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‘Co-ordinating’ the past

Achievement Objectives:

Achievement Objective: GM3-1: Use linear scales and whole numbers of metric units for length, area, volume and capacity, weight (mass), angle, temperature, and time.
AO elaboration and other teaching resources
Achievement Objective: GM3-5: Use a co-ordinate system or the language of direction and distance to specify locations and describe paths.
AO elaboration and other teaching resources
Achievement Objective: S3-2: Evaluate the effectiveness of different displays in representing the findings of a statistical investigation or probability activity undertaken by others.
AO elaboration and other teaching resources


The purpose of this unit is to develop an understanding of the time line of the growth in the population of New Zealand. Immigration, the locations of places of origin, and the directions of the different paths immigrants have taken to reach Aotearoa, are considered.

Specific Learning Outcomes: 
  • Order events on a timeline, giving consideration to scale.
  • Describe early Polynesian migration routes using grid references and compass points.
  • Write grid references and compass points to identify a specific location.
  • Locate NZ places with Māori names on a map, using grid references and compass points.
  • Develop understanding of the context for early migrants to NZ.
  • Read and interpret data.
  • Present migration data on a line graph.
Description of mathematics: 

In understanding some dynamics of immigration, students are better placed to understand New Zealand’s cultural diversity.

The title of this series of teaching sessions is “Co-ordinating the past”. As level 3 students consider a simple history of migrants coming to NZ, they are learning to locate places of origin using co-ordinate references such as A3, or E5. They are also learning to describe the geographic movement people journeying from places of origin to NZ, using these co-ordinate references. To further refine their descriptions of movement and to define specific routes, they must of course learn to use and apply compass directions (N S E W). In these lessons students are not required to interpret the scale of maps or to calculate the large kilometre distances travelled.

Measurement involves quantifying an attribute using units, recognising that these units should be uniform in size. In this series of lessons, as students sort and order a selection of immigration events by date, they must consider the units of time they will use for a timeline spanning some 800 years. The creation of a linear scale with equally spaced units of time requires a practical application of number and measurement knowledge and strategies.

As students encounter immigration data in a table and present this in a line graph, they refine their understanding that line graphs are like scatter plots in that they record individual data values as marks on the graph, but that line graphs connect each point with a line. In this way the change between any pairs of points is made clear and the overall trend can be seen. Students also learn how to plot two data sets on the one display, and to use colour to differentiate these clearly. Comparing the effectiveness of the table and the graphical data display, brings into focus the different ways of showing the relationship between variables, and that some displays are more ‘powerful’ in their clarity and impact than others. It is important too that students can accurately read a line graph, interpreting the scale on the y axis in particular, and understand the information that is presented.

Associated Achievement Objectives

Social Sciences
Social Studies

  • Understand how early Polynesian and British migrations to New Zealand have continuing significance for tangata whenua and communities.
  • Understand how the movement of people affects cultural diversity and interaction in New Zealand.
Required Resource Materials: 
Atlases/ Google access
Pencils and erasers
Paper and paper strips
NZ history reference sources/Google
The House that Jack Built, by Gavin Bishop

Learning activities
Whilst this unit is presented as sequence of five sessions, more sessions than this may be required. It is also expected that any session may extend beyond one teaching period.

Session 1

This session is about creating a timeline of key events in New Zealand’s immigration history and identifying some immigrant populations.


  • Order events on a timeline, giving consideration to scale.

Activity 1

  1. Begin by writing this statement:
    New Zealand was once a land with no people.
    As at Monday, 04 Nov 2013 at 01:58:22 pm, New Zealand had a population of 4,490,236*

    How do you explain this? (Initially, immigration)
    *Check current population at:  http://www.stats.govt.nz/tools_and_services/population_clock.aspx
    Make available paper, pencils.
    Set a short time limit. Have students work in pairs to brainstorm together and record their knowledge/understanding of the ‘peopling of NZ’.
  2. Have students pair share their ideas, and then discuss and record these as a class.
    Highlight the fact that the New Zealand population is now culturally diverse because of the significant movement of people over time.

Activity 2

Make available pencils, rulers, erasers, strips of paper, scissors and glue (optional)

  1. Distribute copies of Attachment 1 (Key immigration events).
    Explain the abbreviate c. for ‘circa’, meaning “around, about” this date.
    Explain that, for this task, where c. is used, the date is, in some cases, indicative of a period of time over several years around this date.
    Read these events together, pointing out that the events as listed are not in order. Together identify the first listed event and the most recent. Have students number the events in order from earliest to most recent. Alternatively, they can cut them out and place them in order of date.
  2. Explain that students should work in pairs to discuss a scale they could use to create a timeline of the listed events. They should consider the endpoints of their measurement scale, the number of years between these, and the units of time that their scale will be partitioned into. They will need to know how to further partition some of the units to locate specific years.
  3. Have each student complete their own timeline, making accurate measurements of the scale on their own paper strips, then writing in the events, or cutting them out and gluing them, at the appropriate places on the timeline.

