Education Technology

It's a Small World

Published on 10/17/2008

Activity Overview

In this activity, students collect population data for the world on 10 different days and then find a model for the data set assuming that over a short period of time the data can be considered linear. Finally, they evaluate the model over a much longer period to determine the validity of the linear model.

Before the Activity

  • Open a new TI InterActive!™ document
  • Record the day- population data from the United States Census bureau web page for 10 days including January, 1st
  • See the attached PDF file for detailed instructions for this activity
  • Print pages 34 - 38 from the attached PDF file for your class
  • During the Activity

    Distribute the pages to the class.

    Follow the Activity procedures:

  • Enter the day number and population values into a list, and plot a graph of day number versus population
  • Choose two points that fit on the graphed line and record their coordinates
  • Use the coordinates to find the slope of the line that best fits the graphed data, and find the y- intercept
  • Using values of m and b form a linear model of the data and compare it to the graph to see how well it fits the data
  • Use the model to find the population on January 1st and compare it to the United States Census bureau data
  • Use the model to find the population on January 1, 2000 and also predict the year when the population was zero
  • Observe that the population calculated for January 1, 2000 by the linear model is too high, and the date of zero population is found to be 1920, which is not true
  • Observe that the model in the linear form is good only for data over a short period of time, and long term population predicting needs an exponential or logistic model
  • After the Activity

    Review student results:

  • As a class, discuss questions that appeared to be more challenging
  • Re-teach concepts as necessary