Photo by English Teacher

We’ve looked at teaching math using inductive thinking. Now we’re going to dive into math games that capitalize on gifted students’ intuitive abilities.

### Nim

Nim is an ancient math game, and there are now several variants of the original. Here’s my favorite:

#### Nim: The 100 Game

Two players begin at zero, and take turns adding between 1 and 10 to the current sum. Whoever reaches 100 wins.

- Student A begins with 5
- Student B can add from 1 through 10, arriving at 6 through 15.
- Student A can then adds between 1 and 10 to the new total
- And so on.
- Eventually, one student will add and make 100, winning the game.

Why is this inductive? After a few games, students will probably catch the pattern and form their first generalization: *The Key is 89*!

From there, students will begin to identify more patterns, building on their first generalization.

Naturally, anyone who can beat the teacher wins a prize! I’ve heard people say they require two wins against the teacher. This gives you a chance to judge whether they understand the strategy before revealing your own.

Build on students’ patterns by changing the rules a bit:

- Reach 21 by adding between 1-3.
- Reach zero by starting at 25 and subtracting up to 4.

#### Nim: Heaps

Another Nim game uses three “piles,” each containing a small number of objects. Players alternate turns, taking any number of objects from a single pile. The object is to be the last one to remove an object.

A | B | C | Move |
---|---|---|---|

3 | 2 | 1 | Starting piles |

1 | 2 | 1 | Red removes 2 from pile A |

1 | 0 | 1 | Blue removes 2 from pile B |

0 | 0 | 1 | Red removes 1 from A |

0 | 0 | 0 | Blue ed removes 1 from C, winning the game |

After a few rounds, kids will start to spot patterns and formulate strategies. If they get abstract enough, they can even reach a *mathematical proof of the winning strategy*!

### Visual Games

Moving beyond purely numeric games, let’s check out some visual games.

### Cram

Cram is a visual game played on a grid of squares. 4×4 or 6×6 are common, but encourage your students to try other (even irregular) board sizes. Two players compete, placing 2×1 rectangles onto the grid. The last player to successfully place a piece wins.

Here is a sample Cram game played on a 4×4 grid. Eventually, red cannot make a move.

### Sprouts

Sprouts is a dot and line game played with just paper and pencil. Students draw a small set of dots to begin (even two dots is enough). The object is to continue connecting those dots with lines.

- Connect two dots with a line (curvy is fine).
- Put a new dot somewhere on that line.
- Repeat.
- Each dot can only have three lines connected to it.
- Lines may never cross each other.
- You lose when you can’t draw another line.

In this sample, there is only one dot remaining in the end with fewer than three connections, so the player cannot make a new line.

### Chomp

In the game of Chomp, players play with a rectangular grid and remove squares each turn.

- Players decide who goes first.
- Players pick a piece near the bottom right and remove it, along with
*all pieces*to the bottom and right of it. - Whoever removes the top-left square loses.

Here’s a sample game:

After a couple plays, kids will realize the importance of taking that last square under the losing box.

### Aren’t These Just Games!?

Sure, these may be games at heart, but you can take them to the next level by requiring students to develop strategies, write them out, and then use them to challenge you to a match!

Unlike a game like chess, these activities are very simple. Students can quickly formulate strategies, test them, and build on them.

These are all great activities for:

- warmups
- “may do” activities for early finishers
- five-minute fillers

Warning! Your kids may get really into these, requiring you to create tournaments, devote wall-space to their strategies, or incorporate other classrooms!

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