Application of Slope: How does Income Relate to Education?
Overview
Subject/SubSubject: Math/Algebra
Title: Application of Slope: How does Income Relate to Education?
Summary:
Students use a graph from 1935 to calculate income and to see how much difference an education makes in earning potential, then compare the data to more current data.
Math relates to patterns in life.
Investigative QuestionCan math help determine trends in earning related to formal education?
Grade(s):  9, 8 
Audience:  General 
Learners:  Used with 9th graders and 6th graders studying Algebra. Students should already possess the skills needed to solve the problem. 
Required Vocabulary:  N/A 
Prior Content Knowledge:  N/A 
Standards
Virginia

Field Tests
Click on the title to expand the description of each field test
June 11, 2007  Madelyn Turner
May 04, 2007  Michael Cohen
April 25, 2007  Nance Cedar
March 02, 2007  Anthony McPhee
December 31, 1969  Pam Juhl
December 31, 1969  Patty Tuttle
December 31, 1969  Becki O'Loughlin

Sources
Application of Slope: How does Income Relate to Education?
Understanding Goal
Math relates to patterns in life.
Required Materials
Web Sites
2005 census data
Directions
Investigation
Step 1  Print out copies of the images for students, or secure technology to display the images to the entire class. 
Step 2  Motivate the students by discussing the Understanding Goal and Investigative Question. 
Step 3  Display or handout the image. Ask students to explain the idea behind the image. What is the difference between the two buildings shown? What is implied from the picture? 
Step 4  Ask students to name the dependent and independent axes units. Ask students to identify the x and yintercepts of the graph. Why are the none? Is this accurate or just a model? 
Step 5  Aid students in determining the difference in earnings at age 18. Based on this number alone, would you anticipate the earnings to be close to each other at age 25? What is the difference in earnings at age 25? How did this compare to the expected difference? 
Step 6  Aid students in determining the slope of the trained and untrained workers earning power. What are the units of the slope? Ask students to describe the effect that slope has on the ending value of this line even though the beginning values at age 18 were not very different. 
Step 7  Instruct the students to write the equation of the lines for the two different earnings. If the rate of change remained the same as it was in 1935, what would the earning power have been in 2005? Depending on the emphasis desired for the lesson, use the equation, or have the students graph the data to determine the answer. 
Step 8  Display, or handout, the data from the 2005 census. Were the numbers predicted from the 1935 graph accurate?Web Sites 
Step 9  Instruct the students to use the 1935 data for a 25yearold and the 2005 data (for 25yearsold and up) to determine the actual rate of change over the time period. NOTE: students will need to convert one set of data so that it is comparable to the other (1935 is in terms of weeks, 2005 is in terms of years) 
Step 10  Determine the ratios of untrained:trained workers at age 18 in 1935, at age 25 in 1935, and at age 25 in 2005. According to these statistics, what will the future hold? 
Step 11  Discuss the variables that make predictions not hold true. Discuss the accuracy of comparing the 25yearold data and the 25yearold and over data. 
Step 12  Revisit the Understanding Goal and Investigative Question and emphasize what students can learn and earn by staying in school! 
Best Instructional Practices
Math relates to patterns in life.
Investigative QuestionCan math help determine trends in earning related to formal education?
Analysis of Student Learning
Students were able to see the importance of gaining a higher education to increase their income and thus to have a higher quality of life. They were able to apply the mathematical concept of slope to a real life situation and see the connection of mathematics to the real world.
Analysis of Best Instructional Practices (learn more)
Teaching for Understanding (learn more)
Explicit Understanding Goal
Students were engaged due to the topic.
Check Misconceptions
Students could describe many ways that the end results would be skewed.
Reflections and Recommendations
Students were motivated by using a topic that they could easily relate to. They enjoyed seeing the old image. Recommendations: Other questions could be asked of the students such as "When did the trained workers earn twice that of the untrained workers?" Another function could be developed by looking at the ratios of untrained to trained earnings over time. Specific data related to one state or race etc. is also available through the census.
Credits
Authors and Contributors
 Susan Lauffer
 WashingtonLee High School, Arlington County Public Schools, Virginia
 Teaching with Primary Sources Northern Virginia
 TPSNVA Staff, Teaching with Primary Sources Northern Virginia, Virginia
 Anne Verville
 WashingtonLee High School, Arlington County Public Schools, Virginia
Library of Congress Items
Library of Congress items used in this Lesson Plan.
Thumbnail  Library of Congress Item 

Hine, Lewis Wickes. 1917? Exhibit panel / L.W. Hine. Library of Congress: Prints & Photographs, National Child Labor Committee Collection .  
Library of Congress. n.d.. Locating International Census Data. Library of Congress: Research Centers, Business Reference Services. 