Zero Out

by Paul Brice

Paul is a math teacher at a junior high school in Encinitas. He is also an avid tennis player and gardener..

Instructional Objective The learner will be able to recognize and combine algebraic-like terms into sets of three. Each set will "zero out" (have a net value of zero).


Learners/Context This game is for students in a pre-algebra course. These students are in grades eight or nine,but the content of the game is appropriate for any student studying like terms. Instructors can use this card game as review or remediation in teaching combining like terms.


Rationale Instruction in a math class can be routine. A card game allows the instructor to provide practice in a particular content area without the drudgery of using a worksheet. Combining like terms involves pattern recognition, which lends itself to a rummy class of card game.


Rules Students sit in groups of three or four. A dealer deals each player seven cards. Players use six cards to make two sets of three cards. They use the seventh card as a discard. The dealer places the remaining cards face down. The dealer turns the top card face up and places it next to the deck as a discard pile.

Players sort their cards by types of terms. They position cards of like terms together. Players take turns drawing the top card from the remaining deck or selecting the top card in the discard pile. During each turn, a player must draw from either pile and discard one card before their turn is over. Each player tries to make two sets of three cards. Each set must contain cards of like terms that "zero out."

A "Freebie" card can count as any value card the player wants, including zero. The deck contains two wild cards. Once a player has two sets that "zero out" ,the player can lay the two sets down and discard the remaining card. The player who successfully goes out, gets a score of zero. The other players will add the absolute values of the coefficients of the terms in their hands to determine their score. The player with the lowest total at the end of a set number of rounds, is the winner.

Card Design Each card contains the Zero Out logo in the center. The upper left and lower right hand corners contain the same algebraic term. The term in the lower right hand corner is upside down. No matter which way you hold the card, the term in the upper left hand corner is always right side up . Cards resemble those of a standard deck of cards with algebraic terms instead of numbers and suits.


Deck Design The deck has 84 term cards and 2 Freebie (wild) cards. There are seven different terms on the term cards. They are: x, xy, y, x2, y2, x2y, and xy2. Coefficients for each term are either: -3, -2, -1, 3, 4, or 5. This provides 42 possible term-coefficient pairings. The deck contains two of each type of pairing (84 term cards). Below is an example of a player's possible hand:

-3x 4xy -2xy -y 3x2y -2y and 5xy.


Design Process In deciding what content to use for the game, I searched for math skills that my students are weak in.and that I could form patterns with. Combining like terms seemed like an appropriate topic. To keep the math simple, I am only using coefficients between -5 and +5. To have enough cards left for play after dealing the hands, I decided to use seven different variables. This would produce 70 different term cards. Having 70 different term cards will allow a player to win a hand without having to reshuffle the discard pile. Having the players search for two sets of three of a kind that "zero out", gives the learners practice at combining like terms. It also makes for a short game with a manageable number of cards to hold at one time.