This will be taught in a calculus class. Using the software and tools as shown in the following links: https://www.vernier.com/ https://www.vernier.com/products/software/lp/, the students will use the equipment to throw a ball in the air and track its position as time goes on. The students will use the data to draw a graph of position vs time for the ball and create an equation which give the position as it is related to the time. The students will then take the slope at different points and use the data to draw a slope vs time graph. They will also create a function for this graph. This will be an introduction activity to derivatives. The students will create a functions of the position vs time as well as create a function for the slope vs time. We will then go into covering the material for derivatives. The students will understand the procedure of how to create a function from a graph or data. They will also understand the concept of what a derivative is and how it relates to the real world problem I have provided. Below you will find the handout I will give the students to guide them through the activity.

The CCSS for this lesson are as follows:

• CCSS.MATH.HSF-IF.B.4: Interpret functions that arise in applications in terms of context
• CCSS.MATH.HSF-CED.A.2: Create equations that describe numbers or relationships.
• CCSS.MATH.HSF-BF.A.1: Build a function that models a relationship between two quantities.

 

 

Ball Throwing Activity

Name:

Date:

1. Set up your iPad such that it is far enough away to get a video of the ball as you throw it straight up in the air. You should make sure the ball stays in the view of the iPad when it is thrown for you should not move the iPad during the experiment.
2. Open the Vernier Probes and Software program. Take a video of the ball as you lightly toss it straight up in the air.
3. Sketch a graph of a position vs time for the ball in the space below. Create a function for this graph.

 

 

 

 

 

 

 

 

 

4. Take the slope of the graph at t=0, at a point before the vertex, at the vertex, at a point after the vertex before the end, and finally at the point just before the ball hits the graph. What are the units of these slopes? What does this tell you about what the number means? Sketch a graph of the slopes as a time vs slope graph. Is it linear? What does that mean? Write an equation for the graph.