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Learning area: Mathematics
Year level: Year 10
Country: Australia, Bangladesh, China, India, Indonesia, Japan, Malaysia, North Korea, Philippines, Singapore, South Korea, Thailand, Vietnam
General capability: Intercultural understanding

This learning sequence explores the theme of human population and focuses on developing student familiarity with data representation and interpretation. It supports the Australian Curriculum for Mathematics: Statistics and probability.

Students are introduced to the concept of population clocks and use data to compare population numbers and life expectancy in Australia and various countries in the Asia region.

Act_4_bigA life expectancy graph

Acknowledgements

Graph: AEF

Related resources

Activity 1: World population clocks

In this activity, you will investigate a number of internet websites that display population clocks which give 'real time' estimates of the world's population and use these for mathematical calculations.

Task 1: Are all world population clocks the same?

  1. Visit at least two world population clock websites and compare their estimates of the current world population. Some websites give information about how the estimates are calculated. Discuss the differences.
  2. Read the article excerpts on world population and discuss them.
  3. An article in The Guardian (United Kingdom) suggested that there are half a million births per day. Does this mean that the world population is increasing by half a million per day? Why/Why not?
  4. Try this calculation:
    • How many days have there been since 31 October 2011?
    • If the world’s population is increasing by 500 000 per day, what would be an estimate for the world’s population today?
  5. Compare this estimate with a population clock estimate. Why is there such a difference?
  6. Half a million births per day is only part of the equation. What other factors must be taken into account to estimate the rate of growth of the world’s population?

Task 2: Mathematical models of population clocks

Population clocks are not real time counters of the population; rather they are mathematical models. The counter has been programmed to give a visual representation of the rate at which the population is changing.

The increasing population numbers are based on statistics rather than an actual count. The clocks do not show the same figure at any instant because they are based on different assumptions about birth and death rates.

The population clock at Tranquileye is based on there being about three more births per second than there are deaths throughout the world.

  1. Using this information recalculate your estimate of the increase in the world’s population since 31 October 2011.
  2. Complete the following steps to calculate this figure.
    • How many days have there been since 31 October 2011?
    • How many seconds have there been since 31 October 2011?
    • If there are three more births than deaths per second, the increase in world population since 31 October 2011 is about …
  3. Compare this figure with the figure shown at Worldometers.
  4. Discuss the difference. The difference might look quite large, but what is the percentage difference between the two estimates?

Task 3: Seven billion people

  1. Read the excerpt The seven billionth resident.
  2. Look at the following websites and record their estimates (approximately – they keep changing) of today's world population.
  3. It's not surprising, then, that not all clocks recognise 31 October 2011 as the day the world population reached 7 billion. Look at Galen again. According to this site, what was the world population on 31 October 2011? (Enter the date as October 31, 2011.)
  4. Write down why you think the estimates on all the websites in this task vary. As a class, compile a list of reasons.

Task 4: What does seven billion mean?

  1. View the video National Geographic Magazine: 7 billion (on the rightabout how many times we could walk around the earth with seven billion steps. Calculate:
    • How many countries in the world would there be if each country had the same population as Australia?
    • If everyone lived in a city the same size as your state or territory's capital city, how many cities would there be in the world?
    • If only one person in a hundred played soccer, Australian rules football, netball, basketball or hockey (choose one) how many teams could you make with seven billion people?
  2. Create your own comparisons of what seven billion people means and ask your classmates to calculate them.
  3. Think of the impact a population of seven billion has on the Earth. You may want to watch the video clip again for ideas.
    • Construct a PMI (Plus, Minus, Interesting) chart.
    • Discuss your observations with the class.

Acknowledgements

Video: 7 Billion, National Geographic Magazine by NationalGeographic ‪Standard YouTube Licence

Image: Excerpt from article from AltertNet 31 October, 2011

Activity 2: Country-specific population clocks

In this activity, you will calculate and substantiate the claim that the rate of Australia's population is increasing by one every 97 seconds.

Task: Compare and analyse population data

  1. Visit the Australian Bureau of Census website or another population clock site which provides details about their statistical assumptions. Is the world population, as shown on the clock, increasing at the claimed rate of one every 97 seconds?
  2. Check this by taking some measurements. Explain how you would do it.

  3. Use the following component settings and calculate the net gain:
    • one birth every 1 minute and 47 seconds
    • one death every 3 minutes and 36 seconds
    • a net gain of one by international migration every 2 minutes and 49 seconds.
  4. Compare your calculation method with others. Hint: A calculation that you could make is 1/107 - 1/216 + 1/169. Can you explain why this is a relevant calculation?

  5. On the U.S. Bureau of Statistics population clock website, the component settings change month by month. Here are the settings for June 2011. This implies that for another month, another year, the settings might be different:
    • one birth every 8 seconds
    • one death every 13 seconds
    • one international migrant (net) every 43 seconds
    • a net gain of one person every 13 seconds.
  6. Does this mean that July 2011 will have different settings? What about June 2012? Give reasons for your answers.
  7. Would the number of births in a month be about the same from month to month?
  8. Conduct a survey amongst students in your class to see which month had the highest number of births.
  9. Visit the Australian Bureau of Statistics CensusAtSchool website.
  10. Select a range of categorical data samples and determine whether there is a common month each year when babies are more likely to be born. Discuss the reasons for your findings.

Activity 3: Life expectancy

In this activity you will compare the life expectancy of inhabitants of different countries and observe the differences between male and female life expectancies and those of different ethnic groups in most countries and cultures. You may choose to construct the table as a spreadsheet, using appropriate software to assist with different sorting and graphing techniques.

Task 1: Factors affecting life expectancy

Conduct an internet search and then discuss the following questions.

