The Factor
Game 
Teacher's
page
Revised: 9.24.07

Resources
needed: A set of fifteen 3 by 5 cards (with tape on the back) numbered from 1 to 15. Game can also be played using the Factor Game microworld. (version 1.0) (Version 1.1) Don't forget to download the Webplayer first. Curriculum:
Key Words: 
Microworlds version. (Webplayer required.) 
Preliminaries Explain the rules for your students. (See Rules of the Game below.) Rules of the Game Two players (or
teams) compete
for the highest score by picking numbers from 1 to 15. Let's say that
Player
A picks 15. This means A gets 15 points. B receives the sum of the
factors
of that number and they are added to B's total. 1, 3, and 5 are the
available
factors of 15 so B has 9 (1+3+5) points. The number chosen and its factors are then removed from
the board or screen. Next its B's turn to
pick a number that is still on the board. Play continues until all the
cards have been selected. 
How to play with your students
Tape fifteen 3 by 5 cards (numbered from 1 to 15) on the blackboard or wall. After explaining
the
rules,
tell the students that your role would be strictly to move the cards.
For
example, if the first team (A) chooses 15 the teacher moves the 15 card
to Team A's total. Team B then has to tell the teacher what cards they
are entitled to (factors of 15 still on the board.) In this case 1 and
5 should move to Team B's hopper. If a team makes a mistake it is the
obligation
of the other team to catch it. This keeps the students attentive and
engaged.
If some errors are not picked up by the students, the teacher should
make
sure they are aware of the problem. Here is an example of a possible game (Initial number chosen is in blue; chosen factors are in red.) 


































































Variations of the Game  Using the Computer Use the "applet" version of this game (see links above.) Project the screen image on the board for the two group game and proceed as in the 3x5 card game. After the group game you can have the students play against each other in a lab situation. You can also easily change the range of numbers. Watch out for time though. A game of 40 can last a full (45 min) period! There are other versions of the Factor Game that you can use as well. See below.Extensions & Additional Activities You can try an interesting variation of the game by taking advantage of the range feature. Ask your students to play a game of 10 (Move your slider to 10 before clicking on start.) Player A always goes first. Assuming that both players are using an optimal strategy, will player A always win? Try it for other ranges? Is there a pattern? The terms prime,
composite,
deficient, abundant, and perfect can be introduced to explain the how
the
numbers work. 18 is an example of an abundant number because the sum of
its factors (not including 18) is greater than 18. (1+2+3+6+9=21). A
variation
of this factor game is used in the Connected Mathematics Project in Prime
Time  Factors & Multiples. Other Resources and Applets
