The key to learning to speak like a native is learning to open your ears to the sounds and rhythm of American English. As you tune your ear to the sounds of English you'll be better at pronouncing them correctly. 

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Listening Exercise #1:

Long /A/ vs short /e/

Paper - pepper

Wait - wet

Taste - test

Late - let

Waste - west

Listening Exercise #2: 

Short /o/ vs Short /u/

Hot - hut

Bought - but

Caught - cut

Lock - luck

Mom - mum

10 examples of words that are spelled different than they are pronounced.