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Housing Costs

Introduction:

Do houses cost more depending on their size? How much more? Should you pay over $100,000 for a two-bed room, one bath home that has 1500 square feet?

Task:

You are going to investigate this question using algebra to determine how much a house probably costs depending on its size.

Resources:

You will need a straightedge and graph paper to complete this activity.

You will need Internet clearance to complete this activity.

Process:

  • Put all of your data in a chart. Data should include:
    1. Price
    2. Square footage
    3. Price per square foot (you will need to calculate this)
  • Plot the data on a coordinate plane as a relation of price per square footage.
  • 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.

Evaluation:

Questions to be completed and attached to your chart and graph: 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 Bellingham?

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 if you decided to purchase a house?

7. List three factors that could make the value of a house more than the expected value as determined by its size.

8. List three factors that could make the value of a house less than the expected value as determined by its size.

9. After examining what different size houses are like, how large a home would you like to own someday?

10. How much would the home cost that you described in #7?

11. Divide your answer in #8 by 3. This is the annual income you will need to have in order to afford this home.

12. What hourly wage will you need to earn in order to afford this home? Divide your answer in #9 by the number of hours worked in a year. This is usually 50 weeks at 8 hours a day.

Extra Credit: Research another location of the county 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.

Conclusion:

Knowing what a house is worth depending on its size is a skill that everyone can use. Knowing that you are paying the right amount for what might be the largest purchase in your life is important.

Lesson courtesy of...

Susan Boone sboone@cs.rice.edu Saint Agnes Academy

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