Pedagogy in Action > Library > Interactive Lectures > Examples > U.S. Population Growth: What Does the Future Hold?

# U.S. Population Growth: What Does the Future Hold?

This material was originally developed through Merlot
as part of its collaboration with the SERC Pedagogic Service.

#### Summary

College Algebra or Liberal Arts math students are presented with a ConcepTest, a Question of the Day and a write-pair-share activity involving U.S. population growth. The results are quite revealing and show that while students may have learned how to perform the necessary calculations, their conceptual understanding concerning exponential growth may remain faulty. Student knowledge (or lack thereof) of the size of our population and its annual growth rate may also be surprising.

## Learning Goals

To enable students to:
• gain some knowledge of the size of our U.S. population and its projected growth
• develop a deeper understanding of exponential growth
• recognize the differences and similarities between linear growth and exponential growth
• recognize the effect and implications of long-term exponential growth even when the growth rate is relatively small

## Context for Use

This activity can be used in a College Algebra or Liberal Arts math class as an introduction to the nature of exponential growth and can be carried out in either a small class or a large lecture setting. A scientific or graphing calculator is required along with Internet access to display specific graphs of population data.

The time required for the entire activity is approximately 25-30 minutes but fewer segments can be offered as a shorter alternative (see Activity Description below for individual segment times).

## Description and Teaching Materials

Activity description
• Students are given a ConcepTest (Rich Text File 26kB Jul9 07) in the form of a straw poll (either show-of-hands or written) concerning the current U.S. population, its current growth rate, and a projection concerning the population in 2050. Each student is asked to make a conjecture and the instructor records the results for the class to see. (~5 minutes)
• The Question of the Day (Rich Text File 17kB Jul9 07) addresses the difference between a ten-year growth rate and an annual growth rate and also addresses the similarities and differences between linear and exponential growth. It begins with three ConcepTest questions and then students work in pairs to share and explain their answers and reasonings in written form. The instructor will need Internet access and a projector to display the specified population graphs for student viewing. (~10 minutes)

• Lastly, students are asked to construct an exponential growth model and calculate future population values with the help of a graphing calculator in a write-pair-share activity (Rich Text File 86kB Jul9 07). They are also asked to describe and record the implications of these projected values. (~5-10 minutes)
• In conclusion, the instructor presents a summary of student results (~5 minutes)

## Teaching Notes and Tips

The ConcepTest reveals how unaware many students are of the size of our current U.S. population and its annual growth rate (they are generally unaware of the sizes and growth rates of their city and state populations as well). In turn, the Question of the Day reveals that many students do not recognize the nature of exponential growth until it is clearly pointed out to them.

Lastly, the write-pair-share activity is designed to bring them to a realization of the dramatic results of our population growth if it were to continue at its present growth rate. Most students have never considered the mathematics involved and are somewhat shocked at the results.

## Assessment

I generally use this assignment as a means to provoke student thinking and reflection; grading is optional.

## References and Resources

U.S. Census Bureau