Activity 3

As students complete their timelines have them identify if they can, from which (if any) of the immigrant populations their own family (ancestors) originate.
Make atlases/Google available for students to locate places of origin.

Session 2

This session is about using compass points and grid references to describe travellers’ journeys and to locate specific places on a map of New Zealand.


  • Describe early Polynesian immigration routes using grid references and compass points.
  • Write grid references and compass points to identify a specific location.

Activity 1

  1. Refer to the timeline created in Session 1. Identify the first people and discuss tangata whenua. Recognise that there are strong Māori traditions for recounting how their ancestors came in great ocean-going canoes (waka).
    Explain that, over time, researchers have suggested possible migration routes for the original Polynesian settlers of New Zealand. It is thought that they discovered the country on deliberate voyages of exploration, using the ocean currents, winds and stars to help them to navigate. It is suggested that they became known by the collective name, Māori, meaning ordinary, upon the arrival of Europeans.
    Students can research further information using: http://www.teara.govt.nz/en/ideas-of-maori-origins
  2. Print and distribute to each student a copy of a map showing the possible migration routes of Polynesian people and suggested time periods that these movements occurred An example can be found at http://www.teara.govt.nz/en/map/2510/pacific-migration-routes, and others may be found by using a search engine. Discuss key movements shown on the maps, noting early Asian origins, movements east, then later, west to NZ. Look at the approximate dates attributed to these movements. Discuss these relative to the timelines created in Session 1, noting how far back the BC dates would be relative to the beginning of the timeline.
  3. Make available a length of thick string. Have students use the timeline scale to calculate how long the length of string would be to reach the 3000BC date. Have two students hold up a timeline, and have other students assist in adding the string length to the timeline to model/demonstrate the complete time scale.

Activity 2

Have students write 8 compass points on or beside their map from Activity 1.
Together draw a grid and write in grid references for the map.
Have students in pairs discuss key movements of Polynesian people, giving dates, grid references and compass directions.

Activity 3

Make pencils and paper/computer available.

  1. Have individual students write their own descriptions, using compass directs, time, and place names to describe several of the migration routes they have discussed, including, in particular, the New Zealand ‘immigration journey’ over time.
  2. As they complete this, have students research and record their ideas about the sorts of challenges the travellers may have faced on their long journeys on their canoes, and what sort of things they may have brought with them.
    For example: food crops such as taro yam, kumara; other tropical plants such as banana, breadfruit or coconut which did not survive in the cooler NZ climate; dog (kuri); their fishing, carving, tool-making, weaving and canoe building skills; rat (kiore) perhaps as stowaways.

Activity 4

Conclude this session by having students present in pairs the routes they have documented, checking the gird references and compass directions.
Have them share their research information about what the Polynesian migrants are thought to have brought with them to NZ.

Session 3


  • Locate NZ places with Māori names on a map, using grid references and compass points.
  • Develop understanding of the context for early migrants to NZ.

Activity 1

  1. Write Aotearoa on the class chart. Discuss the suggested origins of its meaning:
    ao: cloud, dawn, daytime or world,
    tea: white, clear or bright,
    roa: long or Aotea = the name of one of the migratory waka that travelled to New Zealand.
    The common translation is "the land of the long white cloud".
    Alternative translations include ‘long bright world’ or ‘land of abiding day’ referring to the length and quality of the New Zealand daylight (when compared to the shorter days found further north in Polynesia).
    For further information see: http://en.wikipedia.org/wiki/Aotearoa
  2. Make atlases/Google available and distribute Attachment 2.
    Have students consider the meaning of the named places, use an atlas/Google to locate each on the New Zealand map, and record its grid reference, and compass direction as appropriate, beside each place.
  3. Have students research local or other national Māori place names and their meanings, and add these to the list on Attachment 2.

Activity 2

  1. Refer to the timeline and to the early arrival of Europeans in New Zealand.
    Read: The House that Jack Built by Gavin Bishop
  2. Discuss the context for an early European settler in NZ.
    Refer to the list of Goods to Trade” on the second inside page of the book. Agree on a definition for trade (students may refer to ‘fair swaps’ that friends make) and discuss why the goods on the list would have been traded.
    (Optional) Note and discuss the imperial units of measurement used and present metric equivalents: 1 pound (lb) is approximately 454 grams (g), 1 yard (yd) is approximately 91 centimetres (cm)

Activity 3

Conclude the session by recording student understanding about the early peopling of New Zealand (migration to NZ). Note that immigrants needed to bring some items from their homeland.

