...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:

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.
 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.

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.

Challenge Level: Increasing complications such as exponents,
absolute values, etc.
To play the
game:
 Read through
the directions and model a game or two for the class.
 Break class
into groups of 2 or 3. Decide on which game to play:
 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.
 Have
individual groups try to solve it or solve it as a class.
 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
