Return to Mathematics IndexVisual Structure of Postulates and Axioms in Algebraic OperationsSanford Olshan Roosevelt High School Chicago, ILObjectives: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.