Life and Riches, Notes for Teachers

Numbers Institute, 9169 W State St #1881, Boise, ID 83714, 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:

Simplified Life Expectancy Table
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
Total: 46,140 Divided by number of people (1,000): 46.1

*Take the number of people beginning each row (B_i), minus the deaths on that row (D), to start the next row (B_i+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.