While most population concepts are firmly rooted in K-12 science and social studies curricula, many of PopEd’s lessons also find a place in the math classroom. Understanding birth, death, and fertility rates, growth patterns, probabilities, and projections are all part of “real-world math”—using relevant data about the world around us to build students’ foundations in mathematical practices and reasoning. Real-world math has long been a priority for the National Council of Teachers of Mathematics (NCTM) and is now integral to the new Common Core Math Standards.

Through math instruction, we can illustrate the different population dynamics of countries and world regions while also building students’ computational skills and understanding of ratios, percentages, logarithmic equations, and modeling.

The feature articles in this issue explore the demographic phenomenon of low birth rates in Europe and East Asia. Several of our math-focused activities compare birth and death rates for a variety of countries. In “On the Double,” middle school students explore these rates for ten countries ranging from high growth to no growth to negative growth, and calculate their populations’ doubling time.

In “The Stork and the Grim Reaper,” elementary students illustrate birth and death ratios using measuring cups and colored water. The “stork” (representing birth rates) and “grim reaper” (representing death rates) take turns “populating” or “depopulating” the water bowl (representing people). The size of their cups varies depending on the ratios they are depicting. When the stork’s cup is larger than the grim reaper’s, the water level rises; when the grim reaper’s is larger, the water level falls.

## On the Double

##### Procedure:

Explain to students that the larger the difference between a nation’s birth rate and its death rate, the greater (or lesser) the population growth rate. Ask students to look at the chart below and hypothesize which countries will have the highest growth rates and which will lose population at current rates.

Now have students determine the rate of annual increase for each country’s population using the following formula: (birth rate-death rate)/10

For example, the world’s current rate of annual increase can be calculated by knowing the birth rate is 20 births/1,000 people and the death rate is 8 deaths/1,000 people. (20-8)/10 = 1.2%

*(Note: These figures represent the rate of “natural increase” and do not include net migration.)*

Based on the rate of natural increase, students can now determine each country’s population doubling time with the following formula: 70*/rate of increase = doubling time

For example, to calculate the doubling time for the world population at the present rate of increase (1.2%), you would use this formula: 70/1.2 = 58 years

For countries that are losing population, the same formula can be used to determine how many years it would take that population to decline by half: 70/rate of decrease = halving time

##### Discussion:

Which figures differ most among countries, the birth rates or the death rates? How would you explain this?

*Birth rates vary more because there is more variability in family size. The birth rate is higher when the average family size is larger. For example, Nigeria (with a birth rate of 39/1,000) averages 5.5 children per family while Germany (with a birth rate of 8/1,000) averages 1.5 children per family. Death rates are affected by age distribution, and most countries will eventually show a rise in the overall death rate, in spite of continued decline in mortality at all ages, as declining fertility results in an aging population (and the elderly die at a higher rate).*

What do you think accounts for variations in death rates among countries? Why do you think the death rate in the U.S. is higher than in Guatemala?

*War, disease, famine, poor health care, and age structure can influence death rates. The difference in death rates between Guatemala and the U.S. can be attributed to the U.S. having a larger proportion of elderly citizens.*

Are countries like Germany or Bulgaria likely to run out of people? Why or why not?

*Not likely. Birth and death rates can change each year due to various social and economic factors. Migration changes demographic profiles as well. For example, the recent influx of hundreds of thousands of migrants to Germany from war-torn countries in the Middle East is likely to increase Germany’s population and also bring down the mean age (and therefore the death rate) because migrants tend to be young.*

* Note: 70 is the approximate equivalent of 100 times the natural logarithm of 2, which is used to determine doubling time.

** Do not make rate of decrease negative. For example, for Germany, divide by 0.3, not -0.3.

“On the Double” and “The Stork and the Grim Reaper” are just two of the more than 70 PopEd activities that teach real-world math concepts. To find more, visit our interactive “Find a Lesson” module at

www.populationeducation.org.