a x b + c | T R E E N E X |
(a + b) x c |

Three Number Expressions

This is a math card game for 2 to 4 players. Materials needed are: paper, pencil, and a deck of cards numbered from 0 to 9. Calculators are optional. For the cards, one can use ordinary playing cards, counting the 10 or joker as a zero (0); or a special deck can be constructed from tagboard or 3×5 file cards. The basic objective is to create expressions of three numbers in the forma × b + cor(a + b) × c. When a player's expression is correctly evaluated, the result is considered to be his/her score for that hand. The rules for a three-player game will be used to describe the general procedure. Then other versions will follow naturally.

1. Each player has paper and pencil for recording his/her results. 2. The dealer deals two (2) cards to each placer face down. Then one card is placed in the center, also face down. This is called thecommon card. 3. The player to the dealer's left turns his cards face up and decides which operation to perform on the two numbers, addition or multiplication. The decision is then announced and the expression is written on paper for all to see. [Note: if addition is selected, the values are written inside parentheses,(a + b). Otherwise, the values are merely written in thea × bform.] 4. The dealer and the other player now turn their cards face up. They, however, must form their expressions using whichever operation the first player didNOTuse for his expression, writing them on their papers in the manner described in the note above. 5. The common card's value is now revealed and utilized by all players to complete their "Treenex" (Three Number Expression) in the following way: (1) if addition was used for the first two numbers, multiplication must be used with the third number; thus forming an expression of the form(a + b) × c. However, (2) if multiplication was used first, then addition is now used to complete the expression in the form ofa × b + c. 6. Each player computes the value of his/her expression. Standard order of operations are followed, namely, the value inside the parentheses is done first for the expression(a + b) × c, followed by the multipication. Or multiplication is done first for thea × b + cexpression, followed by the addition. (Each result may be verified by the other players to avoid controversy. Here calculators may be used if the need is felt.) 7. Scores are duely noted, and play passes to the 2nd hand. This time the third player makes the "first operation decision", thus forcing his/her opponents to use the other operation in their initial positions. (Of course, for the 3rd hand, the dealer takes his turn to make that "first operation decision".) Play proceeds as described above (#2-#6). After the third hand, the scores are totaled. The player with the high score is declared the winner. Again calculators might be used for this.

VARIATIONS The winner can also be declared to be the person who has the LOW score, or even the MIDDLE score. This must be agreed upon before play begins, naturally. This obviously chages the thinking strategies for the player who makes the "first operation decision" in each hand. Also the rules for the 3-player game can easily be adapted for 2 to 4 players. First in this case, four hands should be played. For 2 players, the "first operation decision" would be made on alternate turns; for 4 players, each one would receive his/her own turn for that. (And of course, more hands could always be played to constitute one "Game".) Next if the players understand negative numbers, subtraction could be substituted for addition. Also a larger deck of cards could be used, or just put larger numbers on the cards [say, 10 to 19, for example]. As one can easily see, there are many possible variants to the basic game. tt(9/26/92)

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