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Population Math

Grade Level:

Activity Overview: This activity uses published statistics from the global population monitors as the input for a variety of mathematical equations.

Problem Statement:

Calculate and explain, from given data, the values of crude birth rate, crude death rate, fertility, doubling time and natural increase rate.

Project Deliverables:

Students should use technology to research various population parameters in order to calculate the following population classifiers:

  • Birth Rate: This metric is the number of births per 1,000 persons in a population over a given period (usually a year). It excludes variation such as sex ratios, age distributions, and postponement or acceleration of marriage age, which all affect actual birth rates. Divide the number of births by the total population and multiply the quotient by 1,000.
  • Death Rate: This metric is calculated the same way as with birth rate, with deaths per 1,000 persons as the numerator.
  • Natural Increase Rate: This metric represents the percentage by which a population is increasing or decreasing. Negative rates of natural increase indicate a declining population. To calculate, subtract death rate from birth rate, then divide the difference by 10 to express as a percentage.
  • Doubling Time: This metric is the amount of time in years required for a population to double in size at a constant growth rate. To calculate doubling time for a population undergoing exponential growth, use the rule of 70. Divide 70 by the growth rate as a percentage (not as a decimal).
  • Total Fertility Rate: The average number of children born per woman in her childbearing years according to a current schedule of age-specific fertility rates. Multiply by 1,000 to determine the number of children born per 1,000 women. Total fertility rate is calculated as a sum of current age-specific fertility rates for single year age groups or x times the sum of current x-year group fertility rates.
    $$total\,fertility\,rate=\sum ASFR_a$$
    $$total\,fertility\,rate=5\sum ASFR_a$$

Example Solution:

The attached document contains solutions for the above population classifiers for the country of Argentina. The data was taken from the 2013 Demographic Yearbook from the United Nations Statistics Division. Students' answers will vary, but correct calculations will follow the instructions outlined on these sheets using the data available from the databases.


The United Nations Statistical Division collects a variety of demographic and social statistics from civil registries worldwide and publishes these data in annual Demographic Yearbooks and also in more specific occasional reports such as the World Fertility Report 2009.



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