Near the end of the episode, Chief Eagle Cloud gives each Brady an Indian name:
Mike: Big Eagle of Large Nest
Carol: Yellow Flower with Many Petals
Greg: Stalking Wolf
Peter: Middle Buffalo and as a second choice Sleeping Lizard
Cindy: Wandering Blossom
Bobby: Little Bear Who Loses Way
Jan: Dove of the Morning Light
Marcia: Willow Dancing in Wind
Alice: Squaw in Waiting
Cindy: (in leaving Grand Canyon)Do you remember us? We're the Brady family.
Bobby: You mean we used to be, now we're the Brady Braves.
Alice makes an ironic reference to real-life Jay Silverheels, when she says, as she goes to get water "If I happen to bump into Tonto"
Jay Silverheels is best known as Tonto in The Lone Ranger.