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Activity 1: Comparative Costs: The Early 19th Century and Today
(Grade Range: 5-7)

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Objectives:

  • Perform calculations involving measurements of land and the value of money
  • Interpret and create graphs depicting the value of money at different time periods
  • Calculate the value of money during different time periods using several methods

NCTM Standards:
Standard 4: Measurement: understand attributes, units, and systems of measurement and apply a variety of techniques, tools, and formulas for determining measurements.

Standard 10: Representation: develop a repertoire of mathematical representations . . . to model and interpret physical, social, and mathematical phenomena.

adobe acrobat Student Activity (PDF File)
Answers (PDF File)

The Louisiana Purchase

Louisiana Purchase Map
Figure 1. The territory acquired in the Louisiana Purchase.
During the presidency of Thomas Jefferson, the United States succeeded in purchasing from France a large body of land known as the Louisiana Territory. The purchase was called the Louisiana Purchase.

On April 30, 1803, Robert Livingston, ambassador to France, and James Monroe, special envoy, concluded a treaty in Paris in which the United States purchased from France the whole of the Louisiana territory for $15,000,000.

The territory (see Figure 1), approximately 800,000 square miles, included the Mississippi River Valley and most of the present-day Midwest, almost doubled the size of what was then the United States.

1. One acre is 43,560 square feet or 4,840 square yards. There are exactly 640 acres in a square mile.

     a. How many acres were purchased?

     b. What was the cost per acre?

2. Today, an acre of land can cost anywhere from $100 to $1,000,000. Assuming $500 per acre as a very low price, how much would the Louisiana Purchase have cost at this rate?

3. The chart in Figure 2 illustrates the value of money between 1800 and 1999. It illustrates that $100 in 1999 had less value than in previous years. For example, $100 in 1999 is the equivalent of $10 in 1920.

Use the chart in Figure 2 to determine the price of the Louisiana Purchase in today's dollars.

Chart showing the value of a U. S. dollar from 1800 to 1999
Figure 2. Chart showing the value of a U. S. dollar from 1800 to 1999.

4. Go to this web site: http://www.westegg.com/inflation/ Use the inflation calculator on this web page to determine the exact cost of the Louisiana Purchase in today's dollars.

5. Use the amount found in problem 4 to find the percentage change in 1803 dollars compared to 1999 dollars.

It might surprise you that the U.S. was able to purchase this large territory for so little money (even in current dollars). Events that might explain this bargain include the fact that Emperor Napoleon of France had just lost an army and the island of Santo Domingo in the Caribbean to Toussaint L'Overture, the leader of a slave insurrection. As a result, Napoleon was no longer interested in maintaining a French foothold in North America. The purchase was ratified through congressional legislation in October of 1803.

Jefferson's Library

Thomas Jefferson offered to sell his library to the federal government in 1814. The government's own library was lost in August when the British burned the Capitol in Washington, D.C.

In January 1815, Congress purchased Jefferson's library of 6,487 volumes for $23,940. It was shipped to Washington by wagon in May. Jefferson's library became the foundation for the collections of the Library of Congress.

6. What was the purchase price per book for Jefferson's library?

7. Use the graph in Figure 2 to determine the cost of Jefferson's library in current dollars.

8. Use the inflation calculator to determine the exact cost of the purchase in today's dollars. ( http://www.westegg.com/inflation )

9. Use the amount found in problem 8 to compute the percentage change from 1815 to 1999 dollars.

10. Explain whether you find this transaction fair to both parties (President Jefferson and the U. S. government).

Presidential Salaries

The President of the United States currently earns $200,000 per year.

Chart of presidents' salaries
Figure 3. Chart of presidents' salaries.

11. What would the value of the president's annual salary be in the following years?

     a. The end of Ronald Reagan's presidency (1983)?

     b. The end of Richard Nixon's presidency (1974)?

12. Use the inflation calculator web page (http://www.westegg.com/inflation) to answer the following questions about presidential salaries if the following presidents had been paid the equivalent of $200,000.

     a. Thomas Jefferson's salary (1809)

     b. Abraham Lincoln's (1865)

     c. Woodrow Wilson (1921)

13. On the blank graph below, extend the information from the presidential pay graph back to 1800. (Hint: use the inflation calculator to find the values. http://www.westegg.com/inflation.)

Blank Graph
14. Explain whether you think the $200,000 per year salary is a fair salary for the president and why.