Identify and discuss the sports played by the rich, the middle class, and the working class.What role did women's sports play in each of these...

Depending on which country you mean, the answer could vary a bit, but the theme is the same.  Cricket, polo, tennis and golf are commonly played sports among the elite in English speaking countries, and among the Ivy League universities in the United States.  Golf in the US in particular was played at clubs that, since they were private, could exclude people on the basis of race, religion or class.

For people in poverty, Football (soccer) is still very common in the greater Colonial World in Africa, the Middle East and Latin America.  Baseball in the US was often stickball, because all you needed was a stick and a ball of twine, with coats or shirts for bases.  You could play it in the streets of major cities or in the rural countryside of Kansas or Texas.  This is how it became the national pastime in America.

Womens' sports in the US came much later on an organized level, really only coming into their own in the 1970s and 80s, after Supreme Court rulings and government regulations opened up women's sports at the public school and university levels.