Technical ReportPDF Available

Abstract

These teaching notes are for teachers of Language, US History, Social Science, Physical Science, Health, and Mathematics. They accompany a Life and Riches poster which shows data on 120 countries in the world. E1. Population. The size of each circle shows population, so China is the biggest circle, in the upper left corner; India is 2nd biggest, in the middle left; and USA is 3rd biggest, in the upper right. E2. Position. The position up and down of each country shows life expectancy (China's is 70.1 years). The position right to left shows average production per person (China has $1,990, at US prices). E3. History. Each point on the zig-zag line shows life expectancy and production of the USA in a specific year (adjusted for inflation). For example the 1890 point is at 44 years and $3,500, which were the conditions then, at 1990 prices. For readers outside the USA this line is useful to show how unsteady progress is. Other data include percent of workers in industry, services and agriculture, fraction of land area covered by forests, radio receivers per 100 people, annual change in life expectancy and GDP per person.
Life and Riches, Notes for Teachers
Numbers Institute, PO Box 1320, Shepherdstown WV
25443, LR@NumbersInstitute.com
These teaching notes accompany a poster which shows
data on 120 countries in the world.
When you put the poster on the wall, explain at least items E1
- E3. Other items can be left until later.
E1. Population. The size of each circle shows population, so
China is the biggest circle, in the upper left corner; India is 2nd
biggest, in the middle left; and USA is 3rd biggest, in the upper
right.
E2. Position. The position up and down of each country
shows life expectancy (China's is 70.1 years). The position
right to left shows average production per person (China has
$1,990, at US prices).
E3. History. Each point on the zig-zag line shows life
expectancy and production of the USA in a specific year
(adjusted for inflation). For example the 1890 point is at 44
years and $3,500, which were the conditions then, at 1990
prices. For readers outside the USA this line is useful to show
how unsteady progress is.
E4. Industrial Structure. Shading in each circle shows how
many people work in industry (darkest shade), services and
agriculture. Note that countries in the upper right corner are
called industrial countries, but most of their workers are in
services.
E5. Forests. A line across each circle shows the fraction of
land area covered by forests (32% in the USA), giving a
connection with environmental issues.
E6. Radios. The number of radios shows how connected
people are to the rest of their country and the world. Radios
also measure wealth in a simple way. A bar graph rises from
the bottom of each circle. The fraction of the circle crossed by
the bar graph shows radio receivers as a percent of the
number of people in each country (over 100% in the USA,
which reports 2.1 radios per person).
E7. Yearly Change. Outside each circle is a short line, which is
like a tail showing change: the vertical rise from the bottom to
the top of this line shows 1 year's rise in life expectancy. The
sideways distance between the ends of the line shows 1 year's
change in production. For example Spain, at the top middle of
the poster, rose .3 years and $300, so its line points up and to
the right. Some countries like Cuba and Russia have no tails
since they lack data. Life expectancy is an average of
extremes: some die as infants and most others live longer than
the average. On production, a few people in each country have
much more than average, so most have somewhat less than
average.
E8. Dates of Data. The population of each country is for 1991.
Life expectancy, production and radios are for 1990. The
number of workers in each sector is for 1989-91. Forests are
for 1989-90. The tail on each country shows a year of change,
based on the average of the last 10 years for production and
30 years for life expectancy. In historical data for the USA,
gross domestic production goes back to 1929 (GDP,
meaning produced in the country, whether owned by
residents or foreigners). It is extended back to 1889 by
changes in gross national production (GNP, meaning owned by
residents, whether produced at home or abroad). The two
measures overlap greatly, since most things are produced in a
country and owned by residents. Change in one is a good
estimate of change in the other.
E9. All Subjects. Ask students to write their own questions or
assignments about the poster, and periodically pick some of
these for the class to work on.
Language Teachers
L1. Countries' Languages. Ask students to list all the
countries that speak the language you teach. You may be
surprised how few countries they know. Then divide the
poster into sections, and have a different student or group of
2-3 students for each section highlight the countries that
speak the language you teach. When they are not sure, they
can refer to almanacs or encyclopedias (see p. 4). Especially
for English, French, and Spanish, students will see how widely
these languages are spoken.
L2. Authors. Ask students to identify authors from a variety
of countries. Write the names on paper next to the poster, and
tie a string from the author's name to the country's position
on the poster. You can do the same with short poems from
different countries.
L3. Choose One Country. Ask students, alone or in teams of
2-3, to choose one of the less known of the countries that
speak the language you teach, and present a report.
