This is a day 2 lesson-activity for AP Calculus.  In just 5 days you can introduce your calculus students to the five many concepts they will be learning about.  

What is in the lesson-activity?

This lesson is made up of an 40-50 minute activity and a 2-page homework assignment with 2 questions similar to those in the activity. Answers to all activities are included. 

How have I used it?   

Behavior of Functions was designed to have students think about how the behavior of a function is changing.  This lessons has the students study the behavior of four functions they have seen since Algebra 2.  I encourage students to see if they can make a sketch without a graphing calculator, but then I also encourage they them to use their graphing calculator to build a window that matches the given graph and then make a sketch from their calculator.  (Notice these windows are not standard windows - a skill students must use on the AP test.)  After creating the four graphs, students are asked to draw a tangent line on each graph at x = 1 and use their graphs to approximate the slope of the tangent line.  Students are asked to describe how the behavior of the function at x = 1 on each graph.  Depending on the slope students could say the graph is increasing, decreasing or neither and relate that to the slope of their tangent line. 

This is a one day lesson-activity that is part of a larger package known as a Jet Tour of Calculus.  

The Jet Tour of Calculus is a set of five one-day lessons, where students are introduced to the five main topics of Calculus,  AB Calculus, and BC Calculus.   The titles of the five lessons are  

1. Instantaneous Rate of Change

2. Behavior of a Function

3. Definite Integrals

4. Using Formulas to find Definite Integrals

5. Limits

The five lessons can be purchased separately or in a bundle.  

Each lesson is designed to engage students in using their graphing calculator to building understanding for the five topics graphically, numerically, analytically, and verbally.  The concept of the five topics is emphasized but the notation does not need to be emphasized since you will be returning to each of these topics to study them further. Upon completion of the five lessons students gain a strong understanding of what they will be studying in the year of calculus that is ahead for them.

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