Begin the lesson with a discussion on the use and importance of population data. You might want to ask questions such as:
 How is population data collected? [Through the Census, which is taken every 10 years.]
 How is population data used? [To determine voting districts,
public services, to make predictions for economic and population
growth, etc.]
 What are some ways of displaying population data? [Tables, line graphs, circle graphs, etc.]
Distribute the History of Populations Activity Sheet to the students.
History of Populations Activity Sheet
Individually, students should describe what they see in the
circle graphs. Ask them to give an explanation of the information shown
in the graphs. Discuss these explanations as a class.
Prior to using the circle graphs, students should create a title for
all four graphs. Students might suggest "Percent of Total U.S.
Population by State." Students should record their title at the top of
the first page of the activity sheet.
Ask the students to:
 describe the information in each circle graph, and
 explain what steps would have been followed to construct the graphs.
Record the following information on the chalkboard or overhead.
Then ask the students to individually figure out the population of the
three states for the four dates.
Population of the United States (nearest million)
 Year  Population  1800  4,000,000  1850  23,000,000  1900  76,000,000  1950  170,000,000 

In pairs, students should compare their solutions and how they arrived at them.
Solutions
 New York: 1800 (400,000); 1850 (2,300,000); 1900 (12,160,000); 1950 (15,300,000)
 Massachusetts: 1800 (400,00); 1850 (690,000); 1900 (3,800,000); 1950 (3,400,000)
 Pennsylvania: 1800 (440,000); 1850 (2,070.000); 1900 (7,600,000); 1950 (10,200,000)
Individually, students should record their observations about
the graphs and share as a class. Some of these observations might
include the following:
 How do the percents for each of the three states and the other states change from one graph to the other?
 What was happening to the population for the three states throughout the time span covered by the graphs?
 Did the percents for the three states decrease from one fiftyyear period to the next?
 Why do you think the percent for New York increased between 1800 and 1850?
Have the students work in pairs to complete the activity sheet,
questions 1 through 4. Ask the students to share their explanations
with their partners, as well as the whole class.
Questions 5 and 6 require other resources, such as web access, in
order to find census data. These can be completed in class, or they may
be assigned as homework.
Solutions for the History of Populations Activity Sheet
Question 1. 31%; decreased (in 1850), increased from 850 (in 1900);
decreased (in 1950). The percent changes were 22% (in 1850), 31% (in
1900), and 17% (in 1950.)
Question 2. In 1800, Pennsylvania had the largest percent of the
population. In 1850, 1900, and 1950, New York had the largest percent
of the population.
Question 3. From 1800 to 1950, Massachusett's population percent
decreased from 10% in 1800 to 2% in 1950, an overall decline of 8%.
Question 4. One possible explanation for New York in 1900 was the number of immigrants coming through Ellis Island.
Question 5. In 1800, there were 13 other states. In 1850, there
were 28. In 1900, there were 42. And in 1950, there were 45. Students
may use an almanac (either in book form or online) to help them answer
this question.
Reference
Irons, Calvin and Irons, Rosemary. The Arithmetic Teacher. October, 1991. vol. 39, no. 2. p 26  33.