In an ordered pair, the two terms have a defined relationship. If that relationship is known, a missing element can be determined or additional ordered pairs belonging to the same set can be generated. Please try the following. It is common for one pattern in mathematics to give rise to other patterns. As a result, patterns form a rich resource for independent investigations driven by student interest.
Patterns occur in an endless number of contexts throughout mathematics.
All employ basic skills in various ways and often in unusual combinations, providing for extensive and meaningful utilization. The following will appear as an activity for students in the next issue of AIMS but is previewed in the event the reader wishes to pick up the challenge. Since it is an original investigation of this writer, there is no algorithm or known path to guide the reader. This arrangement was studied for a pattern. Hopefully, the reader will have the same experience.