# A Look at High School Dropout Rates: Average Rates of Change and Trend Lines

This material is replicated on a number of sites as part of the SERC Pedagogic Service Project

#### Summary

In this Spreadsheets Across the Curriculum activity, students calculate the average rate of change and graph a scatter plot of status high school dropout rate for 1975-2002. They compare the average rate of change determined by the total net difference divided by the length of the time period to the slope of the trend line fitted to the data on the scatter plot. In the end-of-module "Show You Know" assignment, the students analyze data for the event highschool dropout rate over the same time period, and they compare the two measures, status vs. event dropout rates. The module combines interpretation of rate of change in the context of a real-world time-series data set with instruction on elementary spreadsheet computation and graphing.

## Learning Goals

Mathematics. Students will:
• Calculate the average rate of change by dividing the net difference between the beginning and final values by the duration of the time period.
• Calculate an average of the annual rates of change and find that it is an incorrect measure of the average rate of change when the values represent unequal time intervals.
• Find that although there is an overall average decline in highschool dropout rate (negative sign), there are intervals within the time period when highschool dropout rate increased (postive sign).
• Labor over the wording of rate of change of the dropout rate.
• Draw a scatter plot of the data and find that the slope is not the same as the average rate of change unless the first and last data point fall on the trend line.
Excel. Students will:
• Build a spreadsheet and calculate the average of a column of data.
• Draw a scatter plot of the data and determine the trend line.
Context. Students will:
• Look at tables and graphs of highschool dropout rates
• See that there are different measures, namely status dropout rates and event dropout rates.
Overall. In the process of this work, students will come to see that there are nuances, and indeed hazards, in the ubiquitous term "average rate of change."

## Context for Use

I plan to use this activity in courses in intermediate algebra, college algebra, and precalculus, where students benefit from working with real-world data. I wrote the module with the intention of its being of interest in courses in education and sociology as well. The general concepts of rate of change and trend lines have widespread applicability, of course, and the module can be easily adapted to fit the context of other courses.

Wherever the module is used, students will need to have PowerPoint and Excel.

## Description and Teaching Materials

SSAC2006.LC142.FCW1.1-student (PowerPoint 386kB Sep11 06)

The module is a PowerPoint presentation with embedded spreadsheets.

If the embedded spreadsheets are not visible, save the PowerPoint file to disk and open it from there.

This PowerPoint file is the student version of the module. An instructor version is available by request. The instructor version includes the completed spreadsheet. Send your request to Len Vacher (vacher@usf.edu) by filling out and submitting the Instructor Module Request Form.

## Teaching Notes and Tips

This activity may best be completed in a computer lab with each student having individual access to a computer. Or, it can be used as a homework assignment following a presentation or discussion in class.

## Assessment

The Show You Know activities at the end of the PowerPoint presentation provide students the opportunity to demonstrate basic skills, explain relevant concepts, and apply the knowledge in a new context. The instructor version includes a pre-test.

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