How to Play the Factor Game
Players start with a simple game board, with the numbers 130 (in the past I've alternated between giving them a preprinted sheet and letting them write their own numbers on their own paper; sometimes I have them play at the whiteboard). Player 1 chooses a number, and marks it (they might circle it, square it, triangle it, color it etc). Player 2 then marks all of the remaining factors of Player 1's choice. Player 1 receives points equal to the number they chose, and Player 2 gets points equal to all of the remaining factors of that number. Next, Player 2 chooses a number (and gets those points), and Player 1 identifies all of the factors of that number, receiving those points. Play continues this way until all possible numbers have been used. *Special rule  players can't choose a number that has no factors available for the other player. If they do, they lose their turn, receiving no points.
When I introduce this game to my classes, we play it on the whiteboard, and I always allow them to go first (the first time). Often, they will choose 30 as their number, since it's the biggest. When I go ahead and mark all the remaining factors of 30 (my points), they are shocked! After the first turn, they have 30 points and I have 42! (I normally have 2 students record our scores on the board, while 2 others keep running totals on a calculator, but points can all be tallied at the end if you want).
For my first turn, my choice would be 27, giving them only 9, since 1 and 3 are already gone. After their experience with 30 and its factors, they start thinking a bit more. They will often consider 25 or 23, but I remind them that they must leave a factor for me, and 1 and 5 are already taken. For the sake of showing further steps, let's pretend that they choose 21. That leaves 7 for me.
The game continues, alternating turns, until all possible numbers are used, as shown in the "finished game" picture.
The second time we play as a group, I choose 29 as my first number, and they are disappointed to only get 1 point! We continue to play the second game, and they get a better idea of what makes a good choice. After our games as a class, I have the students work in partners, and they normally get one or two games played before we stop to discuss at the end of the period. We always talk about what the best and worst first choices are, and bring the idea of prime and composite into the discussion. I have been playing this game with students for at least 15 years (I think), and every set of students has loved it! I found the game when I was involved with Mathline, so long ago. If you'd like to see the original lesson plan, with extension ideas, click here. Have you played the Factor Game?
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2 Comments
Andrea
1/9/2019 01:34:06 pm
Could you make this game higher than 30...perhaps 45 or 60? Would it work?
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Ellie
1/10/2019 08:44:27 pm
I haven't tried it, but I don't see why it wouldn't  students would have more factors to find when they choose the bigger numbers, so they might miss some, but that could be a good challenge!
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