Module 6

Do you like to play games? Games come in a variety of different forms. There are card games, board games, and video games; individual games and team games; role-playing games and reality-based games. Sports can be considered games on a large scale as well.

 

Even if you don’t like to be in the midst of the action, you might enjoy watching other people play. After all, games can be entertaining for the spectator too! In this module you will discover that math can be used to describe various aspects of games, from their playing surfaces to the strategies used to achieve the best results.

 

This module will introduce you to rational expressions and rational equations. You will learn how to add, subtract, multiply, and divide rational expressions. You will have an advantage going into these lessons because you already know how to perform those same operations on rational numbers. Simplifying rational expressions is similar to simplifying rational numbers.

 

You will also study rational equations and their applications. You will see how rational expressions and equations can be used to describe the properties of, and predict the outcomes of, different games.

 

In this module you will investigate the following questions:

• How are rational expressions an extension of rational numbers?
  
  
• How can rational expressions be used to model situations related to competition and cooperative games?
  

To investigate these questions you will focus on the lessons and questions in the table.

 

Lesson	Topic	Lesson Questions
1	Simplifying Rational Expressions	How is the process of simplifying rational expressions similar to the process of simplifying rational numbers?
		Why is simplification desired in mathematics?
2	Multiplying and Dividing Rational Expressions	How are multiplying and dividing rational expressions similar to multiplying and dividing rational numbers?
		How are non-permissible values determined when multiplying and dividing rational expressions?
3	Adding and Subtracting Rational Expressions	How are adding and subtracting rational expressions similar to adding and subtracting rational numbers?
		What patterns can be used to prepare rational expressions for addition or subtraction?
4	Solving Rational Equations	What principles are common to the strategies for solving rational equations and how are these principles helpful?
		Why are some values of the variable obtained in solving rational equations not roots of the equations?
5	Applications of Rational Equations	What types of problems related to co-operative and competitive games can be solved by rational equations?
		How can real-world problems be modelled with rational expressions and rational equations?

 

The entertainment value of games cannot be overstated. In fact, the television industry has been capitalizing on this idea for a long time. Game shows and reality-based television programs feature contestants singing, dancing, playing, and otherwise competing against one another for supremacy.

 

In Module 6 Project: Game Challenge you will design your own game—a board game, video game, or reality-show challenge. You will incorporate the mathematics in this module to address aspects of your game, such as game play, game environment, and best strategies. You will collect real data as you and your friends test your game by playing it!