"...samples of growing pattern problems created by ED 556 students at Monmouth University in West Long Branch, NJ during the Fall 2004 session. In each case, students should draw and/or describe the next couple of stages in the pattern and create an input/output table to describe the relationship between the stage and the number of blocks used. Students should be challenged to write a rule in words and more capable students should be challenged to write a general mathematical rule that would calculate the number of blocks needed for any given stage."
Links are listed for on-line practice with function machines. They also recommend several children's books to introduce functions as growing patterns: Two of Everything, One Grain of Rice, The King's Chessboard. (Also see pdf files and lesson plans available for the books.)