L4. Radio Scripts. The bar representing radios, inside each
circle, shows how connected people are to other parts of their
country and the world. Even in the poorest countries, there
are usually several radios per village. These are owned by
churches, officials, store owners, etc., and people gather
around for important broadcasts. Ask students to design radio
broadcasts to teach people about development: how to build
efficient stoves, get immunized, stop erosion, use fertilizer,
meet customers' needs in stores and offices, build boats, or
whatever else students think would be useful and can find out
how to do. This exercise will teach them a lot about their own
and another culture. They can also search the web for
programs or listings of what is actually broadcast.
L5. Rewriting. Ask students to reword (or translate) the
labels and titles on the poster. What would be
clearest? Reword labels and titles in textbooks and
newspapers too.
US History
U1. Health Changes. For each date on the diagonal line, you
can look left to the life expectancy scale and see what life
expectancy was that year. It rose from 44 years in 1890, to 48
years in 1900, 64 years in 1940, and 76 years in 1990. It fell to
39.1 in the worldwide 1918 flu epidemic. Life expectancy was
low then, and is low in other countries now, mostly because of
infant mortality, not because of deaths at age 39. Life
expectancy is an average of children's and adults' deaths. The
rise shows the real strides in public health, and the effect of
inventions like antibiotics. Ask students to find the age at
death of famous people in the past, and how many of their
children died young. Also, the web (especially wikipedia.org)
shows dates of various discoveries, like antibiotics,
antiseptics, pasteurization, immunization, anesthetics, and
vitamins.
U2. Income Changes. From each date on the line, you can also
read up to the top scale, to find production per person that
year. The numbers are adjusted for inflation, so the change
from $3,500 in 1890 to $21,400 in 1990 means the country
did produce 6 times as much per person as 100 years before:
more clothes, furniture, roads, vehicles, machines, books,
thicker newspapers, etc. Ask students to find data to make
some of these comparisons, or measure trends in other
countries. The line moves left in 1930, showing lower
production in the Great Depression. Point this out when you
teach that period.
U3. Presidents' Terms. Ask 2-3 students to mark Presidents'
terms on the US line. Discuss what happened during these
terms. Point out the declines in production during the
Depression and after World War II. Point out the flu epidemic
in 1918.
U4. War Deaths. Life expectancy fell in 1943. The cause was
not just battle deaths, but high death rates among the elderly
(who are mostly women).
Chance of Death
Males
Both Sexes
Age
15-24
25-34
75-84
85+
1942
.0023
.0032
.1016
.2111
1943
.0026
.0032
.1075
.2303
Change
.0003
0
.0059
.0192
The table shows that at age 85 and over, an extra 192 people
died out of every 10,000 (maybe from shortages and
rationing), compared to 3 extra men age 15-24.
U5. Comparing Past and Present. Ask students to pick a
Presidential term and compare life in the USA then, with life
today in some country having about the same production per
person.
Social Science
S1. Current Events. When countries suddenly appear in the
news, teachers and students can find them on the poster and
immediately learn some background and comparisons with
other countries. You can put news articles next to the poster,
and use string to connect each one to the country it describes.
S2. Remember Countries. Ask students to learn the positions
of some countries. They should be able to draw them in the
right locations on a test. Remembering positions will give
them a sense of which countries are rich and poor, and will let
you see any misperceptions.
S3. Small Countries. The smallest countries on the poster,
with 3,100,000 people each, are the Central African Republic
(bottom left, next to Rwanda), Costa Rica (above and to the
right of China), and Uruguay (below and to the right of Costa
Rica). If students are curious about other countries, which are
too small to be on the poster, like Iceland, Kuwait, or
Singapore, ask them to look up the facts on the web.
S4. Number of Radios. Radios reflect, in a simple way, how
many possessions people in different countries have. Ask
students to count how many radios their home has, including
car radios, alarm clocks, etc. Compare the average for the class
to the figures for other countries.
S5. Radio Scripts. See item L4 under Language.
S6. Choose One Country. If you sometimes ask students to
pick one country to write about, the poster gives them a
starting point to decide which country might interest them.
S7. Compare Countries. The poster shows visually which
countries are similar. Ask teams of 2-3 students to pick
countries that are similar on some of the items in the poster,
and compare the countries.
S8. Compare Jobs. Each pie chart is divided into 3 parts,
showing what work people do. Ask teams of 2-3 students to
learn about some typical jobs in each category. They can find
out pay and working conditions, and then estimate what can
be bought with that much money. Ask them to imagine or
research some facts about daily life for these workers and
their children. They can start in their own country, and then
compare to others. Libraries may have books on daily life in
specific countries. At a more advanced level, this topic is
covered by Anthropology, Sociology and Labor Economics
books.
