SISL > 2012 Sustainability in Math Workshop > Activities > Population Growth, Ecological Footprints, and Overshoot

Population Growth, Ecological Footprints, and Overshoot

This page is authored by Rikki Wagstrom, Associate Professor of Mathematics at Metropolitan State University, Saint Paul, MN.
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In this activity, students develop and apply linear, exponential, and rational functions to explore past and projected U.S. population growth, carbon footprint trend, ecological overshoot, and effectiveness of hypothetical carbon dioxide reduction initiatives.

Learning Goals

From a sustainability perspective, this activity explores some basic ideas that will engage students in civil discourse leading to more effective decisions:

From a mathematical perspective, this activity utilizes the following concepts and skills:

Context for Use

This activity is designed for an intermediate or college-level algebra course, or in a pre-calculus course. Students are expected to be familiar with linear and exponential functions. We use this activity as a follow-up to an earlier activity which introduces the idea of a footprint and the mathematics of footprint estimation.

Description and Teaching Materials

The student handout for this activity is found in the following pdf file.

Student Handout for Overshoot Exploration (Acrobat (PDF) 424kB Mar16 13)

This is a three-part activity. The first part deals with population growth, the second part deals with the relationships between population growth, Ecological Footprint, and Biocapacity, and the third part explores hypothetical initiatives to end overshoot. The three-part nature of the activity allows instructors flexibility in how they use it in their classroom:

Teaching Notes and Tips

If students are completing the activity independently, it is advisable to assign and grade the project in stages to allow students to receive feedback and correction along the way. This gives students the best possible chance of reaching the end of the activity without being confused or misguided.

For instructors that intend to do the bulk of the activity together with their class, a nice stopping point is right before exercise (20). Instructors can then assign the final three exercises as homework.

This activity requires students to keep track of several quantities. At some point, students may start to mix up Ecological Footprints and Biocapacities, per capita amounts and total amounts, and Carbon Footprints and Ecological Footprints. Instructors might encourage students to write down a list of all variable names and what they represent.

The amount of time required for this activity will depend entirely on how the instructor uses the activity. Parts one and two can be completed in a one-hour class period. Part three will require an additional class period.


Exercises (20)-(22) in this activity address the primary learning goals of this activity and can be used to assess student learning.

References and Resources

This activity was written in collaboration with the Global Footprint Network.

Population data in this activity were obtained from the World Population Prospects, the 2010 Revision developed by the Population Division of the Department of Economic and Social Affairs, United Nations.

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