HCPSS Worthwhile Math Task
Land Purchases in U.S. History
Common Core Standard
8.EE.4. Perform operations with numbers expressed in scientific notation, including problems
where both decimal and scientific notation are used. Use scientific notation and choose units of
appropriate size for measurements of very large or very small quantities (e.g., use millimeters per
year for seafloor spreading). Interpret scientific notation that has been generated by technology.
The Task
Read 3 brief paragraphs that outline major land purchases made throughout U.S. history. Using
information from the paragraphs, determine the purchase price per square mile and per acre.
What would the purchase price be now?
Facilitator Notes
1. Introduce the task to the students. Allow 10-15 minutes for students to read the attached
articles about U.S. purchases in history.
2. Students will work with a partner using the solution method of their choice.
3. Additional Resources for Students:
Alaska Purchase Video Clip from www.discoveryeducation.com
Link:
http://player.discoveryeducation.com/index.cfm?guidAssetID=F64D270DD716-4075-9A2A-DB4B1F50D2C1&productcode=US
Gadsden Purchase Video Clip from www.discoveryeducation.com
Link:
http://player.discoveryeducation.com/index.cfm?guidAssetID=39EBA09EE174-4F38-ADCA-F6F4162B4E6C&productcode=US
Follow-Up
Questions
The Louisiana Purchase Video Clip from www.discoveryeducation.com
Link:
http://player.discoveryeducation.com/index.cfm?guidAssetID=43B63AF860F7-4A02-BE55-668EC473E925&productcode=US
Howard County Public Schools Office of Secondary Mathematics Curricular Projects has
licensed this product under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0
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HCPSS Worthwhile Math Task
1. What are some factors that could have affected the purchase price of the different lands?
2. Of the 3 purchases, Alaska, Louisiana, and Gadsden, which was the best purchase made
by the U.S.? Justify your answer.
3. If the U.S. had purchased an additional 205, 000 square miles of land in 1803, what
would the purchase price have been?
Solutions
Students may use a variety of strategies to solve. Here is one sample answer:
The Louisiana Purchase
1.5  10 7
 .1812  10 2  1.812  101  $18.12 /sq.mile
8.28  10 5
Cost per square mile
Cost per acre


Cost Today

(8.28 105 )(6.4 102 )  52.992 107  5.2992 108
(number of acres purchased)
1.5  10 7
1
 2.83  10 2  .0283  $0.03/acre
8  .283  10
5.2992  10
(1.5 107 )(2.041101)  3.0615 108
$306,150,000

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licensed this product under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0
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HCPSS Worthwhile Math Task
The Gadsden Purchase
Cost per square mile
1  10 7
3
2
4  .3378378378  10  3.378378378  10  $337.84 /sq.mile
2.96  10

2.96  10 6.4  10   18.944  10
4
Cost per acre

2
 1.8944  10 7
(number of acres purchased)
6
1  10 7
0
7  .52787  10  $0.53/acre
1.8944  10
(1107 )(2.941101)  2.941108
Cost Today

The Alaska Purchase
$294,100,100

(7.2 106 )
1
5 1.227805707 10  $12.28 /sq.mile
(5.86412 10 )
Cost per square mile
Cost per acre

7.2  10 6
2
 $0.02 /acre
8  1.918446417  10
3.7530368  10

(1.538 101)(7.2 106 ) 11.0736 107 1.10736 108
Cost Today

Follow Up Questions:
(5.86412 105 )(6.4 102 )  37.530368 107  3.7530368 108
(number of acres purchased)
$110,736,000

1. Location, Resources, time period, etc.
2. Student responses will vary. As long as their reasoning and justification make sense and
support their decision, all answers are acceptable.
3. Total Land Purchase in 1803:
(8.28 105 )  (2.05 105 ) 10.33 105
Note: This answer is not expressed in scientific notation. Students must convert to
scientific notation. Correct answer: 1.033  10 6 square miles purchased.
 Howard County Public Schools Office of Secondary Mathematics Curricular Projects has
licensed this product under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0

