Walter's dream is to be financially successful, which he hopes to accomplish through opening a liquor store with his friend Willy. He works as a chauffeur to wealthy people in Chicago and, at one point in the play, expresses a wish to be as rich as one of the men whom he chauffeurs and to have the money to put pearls around his wife Ruth's neck. There is a conflict between his materialism and doing what is sensible for his family. In other words, it was not at all sensible to trust Willy with half of the money from his father's insurance policy, and it was unfair to give Willy the money without consulting his family.
Beneatha's dreams are to become a doctor and to achieve a sense of identity that is rooted in Afro-centrism and burgeoning feminism. She does not embrace her mother's values (e.g., she is an atheist), but she is committed to her family's upward mobility, which she seeks through her education. Beneatha's American dream is, thus, rooted in individual freedom and self-definition.
Ruth's is a simpler woman than her husband and sister-in-law, and her dream relates to her own family values. She learns that she is pregnant and considers having an abortion to avoid the financial burden that another child would place on the family. When she learns that they may not be able to buy a house due to Walter's foolish scheme, she says that she will scrub every floor in town to ensure that her family gets out of the tenement. She seems to desire harmony within the family, as well as the prospect of a better life for her son, Travis. Her American dream is more rooted in the family.
Mama Younger's American dream is also rooted in family. She differs from her children due to her religious faith and her relative indifference toward materialism. Her wisdom and resourcefulness lead her to retain half of the money from the insurance policy to buy a house in Clybourne Park. The tree that she maintains throughout the play is symbolic of her hope that her family will one day have its own plot of land, a dream that her husband, who had worked himself to death, could never achieve during his lifetime.