Learning about Rate of Change in Linear Functions Using Interactive Graphs

In this two-part example, users can drag a slider on an interactive graph to modify a rate of change (cost per minute for phone use) and learn how modifications in that rate affect the linear graph displaying accumulation (the total cost of calls). In this first part, Constant Cost per Minute, the cost per minute for phone use remains constant over time. In the second part, Changing Cost per Minute, the cost per minute for phone use changes after the first sixty minutes of calls. Understanding the relationship between change and accumulation is a precursor to understanding calculus. This example illustrates the use of dynamic graphs to learn about change and linear relationships, as described in the Algebra Standard.

Individual Lessons

Lesson 1 - Constant Cost per Minute

In this two-part example, users can drag a slider on an interactive graph to modify a rate of change (cost per minute for phone use) and learn how modifications in that rate affect the linear graph displaying accumulation (the total cost of calls). In this first part, Constant Cost per Minute, the cost per minute for phone use remains constant over time. In the second part, Changing Cost per Minute, the cost per minute for phone use changes after the first sixty minutes of calls. Understanding the relationship between change and accumulation is a precursor to understanding calculus. This example illustrates the use of dynamic graphs to learn about change and linear relationships, as described in the Algebra Standard.

Lesson 2 - Changing Cost per Minute

In this two-part example, users can drag a slider on an interactive graph to modify a rate of change (cost per minute for phone use) and learn how modifications in that rate affect the linear graph displaying accumulation (the total cost of calls). In the first part, Constant Cost per Minute, the cost per minute for phone use remains constant over time. In this second part, Changing Cost per Minute, the cost per minute for phone use changes after the first sixty minutes of calls. Understanding the relationship between change and accumulation is a precursor to understanding calculus. This example illustrates the use of dynamic graphs to learn about change and linear relationships, as described in the Algebra Standard.