The activity uses Cabri Jr. and TI-Navigator™ to explore the angle between the branches of an absolute value function. By the end of the activity, absolute value functions will be connected to trigonometry. This activity can be used in an algebra 2/pre-calculus course where students are already familiar with absolute value and trigonometric functions. It can also be used to introduce students to the connections between functions in an algebra 1 or geometry course.
Before the Activity
All of the student calculators need to be loaded with Cabri Jr.
TI-Smartview will work with this activity, but since Cabri Jr. is being used, a view screen is preferred. Also, load the activity settings into Navigator.
During the Activity
I have attached two documents to this activity. One of the documents gives the instructions for using TI-Navigator with this lesson. The second gives an option if you do not have TI-Navigator.
To begin the activity, the students need to create a file on Cabri Jr. that simulates an absolute value function. These directions are in the attachment. Once the file is created, students will then measure the angle between the branches of the absolute value funtion. The students should record the measure of the angle as well as the slope of each branch of the function. This data is then sent through Navigator to create a data list from all of the students. (This can be done without Navigator by typing in the data into the STAT editor).
After all of the data is collected, the students are challenged with the task of finding an equation that will fit the data. Advanced students will try several types of regressions while the students who are becoming acquainted with absolute values functions will need to be lead through the investigation.
To help the students through the investigation, I have included a document titled "teacher notes" with a graphic that will help the students make the connection between the absolute value and trigonometric function.