Session 4

This session is about using compass points and grid references to describe the journey of European immigrants to New Zealand.


  • Describe European settler journeys using compass points and grid references.

Activity 1

  1. Have students refer to the timelines created in Session 1.
    Discuss selected migrant groups.
    Brainstorm and record student ideas about why people from other nations might want to come to live in NZ. List these in two headings: For example:
    Why leave their own country?Why come to NZ?
    a war is going on
    poor living conditions
    a peaceful, safe place
    NZ is not crowded
  2. Discuss how immigrants travel to New Zealand now (by air, over land and sea).
    Ask how immigrants travelled to NZ in times past (by sea, around land).
    Point out that the first commercial flights to and from the Pacific began in 1947 and the first jets were bought by Air New Zealand in 1963, with the first Auckland to Los Angeles flight happening in that year.
  3. Distribute a copy of Attachment 3 to each student.
    Make available Atlases/Google, pencils.
    Have student pairs work together to discuss, and locate on their own world maps, the country of origin of at least 5 of the migrant groups on their timeline, and mark on their map the route that the immigrants were likely to take to NZ, depending on the time of immigration.
    Have them record a description of the route taken to NZ, using compass directions and grid references, and explain their rationale for the identified route.

Activity 3

Have students research and write a short profile about one of the immigrant groups, including the predominant place of settlement in New Zealand of this immigrant group (if this is known).

Activity 4

Conclude by having students pair share their maps, explaining their routes to each other.

Session 5

This session is about interpreting immigration data.


  • Read and interpret data.
  • Present migration data on a line graph.

Activity 1

Begin the session by referring to the timeline created in Session 1.
Have students share information about immigrant populations from Session 4, Activity 3.

Activity 2

Distribute a copy of Attachment 4 to each student.

  1. As a class discuss the trends that can be seen in the data in Figure 1. (the number of immigrants continues to increase, but this has decreased over time relative to the numbers of people born in NZ).
  2. Make graph paper available.
    Explain that students are to make a line graph using the Figure 1 data.
    Both data sets should be plotted on the same graph, but different colours should be used.
    Look at the population data, model and agree on how to round each of the population figures to the nearest 1000. Students should record these on the table beside the actual figures.
    Identify the range within both sets of data and discuss a sensible scale for the y axis.
    Model this as appropriate.
  3. Have students make their graphs, taking care to label axes and the graph appropriately.
  4. Have students write their own statements about the trends in their graphs and suggest implications for these.
  5. Discuss Steps 3 and 4 as a class, sharing ideas. (Note that the data spans 100 years only ending in 1961. Discuss the different trends in each line and the relationship between these).
  6. Have students evaluate the data displays, stating which display, the table or the graph, tells the story about the immigration trends the most powerfully. Discuss their reasons.

Activity 3

  1. Introduce Figure 2. Give students time to interpret and make sense of what it is showing.
    the years it represents, the scale on the y axis, the non NZ citizens who are arriving and the NZ citizens who are leaving, and the points made below the graph.
  2. Write net migration on the class chart. Discuss its meaning: the difference between immigrants (those arriving) and emigrants (those leaving) in a certain period of specified time.
    Discuss in rounded figures the net migration for at least two of the given years.
    For example:
    1973: 40 000 non NZ immigrants and 10 000 NZ citizens leaving NZ: net migration approx. +30 000
    1980: 8000 non NZ immigrants and 37 000 NZ citizens leaving NZ: net migration approx. -29 000
  3. Have students write statements describing the net migration for at least four other years and suggest possible reasons (NB. Note below Figure 1. Government immigration policy).

Activity 4

Referring to content from Sessions 2 and 3, conclude this session by recording students’ ideas about which migrant groups are contributing to the immigration figures for particular years (and why).

Activity 5

Conclude with any of the following:

  • Together research immigration statistics from the most recent census. Note trends.
  • Have students, in pairs, discuss and record their predictions for the NZ population and for immigration dynamics for the year 2025, and give their reasons. (these may include references to changes in modes of travel, given ‘carbon footprints’, fossil fuel supplies etc.)
  • Have students write an explanatory paragraph about the origins of the cultural diversity of the NZ population, highlighting its richness.


Coordinating_cm1.pdf404.57 KB
Coordinating_cm2.pdf464.69 KB
Coordinating_cm3.pdf265.43 KB
Coordinating_cm4.pdf411.82 KB