ALGEBRA TIC-TAC-TIMES
by Richard J. Crouse and Marilyn J. Sweeney from the The Mathematics Teacher
"Algebra tic-tac-times" combines mathematical
skills with a competitive strategy. It
is a highly motivational skill-review exercise
that involves the problem-solving strategy of
working backward.
Directions for Play
Objective
The object of the game is similar to that of
tic-tac-toe; the winner is the first of two
players to place four tokens in a row, either
vertically, horizontally, or diagonally.
Materials
The materials necessary to play algebra
tic-tac-times include a factor board and a game
board (fig. 1) and forty translucent tokens of
two different colors. One token of each color
is used as the factor marker, and the remainder
are used as game tokens. The game
board should be laminated so that it can be
saved from year to year. The tokens should
be stored in a bag so that they don't get lost.
Method of play
Player 1 begins the game by placing a factor
marker and one of player 2's factor markers
on any factors on the factor board. The product
of these factors determines the placement of
player 1's game token. In figure 1,
player 1 placed a factor marker on x + 1 and
player 2's marker on x -1. Player 1 then
placed a game token on x^2 -1 because
(x -1)(x + 1) = x2 -1.
Note: factor markers can be placed on the
same factor, resulting in squared factors.
Player 2 can move only player 2's factor
marker (player l's marker remains in place)
to another factor on the factor board, as
shown in figure 2. In this example, player 2
could move a factor marker to x. The product of
these new factors determines the placement
of player 2's game token. In this example,
player 2 would place a game token on the product
of x + 1 (player l's marker) and x (player 2's
marker), or x^2 + x, on the game board.
Players must use a strategy of working
backward to determine which products com-
bined with the available factors will win the
game. These same problem-solving strate-
gies become a part of the defensive play of
the game when a player wishes to block an
opponent.
Penalties
A player is penalized when a product that
has already been covered is used or when an
incorrect response to the factors is given. A
move is considered to be completed when a
player's hand is removed from the factor
marker in the event of a duplicate product or
from the game token in the event of an
incorrect response. In the event of a penalty,
the opposing player has the opportunity to
move both factor markers, as in the begin-
ning of the game.
