Goal
Students move from actual or physical experience with objects (variables), and their relationships (functions), toward a symbolic notion of the concepts.

Objectives

• Students see patterns when represented numerically
• Understand relationships between shapes and perimeter
• Describe the patterns of change among variables
• Call those patterns of change a function
Time
About an hour of direct instruction from the teacher followed by up to week of self-paced exploration and expansion of the initial idea by students.

Materials

Activity
Students rotate in groups through the following stations in order to gain more experience with relationships in the real world.

1. Length of the side of a square to number of squares: Squares from squares
2. Number of triangles to distance of perimeter: Row of triangles
3. Number of pentagons to distance of perimeter: Row of pentagons
Teacher models each station for the entire class.

Students make a T-Chart in each of their journals for each of the stations while gathering data.

Closure
Students respond to the following questions in their observation and reflection journals: What are the variables for each activity? What are the factors for each activity? What is the pattern or function (the rule you wrote) in each activity? What are some other patterns you noticed?

Assessment
Teacher reads and responds to journals in order to determine whether or not students are able to collect data in an organized way and if they are beginning to use the vocabulary in an accurate way. This is an opportunity for the teacher to catch misconceptions students may have and write questions to the students which may help eliminate those misconceptions.

Plan B
Students rotate one person at a time through the stations while others read silently if the groups do not work well together.

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