Virginia Population Density Reporting category Computation and Estimation/Patterns, Functions, and Algebra Overview Given the population numbers of Virginia and West Virginia and the number of square miles of land in each state, students will determine population density for each state and then decide which state has the greater population density. Based on this information, students will develop a strategy that will help them determine how many citizens of one state would have to move to the other state to make the population densities equal. Related Standards of Learning 8.3, 8.17 Objective The student will work with population densities and unit proportions to understand the relationship of population to available area as a population density. Materials needed Calculators ―Virginia Population Density Recording Sheet,‖ one copy for each student Note: It is helpful for the students to first complete the ―Population Density‖ activity in order to understand the concept of unit proportions. Refer back to the concept of mean or average population. Instructional activity 1. Initiating Activity: Give the students copies of the ―Virginia Population Density Recording Sheet‖ and the following data taken from the 1990 Census: Virginia West Virginia Population 6,187,000 people 1,793,000 people Land Area 40,767 sq. mi. 24,231 sq. mi. 2. Ask the students to develop a strategy to determine the population density of each state and then calculate the population densities. 3. Instruct the students to determine which state has the greater population density and then to determine how many citizens of one state would have to move to the other state to create equal population densities (not equal populations). Remind the students that they should be prepared to describe the strategy used and to explain their reasoning. 4. Closing Activity: When the students are finished, have them explain their strategies for solution to the class. Their solutions should include information about how many citizens would have to move from one state to the other. Answers should include all calculations. Sample assessment Monitor the class as the students work on and develop the following solutions. If incorrect strategies are conceived, note where the students lost the right track and lead them back to the proper process by asking questions. Solutions To determine the population densities of the two states, make sure the students set up the proper ratios and solve them correctly: 6187000 people x people Virginia: = 1 sq. mi.; therefore, x = 151.76 people per 40767 sq. mi. square mile, which is the population density of Virginia. 1793000 people x people West Virginia: = 1 sq. mi.; therefore, x = 74.00 people 24231 sq. mi. per square mile, which is the population density of West Virginia. Now the students can see that Virginia has a higher population density than West Virginia. An alternative method of representation is the following: 40767 sq. mi. Virginia: = .007 square miles per person in Virginia 6187000 people 24231 sq. mi. West Virginia: = .013 square miles per person in West 1793000 people Virginia While this method does not yield population density, it does show that with less area of land per person, Virginia is more densely populated than West Virginia. It is plain that Virginia citizens would have to move to West Virginia to equalize the population densities. There is more than one way to find out how many people would have to move. A possible solution using proportional reasoning is the following: Find the total area in both states. (64,998 square miles) Find the total population of both states. (7,980,000 people) Find the ratio of the total population of both states to the total area of both states; this ratio represents the mean or average population density that needs to be achieved if the population densities are to be equalized. 7980000 people x people ( = 1 sq. mi.; therefore, x = 122.77 people per square mile) 64998 sq. mi. Subtract this average population density from the population density of Virginia. (151.76 – 122.77 = 28.99 people per square mile) This tells the number of Virginia citizens per square mile who would have to move to West Virginia. Multiply this number of Virginia citizens per square mile who would have to move times the total number of square miles in Virginia (28.99 40,767 = 1,181,835 people). This is the number of Virginia citizens who would have to move to West Virginia to equalize the population densities. Follow-up/extension Have the students confirm or prove their solutions to the problem of how many Virginia citizens would have to move. Have them subtract this number of people (1,181,835 people) from the total population of Virginia and then add this same number of people to the total population of West Virginia, thereby creating the census after the move takes place. Then have them use these new population numbers to refigure the population densities of both states. They should quickly discover that the new population densities are the same — 122.77 people per square mile. Virginia Population Density West Virginia Virginia Population: 1,793,000 people Population: 6,187,000 people Area: 24,231 sq. mi. Area: 40,767 sq. mi. 1. Which state, West Virginia or Virginia, has the greater population density? Show your work. 2. How many citizens of one state would have to move to the other state to create equal population densities? Be prepared to tell the strategy you used and explain your reasoning.