Coloring Formulas for Growing Patterns

Recognition and extension of patterns is a recurrent theme in the algebra strand of Principles and Standards for School Mathematics (NCTM 2000). Work with repeating patterns begins as early as prekindergarten, with students learning to extend patterns. Later, they recognize that the same pattern may be shown in different ways, and they translate patterns from one form to another, for example, changing ABABAB to * ∧ * ∧ * ∧. Such pattern activities allow students to develop logical reasoning skills, make conjectures, and test their ideas about them. As children become older, work with repeating patterns continues; but experiences with growing patterns, in which each element of the pattern is an extension of previous elements, become increasingly important. Geometric growing patterns can often be translated into number relationships and can thus be used to introduce ideas related to functions. A common method of introducing