Module 5 Introduction

Math 10C Module 5 Introduction

Module 5: Linear Functions

Module 5 Introduction

This shows a photo of the Olympic flag surrounded by the flags of some of the participating countries.

Hemera/Thinkstock

The first Olympic athletes stepped into the great stadium at Olympia, Greece, in 776 BC. Since then, the Olympics have evolved to become a worldwide spectacle. At one time, both the Summer Olympics and the Winter Olympics were held in the same year. Now the summer and winter games alternate on even years. In addition, the number of official Olympic events or disciplines has expanded significantly.

As many as ten years before an anticipated Olympic Games, cities will vie for the chance to host the Olympics. Factors such as facilities and accommodations as well as scheduling, transportation, and efforts to promote environmental sustainability all need to be adequately addressed for a bid to be considered.

The successful city will spend the years leading up to the Olympics preparing for the Games by building and improving infrastructure and by constructing and repairing buildings and public roadways. This activity stimulates the local economy by providing jobs and inviting business and trade. Above all, a city that hosts the Olympics receives a lot of attention on the world stage by promoting itself and its country on the world’s largest stage.

One of the benefits of having the Summer Games and Winter Games hosted in different cities for each Olympic year is that each city has a different way of staging the event. The athletic events will be conducted according to standard rules, but the venues, courses, and atmosphere will all be different.

At the beginning of Module 5, you will prepare as a host city prepares for an upcoming Olympic games. You will study linear relations and functions. You will analyze their properties and investigate their different representations. You will lay the groundwork for further studies in the next unit where you will investigate linear equations and systems of linear equations.

In the second half of Module 5, you will study a variety of forms of linear functions. These are the slope-intercept form, slope-point form, and general form. All of these forms are different ways to express linear functions. These forms are different in the same way that one Summer Games is different from the next one. Each form can be used to represent the same linear function, but each one has different properties and features.

In this module you will investigate the following questions:

What are linear relations and functions?
What techniques are involved in working with linear relations and functions to solve problems and communicate understanding?

To investigate these questions, you will focus on the following lessons and consider the listed lesson questions.

Lesson	Title	Lesson Questions
1	Identifying Linear Relations	How can you distinguish a linear relation from a non-linear relation? How can the concept of slope be used to identify a linear relation?
2	Properties of Linear Functions	How are linear functions uniquely defined by their properties? How can the properties of linear functions be used to solve problems?
3	Slope-Intercept Form	How does the equation of a linear function relate to its graph? How are the properties of linear functions applied to studying and solving problems?
4	General Form and Slope-Point Form	How are the general, slope-intercept, and slope-point forms different from each other? Why are there multiple ways of expressing linear functions?
5	Graphing Linear Functions	In what ways can you verify that you have properly graphed a linear function? How is graphing a linear relation similar to solving the corresponding equation?

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 this module 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 concepts; and you will work through short, interactive lessons that allow you to apply those concepts. You will solve reality-based problems that will help you to see how these concepts are applied in day-to-day living.

You will continue to do exciting project work, which will reinforce your understanding of key mathematical ideas. Your project work will involve, among other things, creating a simulated bungee jump!

Keep your calculator handy throughout the module as you will find some calculations are much easier to complete that way.