Are ‘such a piece’ and ‘at hand’ correctly used in the sentence? Should I say ‘instructed’ or ‘called,’ ‘from’ or ‘out of’?

Are ‘such a piece’ and ‘at hand’ correctly used in the sentence? Should I say ‘instructed’ or ‘called,’ ‘from’ or ‘out of’?

Mr. Parker handed pieces of paper to the students and asked each of them to get a piece, pass the other pieces, write his/her favorite word on such a piece, and drop it into the box at hand. Then, she (instructed, called) each of them to draw a piece of paper (from, out of) the box, read and explain the word written on it, and tell about his/her expectations of her as his/her teacher.