S9. Service Economy. The term 'services' includes
government, education, health, transportation, retailing,
wholesaling, entertainment, etc. Ask students to count how
many service workers they meet in a day (teachers, bus
drivers, retailers, custodians ...). Then point out that most
developing countries have only a third as many service
workers as the developed countries. Ask students to imagine
how different their country would be if many service workers
were farmers instead (larger classes, fewer buses, stores
closed ...). Ask who would prefer that simpler life, with more
farmers and fewer service workers.
S10. Economics. All production has been converted to 1990
US prices, so you can compare countries fairly. If two
countries have the same food, clothing, etc., they are counted
the same on the poster, even if they have different prices.
Totals include goods and services produced for sale, and
even goods produced and used inside a household, like
subsistence farming. But we exclude services inside a
household (like cooking) and things not sold (like the pleasure
of a sunset or forest). This is gross production, rather than net,
so figures include waste too. A process that creates poisonous
waste is counted in production, and cleaning it up is also
counted, but depletion and deterioration of mines, forests,
machinery, etc. are not subtracted out. Term papers can study
any of these issues: exchange rates (we use 'purchasing power
parities'), subsistence farming, depletion and net national
production.
Physical Science and Health
P1. Human Biology. The range in life expectancy reflects
differences in public health (infectious water and food, lack of
calories and vitamins) and lack of infant health care, before
and after birth. Students can study (a) human biology: how
infections start and spread, both within a body and between
people; and (b) how medicine uses chemical and biological
means to control disease.
P2. Nutrition. Both the life expectancy and the agriculture
data can lead to asking students to find what the most
common foods are in different countries, and what nutrients
these have. More specifically students can study what the lack
of each protein, vitamin or other nutrient causes, and how
experiments were designed to find these nutrients and their
effects.
P3. Forests. Each circle has a line across it showing the
fraction of the land area covered by forests. This includes
ancient forests like tropical rain forests, second growth forests
where fields return to trees, and commercial forests planted
as self-sustaining crops. Students can compare the amount of
forest in different countries, and how it is changing. They can
also study the kinds of wood, other plants, and animals in each
forest. They can study the properties of different kinds of
wood and soil.
P4. Radios. Radios can be short wave or medium wave, and
amplitude modulation or frequency modulation (AM or FM).
Students can study (a) how far you can hear broadcasts of
different types and wattages (web research, and emailing to
radio stations), (b) how the inventions work that made radios
possible (crystals, vacuum tubes, transistors, speakers,
microphones, amplifiers, etc.), (c) how radio frequencies are
divided, among countries and inside a country.
Mathematics
M1. Types of Graphs. This poster is an x-y graph, but it is also
filled with pie charts (workers), bar charts (radios), area
charts (population and forest) and a line graph (US history).
The horizontal scale is stretched to the 3/4 root, to give more
space on the left (milder than a logarithmic transformation).
Use of the poster is in line with NCTM's recommendations for
more statistics, practical applications and estimation.
M2. Graphical Analysis. Ask students to draw x-y graphs of
other data. They can get data from the web and other sources:
area and population of countries, area and depth of lakes,
latitude and longitude of cities (a map!), number of men and
women mentioned in newspaper stories or television
programs, etc.
M3. Averages for Smoothing Data. The line graph of US
history uses 3-year moving averages for life expectancies from
1900-1916 and 1920-1942, since the raw numbers fluctuate
sharply. Following are the actual life expectancies:
Life Expectancy at Birth in
the USA
1899 46.9
1900 47.3
1901 49.1
1902 51.5
1903 50.5
1904 47.6
1905 48.7
1906 48.7
1907 47.6
1908 51.1
1909 52.1
1910 50.0
1911 52.6
1912 53.5
1913 52.5
1914 54.2
1915 54.5
1916 51.7
1917 50.9
1918 39.1
1919 54.7
1920 54.1
1921 60.8
1922 59.6
1923 57.2
1924 59.7
1925 59.0
1926 56.7
1927 60.4
1928 56.8
1929 57.1
1930 59.7
1931 61.1
1932 62.1
1933 63.3
1934 61.1
1935 61.7
1936 58.5
1937 60.0
1938 63.5
1939 63.7
1940 62.9
1941 64.8
1942 66.2
1943 63.3
1944 65.2
1945 65.9
1946 66.7
Ask students to graph the exact numbers over time. Then have
them calculate and graph 3-year moving averages (plot at
1900 the average of 1899-1901, plot at 1901 the average of
1900-02, etc.). See which approach shows trends better. Ask
them to graph other data in raw form and with moving
averages, to see the trends. They can use daily low
temperatures, stock prices, or sports statistics.
