Learning Resources

Outcomes

In this lesson you will

• Explore a table of data describing a car trip.
• Calculate speed as the average rate of change over time for various parts of the trip.
• Explore how information about speed is useful in describing a situation.

By the end of this section you should be able to:

• Demonstrate an understanding of the concept of rate of change in a variety of situations.
• Demonstrate an understanding that slope depicts rate of change.
• Calculate average rates of change.
• Describe and apply rates of change by analyzing graphs, equations, and descriptions of linear and quadratic functions.

Introduction

In this section you will focus on the contexts in which rate of change might be considered. You will see that you can calculate average rate of change by comparing the total change in one variable to the total change in another. A variety of contexts will be used, but in particular, speed as the rate comparing change in distance with change in time is examined.

This section will provide opportunities for you to define rates of change by examining graphs, tables, and/or functional descriptions of situations and explores the idea that linear relations are those with a constant rate of change.

You will also see in this section that rates of change vary in a consistent pattern for quadratic relations. You will see the following:

• When a rate of change is positive, the graph goes up from left to right.
• When the rate of change is negative, the graph goes down from left to right.
• When the rate of change is zero, the graph is horizontal.

This section should take you about 3 hours to complete.

Prerequisites

To be successful in this lesson, it would be helpful to know the following:

• How to find the average (mean) of a set of data.
• The concept of average speed as distance/time.