Activity Plan

Title: Velocity and Position Are Buddies.

Topics: The relationship between velocity and position.

Connection to Core Curriculum: This activity covers objectives that are geared toward calculus students, a course which is not covered as part of the core curriculum. It should be noted, however, that even though the following are not specified objectives for the activity, students will gain experience and further knowledge in areas connected to the core curriculum by engaging in the activity:

High School: Functions >> Interpreting Functions>> Interpret functions that arise in applications in terms of the context. >> For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. >> Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.

High School: Statistics and Probability>> Interpreting Categorical and Quantitative Data>> Summarize, represent, and interpret data on two categorical and quantitative variables >> Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models.

Overview: Students will discover that computing area under a velocity function gives the position or total distance traveled. Students generate velocity over time and then compute the area given by those velocities to find area in a discrete and continuous case. Note that this activity can be modified for a bus trip or other real-world application where velocity can actually be measured and recorded over time.

Objectives:

• Students will use and apply a velocity to a real world problem and gain broader understanding of what a velocity function represents.

• Students will discover the relationship between velocity and position.

• Students will discuss and explain briefly why the integral of velocity is position.

Activity Plan:

• Announce that we will be working individually with an applet and then discussing what we learned in groups.

• Hand out the task sheet and set a timer for 16 minutes.

• After the timer goes off, split students into groups of 3-4 and given them another 10 minutes to discuss what they discovered from the applet.

• End the group discussions and set a timer for 6 more minutes to allow students to record their discussion and findings on the back of their task sheet.

• Lead the class in a short (3-4 minutes) overview of what students discovered (the integral of velocity is total distance traveled, or position) and why (we know that the area of a rectangle is given by base x height and that distance = speed x time, which is given by our vertical and horizontal axis. The continuous case (integral) is used because speed is a continuous function- we don't suddenly go from one speed to another, we accelerate from one to another.)

Background: (optional)

Extensions: (optional)

Included documents: Task sheet: What if the Odometer is Broken?

References: (As appropriate)