Lesson #159 Equations of Conics

  
Quotes of the Day:
"Cogito, Ergo Sum.  I think, therefore I am."  -- Descartes

"I think, therefore I laugh." -- John Allen Poulos

"I do not think -- therefore I am not."


Objectives:
1. The student will solve equations of conics while playing the game of Tracker.

2. The student will relate graphs to their equations.

3. The student will apply transformation concepts to graphs of equations.

4. The student will generalize strategies for use with many types of graphs.

5. The student will analyze characteristics of various types of graphs.

6. The student will apply geometric properties, such as symmetry.



Lesson:
1. Remind students that Descartes was the French 
   mathematician who developed the coordinate system.  In 
   fact, the rectangular coordinate system is often called 
   the Cartesian Coordinate System.  

2. Go over homework problems.  Discuss hyperbolas which 
   are rotated 45 degrees, such as  xy = 1.

3. Explain the Tracker game.

   In the TRACKER game, graphs are hidden on a coordinate grid. 
   Students gather clues about the location of the graphs by using 
   "probe shots."  These probe shots are horizontal and vertical lines.  
   Each point where the probe crosses the hidden graphs is marked on 
   the screen.  After using probes to locate a graph, students send a
   "tracker" along the graph by entering its equation.

   We will play the Novice Game.
   In the Novice Game, you choose two types of graphs to be hidden on the grid.  
   There are always three hidden graphs: two of one type and one of the other.
   One type of graph is marked with X's and the other with O's when crossed by 
   a probe shot.  If a hidden graph is a hyperbola, it could be of either kind 
   and not necessarily the same kind as another hidden hyperbola. 
   The game ends when you have found all the hidden graphs. When you finish a 
   game with a positive score, the program compares your game score to those 
   in the TRACKER Novice Game section of your Records file.  If your score is 
   higher than the lowest score currently in the Novice Game section, or the 
   Novice Game section has fewer than ten scores saved in it, you will be 
   offered the opportunity to add your game to the Records.  A game added to 
   the Records will be erased when it is no longer in the top ten scores for 
   that game. 


4. Distribute copies of the Worksheet #1 and Worksheet #2.
   Explain the scoring of the game.

        Worksheet #1

        Worksheet #2

5.  Have students play "Tracker" on the computer using 
    ellipses, hyperbolas, parabolas, circles, and lines.

6. Students should record the results of their games on 
   Worksheet #2.
Lesson #159 Equations of Conics

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