What do the motifs Colours, Violence, Race, and Sports have to do with Daisy Buchanan and Nick Carraway in The Great Gatsby?
For an examination of the way race factors into the novel, there is a scene early on when Nick first meets up with Tom and Daisy. During this afternoon tea, Tom encourages Nick to read a book about the advancement of the black race and the threat that it poses on American society. This was a time during which the Harlem Renaissance had begun to make Black artists, in particular, a household phenomenon. The music of the Jazz age comes from the African American tradition. Music permeates the novel because music permeated the era. It was acceptable to associate with black son that level, but not to allow them access into the social circle to which Daisy belongs and into which Nick skirted along the periphery.
Violence is most readily apparent in the scene during which Daisy strikes and kills Myrtle, but Nick is also exposed to violence when Gatsby takes him to meet with Meyer Wolfsheim and Wolfsheim relates the story of the man who is eating dinner, steps outside to "take care of something" and is shot dead. This, apparently, is not an uncommon occurrence if you are a part of the underground/bootleggers circle. Nick is shocked by this violence. Also, Nick is affected by violence when he goes with Tom to the city (when Tom takes Myrtle) and Tom ends up striking Myrtle for mentioning Daisy. Nick also sees the aftermath of violence both with Myrtle's death and Gatsby's death. Up until this particular summer, Nick had been sheltered from the violence that human kind is capable of, and seeing it up close changes him (as well as makes him decide that he wants no part of it). Daisy, on the other hand, is unaffected by the violence. She is a member of the rich - those who are untouchable and can break things only to rely on their wealth to get them out of trouble.
The best mention of color that I can think of immediately is the light that is at the end of the dock. Daisy is on one end of the light and Nick (as well as Gatsby) is on the other end. That green glow is significant - green is often associated with jealousy as well. Also, the color of the car is a factor. Tom is driving Gatsby's yellow car on the way in to town, but it is Daisy who is driving the car when Myrtle is killed. The yellow is what makes the car memorable.
Sports - Jordan is a golf player, and she is, in some ways, more defined by her sport than by anything else. She is a champion, a pro, and, as such, out of Nick's league. Tom plays polo. Nick is not a sports player at all. The other references to sport include the rigging of the world series by Wolfsheim.
I must admit I have some difficulty finding ways that the motifs of colours (without a very specific investigation of the text) race and sports have a great deal to do with Daisy and Nick. The violence one is also a tad difficult, but can possibly be explicated as follows:
Daisy is a person who practices violence on all the people around her but in a mental way rather than a physical one. She is willing to manipulate people to get whatever she wants, she will lie or lead anyone on and in the end destroys Gatsby by allowing him to take the fall for her crime.
Nick on the other hand in some ways is entirely free from the violence of the novel, mental or otherwise. You could likely make the argument that he is affected by it as the most astute observer of the action of the play. He is affected in terms of the impression he has and his emotional loss at the failure of Gatsby to find the success he is looking for.
But I will admit to finding it rather difficult to connect the other motifs, particularly sports. I will be curious to see how some others can connect that to the two characters.