In The Miracle Worker, what are things Helen does that demonstrate her intelligence and understanding of the world around her?

Helen cannot see or hear, but this does not make her unaware or unintelligent.  One day, her mother puts on her bonnet because she is going out.  Helen feels the bonnet on her mother's head and knows that she is about to leave the house.  She does not want her mother to go, and she tries to remove the bonnet.

When Miss Annie Sullivan arrives, she hands Helen a key.  The girl uses it to unlock Annie's suitcase.  Later, Helen locks Annie in her room and hides the door key.  It is later revealed that Helen hid the key in her mouth.  After Helen removes the key from inside her mouth, "she takes it in her fingers, stands thinking, gropes to the pump, lifts a loose board, drops the key into the well, and hugs herself gleefully" ("The Miracle Worker," Act One, Scene 8).  Helen is not pleased with Annie being in the house, so she locks the woman in her room and tries to remove any means of letting her out.