1- 2 Nim
Math Concepts
Counting, Add / Subtract numbers 1- 9
Materials
Paper & Pencil- or- Small pile of little objects
Players
2
Set up
Write the starting “current” number, 10, on your shared piece of paper. One player, usually the less experienced, is given the choice of going first or second.
Play
Players take turns subtracting one or two from the current number and updating the number on the paper.
Goal
The player who makes the current number 0 wins.
Example:
The weaker player, cleverly, elects to go first. The players make the following moves:
(1) 10- 1 = 9. (2)9-2=7,
(1) 7- 1 = 6,
(2) 6- 1 = 5,
(1) 5- 2 = 3,
(2) 3- 1 = 2,
(1) wins with 2- 2 = 0!
Discussion and Tips
This is an ideal activity for practicing the problem solving technique of “Learn from simpler versions of a problem.” Lead a discussion where you keep track of who wins if you start at 1, at 2, at 3, at 4, at 5, at 6. What is the pattern that emerges?
Variations
Piles of objects: If your players are not comfortable with numerals yet, use a pile of objects. Remove objects from the pile with each move until no objects are left and you have a winner.
Number line: Use a marker on a number line. Start the marker at 10 and slide it one or two places to the left with each move.
Adding: Practice adding by starting with 0 and adding 1 or 2 for each turn. The player who reaches the target number wins.
Target loses: You can play that the player who is forced to 0 (or the target number) is the loser.
Target number: Use smaller target numbers for beginning players and larger target numbers for more experienced players.
Different step sizes: For the upper grades in this range, Instead of adding or subtracting 1 and 2, use other groups of numbers. Use 1, 2, and 3; or even 1, 2, and 4.