SISL > 2012 Sustainability in Math Workshop > Activities > Fitting and Estimating Rates of Change in the Functions Underlying Earth's Bio-Development Over Time

# Fitting and Estimating Rates of Change in the Functions Underlying Earth's Bio-Development Over Time

#### Summary

Students will explore a geologic history app, showing the movement of continents, as well as the corresponding changes in biodiversity, and the related variables oxygen, carbon dioxide, and temperature. Once familiar with the data through user-friendly UI in the app, they will download the source data and analyze it Excel. Analysis steps including parsing 2 column data, plotting, and basic function fitting.
Students then compare numerical estimates of rates of change with rates obtained by differentiating the fitted functions. Finally, students go back to the data on their own, and make a case as an advocate for an environmental or business group about the impact of environmental variables on biodiversity.

## Learning Goals

Present relationships between global environmental factors (oxygen, carbon dioxide and temperature) and biodiversity.

Engage students in civil discourse and communications that lead to more effective decisions.

Advance student literacy around sustainability issues.

Encourage self-reflection and personal development of student voices for solving societal challenges.

Promote critical thinking and data analysis.

## Context for Use

Designed for Calc I classes. Roughly one hour for the main interactive activity, with post-class analysis and report writing.

## Description and Teaching Materials

Part 1: To begin, we will be investigating the time period from 1970-1985. Go to the Biointeractive website and enter the data for years, temperature, carbon dioxide, and biodiversity into an Excel spreadsheet.

1. Create a scatterplot of year and carbon dioxide. For simplicity sake, call year 1970 time 0. Your x-axis should range from 0 to 15.
2. For the year 1983, pick two points (one before, one after), and calculate the slope. Include units in your answer.
3. Now click on your graph, and under chart tools and layout, click on "Add Trendline" and select "More trendline options."
4. Experiment with the different trend lines to find a function that best fits through the data. Select "Display Equation on Chart" at the bottom. If using a polynomial function experiment with the order (i.e. quadratic, cubic, quartic, etc).
5. Using your equation, calculate and interpret the derivative for the year 1983 in context.
6. How do your two derivative estimates compare?
7. Repeat the process for year with temperature and biodiversity. Note if the points are really scattered the function will probably not fit perfectly.
8. For the graph for biodiversity, what happens in 1976?
9. What overall conclusions can you make? Write a paragraph summarizing your results.

## Teaching Notes and Tips

Teaching Notes 1.

## Assessment

Assessment Notes 1.

Resources 1.