Best for
Direction and turn lessons, grid-reference practice, integrated maths inquiries, and respectful introductions to Pacific and Māori navigation knowledge.
Pāngarau / Mathematics • Years 7-10 • Geometry, direction, and mapping
Star Navigation Mathematics
Use this handout to help ākonga explore how mathematical ideas such as direction, turn, angle, and positional systems support wayfinding. The teaching goal is respectful: use mathematics to notice the precision within navigation traditions, not to reduce them to a worksheet trick.
Free integrated maths base, premium adaptation path
This page already provides the direction prompts, grid tasks, and angle reasoning. Te Wānanga becomes useful when you want the same structure rebuilt around a local map, a school navigation task, or a class inquiry into wayfinding.
- Generate a simpler grid-reference version or an extended angle-and-bearing challenge.
- Swap in local landmarks, coastal routes, or school-ground mapping tasks.
- Save an adapted version in My Kete and refine it later in Creation Studio.
Kaiako planning snapshot
- Use length: 35-50 minutes.
- Grouping: Whole-class context build, then partner map work, then independent reflection.
- Prep: Compass rose or projected map if available.
- Teaching move: Be explicit that this is a maths support lens, not a full cultural study of navigation knowledge.
Resources already provided
- Direction and turn reference
- Grid-navigation task
- Angle and route reasoning prompts
- Support, core, and stretch pathways
- Teacher-only curriculum companion
If the lesson mentions compass directions, grid locations, or turn-based navigation reasoning, those materials are already on this page.
Ngā Whāinga Akoranga / Learning Intentions
- We are learning how direction, turn, and angle language support navigation tasks.
- We are learning how to read and use simple grid references.
- We are learning how mathematics can illuminate real navigation practices with respect and care.
Paearu Angitu / Success Criteria
- I can use compass directions and turn language accurately.
- I can locate and describe positions on a simple grid.
- I can explain how a route uses angle or turn reasoning.
Curriculum integration / Te Mātaiaho alignment
The companion page links this handout to Phase 2 geometry expectations around grid references, direction, and benchmark turns, with an integrated pathway for angle reasoning.
Why this matters in Aotearoa classrooms
Wayfinding traditions across Te Moana-nui-a-Kiwa relied on careful observation of stars, winds, currents, horizons, and direction. Mathematical thinking is part of that precision, even though the knowledge system is richer than mathematics alone.
Through a mātauranga Māori and Pacific navigation lens, students can see that direction, pattern, and spatial reasoning are living forms of knowledge. That demands respectful teaching language and clear limits about what a short maths handout can and cannot do.
Direction and turn reference
Quarter turn
A quarter turn changes direction by 90°.
Half turn
A half turn changes direction by 180°.
Compass language
North, east, south, and west can be combined with half and quarter turns to describe route changes clearly.
Grid language
An alphanumeric grid reference identifies a location using a row letter and column number, such as B4.
Te Kāpehu Whetū — Interactive Star Compass
Explore the 32 whare (houses) of te kāpehu whetū, the Māori star compass. Hover or click a house star to see its name, meaning, and bearing. Drag or click to rotate the waka in the centre and steer.
The star compass was developed by Hawaiian navigator Nainoa Thompson, building on the teaching of master navigator Mau Piailug of Satawal. Jack Thatcher adapted it into te reo Māori for navigators of Aotearoa. House names and meanings here follow the Science Learning Hub.
Navigation grid task
Imagine a simple navigation map where a waka starts at B2.
| Instruction | New location or direction | What turn is involved? |
|---|---|---|
| Move two squares east. | ________ | ________ |
| From there, make a quarter turn and travel south one square. | ________ | ________ |
| Make a half turn and return two squares. | ________ | ________ |
Route reasoning
Angle challenge
If a route turns from facing north to facing east, what size turn has happened? How do you know?
Observation challenge
Why is direction alone not enough for safe navigation? What other observations would a real navigator need?
Support, core, and stretch pathways
Support
Focus on cardinal directions, quarter turns, and simple grid moves with teacher modelling.
Core
Use turns, directions, and grid references together to describe and follow a route.
Stretch
Create your own navigation path with at least four route instructions and one angle clue for a partner to solve.
My reflection
What did mathematics help you notice about navigation, and what still sits beyond the maths lens?
Hononga Marautanga · Curriculum Alignment
Curriculum alignment for this handout has not yet been verified against the live curriculum statements. A generated placeholder that stood here was removed on 2026-08-29 because it matched no real statement.
Aronga Mātauranga Māori
This resource sits within a kaupapa that recognises mātauranga Māori as a living knowledge system with its own frameworks, values, and ways of understanding the world. The New Zealand Curriculum calls for learning that reflects the bicultural partnership of Te Tiriti o Waitangi, which means every subject area has an obligation to engage authentically with Māori perspectives — not as cultural decoration but as substantive contributions to how we understand our topics. The concepts of manaakitanga (care for others), kaitiakitanga (guardianship), whanaungatanga (relationship and belonging), and tino rangatiratanga (self-determination) provide a values framework applicable across all learning areas, and all are relevant to the work in this handout.
Tuhia ōu whakaaro · Write Your Thoughts
Reflect on what you have learned today. What was the most important idea? What question do you still have?
Ngā Rauemi Tautoko · Support Materials
This handout is designed to be used alongside the broader unit resources available at Te Kete Ako handouts library. Related resources from the same unit are linked in the unit planner. All resources are provided — no additional preparation is required to use this handout in your classroom.
Curriculum alignment
- This handout has no verified curriculum statement attached yet. The two statements previously listed here cited New Zealand Curriculum Level 1 mathematics — new-entrant counting and equal sharing — on Years 7–10 geometry and direction work, an error of about eight year levels. They have been removed rather than swapped for a plausible-looking replacement. The material sits at roughly NZC Level 4–5 mathematics (angle, bearing and grid reasoning); confirm the alignment against the live curriculum before you report against it.