## MAT Exam Expository Papers

#### Title

The Four Numbers Game

#### Date of this Version

7-2007

In partial fulfillment of the requirements for the Master of Arts in Teaching with a Specialization in the Teaching of Middle Level Mathematics in the Department of Mathematics. Jim Lewis, Advisor July 2007

#### Abstract

The Four Numbers Game is a fun way to work with subtraction and ordering of numbers. While trying to find an end to a game that is played with whole numbers, there are several items that will be investigated along the way. First, we offer an introduction to how the game is played. Second, rotations and reflections of a square will be presented which will create a generalized form. Third, we explain how even and odd number combinations will always end in even numbers within four subtraction rounds. Fourth, we argue that the length of the game does not change if multiples of the original numbers are used to create a new game. Fifth, we show that all Four Numbers Games will come to an end. Sixth, we offer an investigation of the general form and some special cases and how they can help predict a more accurate end. Finally, there will be an example of how this problem could be used in a sixth grade classroom.

COinS