Growing patterns involve a progression from step to step which make them more difficult for students than repeating patterns. Students must determine what comes next and also begin the process of generalization, which leads to the foundation of algebraic reasoning. Students need experiences identifying what changes and what stays the same in a growing pattern. Growing patterns may be represented in various ways, including dot patterns, staircases, pictures, etc.
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Mathematical relationships exist in patterns. There are an infinite number of patterns.
Describe numerical and geometric patterns formed by using concrete materials and calculators.
Identify, create, describe, and extend patterns using concrete materials, number lines, tables, or pictures.
Students in grades three and four had experiences working with input/output tables to determine the rule or a missing value. Generalizing patterns to identify rules and applying rules builds the foundation for functional thinking. Sample input/output tables that require determination of the rule or missing terms can be found below: [Graphic cannot be reproduced].
The student will describe the relationship found in a number pattern and express the relationship.