the federal holiday honoring the late civil rights leader.

"When he signed the bill, he reminded us of what Dr. King called life's most persistent and urgent question: What are you doing for others?" she said. "And in my family, the only wrong answer to that question is 'nothing.' "

Later Saturday, singer Katy Perry headlined a concert for children of military families and Washington schoolchildren, hosted by Michelle Obama and Jill Biden. Singer Usher and the cast of the TV show "Glee" were among others who performed.

The Saturday event was to recognize the sacrifices and "level of maturity that is required from military kids," the first lady said.

"It means always thinking about things that are so much bigger than yourself. It means growing up just a little faster and working just a little harder than other kids," she said. "And it means doing the greatest thing you can ever do with your life at such a young age, and that is to serve our country."

Sunday evening, the Obamas will watch Latino acts at "In Performance at the Kennedy Center," which is followed by the Let Freedom Ring concert. The Red, White and Blue Inaugural Ball and Hip-Hop Inaugural Ball are also scheduled in the capital.

The president will speak to donors at a candlelight celebration at the National Building Museum on Sunday night.

Monday's events will be downsized from Obama's first inauguration. After events in front of the Capitol, the Obamas and Bidens will lead the traditional parade down Pennsylvania Avenue to the White House. There are only two presidential balls this year, down from the 10 staged in 2009.

While the anticipated crowd for Monday's events is expected to be about half the size of the one that gathered four years ago, the temperature will be a bit higher than in 2009, when the high hovered around the freezing mark. While the early morning temperature this time will be in the 20s, the forecast calls for a high temperature in the upper 30s or low 40s. Still, organizers cautioned attendees to bundle up because they're likely to experience prolonged exposure to the cold as they watch the events and make their way to and from them.

CNN's Tom Cohen, Dana Davidsen, Brianna Keilar, Kevin Liptak, Dan Lothian and Gregory Wallace contributed to this report

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