Number Patterns from Digit Sums

L/iscovery can be an important process in elementary mathematics education. The unit described here encourages self-discovery and allows the student to occasionally make a discovery that is new even to the teacher. All that the unit requires is a pencil, some paper, a creative imagination, and a "Let's see what would happen if . . ." attitude toward the problem. It is based on the concept of the digit sums of numbers, specifically of sets of numbers that have a pattern linking them together. The topic of digit sums (or digital roots) is an old one, sometimes referred to as "casting out nines," that is experiencing a revival in many textbooks. The topic is simple enough for elementary school children to handle with ease (this article is based upon experiences with fourth-grade children), yet it is one that appears in advanced-level number theory. The ideas are more than mere curiosities.