Lesson Plans
Back to lesson plans archive June 14, 2013Are colleges affordable? – Lesson Plan
By Mary F. Klein a mathematics teacher from Urbana, Illinois
Subject(s)
Secondyear algebra courses and beyond, high school mathematics
Time
One to two class periods
Objectives
A mathematical model is a method of understanding a complex real world process involving multiple variables. To design a model, important features are identified and quantified symbolically using a number of mathematical tools. Once designed, a mathematical model must be evaluated and critiqued for accuracy, advantages, and limitations.
In this lesson, the students investigate a mathematical model that compares the cost of education to potential earnings in order to decide if the investment is a good one. The students compute the amount to be repaid each year for the life of the loan and then they compare the answer to some probable starting salaries. Finally, the students critique the model discussing which other factors (demand for the job, other costs, etc.) should be taken into consideration.
Overview
This lesson and activity are designed to help students understand the idea of a mathematical model and, at the same time, provide a tool that may be useful to them when they choose a college and evaluate the potential debt that may result.
Procedures
 Distribute the Online NewsHour story, ‘Paying More For College, Getting Less’ for students to read. Briefly discuss the story. Bring up the idea that one goes into debt to finance a house. Does it pay to borrow to finance future earnings? Point out that borrowing for a house or an education can be considered an investment, while borrowing for a car is not an investment since the car depreciates in value. Tell the class that today’s goal is to use mathematics to investigate the relationship between how much we borrow and how much we can afford to borrow.
 Tell students that the power of mathematics is that it can be used to help us understand our world and that an important tool is the mathematical model. Define ‘mathematical model’. Distribute the handout, ‘The Mathematical Model,’ and the worksheet.
 Go over the parts of the model and then work out the details of the first problem on the worksheet.
 Point out that since we know the amount of the yearly payment, we can consider the yearly payment to be a constant. Equation D can be simplified to y = (205,800) / x. What sort of graph can we expect? A hyperbola! Graph equation D. (Let 0 < x < $60,000 using increments of $10,000 and let 0 < y < 100% using increments of 10%.)
 Discuss how to interpret the graph. (As earnings increase the percent of income used to repay the debt decreases). The financial industry standard is that total debt (including housing) should be less that 36% of gross earnings. Is the value we found for A in fact a reasonable debt ratio for a first year teacher earning $28,132 (the median income for a teacher with a BA in Illinois)? The minimum starting salary for such a teacher is $20,299. Discuss how low that first year starting salary could be and still support a reasonable debt ratio. (Use a graphing utility to plot y = 36. Find the intersection of the graphs.) Would it matter if there were a glut or a shortage of teachers in a particular field?
 Assign students to groups and have them present their findings. (To save time, you might assign just 1 or 2 problems to each group.)
 Check answers.
 Discuss the model itself. Is it a good model? What hidden assumptions does it make? What are its limitations? What would the students change?
Extension Activity
 Investigate the effect on the debt ratio if a student charges daily expenses to a credit card and makes only the minimum payment each month.
 Borrow a copy of Peterson’s Complete Guide to Colleges from a high school counselor. Choose a number of colleges or universities and look up ‘the average debt incurred by students the previous year’ for each school. Compare the debt ratios for the different schools.
Sources
Robert Andersen, Associate Director of Financial Aid, University of Illinois at UrbanaChampaign
Chris Hopkins, Counselor, Urbana High School
Author Mary F. Klein is a mathematics teacher with experience at the high school, middle school, and junior high school levels. She is the author of several Webbased lessons on mathematics and basketball. She lives with her husband and son in Urbana, Illinois.
Tags:
The Materials You Need
Tooltip of materials
 NewsHour Extra: Paying More for College, Getting Less
 One graphing calculator per student or group of students (a scientific calculator and graph paper could also be used)
 Student Worksheet
 The Mathematical Model Handout
 Answer Key
 Chalkboard or overhead
 Overhead graphing utility (optional)
Standards
Tooltip of standarts
Relevant National Standards:
 Students should use mathematical models to represent and understand quantitative relationships
 Students should analyze and evaluate the mathematical thinking and strategies of others
 Students should represent and analyze mathematical situations and structures using algebraic symbols
National Council of Teachers of
Mathematics Standards
Related Stories
Tooltip of related stories
More Articles
Tooltip of more video block
RSS Content
Tooltip of RSS content 3

Fewer Republicans hold town hall meetings in face of critical crowds
Members of Congress customarily hold town hall meetings in their home districts while on recess. However, fewer than 30 Republicans have held such gatherings due to local protests and rowdiness. Continue reading
CongressdemocracyGovernment & CivicslawmakersSocial Studiestown halls 
Baltimore program hopes to overcome violence with mindfulness
Schools in Baltimore, Maryland are experimenting with meditation as a way to help students deal with stress and trauma. Continue reading
meditationmindfulnesspovertystresstraumayoga 
75 years later, Japanese internment executive order remembered
February 19, 2017, marked the 75th anniversary of President Franklin D. Roosevelt’s controversial executive order, which allowed the government to incarcerate Japanese Americans after the attack on Pearl Harbor in World War II. Continue reading
Executive OrderGovernment & CivicsimmigrationinternmentJapanese internment campSocial StudiesWorld War II 
Local sheriff shares concerns over federal immigration laws
Dozens of cities throughout the United States have been deemed “sanctuary cities,” where local governments resist cooperating with federal immigration officials, including handing over undocumented immigrants who have may committed very minor offenses. Continue reading
Government & Civicsimmigrationlaw enforcementsanctuary citySocial Studies 
Community comes together to help homeless students and families
In order to address the homelessness problem facing students, a school district in Kansas City, Kansas, with over 1,000 homeless students, partnered with Avenue of Life, a nonprofit organization that brings students out of homelessness by supporting the entire family. Continue reading
Government & CivicshomelesshomelessnesspovertySocial Studies