# Using functions in an introductory geoscience course

#### Summary

_{2}increase are two exercises that are included to help teach exponential growth and decay. The template and exercises guide faculty through helping students to make connections between datasets, graphs and functions.

## Learning Goals

- use data to plot a curve or a line
- read information from a plot
- recognize different functions, in numerical, graphical, and algebraic forms
- calculate slopes of functions
- interpolation and extrapolation
- (optional) learning to use appropriate technology (e.g., Excel)

## Context for Use

## Teaching Notes and Tips

We envision this template as an outline for teachers of introductory geology classes (physical, historical, environmental, etc.) who want to develop the graphical literacy of their students. They will be able to adapt this template for any graph or function of interest. Similarly, it can be adapted to illustrate functions in a pre-calculus course.

We guide you through reasoning for giving students CONTEXT, showing them and guiding them through exploring DATA, preparing students to GRAPH, exploring the GRAPHICAL expression, introduction and use of EQUATION, and ANALYSIS. Each graph will be different but we also encourage you to have students to think deeply about the mathematics and geology behind what you have shown the students by asking thoughtful questions.

## Teaching Materials

- Template for teaching functions (Acrobat (PDF) 144kB Jan20 04) with guidelines for helping students to make connections,
- Exercise dealing with population growth (Acrobat (PDF) 160kB Jan20 04) and exponential functions,
- Exercise dealing with exponential functions in relation to atmospheric carbon dioxide increase (Acrobat (PDF) 152kB Jan20 04) through time.

## Assessment

These exercises are most easily assessed by giving them as homework and grading them.

However, the template may be used as a part of a lecture and if this is the case, questions on an exam in which students must interpret a graph or choose the equation that is most like its graphical representation may be appropriate.

## References and Resources

### World population

- The United Nations has an informative site on world population. You can download comma-delimited files of population from 1950 projected to 2050.
- The US census has world population information from each year (1950-2050) and estimated historical information (before 1950).

### Atmospheric CO_{2} increase

- Online trends provides a number of ice core data sets that contain atmospheric carbon dioxide and carbon isotope information.
- QELP has infomation about carbon dioxide changes on Mauna Loa.

### Functions

- Wolfram has an entire site dedicated to functions. They have information on all types of functions from elementary to elliptical integrals to polylogarithmic functions.
- MathHelp has a number of pages on equations and functions: equations and functions, coordinates and graphs, linear functions, and quadratic equations.

## Controlled Vocabulary Terms

**Resource Type**: Activities:Classroom Activity:Short Activity, Activities:Problem Set, Classroom Activity

**Special Interest**: Quantitative

**Grade Level**: College Lower (13-14), :Introductory Level

**Quantitative Skills**: Vectors and Matrices, Probability and Statistics:Data Trends:Curve Fitting/Regression, Problem Solving:Equations, Arithmetic/Computation, Graphs, Geometry and Trigonometry, Algebra, Logarithms/Exponential Functions:Logarithms

**Ready for Use**: Ready to Use

**Quantitative Skills Activity Type**: Short Activity, Problem Set, Classroom Activity