Unported License.
HCPSS Worthwhile Math Task
Louisiana Purchase
The Louisiana Purchase (French: Vente de la Louisiane "Sale of Louisiana") was the
acquisition by the United States of America in 1803 of 828,000 square miles (2,140,000 km2) of
France's claim to the territory of Louisiana. The U.S. paid 60 million francs ($11,250,000) plus
cancellation of debts worth 18 million francs ($3,750,000), for a total sum of 15 million dollars
for the Louisiana territory.[1][2][3]
The Louisiana territory encompassed all or part of 15 current U.S. states and two Canadian
provinces. The land purchased contained all of present-day Arkansas, Missouri, Iowa,
Oklahoma, Kansas, and Nebraska; parts of Minnesota that were west of the Mississippi River;
most of North Dakota; most of South Dakota; northeastern New Mexico; northern Texas; the
portions of Montana, Wyoming, and Colorado east of the Continental Divide; Louisiana west of
the Mississippi River, including the city of New Orleans; and small portions of land that would
eventually become part of the Canadian provinces of Alberta and Saskatchewan.
Source: http://en.wikipedia.org/wiki/Louisiana_Purchase
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HCPSS Worthwhile Math Task
Gadsden Purchase
The Gadsden Purchase Was Signed in Mexico City
December 30, 1853
Meeting in Mexico City on December 30, 1853, James Gadsden, U.S. Minister to Mexico, and
General Antonio López de Santa Anna, president of Mexico, signed the Gadsden Purchase. The
treaty settled the dispute over the exact location of the Mexican border west of El Paso, Texas,
giving the U.S. claim to approximately 29,600 square miles of land in what is now southern New
Mexico and Arizona, for the price of $10 million.
U.S. Secretary of War Jefferson Davis influenced the president to send Gadsden to negotiate
with Santa Anna for the land. Davis valued it, as others did, as the perfect tract for the
construction of the southern transcontinental railroad. The railroad line would connect western
territories to the east and north, greatly increasing the accessibility of these new lands. By 1869,
the "big four" of western railroad construction--Collis P. Huntington, Leland Stanford, Mark
Hopkins, and Charles Crocker--had pushed the Central Pacific Railroad line eastward over the
Sierra Nevada Mountains to Utah to join with the Union Pacific, completing the first
transcontinental railroad.
After completing the Central Pacific Railroad from California to Utah in 1869, the big four
started the Southern Pacific as a branch line into southern California. The railroad reached the
Arizona border in 1877, and in 1883 it was joined to other railroads built west from New Orleans
across Texas and New Mexico, territory that was acquired in the Gadsden Purchase. This
transcontinental system sped up westward expansion of the U.S.
Still in operation today as the Union Pacific Corporation, the company controls most of the railbased shipping in the western two-thirds of the country.
Source: http://www.americaslibrary.gov/jb/reform/jb_reform_gadsden_1.html
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HCPSS Worthwhile Math Task
Alaska Purchase
The Alaska Purchase was the acquisition of the Alaska territory by the United States from
Russia in the year 1867 by a treaty ratified by the Senate. The purchase, made at the initiative of
United States Secretary of State William H. Seward, gained 586,412 square miles (1,518,800
km2) of new United States territory. Originally organized as the Department of Alaska, the area
was successively the District of Alaska and the Alaska Territory before becoming the modern
state of Alaska upon being admitted to the Union as a state in 1959.
Russia was in a difficult financial position and feared losing Russian America without
compensation in some future conflict, especially to the British, whom they had fought in the
Crimean War (1853–1856). While Alaska attracted little interest at the time, the population of
nearby British Columbia started to increase rapidly a few years after hostilities ended, with a
large gold rush there prompting the creation of a crown colony on the mainland. The Russians
decided that in any future war with Britain, their hard-to-defend region might become a prime
target, and would be easily captured. Therefore the Tsar Alexander II decided to sell the territory.
Perhaps in hopes of starting a bidding war, both the British and the Americans were approached.
However, the British expressed little interest in buying Alaska. The Russians in 1859 offered to
sell the territory to the United States, hoping that its presence in the region would offset the plans
of Russia’s greatest regional rival, Great Britain. However, no deal was brokered due to the
American Civil War.[1][2]
Following the Union victory in the Civil War, the Tsar then instructed the Russian minister to the
United States, Eduard de Stoeckl, to re-enter into negotiations with Seward in the beginning of
March 1867. The negotiations concluded after an all-night session with the signing of the treaty
at 4 a.m. on March 30, 1867,[3] with the purchase price set at $7.2 million.
American public opinion was generally positive, as most editors argued that the U.S. would
probably derive great economic benefits from the purchase; friendship of Russia was important;
and it would facilitate the acquisition of British Columbia.[5]
Source: http://en.wikipedia.org/wiki/Alaska_Purchase
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HCPSS Worthwhile Math Task
According to http://www.davemanuel.com/inflation-calculator.php,
Year
Value of $1 now
1800
1801
1802
1803
1804
1805
1806
1807
1808
1809
1810
1811
1812
1813
1814
1815
1816
1817
1818
1819
1820
1821
$18.18
$18.18
$21.28
$20.41
$19.61
$19.61
$18.87
$19.61
$18.18
$18.52
$18.52
$17.54
$17.24
$14.29
$12.99
$14.93
$16.39
$17.24
$18.18
$18.18
$19.61
$20.41
Howard County Public Schools Office of Secondary Mathematics Curricular Projects has
licensed this product under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0
Unported License.