# A FUNCTIONAL HOUSING MARKET

Susan Boone
Subjects: Algebra I ( linear equations)

### Topic: Linear Equations (regressions)

Purpose: Students will access the Internet to search for housing prices in Houston, Texas,(the location can be changed to accommodate any location) and compare the prices to the number of square feet found in the living area of a house. A linear equation will be derived from these data on a coordinate plane. Any "best- fit" method for determining the graph of the line can be used. Using information from the graph of the data and the equations of the function, students will answer questions about housing prices.

Materials: Internet connection, graph paper, and ruler.

Prior knowledge: Students should be able to plot points on a coordinate plane and write an equation in slope-intercept form from a linear graph.

Description: Often, actual data do not represent an actual linear function. Students will be asked to access data from the Internet and derive a linear regression from their set of data. These data will be used to answer questions on average cost per square foot, land values, and to predict the cost of various sized homes.

Time: Two class periods (one for data collection and one to determine regression)

Procedure: Students will "search" for information on housing prices on the Internet.

Suggested Houston area URLs

A Net Search can also be done on real estate. Students should collect data from at least six properties in the Houston (or other specified) area. The data should include the price of the property and the square footage of the house. Calculate the square footage from given room dimensions. Plot the data on a coordinate plane as a relation of price per square footage. After students have plotted their data, instruct them to find a line of "best-fit" so most of the points are close to the ruler. There are several methods to do this, but for this lesson I recommend that a ruler be placed on the graph so that about half of the data points are above the ruler and about half are below. Draw the line, and then write an equation in slope-intercept form.

Include a copy of the page that includes the dimensions of the rooms of your house.  Be sure to include the URL.  Show all of the work you did to calculate the square footage.  Do not use any given saure footage since you do not know what measurements were included.

Questions: Be sure to include the URL for the location of each of the sites used for your data. (Include the room measurements.) After completing your graph and writing your equation, answer the following questions.

1. How much does a 5,000 sq. ft. home sell for in the location that was researched?

2. What does the slope m, of the equation represent?

3. What does the b value in the slope-intercept form of the equation represent?

4. What does the line represented on the graph indicate about the cost of housing?

5. How would this graph vary if data was collected from other parts of the country?

6. How could this graph help you decide if you wanted to purchase a house?

7. If the graphs of new home prices vs. house size from two cites are compared, the cost of lots is about the same in the two cities. How will this fact affect the two graphs?

8. If the graphs of new home prices vs. house size for two cities is compared, the construction price per square foot for building a house is about the same in the two cities. How will this fact affect the two graphs?

Extension: Research another location of the country and go through the same procedure in this lesson. Students could work in groups of 3 or 4, compare data and write a summary regarding housing prices in various parts of the country.

Gender Issues: Determine the ratio of male to female Realtors listed on the real estate locations at were used to research data. (It may not be able to determined gender of some of the Realtors). Discuss possible reasons the ratio of men/women is such that it is. Decide whether realty is a profession requiring math? If so, how much and what type? Research careers on the Internet. Site at least three URLs used and list the required education needed to get you realty license.

Special thanks fo Joe Dan Austin.
Reference: Austin, J.D., Howard, C., Thomas, R.D. Mathematics of Money, Second Ed., Section 3.6