Number Patterns and Sequences

Behind every equation or function there is a situation, a table, and a graph... that's the "Rule of 4."  There is also a sequence, a pattern of values that we expect students to perceive and understand, sometimes without even realizing it.

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Many teachers nowadays use Visual Patterns to give students a fun, engaging, and accessible way to explore patterns of growth.  They learn to reason about growth and learn to use algebra to represent the patterns they see in the figures.  I want to collect some ideas for giving the students the same kind of accessibility to the next level of abstraction.  By working with sequences before they work with tables or graphs, students can focus on the patterns they see and reason about them.  They can explore and compare proportional, linear, and non-linear patterns; make predictions; and link them to algebraic functions and equations.  As a result, students can have a better understanding of the sequential patterns present in a graph or table, where the patterns are sometimes more subtle or obscured.