The Function Machine Game
Math concepts: odd numbers, even numbers, greater-than/less-than, rounding off, addition, subtraction, multiplication, division, fractions, negative numbers, prime numbers, square numbers, problem solving, mental math
Number of players: two or more
Equipment: pencil (or pen) and paper for every player
Each player needs pencil and paper of his own. One person plays the role of the function machine, and he must make up a rule for calculating with whatever numbers the other players will give him. In math, a function is any rule that turns one number into another*, such as:
- Double the number, and then add seven.
The function machine should write his function rule on a piece of paper and slip it in his pocket.
All the other players make themselves a chart to keep track of the game.
*[In reality, the definition of a function is a bit more complicated than that, but it suffices for this game.]
How to Play
Play proceeds to the left around the table.
- Each player in turn says any number he wishes, and all players write that number in their Input columns. The function machine calculates with that number, mentally or on scratch paper, and says only the answer to his calculation.
- If that input number is too difficult for the player to work with, he should say, “That’s too hard,” and ask for a different number. Occasionally, players will give an input number that does not make sense with the chosen rule, in which case the machine answers, “That does not compute.”
- Whatever answer the machine gives, all other players write it in their Output columns.
- After receiving an answer, the player whose turn it is may make a guess at what calculation the machine is doing. Other players may not guess at the function rule until their own turns.
The first player to guess the rule of the function machine wins that round. If you have time to play a full game, where every player has a chance to be the machine, then the winner of the game is the player who gave the most output numbers before the others guessed his function rule.
My math club students have always enjoyed this game, especially when it is their turn to be the function machine with the secret rule. But some freeze mentally at the task of creating their function rule, while other students make up rules that are so complex they are nearly impossible to guess. You may want to make a list of suggested function rules in advance, writing the rules on index cards and letting each player draw a rule from your deck.
Here are some function ideas to get you started:
- Add 15 to the number.
- Subtract 4 from the number.
- Multiply the number by 8.
- Cut the number in half.
- Cut the number in half, and then add one.
- Double the number, and then subtract three.
- Add the next larger number, so an input of 3 gives an output of 3 + 4 = 7.
- Multiply by the next larger number, so an input of 5 gives an output of
5 × 6 = 30.
- Triple the next larger number.
- Subtract the number from 25.
- Square the number, and then add one.
- Say the largest multiple of 3 that is less than the number.
- Round off to the nearest hundred.
- Double the odd numbers, but cut the even numbers in half.
- All odd numbers are 17, but all even numbers are 12.
- Say the ones digit of the number.
- Add the digits in the number together.
- If the number is prime, say the number. If the number is not prime, say 1. Remember that one, zero, and all negative numbers are not prime.
- Say the tenths digit of the number (the first digit after the decimal place). The student may need a calculator to rapidly convert fractions to decimal numbers.
This is a great game to play in the car on family trips, since there are no little game pieces and the paper does not need to be passes around. Even the driver can join in the fun.
Beware that some function rules can be described in more than one way. For example, the rule:
- Double the number, and then add two.
…could also be written as:
- Double the next higher number.
It helps to have a referee who knows algebra to judge the guesses. “Double the number, and then add two” is written as , while “double the next higher number” is , and anyone who knows algebra can easily see these are the same. The player who tries to guess the rule does not have to put it in the exact words the function machine used, as long as the statements are equivalent.
Edited to Add
You can play an interactive online version of the game here: