1. Demonstrate the game with volunteers for at least three games (or many more!), until you are certain everyone understands it and is excited to play.
2. When demonstrating 1-2 Nim, narrate the game out loud, using mathematical language, and leaving empty space for students to chime in: “My opponent just took 2 leaving… [wait for students] 5 in the pile. Who has a advice for what I should do next?”
3. Remind students that they will lose many games as they play, and that every loss is an opportunity to learn. Can they steal the strategy of the person who just beat them? Point out how students are trying out new strategies as they play you in demonstration games.
4. As kids play each other, circulate to see what strategies they are developing. Challenge them to play you, and see if they can beat you.
5. Encourage student conjectures, but do not call them as true or false. Challenge students to break their own conjectures.
6. This game is great for station work once students already know how to play it.
7. We use the term “the 3 trap” to describe what happens when you give your opponent a pile of three counters. Understanding how to win boils down to understanding what pile sizes you want to leave your opponent with.
8. There are two incredibly powerful approaches to solving Nim. The first is to simplify. How could the game be easier? What if the pile had only one counter? From this place of almost absurd simplicity, we slowly raise the difficulty. What about two counters? Three counters?
The second approach is to organize the data in a coherent way. A table does this very nicely.
9. If kids want to play three-player, keep in mind that we discourage it. Normally trying out different numbers of players is a great impulse. In nim, it leads to spoilers, who can’t win, but can choose who does win.
10. Homework: have kids teach 1-2 Nim to a friend or family member.
References: http://wordplay.blogs.nytimes.com/2011/06/13/numberplay-1-2-nim/