Introduction

The concept of "average rate of change" has been discussed in a previous lesson. Recall that the average of change is the rate at which the y-values of a function change with respect to the x-values.

The average rate of change discussed previously was constant or stayed the same. When the average rate of change is constant, the function is linear. When the function is linear the rate of change is called the slope.

Take a look at the following nonlinear relationships and think about each rate of change.

Parabola opening upward with vertex of 0,0 Scatterplot showing no linear pattern
Exponential function Function with varying amounts of increase and decrease

Lesson Objectives

Following successful completion of this lesson, students will be able to...

  • Estimate a curve of best fit from tables of values to model a set of data.
  • Construct scatter plots to analyze data and produce equations to solve problems.
  • Use mathematical skills for solving application-based problems based on a set of data.
  • Determine correlations between variables.

Essential Questions

  • How is math used in different industries?
  • What math is used for optimization?
  • How is math used to solve real-world problems?
  • What math strategy or algorithm is needed to solve a real-world problem?
  • How can math connect different aspects of everyday life?

Enduring Understandings

  • •Mathematics can be used to analyze trends and to optimize products or performance.
  • Mathematical problem solvers apply various skills and strategies to make decisions about everyday-life activities and to solve real-world problems.

The above objectives correspond with the Alabama Course of Study: Career Math standards: 5a, 7a, 13, 13b.