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Thursday, October 21, 2010

Game of Nim

Wow! While I was cleaning out my purse today, I found a clipping from a Highlights Magazine explaining how to play the game Nim. The game uses alot of problem solving and logic, so I decided to play it with a kindergarten student that I tutor.

How to Play:
  • Have your child find 15 small things—for example: buttons or coins.
  • The first player will take one or two "buttons" away.
  • Each player will take turns doing this.
  • The loser is the player who takes the last button.
Note: You can give the game a twist by using a different number of objects or by taking away different amounts. Also, you can have the winner pick up the last item instead of the loser.
Above is the 21 coin circle that we used to play Nim. We were able to take away 1, 2, 3, or 4 coins. The player who had to take the last coin lost.

Questions to Ask During and After Play:
*Based on a game were you pick up either 1, 2, 3, or 4 items... and the loser is the player who picks up the last item.*
  • Is this game fair regardless of who goes first or second?
  • How many circles do you need your opponent to leave you to ensure that you will win? (2, 3, 4)
  • What strategy did you use during this game?
  • How would your strategy change if the number of items you could pick up changed?
I went and looked up Nim online and found that it is actually very mathematical based. Stuff that even as a teacher I didn't understand. I found a research paper/thesis on one site. Here are some of the higher level actives they used to engage the students.

Activity 1: Understanding the Game: making pairs to try to find ways of winning the game
  • You will need 20 snapable units of yellow.
A teacher could use unifix or snap cubes. At home, legos would work well.
  • You will need to add one black unit to the end.
  • Students alternate turns taking from one to three cubes. The student who takes the last cube is the winner.
Activity 2:
Modifying the Game: Students are assigned to modify the game by changing or adding some conditions to the rules of the game.

1. Present an example of a new game modified by one student.
  • Place a black-colored cube at the center with 7 yellow cubes connected on its left side, and 13 red cubes on its right side.
  • Students take turns removing from one to three cubes of the same color. They may take cubes from either the right or left side.
  • The student who takes the black cube will be the loser.
2. Discuss the demonstrated game.

3. Students make their own modified versions of the game.

Note: Showing children the modified version will get their minds working and thinking about other alternatives to the directions. They will be engaging in high level problem solving and logic.

*Most of the research I found was based on children in middle school and high school. I really do not see why this game would not be perfect for even preschoolers. Just modify the number of items to 5 or 10.

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One Pink Fish

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