Question

Why do you think Walter gives Travis the 50 cents?

Answer 1

   The choice Walter makes to give Travis more money than he needs for school has bearing on Walter's character and also serves to subtly imply his state of desperation.  

   Walter does not like his job as a chauffeur. He feels that it is beneath him to serve someone else in this capacity. He also does not get paid very well. Both of these circumstances make Walter's sense of his own position rather painful, especially in relation to his son.  

   He yearns deeply to change his position. He is willing to act recklessly to change things, as we see Walter's choice to give Travis extra money. In doing this Walter makes a play to change himself in his son's eyes at least, asserting his manhood at the same time.  

   In summation, Walter gives Travis more money than he needs as a demonstration of his feelings, his rather desperate need to find a position of greater pride and dignity.  

Hope this helps! ;)