The problems below are a selection of real world problems developed for the teaching of sustainability/conservation related College classes. The exercises are designed to foster quantitative competence (numeracy) as well as critical thinking and systems thinking. They are basic but realistic and all data used are taken from the published scientific literature and from public online databases maintained by official organizations such as FAO and EIA. No advanced Mathematics is required, yet these problems are challenging for most students. Many students need help to overcome a certain math anxiety or even phobia. These exercises must be accompanied by intensive discussion, assistance, and feedback. Students who complete these assignments successfully experience the power of even basic quantitative methods. They learn that informed citizens do not have to rely solely upon the advice of experts – with reasonable effort they can gather and interpret information and come up with approximate answers to important, non-trivial real world questions.

1. 1 | T. Menninger, Quantitative Exercises in Sustainability Education and Energy Literacy, © 2013
Quantitative Practice Problems in Sustainability Education
and Energy Literacy
Toni Menninger, toni.menninger at gmail dot com
http://www.slideshare.net/amenning/presentations
The problems below are a selection of real world problems developed for the teaching of
sustainability/conservation related College classes. The exercises are designed to foster
quantitative competence (numeracy) as well as critical thinking and systems thinking. They are
basic but realistic and all data used are taken from the published scientific literature and from
public online databases maintained by official organizations such as FAO and EIA.
No advanced Mathematics is required, yet these problems are challenging for most students.
Many students need help to overcome a certain math anxiety or even phobia. These exercises
must be accompanied by intensive discussion, assistance, and feedback. Students who
complete these exercises successfully experience the power of even basic quantitative
methods. They learn that informed citizens do not have to rely solely upon the advice of
experts – with reasonable effort they can gather and interpret information and come up with
approximate answers to important, non-trivial real world questions.
I am putting the exercises below in the public domain for educational purposes. Feel free to use
them or adapt them for your own instruction. Feel free to contact the author with questions or
comments or to request an instructor version. Any feedback is welcome!

2. 2 | T. Menninger, Quantitative Exercises in Sustainability Education and Energy Literacy, © 2013
Agricultural Productivity and Food Security in a World of 7 billion
In this exercise, you will explore the sustainability of the global food system. Read the instructions
carefully, follow the order of the exercise and be sure to understand what is asked. All information
required to complete the assignment is found in the instructions – you do not need to look up any data. It
is helpful to use a spreadsheet. Enter the data into your spreadsheet and label each. Note the exact units.
Perform the calculations step by step, label each result, and keep track of all units. Check your results!
Double check all your conversions and think about whether each result appears plausible and consistent
with what you know from other sources. Remember that the year has 365 days. All units are metric.
Hint: Google can help you with conversions.
1T [metric tonne] =1,000 kg, 1 Ha [hectare] = 10,000 m
2
and 1 km
2
=1,000,000 m
2
= 100 Ha.
1. Grain Production
The Food and Agriculture Organization of the United Nations (FAO) maintains an extensive
database (faostat.fao.org) reporting data about growing area, production and yields for
numerous crops for each country and region. In 2010, the global cereal harvest (mainly rice,
wheat, and maize) was 2.43 billion metric tonnes grown on 6.8 million km2
of cropland and the
average yield of cereal crops was 3.6 T/Ha. The caloric content of grain is about 3,200 kcal/kg.
It depends of course on the variety and other factors such as moisture content. The world’s
arable land area is about 13.8 million km2
; this does not include pasture land. Assume that a
human on average needs about 2,700 kcal per day and the number of people is 7 billion. In this
analysis, we only take into account the calorific (energy) content of grain. Of course, a healthy
diet must be balanced and diverse.
a) How much grain (in kg per year) can feed a person?
b) How much cropland, in m2
, can feed one person?
c) How much grain (in T per year) can feed the world?
d) What percentage of the 2010 harvest does that represent?
e) How much cropland, in km2
, is required to grow enough grain to feed the world?
f) What percentage of the world’s arable land area does that represent?
g) Interpret your results. Is there enough food for everybody? Is food security threatened by
insufficient agricultural productivity?

3. 3 | T. Menninger, Quantitative Exercises in Sustainability Education and Energy Literacy, © 2013
2. Meat Production
FAO also reports data on each country’s average diet. The American diet includes an average of
124 kg of meat per year (the global average is 40 kg). Note that the calorific content of meat is
about half that of grain (depending on the fat and moisture content). FAO assumes that on
average about 3kg of grain is needed as feed for each kg of meat produced.
a) How much feed grain (in kg per year) is needed to support the average American meat diet?
b) How much feed grain (in T per year) would be needed if the entire world adopted the
American diet?
c) What percentage of the 2010 harvest does that represent?
d) How much cropland, in km2
, is required to grow this amount of feed grain?
e) What percentage of the world’s arable land area does that represent?
f) What do your results imply? Is a meat-based diet a sustainable option for feeding the world?
What are the likely consequences when developing countries like China increase their meat
consumption? What, in your view, does this mean for citizens of developed countries?
Additional Background Data (not needed for completing the exercise)
Average diet according
to FAO
Total food
kcal/day
Animal products
kcal/day
Meat supply
kcal/day
Meat supply
kg/year
US 3750 1030 450 124
World average 2800 481 218 40
Least developed
countries
2160 146 59 11.3
The US diet according to FAO data contains 3750 kcal per person per day and is composed of
22% cereals excl. beer, 17% sugar and sweeteners, 18% vegetable oils, 12% meat, 10% milk excl. butter,
4% alcoholic beverages, 3% fruits excl. wine, 3% animal fats, 3% starchy roots.
For comparison Mexico: 44% cereals excl. beer, 15% sugar and sweeteners, 8% vegetable oils, 9% meat,
5% milk excl. butter, 4% fruits excl. wine, 4% pulses, 2% animal fats.
Sources and further reading
 FAOSTAT: faostat.fao.org
 UNEP: World Food Supply, http://www.grida.no/publications/rr/food-crisis/page/3562.aspx
 Pimentel and Pimentel (2003). Sustainability of meat-based and plant-based diets and the
environment. www.ajcn.org/content/78/3/660S.full

