Module 4 Introduction: Module 4 Introduction

Math 10C Module 4 Introduction

Module 4: General Relations

Module 4 Introduction

This photo shows three female hockey players listening to instructions from a coach.

Hemera/Thinkstock

An Olympic athlete trains for years in order to prepare for competition in the Olympic Games. This preparation comes in the form of long hours of practising his or her discipline, training in the gym, and following a prescribed diet. These areas of focus are critical for the athlete to do well in competition. Another critical component of an athlete’s success is coaching. A good coach will be able to motivate the athlete and help the athlete build on his or her strengths and address areas of weakness.

One important skill of a good coach is the ability to see relationships among variables that can help the athlete excel. For example, a swimming coach may record the time that a swimmer takes to complete each lap of an endurance swim in order to help the athlete swim faster. A discus coach may observe a relationship between the angle of a throw and the distance gained. A volleyball coach will know of the relationship between players with longer reaches and their abilities to attack and defend at the net.

With the data collected on the athlete’s performance, a coach can create graphs that help assess progress. Trends in the graphs are analyzed, and subsequent corrections can be made to help the athlete improve.

In this module you will learn the mathematics of relations and functions. You will learn that in any relation, there is an independent variable and a dependent variable. These variables will often exhibit a pattern that can be used to predict other values. You will see that relations can be described not only as graphs, but also as ordered pairs, tables, and arrow diagrams, to name a few. You will learn about special types of relations known as functions. You will also discover how to determine the domain and range of a relation.

Throughout the module you will have the opportunity to create and interpret graphs for given contexts. Like a coach, you will analyze graphs for patterns. In the module’s second half you will examine the concept of the slope of a line. You will learn how to differentiate slopes that are positive, negative, zero, and undefined. You will solve contextual problems involving slope, and you will interpret slope as a rate of change.

The lesson questions you will investigate in this module include the following:

Lesson	Title	Lesson Questions
1	Sketching and Interpreting Graphs	How do you know whether a variable is dependent or independent? How can a graph be used to describe a situation?
2	Relations	Why is it appropriate to connect the points on some graphs but not others? How can you determine any limitations on the domain and range of a relation?
3	Functions	Why is it that some relations are not functions? How can you tell if a relation is a function?
4	Slope	How can slope be used to describe the properties of objects? Why is it possible to use any two points to determine the slope of a line?
5	Slope as a Rate of Change	How is the slope of a line related to the dependent and independent variables of a graph? How can slope be used to make predictions about the outcome of certain events?

All of the lessons in this module refer to sports and recreation, with a special emphasis on Olympic sports. You will learn the outcomes in a variety of ways—through Math Labs, interactive applets, and videos. You will work with distance-time graphs and also examine the steepness of a staircase in your home.

You will use the Internet to explore the concepts presented in the lessons, and you will play games to reinforce your understanding of those concepts. You will apply the concepts you learn to real-life problems. Keep your calculator handy throughout the module, as you will find some calculations are much easier to complete that way.