Module 5

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 are some values not permitted in a rational expression?
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?
		Can you use the patterns of adding and subtracting rational numbers to determine, in simplified form, the addition or subtraction of rational expressions?
4	Solving Rational Equations	What are the different strategies used, and how are they helpful in solving rational equations?
		Why are some values of the variable obtained in solving rational equations not roots of the equations?
5	Applications of Rational Equations	How can real-world problems be modelled with rational expressions and rational equations?

 

In Module 5 Project: Dice Game Competition, you will design, build, and play a dice game that will incorporate the mathematics in this module to address aspects of your game as well attempt to use strategies to maximize your score.

 

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