...an idea that originated from the game Stop That Creature found at PBS's Game Central.  The black box method uses an imaginary device (the black box) that modifies the input number according to a specific formula.  The formula is hidden in the black box so to a viewer the number mysteriously changes. 

The key is to understand the underlying pattern to the changes as successive numbers are input.    By observing what happens to numbers that are input to the box students can determine what the box is doing to generate the output number.    This models the scientific method where scientists would develop a hypothesis concerning the cause of the observed effect the box has on the input number.  The game is excellent practice and develops students skills at detecting underlying patterns to numbers and can be done at any level.

There are a number of variations to the game:

1. Fraction Black Box: Use only one operation (limit to plus and minus or use all four operations) and number.  From the output determine what has happened to the input fraction.  Input must be a fraction. 
2. Basic Integer Black Box: Use only one operation and number.  From the output determine what has happened to the input number. Input can be a positive or negative integer.  Consider using absolute values to make it challenging. 
3. Advanced Integer Black Box: Use two operations (one is addition or subtraction and the other multiplication or division) and two numbers.  From the output determine what has happened to the input number.  Group must either accept any correct answer or tell what operations were used and the order they were used.  Input can be a positive or negative integer.  Consider using absolute values to make it challenging. 
4. Challenge Level: Increasing complications such as exponents, absolute values, etc. 

To play the game:

1. Read through the directions and model a game or two for the class.
2. Break class into groups of 2 or 3.  Decide on which game to play:
3. Each group tries their black box on the class.  They can write their solution on a piece of paper and stick it on the board. 
4. Have individual groups try to solve it or solve it as a class. 
5. The group that has the most unsolvable black box wins.

Use Excel to illustrate relationship to equations:

These games are meant as an informal introduction to equations.  Inputting x, the black box spits out y.  If you input a formula into Excel, you can then project the game and allow various solutions to be tried.  The x and y could then be graphed in Excel to discover the equation of a line.  Basically, the possibilities are endless.

Try Our New Internet Game: The Mystery Box