  1. What is life expectancy? How is it calculated?
  2. What is the average life expectancy of Australians?
  3. What is meant by the following statement: The life expectancy of Australian males is 76.9 years.
  4. Is there a guarantee to say that the life expectancy of all Australian females is 82.7 years?
  5. To what extent does the life expectancy of Indigenous Australians differ from non-Indigenous Australians?
  6. Which country has the highest life expectancy? Which has the lowest?
  7. To what extent does life expectancy vary from one country to another?

Task 2: Aboriginal and Torres Strait Islander life expectancy

  1. Visit the Australian Bureau of Statistics — Australian Social Trends, March 2011 and scroll down to Aboriginal and Torres Strait Islander Life Expectancy. Carefully read the text.
  2. Using this information, complete the following table. Notice that the data presented concerns life expectancy at birth. Life expectancy at birth data takes into account the likelihood of infant and childhood illnesses.
Life expectancy of males Life expectancy of females
Indigenous Australians
Non-Indigenous Australians
Indigenous Australians living in NSW
Indigenous Australians living in the NT  

Task 3: How does the life expectancy of Australians compare with other nationalities?

  1. Search the website People Facts – Life Expectancy which provides details of the life expectancy for 225 countries both by gender and for the total population.
  2. Extract the necessary data to complete the Life expectancy table showing life expectancy details for a range of countries from the Asia region. This information will be used to make comparisons in Activity 4.
Life expectancy data table
Country Male life expectancy Female life expectancy Population life expectancy
Australia
China
Japan
North Korea
South Korea
Bangladesh
India
Nepal
Pakistan
Cambodia
Indonesia
Malaysia
Philippines
Singapore
Thailand
Vietnam

Activity 4: Graphing data

In this activity you will use data completed from Activity 3 to create graphs and analyse information. You will choose or be allocated one Asian country to research.

  1. Using the data from your life expectancy table, draw a clustered column graph (as shown) showing the male, female and population life expectancies on the vertical axis, and countries on the horizontal axis. 
  2. Use information in the graph and table to answer the following questions.
    • Which country has the greatest life expectancy
      • for females
      • for males
      • for the population?
    • Which country has the lowest life expectancy
      • for females
      • for males
      • for the population?
    • In which Asian country is the difference between female and male life expectancy the greatest?
    • Why is the life expectancy of the whole population not always the average of the figure for females and males? Under what circumstances would the life expectancy of the whole population be the average of the female and male life expectancies?
    • How does the life expectancy of Australians (male, female and population) compare with the life expectancy in the Asian countries on your graph? Discuss the similarities and suggest some possible reasons for the differences you have observed.
  3. Notice that the Life expectancy table on the website you used is sortable.
  4. Use this feature to find and list the three countries with the highest life expectancies and the five countries with the lowest life expectancies.

Acknowledgements

Graph: AEF

This learning sequence is designed to assist students to evaluate statistical reports to compare population numbers and life expectancy.

Students explore population clocks and learn that they are not real time counters of the population; rather they are mathematical models. The counter has been programmed to give a visual representation of the rate at which the population is changing. Our world population is increasing and the clocks are based on statistics rather than an actual count. They do not show the same figure at any instant because they are based on different assumptions about birth and death rates.

A range of tasks has been provided for each activity and you may wish to choose which ones are used according to student ability. Materials can be taken from each activity to construct worksheets for students to record their discussions, calculations and findings.

Activity 1: World population clocks

A number of internet websites display population clocks which give 'real time' estimates of the world's population. Links to some of these websites are provided and will be used for mathematical calculations.

On their website, United Nations Day: 24 October 2011, the United Nations Organisation deemed that the world's population had reached seven billion on 31 October 2011.

Refer students to the video of World population: 7 billion. It is important to note, however, that the various websites with population clocks are not synchronised and some organisations maintain the seven billionth inhabitant arrived at a later date.

Activity 2: Country-specific population clocks

Some students may need some assistance to calculate and substantiate the claim that the rate of Australia's population is increasing by one every 97 seconds as shown on the Australian Bureau of Census website population clock. The site provides details about the statistical assumptions to assist with this process.

World population clocks are based on birth and death rates. Country-specific population clocks require more data than world population clocks. A population clock for Australia considers birth and death rates as well as migration and immigration rates.

Activity 3: Life expectancy

The activities provide students with the opportunity to develop their spreadsheet skills. Some students may require some scaffolding activities prior to creating their own spreadsheets. As a starting point, students should complete the Life expectancy data table using information collected from People Facts: Life Expectancy.

When comparing countries, the life expectancy of its inhabitants can differ significantly. There is also a difference between male and female life expectancies in most countries and cultures.

Within a country's population, life expectancy can vary quite a lot between different ethnic groups. In Australia the most obvious difference in life expectancy is that between Indigenous Australians and the non-Indigenous population.

Students might choose to construct the table as a spreadsheet, using appropriate software. This will facilitate different sorting and graphing techniques.

Activity 4: Graphing data

Students will use the Life expectancy data table to create a graph. The table is a useful way to organise data, but graphs are useful in exposing patterns and differences in the data.

Useful websites

Population clocks
  • Current world population – continuous update of population statistics (from Worldometers)
  • World clocks – ongoing clocks including world population and productive, or arable, land (from Tranquileye)
  • Human population – continuous updating of the human population from the Galen Huntington website
  • U.S. and world population clock – continuous data updates including the top ten most populous countries, and a graph for the US population by age and sex from the United States Census Bureau
  • Australian population clock – data updated on the Australian population from the Australian Bureau of Statistics

It is recommended that teachers preview websites to ensure they are suitable for their students prior to use in class. Content accessed via these links is not owned or controlled by the Asia Education Foundation and is subject to the terms of use of the associated website.

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