4. 4 | T. Menninger, Quantitative Exercises in Sustainability Education and Energy Literacy, © 2013
3. US Corn Ethanol
You earlier examined the efficiency of using grain to feed either people or livestock. Grain is
also used to “feed” cars. The federal government has been supporting and subsidizing the
production of corn ethanol for fuel. The Energy Independence and Security Act of 2007 includes
a mandate to produce an increasing amount, currently 13 billion gallons per year, of ethanol,
mostly from corn, which is then blended with conventional gasoline. The process involves
fermentation and distillation and yields about 400 liters of ethanol per ton of corn. The energy
content of ethanol is 33% lower than conventional gasoline – 1.5 L of ethanol is needed to
substitute 1 L of gasoline. A typical US passenger car consumes about 550 gallons of gasoline
per year (source). 1 gallon = 3.78 L.
In the US, the average corn (maize) yield in 2010 was 9.6 T/Ha (notice that this is much higher
than the world average). This year’s harvest will be much lower because of the record drought
throughout the Midwest but we will use the higher number for this exercise.
a) How much corn (in T) is needed to make enough ethanol to run the average car for a year?
b) How many people could be fed by that corn (use the result from 1.a assignment 3)?
c) How many square meters of US cropland can “feed” a car? Compare this to 1.b assignment 3!
d) The US motor vehicle fleet in 2011 consumed 507 billion liters (134 billion gallons) of
gasoline (source: EIA). How much corn (in T) would need to be grown to substitute 100% of this
fuel with corn ethanol?
e) How much cropland, in km2
, would that require? Compare to the total US arable land area,
1.6 million km2
.
f) Interpret your results. Is corn ethanol production a sustainable option?
4. Agricultural Conversion of Solar Energy
Agriculture is a process of capturing, via photosynthesis, and storing solar energy in a form
useful to humans. We can therefore analyze agricultural productivity in energetic terms: how
efficient are crops in capturing and storing solar radiation?
Average insolation (the amount of solar energy reaching the surface of the earth) in the United
States is about 200 W/m2
. This amounts to 1750 kWh per year per square meter (remember
that W [Watt] is a unit of power, that is energy flow over time; kWh [kilowatt-hour] is a unit of
physical energy; the year has 8,760 hours). Assume that the caloric content of corn is about
3,200 kcal/kg. Ethanol energy content is 6.5 kWh/L and 1 kcal = 0.001163 kWh.

5. 5 | T. Menninger, Quantitative Exercises in Sustainability Education and Energy Literacy, © 2013
a) Estimate the energy output of growing corn in kWh/m2
.
b) What percentage of the total solar energy reaching a cornfield does that represent?
c) How much ethanol, in L/Ha, can a US cornfield be expected to yield?
d) Estimate the energy output of corn ethanol production in kWh/m2
.
e) What percentage of the solar energy does that represent? In other words, we are analyzing
the conversion efficiency of converting solar energy into ethanol.
f) What energy output could be expected, in kWh/year/m2
, from photovoltaic panels with a
conversion efficiency of 12%? Compare to your results in a) and d). Which method of capturing
solar energy is more efficient, and by what factor?
5. In a one page essay, summarize your main findings. Which of them surprised you? Which of
them would you want to share with a policy maker? Being an informed citizen but not a
scientific expert, how confident are you of the validity of your conclusions? Have you learned
anything about “systems thinking”?
Sources and further readings
 EIA: Biofuels in the U.S. Transportation Sector,
http://www.eia.gov/oiaf/analysispaper/biomass.html
 Baker and Zahniser (2006): Ethanol Reshapes the Corn Market, Amber Waves
 USDA: Bioenergy, http://www.ers.usda.gov/topics/farm-economy/bioenergy/background.aspx
 National Geographic: Biofuels, http://ngm.nationalgeographic.com/2007/10/biofuels/biofuels-
text
 George Monbiot: Hunger Games
 BBC: US biofuel production should be suspended, UN says
 Tom Murphy: Do the Math, http://physics.ucsd.edu/do-the-math/ (Solar potential, Food energy)