Never get lost


This extended, cross curricular unit supports students to learn and apply theories around scale, bearings and compass directions in a context that enhances their engagement and produces an authentic and useful outcome.

Achievement Objectives
GM5-5: Deduce the angle properties of intersecting and parallel lines and the angle properties of polygons and apply these properties.
GM5-8: Interpret points and lines on co-ordinate planes, including scales and bearings on maps.
Description of Mathematics

At its heart, the idea of this unit is that students learn about how to understand angles and use maps.

The main mathematics within the unit is using working with angles and applying directions and scale.

Associated Achievement Objectives:


Static image

  • Select and use a range of language features appropriately, showing an understanding of their effects.
  • Organise texts, using a range of appropriate, effective structures.
  • Integrate sources of information, processes, and strategies purposefully and confidently to identify, form, and express increasingly sophisticated ideas.
Required Resource Materials
  • Google Maps
  • Rulers
  • Protractors – Template included (photocopy onto OHT sheets and cut out Copymaster 1)
  • Worksheets for activities included

Session 1

This week is about introducing the topic. It is intended that it would take two to three lessons to complete.


  • Establish a link for the students between the two subject areas. 
  • Become familiar with the ideas and language that will be used later in the unit.

Activity 1

Introduce the topic, discussing finding your way, use of maps, and descriptions of areas that are special to students.

Activity 2

Introduction to the English component of the unit.  The main focus is static images.  An introduction to static images is likely to include the use of visual and verbal techniques for example, framing, use of colour and line, the concept of the intended effect on the viewer, language features used to support the visual features, language features of slogans e.g. repetition or assonance. This is a good time to introduce and elicit ideas around turangawaewae (places which students regard as where they belong, places that are special to them).

Students are also introduced to the product of the unit: a tourist brochure for a local area that contains a walking tour with information about specific points of interest along the walking tour. 

Sessions 2-3

In these activities, students learn about geometric reasoning and apply it to solving problems.


  • Learn angle rules for basic geometric reasoning and be able to apply them to problem solving

Activity 1

Learning about angle rules for lines, point, and vertically opposite angles.

Apply them to real life situations.

Activity 2

Learning about triangle and other polygon angle rules

Apply to real life situations.

Activity 3

Learning about angle rules with parallel lines

Apply to real life situations (bringing maps into some of the practice).

Students practice using angle rules to solve problems in a variety of contexts using textbooks, workbooks, or other materials that the school has.

Session 4

The activities described and resources provided for this session are centred around the mathematics content.  However, at the same time the mathematics activities are interspersed with static image activities. This will include making site visits for ideas for their walking tour project, making sketches and gathering material from each site.  Back in the classroom students will choose one of the places to make and present a mini image.  This includes researching the place and producing a mini image that uses visual and verbal features with limited colour use.


  • Be able to measure directions through compass directions and bearings

Activity 1

Students look at protractors, both 180° and 360°

  • How to read the numbers and the scale.
  • How to measure angles with them.

Activity 2

Students are instructed in how bearings work and are measured.

Activity 3


Students work in pairs and are given a map which mainly centres around the Waitakere Ranges where a large part of the movie – Hunt for the Wilderpeople – was filmed.  This is the movie that will be watched and analysed for English later in the topic. Alongside this the students are given a bearing list with locations to find. Ignore the scale at this point and give measurements in centimetres. Teachers to create their own map relative to the movie or context they are using.

The English activities mainly centre around interpreting scenes and the effects of colour and lines in an image.

Session 5


  • Students learn how to describe locations using grid references.
  • Students learn how to use compass directions. E.g. N30°W.

Activity 1

Students look at how to locate things by using grid references. Map examples such as local tourist maps are useful as these usually have grid references. Students can also play a few rounds of battleship in pairs (see Copymaster 2 for a template for battleships).

Activity 2

Looking at N E S W in reference to bearings, the students are introduced to giving directions in the form of   S30°W.  Extra practice can be done with the Shipwreck Exercise (Copymaster 3).


Students are given two sheets. One has start and end points and several obstacles (e.g. rocks, sandbars, etc.) in between. The student uses a ruler and plots a course with at least five legs to it.  They then write down all the compass directions and distances (scale is 1 cm = 1 km). The student then gives the directions to a partner who tries to plot the course on the 2nd sheet of paper which only has the start and end points with no obstacles shown.  When finished the students can put their sheet on the obstacle sheet on the window or to the light and see if they made it or were shipwrecked.

Session 6


  • Applying map scales to work out real life distances

Activity 1

Discuss ratio and scaling in general.  Look at how it applies to the scale for maps. Do some basic conversion exercises.

Activity 2


Copymaster 4 has six different New Zealand communities. Students need to work out the scale of each map and determine the distance between key points in the town

Session 7


  • Understand and use bearings, including to triangulate a location.

Activity 1

Introduce students to the concept of triangulation and how a location can be found as an intersection of bearings from different locations. For example, emergency beacons transmit a pulse that is picked up by different receivers and the bearing information compiled to work out a location. 


Students are given a map of Thames (Copymaster 5) that has three “listening points” marked on it. They also receive a list of known spies that are transmitting signals and the corresponding bearings picked up by the listening stations. Students trace the bearings on the map to find the spies. 

Activity 2

Show students how to use a compass and practice following bearings by moving around according to a course written on the whiteboard. 


Lay out a number of waypoints on the school field, each with a different letter. First students work out the length of their stride. Then they work in pairs to create a course (one with the compass and one marking distance), between a number of the waypoints, including bearings and distances converted from the number of strides it took for them. Pairs should then swap courses with another pair and complete the course checking that the letter sequence is correct.

Session 8


  • Use bearings and distances to describe a path.

Activity 1

Students combine their knowledge of bearings, compass directions, and scale to describe courses between set points on a map.


Two starting points and two destinations are labelled (Copymaster 6). Students need to work out the bearing and distance a drone would follow to fly directly between the points and then for a robot that would need to travel on the roads using compass directions.

Activity 2

Watch the Movie “Hunt for the Wilderpeople”, taking breaks while watching the film to discuss the make-up of different scenes.  Exploring cinematography and the effect on the viewer e.g. lighting, focus, angle of camera, size of the shot, etc. and signalling some of the effects.  The film connects strongly to turangawaewae, where do you stand, where do you belong. This sense of connection is key for the place that students chose to do for their static image – ideally a place they are close to.

Session 9


  • Apply the ideas learned during the unit to a final project.

Activity 1

Students choose an area that is meaningful to them that should have a few different spots that they could go to. On the English side, each waypoint could serve as its own static image or a single waypoint could be the static image, or the area in general. 

ASSESSMENT  (Copymaster 7)

  • Students determine the area they want to create a “tour” for.  It could be a place that is special for them.
  • Find a scale map of chosen area
  • Determine waypoints (points of interest for their walking tour)
  • Give directions and distances between waypoints
  • Bearings and distances for flying a drone
  • Compass directions and distances for walking 
  • Students create an image for 2-3 of their waypoints (points of interest)
  • Students complete the tourist brochure (static image) and present orally
  • This could be to someone locally who is involved in promotion of the town or location, e.g. contact the City Council.
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Level Five