# Students and Teachers

Author David Graser, Yavapai College, Prescott, AZ (David_Graser@yc.edu)

### Abstract This project grew out of the highly publicized reports of teacher shortages in public schools. At about the same time, many reports also publicized a nursing shortage. I asked my students, “How would you document such a shortage?”

The data for this project are from the Statistical Abstract of the United States at Fedstats. Most textbooks emphasize time series and this data allows other representations of the data (see Notes below). In this project, I chose to focus on a recommendation by the NEA that the student to teacher ratio be 15 to 1 in classrooms. Students look at national and state data and form student to teacher ratios for the time period from 2000 to 2006. All students complete a common component on the national data and then apply what they learn to state data that they are assigned. The ultimate goal is to determine the year in which the state and national student to teacher ratio reaches 15 students per teacher.

• Content Area – College Algebra
• Time Frame – 2 to 3 weeks with Mini Lectures
• Published – May 27, 2008
• Keywords – linear, modeling, ratio

### Project Content

Project Letter (DOC | PDF)
Project Data (Excel | PDF)

### Scaffolding Resources

Technology Assignment : Graph Formula (DOC | PDF) In this tech assignment, students learn how to graph a simple linear formula on a graphing calculator and in Excel.

Technology Assignment: Scatter Plot (DOC | PDF) In this tech assignment, students learn how to make a scatter plot on a graphing calculator and in Excel.

Technology Assignment: Line Through Two Points (DOC | PDF) As a precursor to modeling data using regression, students learn how to draw a line through two points on a scatter plot on a graphing calculator and in Excel.

Technology Assignment: Linear Regression (DOC | PDF) This tech assignment helps students to learn how to model data in a scatter plot using linear regression. Instructions are detailed for a graphing calculator as well as in Excel.

Fitting Lines to Data (Video)

Solving Models with Excel and Mathtype (Video)

Formatting Numbers and Adding a Second Curve to a Graph in Excel (Video)

How to Find a Point of Intersection on a TI Graphing Calculator (PDF) This document shows how to put in two equations and find the point of intersection using the intersect command from the CALC menu.

How to Find a Point of Intersection in Excel (PDF) This document shows how to find the point of intersection using GOAL SEEK in Excel.

### Notes

• Data has been updated through the 2006-2007 school year in both the Excel file and the PDF data file.
• Some of the Scaffolding Resources from the College Costs Project might be helpful.
• Most states have student to teacher ratios higher than 15 to 1 and are decreasing. A few have ratios lower than 15 to 1 and are increasing. Be cautious in assigning states!
• An interesting project could be created by having students graph a scatter plot of students versus teachers in each state. The slope of the model would have units of students per teacher. How are these units different from the student to teacher ratio?
• You can also find data on nurses and doctors in the Statistical Abstract of the United States under Health & Nutrition. If you have a large nursing students population, this same analysis could apply with students changed to nurses and teachers changed to doctors. Then the ratio you are interested in is the nurse to doctor ratio.
• The four technology assignments are provided to help students step through the steps in the project. They are given over a four week period and gets them started and allows you to see their progress.