The shape of the nation


Students are introduced to a graphic way of presenting population data that provides, by its shape, important information about the age and structure of a population.

Achievement Objectives
S3-1: Conduct investigations using the statistical enquiry cycle: gathering, sorting, and displaying multivariate category and whole-number data and simple time-series data to answer questions; identifying patterns and trends in context, within and
Specific Learning Outcomes
  • Record data in tables
  • Display data in an appropriate format
  • Make a statement about a data display
  • Make sensible statements about information with reference to supporting evidence.
Description of Mathematics

Students are learning what population pyramid is and what it says about a population. The most important demographic characteristic of a population is its age-sex structure. A population pyramid (also known as an age-sex pyramid) is used to show the characteristics of a population – the number or percentage of males and females in different age groups (usually in 5-year age groups). When the population is plotted in this way, the graph looks like a pyramid because there are generally more younger people than older people.

Students are introduced to three types of population pyramids each of which tells a distinctive story about a population. From a given data set students create two back-to-back histograms placed on their sides. These form a pyramid of a distinctive shape which the students then learn to ‘interpret’.

As the graph is created, have your students understand how the axes are drawn and labelled and how the bars are drawn. Each bar represents the proportion of the population, not the number of people, in that particular age band. This means that the sum of the lengths of the bars in any population pyramid will be 100.

Population pyramids are useful because they tell us about population change. By comparing population pyramids from different years you can tell whether the population is changing over time – for example whether the population is getting younger or older.

Students learn that the distinctive features of a population pyramid give useful insights into the possible needs of that population in the future. We have to take care to interpret information accurately.

Required Resource Materials
  1. Ask students what might be meant by the words, ‘the shape of the nation’, or ‘population pyramid.’ Discuss.
  2. Distribute Copymaster 1 to student pairs. Have them read it together, identify key structural features of the graph, write three statements and three questions about the population pyramids shown.
  3. Have students suggest what shape they think the current NZ population data may take and explain their reasons.
  4. Distribute Copymaster 2 and have students investigate this trial data set, and understand the process of creating a pyramid for this unidentified population.
    Have them explore and understand that sum of the lengths of the bars in any population pyramid will be 100.
    Have students discuss the shape and the features of their completed population pyramid.
    Talk about what this might happen to the shape of this pyramid as the years pass.
  5. Access current New Zealand data for age and sex.
    Distribute Copymaster 3 and have students use raw data to create a NZ population pyramid using the most recent census data available.
    Model and discuss the necessary percentage calculations.
    Have students check their predictions in (3) above and answer a range of pertinent questions such as:
    • What percentage of New Zealanders are male aged 10–14?
    • What percentage are preschool girls?
    • At what ages is there a ‘bulge’ in the graph?
    • In which age group is there a dip?
    • What are the possible reasons for this change?
  6. Have students suggest the shape that the current pyramid may take as the years pass, and suggest what this might mean for planners catering for the needs of our population in the future.

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