This month's Puzzle Corner deals with some common sequences, or ordered lists of related items. One of the first sequences students encounter in kindergarten is the alphabet. Mathematicians are interested in number sequences like the square numbers (1, 4, 9, 16, …...). Some sequences are finite and consist of a limited number of items. Other sequences go on forever and are infinite.The alphabet is an example of a finite sequence and the square numbers are an example of an infinite sequence.
In this activity five different sequences are presented—three are finite and two are infinite. If the first few words describing the items in each sequence were spelled out, the sequence would be instantly recognizable and could easily be completed (for a finite sequence) or extended (for an infinite sequence). What makes this Puzzle Corner challenging is that only the first letters of the words in each sequence are provided. Anyone attempting to solve the puzzles must figure out what common sequence is represented by each of the lists of letters. When the sequence is determined, the blanks can be filled in and the first few items in each sequence listed.
While this activity can be done in groups, it is preferable to have students work individually. This gives students a better chance of uncovering the hidden sequences for themselves. If students work in groups, the chance to experience the joy of discovery is often ruined by one member blurting out the answer before others have discovered it.
I have used activities like this one by introducing them to my class at the end of the math period on Mondays. I would ask students not to share their solutions with other students until Fridays, when we had a whole-class sharing session at the beginning of the math period. If students wanted individual confirmation before that time, they could share their solutions with me. I firmly believe that given enough time, most students will find at least a few of these solutions. When they do, they will experience a powerful sense of accomplishment and satisfaction.
I hope that you and your students enjoy these puzzlers.