Subject/Sub-Subject: Math/Algebra

Title: Application of Slope: How does Income Relate to Education?


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.

Understanding Goal

Math relates to patterns in life.

Investigative Question

Can 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

A.6 The student will select, justify, and apply an appropriate technique to graph linear functions and linear inequalities in two variables. Techniques will include slope-intercept, x- and y-intercepts, graphing by tranformation, and the use of the graphing calculator.

A.7 The student will determine the slope of a line when given an equation of the line, the graph of the line, or two points on the line. Slope will be described as rate of change and will be positive, negative, zero, or underfined. The graphing calculator will be used to investigate the effect of changes in the slope on the graph of the line.

A.8 The student will write an equation of a line when given the graph of the line, two points on the line, or the slope and a point on the line.

A.16 The student will, given a set of data points, write an equation for a line of best fit and use the equation to make predictions.

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


Application of Slope: How does Income Relate to Education?

Understanding Goal

Math relates to patterns in life.

Click on an image for more information.

Slideshow Icon View as a slideshow
Exhibit panel / L.W. Hine Locating International Census Data

Required Materials

Web Sites

2005 census data



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 y-intercepts 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 25-year-old and the 2005 data (for 25-years-old 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 25-year-old data and the 25-year-old and over data.
Step 12 Re-visit the Understanding Goal and Investigative Question and emphasize what students can learn and earn by staying in school!

Best Instructional Practices

Understanding Goal

Math relates to patterns in life.

Investigative Question

Can 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 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.


Authors and Contributors

Susan Lauffer
Washington-Lee High School, Arlington County Public Schools, Virginia
Teaching with Primary Sources Northern Virginia
TPSNVA Staff, Teaching with Primary Sources Northern Virginia, Virginia
Anne Verville
Washington-Lee 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
Exhibit panel / L.W. Hine Hine, Lewis Wickes. 1917? Exhibit panel / L.W. Hine. Library of Congress: Prints & Photographs, National Child Labor Committee Collection .
Locating International Census Data Library of Congress. n.d.. Locating International Census Data. Library of Congress: Research Centers, Business Reference Services.