Teacher to Teacher: A Number Line with Character

Abstract

Vince and Sarah are playing the Factor Game, a two-person game in which me first player selects a number from 1 to 30 (see game board in fig. 1). The second player then selects all the divisors of the first number that are less than that number. If Vince begins the game by choosing 13, Sarah would select 1 because the divisors of 13 are 1 and 13 and Vince has already elected 13. The score is then 13 to 1 in favor of Vince. During the second round of play it is Sarah's turn to go first. She chooses 24 and has a total of 1 + 24 = 25 points. However, next Vince can select 2, 3, 4, 6, 8, and 12 (the remaining divisors of 24), which, added to his previous score of 13. will give a total of 48 point. Once a number is chosen, it is out of play and can be marked off or covered up. A play is legal only if a divisor remains on the board for the opponent to select. A player making an illegal move gets to keep the number chosen, but loses his or her next turn. The game ends when no more legal moves are possible. The highest sum wins. The Factor Game is the first activity in Factors and Multiples, a unit of the Middle Grades Mathematics Project (Fitzgerald et al. 1986).