Education Technology

# Activities

• ##### Subject Area

• Math: Calculus: Derivatives
• Math: Calculus: Applications of the Derivative
• Math: Precalculus: Logistic Functions
• Math: Calculus: Limits of Functions

9-12

30 Minutes

• ##### Device
• TI-83 Plus Family
• TI-84 Plus
• TI-84 Plus Silver Edition
• TI-Navigator™
• ##### Software

LearningCheck™ Creator

• ##### Other Materials
• Overhead view screen calculator for instruction/demonstration
• Student handout
• Transparency
• USA TODAY newspapers (recommended)

## Math TODAY - World Population Milestones

#### Activity Overview

Students will create a scatter plot of the world population for the years 1950 through 2050. The United Nations Population Division data will allow students to explore real-life data that will be modeled by a logistic function. Students will have the opportunity to explore the end behavior of this model and explain what this means about the world population estimates. The derivative will be used to explore when the world population increased most rapidly during this time period.

#### Before the Activity

See the attached Teacher Edition PDF file for notes and guidelines for this activity. The Technology Guide PDF file includes step-by-step calculator instructions with screen shots.

If you are using the TI-Navigator™ Classroom Learning System, see the TI-Navigator Basic Skills Guide PDF file for information on how the system can be integrated into your activity.

#### During the Activity

Students will:

• model real-life data with a logistic function.
• determine and interpret the limiting behavior of the logistic function.
• interpret the instantaneous rate of change at the inflection point of a graph.

• Directions
• Distribute the Student Edition PDF file to your class.
• Follow the activity procedures outlined in the student document.
• You may use the Transparency PDF file to display a large image of the USA TODAY graphic during the activity.
• #### After the Activity

Distribute the assessment questions or send the attached LearningCheck™ assessment to your class to gauge student understanding of the concepts presented in the activity.