Visual Structure of Postulates and Axioms in Algebraic Operations

Sanford Olshan                 Roosevelt High School
                               Chicago, IL

Objectives:
     To reinforce and retain the use of axioms and postulates in various proofs 
and linear transformations of equations. 
     To have student build a physical model of the game of "PRUFF" either as a 
card game  or as a board game. 
                           
Materials:
     Approximately 40 cards listing postulates, axioms, and definitions as taken 
from your text book.  It is a good idea to put examples of each either below or on 
the back of each card.  Make up about 25 problem cards with current problems from 
your text answer should be placed on back. Try to avoid problems that require 
paper to solve.  About 20 cards which have proofs on left hand side you show 
statements and the reasons are placed on the back of card.  
     You may use these cards either as a Card Game as they are or design a Board 
Game as you will find in description of game. 

Strategy:
     From the beginning of the semester student must place each definition, axiom, 
postulate, or property on a card the size of, or smaller than an index card. These 
cards are to be called P-Cards.  Each card should have examples describing the 
Axiom or Postulate on the back of the card. During the sixth week or at the end of 
third chapter we are ready to begin playing the game.  The instructor writes out 
ten or more proofs or solved equations giving the reasons on the back.  The 
students separate into groups of about 2 to 6 in each.  They each take 5 cards and 
try to find the reasons for the proof statement.  If they have one they place it on 
the table and look for a second,  If they do not have any they pick a card from 
their deck and the turn goes to the next person. The person with the least cards 
after the time allotted is the winner. 
     To play the Board Game "PRUFF" you make another set of cards called problem 
cards, these are selected from current problems in the text. Each player selects a 
marker and rolls the die to see who goes first.  Highest roll shakes die and moves 
marker that number of squares.  He can either land on a problem or a pruff.  If it 
is a pruff, he looks at the top statement on the Proof Card if he has a reason he 
places P-card on table and looks for second reason.  If he does not have p-card to 
fit reason he draws one from deck thus completing his turn.  When one lands on 
problem card she selects top problem and tries to solve it.  If she can she 
discards one p-card from hand.  If it is incorrect she must take a p-card from 
deck. 
     If you are sent to Cage you must skip one turn after you roll the die you 
follow the alternate path.  Follow path until the end.  When you reach the end 
without any 'P'cards, You Win!!!  If you have one "P" card, go to start to 
continue play (you do not have to take any new cards!) If you have 2 or more cards 
in your hand, return to start, take five additional "P" cards and continue playing 
until someone wins! (no cards at the end, or least cards when time is called.) 
Note:"The problems can be written in different degree of difficulty so that the 
students may be of various math levels.