Julianne Moore, Dr. Delaney Gracy and Khaliyah, age 5, tour a Children's Health Fund mobile medical clinic
Mark Von Holden/Wireimage
08/22/2014 AT 06:45 PM EDT
While growing up in a famous household sometimes equals a sense of entitlement, that's not the case for Julianne Moore
"We talk about how lucky we are as a family to have what we need, that the kids are able to go to grade school and whenever we need to go to the doctor, we can go to the doctor," the actress tells PEOPLE of her kids Caleb, 16, and Liv, 12, with director husband Bart Freundlich.
"They have lots of opportunities, and they're aware that they're lucky that way," she says, adding that they already have a feel for philanthropy. "We do talk about giving back or giving to charity or what it means to be less fortunate – they're aware of everything."
One cause close to the four-time Oscar nominee's heart: the Children's Health Fund
, which she helps with fundraising.
"They are amazing," Moore, 53, says of the organization, which provides health care to underserved children in New York City and across the country. "I was really impressed with how practical Irwin [Redlener, co-founder] and Karen [Redlener, executive director] have been with their pursuit in giving everybody an equal shot in life."
In addition to backing pediatric programs and educating the public, the Children's Health Fund uses mobile care units that visit underserved areas.
"We're supposed to be able to have our opportunities in front of us," Moore says. "They're trying, in a sense, to level the playing field and give these kids a real opportunity."
Last year on Sept. 11, Moore volunteered for the Cantor Fitzgerald Relief Fund
and asked for donations to go to CHF. (Every 9/11, Cantor, which lost 658 employees that day, designates all brokers' commissions be donated to various charities, including CHF. )
Moore, a New York mom, says supporting Cantor's efforts "is a wonderful way to support the people that need it and honor those who died in a positive way." (The public can also donate to the fund.)
Reporting by LIZ McNEIL