It may be best to identify the play's conflicts here as these represent the narrative threads that culminate in the play's climax where they are (mostly) concluded.
There are several minor conflicts in the play, though each is important to the characters and to the thematic content of the play. These minor conflicts include Ruth's pregnancy (Will she keep the baby or not?), Beneatha's relationships with Murchison and Asagai (Will she choose assimilationist ambition or Pan-African seperatism?), and Walter's plan to open a liquor store.
Each of these conflcts drive the action of the play and contribute to the play's larger conflict, which is essentially defined by the question of what will happen to the family and symbolized by the house that Mama buys in the Caucasian neighborhood. Will they move (and stay together) or will they fail to grow and change positively together and, in so failing, fall apart?
The rising action then will include conversations on each of these topics and the play's climax comes in the moment of decision when Walter stands up to Linder and defies him, saying that the family will be moving into the new house. Walter fulfills Mama's earlier exhortation here to "be the head of this family from now on like you supposed to be."
The rising action in the play A Raisin In The Sun begins with the exposition of the family receiving an Insurance Check and Ruth finding out she is pregnant. After receiving the check mama makes a downpayment on a house in a new neighborhood and decides to give Walter the rest of the money to invest in the liquor store. Mama's only request is that he puts 3,000 dollars in the bank for Beneatha's medical school.
The falling action begins when Walter refuses Mr. Lindner's offer not to move into the new house in Clybourne Park and Mama states "he finally came into his manhood today, didn't he"? Beneatha also finds new strength from Asagai.