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11. Graph and Guess My Rule:
Analyzing patterns with a graphing calculator

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	SREB Readiness Indicator Represent, analyze, extend and generalize a variety of patterns. > Additional indicators
	Skills Complete and extend geometric and numeric patterns Analyze and create rules from patterns Write pattern rules as algebraic statements Use multiple representations for relationships found in patterns
	Figure 1: Graphing calculators

Overview

Students use a graphing calculator (Figure 1) to record and explore geometric patterns. Using the table function of the calculator in conjunction with the graphing function, students are asked to find an equation that expresses the pattern of growth they observe in a geometric model. They then use the graphing calculator to verify that the equation they recorded can be used to extend the pattern to find any term.

The Value of This Technology

The graphing calculator is a welcome partner in the investigation of geometric patterns. It eliminates the time-consuming task of graphing multiple lines with pencil and paper and allows students to extend, analyze, and generalize a great many patterns in a short period of time. With the graphing calculator, the student can immediately see how a change in an equation affects its graph, encouraging the kind of experimentation that is essential in developing an understanding of the relationships between the equation and the graph.

Look in the Classroom

The students in Ms. Zeno's class have been working with patterns by expressing the relationships in a table and then trying to "guess the rule" for the relationships they see.
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