```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
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.

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