M4. Area Graphs. Each circle's area is proportional to
population, so radius is proportional to the square root of
population. China has 4 times as many people as the USA so its
circle has 4 times the area and twice the radius of the USA.
(Area makes the biggest impression on viewers, so most
critics think it is better to keep population in proportion to
area, not radius. If the circle's radius were in proportion to
population, China's circle would get 4 times the radius and 16
times the area of the USA.) Ask students to measure radius or
diameter on several circles, including the standard circle in
the key (its radius is 4.5mm or .18in). That standard circle
represents 25,000,000. Students can calculate areas of other
circles, A=πr2, and estimate populations by proportion:
Population of a country = Area of country's
circle x 25,000,000 / Area of the circle in the key
A related approach is to say the circles are scaled at about
400,000 people per square millimeter or 250,000,000 people
per square inch. After the students have measured and
calculated a few populations, have them estimate other
populations by eye. You can transfer the interpretation and
estimation skills to test questions on other topics, where you
draw circles or squares of different sizes, and ask students to
estimate proportions.
M5. Mathematics of Life Expectancy. Where life expectancy
is low, for example 42 in Sierra Leone, it is because infant
deaths are bringing down the average, not because a lot of
people die at age 42. For example Sierra Leone reports that
15% of babies die before age 1, while China reports 3%,
resulting in a longer average life expectancy in China. Life
expectancies are usually calculated from a Life Table, like the
following simplified example that follows a hypothetical group
of people at current death rates:
A
B
C
D
E
Age
Number of
People
Beginning
Each Age*
Death
Rate
during
That Age
Number
Dying
Contribution
to Average
Life**
(B x C)
((A+1/2) x D)
0
1,000
0.20
200
100
1
800
0.05
40
60
2
760
0
0
0
3
760
0
0
0
. . .
59
760
0
0
0
60
760
1
760
45980
61
0
0
0
0
*Take the number of people beginning each row (Bi), minus
the deaths on that row (D), to start the next row (Bi+1).
**Average length of life is calculated by multiplying the
number of people who live each particular length of time
(column D, which shows that 200 people live 0-1 years, 40 live
1-2 years, 760 live 60-61 years), times the approximate years
they live (A+1/2), all added up (in column E, with a total of
46,140), and divided by the total number of people at the
beginning (1,000), so the average life expectancy is 46.1 years.
Beginning with 1,000 people is arbitrary; any other beginning
number gives the same average. The numbers that determine
the outcome are in column C. Have the students try another
beginning number.
In this example 1,000 people are born on the first line,
marked age 0. 20% of them die in their first year, so only 800
appear on the second line at age 1. 5% of these die in their
second year, or 40 deaths between age 1 and 2. All the rest
live to age 60. The average life time is calculated as: 200
people living an average of 1/2 year each, plus 40 people living
an average of 11/2 years each, plus 760 living an average of
601/2 years each ( = [200 x 1/2] + [40 x 11/2] + [760 x 601/2]
= [100] + [60] + [45,980] = 46,140). The resulting total years
of life are divided by the total of 1,000 births to give the
average years of life per person born ( = 46.1 years). This
average is multiplied out, added up, and divided in column E.
(Note: our example assumes people die evenly through the
year, so on average they would live half way through. But at
age 0 most deaths are in the first weeks, and they really live
on average 1/7 year at that age, not 1/2.)
You can give students arithmetic practice by explaining this
example and then asking them to calculate the life expectancy
if some fraction live to age 80. If students have access to a
computer with a spreadsheet program, they can put in
different death rates for each age, and vary them to see how
life expectancy changes. USA rates can be approximated as:
(age-7)2/(age+10)3.6+ (age/130)6+ .0002. They may also
compare actual death rates and life expectancies of males,
females and ethnic groups. They can research the death rates
by age on the web, as published by each country's Vital
Statistics office.
References
Most data come from the UN report mentioned on the poster.
That and other reference books from UN agencies have many
useful statistics.
There is also useful information in encyclopedias and national
reports like the Statistical Abstract of the US (which lists most
countries). Data from different sources will often not agree,
but should be about the same. For US history, many libraries
have Historical Statistics of the US-Colonial Times to 1970.
We welcome comments and criticisms to improve these notes.
Also, if you write to a teacher magazine about how your
classes use the poster, we'd like a copy.
ResearchGate has not been able to resolve any citations for this publication.
ResearchGate has not been able to resolve any references for this publication.