Education Technology

Trivialization and Dynamisation

Activity Overview

This activity will illustrate how classic exercises from elementary vector geometry can be solved using the Computer Algebra System CAS tool.

Before the Activity

  • Install the Cabri Geometry™ software on the computer
  • See the attached PDF file for detailed instructions for this activity
  • Print pages 1 - 10 from the attached PDF file for the class
  • During the Activity

    Distribute the pages to the class.

    Follow the Activity procedures:

  • Use Cabri Geometry to draw an ellipse
  • Determine the equation of the ellipse and convert it into the standard form
  • Solve the ellipse equation and draw the functions for some values of the variables
  • Satisfy the equation and draw the parametric representation of the ellipse
  • Perform the above steps manually (by hand), compare the results with those from CAS
  • Examine the different solution methods provided on the activity sheet

  • Study the vectorial representation of two points and the straight line
  • Determine all points on the straight line with a certain ratio
  • Replace a component in the direction vector of the straight line by a variable
  • Determine values of the variable which results in one, two, or no solutions
  • Find the locus of the intersection points and determine its characteristic quantities
  • Write the equation of the locus
  • After the Activity

    Students complete the exercises listed on the activity pages.

    Review student results.

  • As a class, discuss questions that appeared to be more challenging
  • Re-teach concepts as necessary