TRIG TIC-TAC-TIMES

"TRIG 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 Trig 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 could place a factor marker on sin(-x) and player 2's marker on cot(x). Player 1 then would place a game token on -cos(x) because [sin(-x)][cot(x)] = -cos(x).

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 In this example, player 2 could moved her factor marker to csc(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 sin(-x) (player l's marker) and csc(x) (player 2's marker), or -1, on the game board. Players must use a strategy of working backward to determine which products combined with the available factors will win the game. These same problem-solving strategies become a part of the defensive play of the game when a player wishes to block an opponent.   ----------------------------------------------------------------------- Listed below are the possible solutions for each of the 45 squares in the gameboard. THIS IS FOR TEACHERS ONLY!!