I’d like to publicize two simple math games for kids that should be more widely known. Both games are hands-on and immediately engaging. Both lead to a number of important mathematical concepts. Both involve a start state, a goal state, and rules for how you can alter a state. And, as you’ll see, there’s no chance in either game.

For each, I’ll first describe a “warm-up” version which kids should begin with.

## Game 1

**Materials**: sticks of different lengths

**Start state**: 5 sticks in a row arranged from shortest to longest

**Goal state**: rearranged so the sticks go from longest to shortest

**Rules**: For each move, you are allowed to pick any 3 adjacent sticks and rotate their positions among themselves. Each stick must move to the position of one of the other two sticks you’ve chosen; none of the 3 sticks you’ve chosen may stay put. You may use as many moves as you wish.

**Example move**:

After the warm-up, start with 10 sticks arranged from shortest to longest.

## Game 2

**Materials**: pencil and paper

**Start state**: the numbers 1 through 5 in a row

**Goal state**: five 3s in a row

**Rules**: For each move, you are allowed to pick any two numbers and change them by adding 1 to one of them and subtracting 1 from the other. You may use as many moves as you wish.

**Example move**:

After the warm-up, change the start state to the numbers 1 through 10 written in a row and change the goal state to ten 5s in a row.

*Have Fun and Good luck!*

Note: The “no chance” here is not exactly the same as the “no chance” in the really fun book *Games of No Chance*, edited by Richard Nowakowski.