Cindy and Bobby are still lost in the Grand Canyon and the family is still looking for them. Cindy blames Bobby for chasing the Indian boy. Then the boy himself reappears and introduces himself as Jimmy Pakaya. Jimmy knows where their camp is, but is reluctant to take them because he has run away from home. Eventually he does so when Cindy and Bobby promise to say nothing about him. They also promise to smuggle him some food when everyone is asleep.
Soon Cindy and Bobby have a joyful, tearful reunion with their family. Mike tells them not to go off again without company of an adult or their oldest siblings. This poses a problem for smuggling food to Jimmy, but Bobby has a plan. So Bobby and Cindy hide some food during a campfire song session and then smuggle it out to Jimmy while everyone is asleep. But they get caught by Greg and Peter, and then by Mike, and are forced to explain.
Mike has a talk with Jimmy. Jimmy says he ran away from home because he wants to be an astronaut and did not know how his grandfather, an Indian traditionalist, would take it. Mike tells Jimmy he is not giving his grandfather a fair chance and he should talk to him about his ambition to be an astronaut. He then lets Jimmy spend the night in their camp.
Next morning, they find Jimmy has disappeared. At first they think Jimmy has run off, but then they find him with his grandfather, Chief Eagle Cloud. Jimmy took Mike's advice and spoke to his grandfather. Chief Eagle Cloud tells Mike, "the foolishness of this child. He thinks because I speak of buffalo, I do not understand blastoff." In gratitude, Chief Eagle Cloud invites the Bradys to his village where they will be welcomed into his tribe and have "a groovy time."
At the ceremony, the Bradys receive Indian names:
Mike: Big Eagle of Large Nest
Carol: Yellow Flower with Many Petals
Greg: Stalking Wolf
Peter: Middle Buffalo (Peter does not like it)
Cindy: Wandering Blossom
Bobby: Little Bear Who Loses Way
Jan: Dove of Morning Light
Marcia: Willow Dancing in Wind
Alice: Squaw in Waiting.
When the Bradys go home, Bobby says they are now the Brady Braves.