Your test scores are strong and in the range for all the schools you listed, however they are all very competitive. I expect your breakdown of scores to show mastery in Math as a perfect score would complement your choice of engineering. Your EC’s are subpar and less than stellar however, so I hope your essays are very strong as well as your rec’s!
Purdue: Low Reach
Georgia Tech: Match
MIT: Reach, only person I ever knew that got in got perfect test scores, gpa, and was the president of the math honor society chapter for the entire state of Florida…
UChicago: Reach-Low Reach
I think you should apply and see what you get! You have a shot at all of these.
please chance back? 
http://talk.collegeconfidential.com/what-my-chances/1727267-homeless-to-harvard-chance-me-chance-back.html?new=1