This exploration for preservice teachers, looks at how the lengths of the sides of rectangles with equal areas are related. The rectangles are constructed so that one vertex is at the origin. The path of the opposite vertex is an example of indirect variation and demonstrates a connection between algebra and geometry. The sketches for this activity are designed to quickly give an introduction to how TI-NSpire can be used to view data in multiple representations.

Review the Instructor and Student note PDF files. Make copies of the student activity file for your class. Transfer the TNS file to the NSpire handhelds using unit-to-unit cables or Connect to Class.

Students will explore the path of the corner of a family of rectangles with equal area are related.
* They will use the locus feature to view the path.
* Data will be collected in a spreadsheet and displayed as a scatter plot.
*An equation for the relationship will be found.
Students will then complete a similar activity on triangles.

Students are not required to complete any constructions in this activity. If the students are familiar with the construction features, a nice extension would be to have students construct their own families of polygons for exploration.
Follow up questions for the preservice teachers are included in the student activity file. A reading on multiple representations of data is also included. (a link is provided to the article)