Education Technology

Trivialization and Dynamisation

Published on 06/09/2008

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