Best for
Bearings, turns, direction, and applied geometry in contexts where students need mathematics to feel purposeful rather than detached from the world.
Pāngarau • Turns, bearings, and estimation • Years 6-10 • Ready to use tomorrow
Traditional Navigation Mathematics
Use this handout to make the mathematics inside wayfinding visible. It helps ākonga see that direction, quarter-turns, estimation, and route decisions are mathematical acts inside mātauranga Māori as well as practical navigation work.
Free maths scaffold, premium adaptation path
This handout is ready to print and teach. If you want bearings tied to a local coastline, a camp map, a school field, or a differentiated numeracy sequence, Te Wānanga can adapt it while keeping the navigation context intact.
- Swap in local landmarks, awa, maunga, or camp routes.
- Create support, core, and extension versions for mixed-readiness groups.
- Save the adapted version and reopen it later in My Kete or Creation Studio.
Kaiako planning snapshot
- Use length: 20-35 minutes depending on whether students complete the route design task.
- Grouping: Whole-class modelling first, then pairs or independent problem solving.
- Prep: Decide whether students will work with quarter-turn language only, formal bearings, or a mixture.
- Teaching move: Keep asking what the number means in the route, not just whether the answer is correct.
Resources already provided
- Direction vocabulary bank
- Quarter-turn and bearing examples
- Two route reasoning tasks
- Explain-your-thinking workspace
- Curriculum companion for teacher planning clarity
If your lesson mentions bearings, turns, or worked examples, those supports already exist here.
Ngā Whāinga Akoranga / Learning Intentions
- We are learning to use turns and bearings to describe direction.
- We are learning to connect mathematical reasoning to navigation problems.
- We are learning to explain how estimation supports a route choice.
Paearu Angitu / Success Criteria
- I can describe a route using turns, directions, or bearings.
- I can estimate or calculate the direction change correctly.
- I can explain what the mathematics means in the route context.
Curriculum integration / Te Marautanga alignment
Use the linked curriculum companion to make the direction, turning, and applied-geometry progression explicit in your mathematics planning.
Why the mathematics matters
Wayfinding does not work through intuition alone. Navigators must estimate, compare, orient, and hold direction with precision. This handout helps ākonga see the mathematics as part of purposeful decision making inside waka traditions and mātauranga Māori, not as a detached worksheet exercise.
Quick direction bank
- North / east / south / west = the four cardinal directions
- Quarter-turn = 90°
- Half-turn = 180°
- Three-quarter-turn = 270°
- Bearing = direction measured clockwise from north
Worked example
Question: A navigator turns one quarter-turn clockwise from north. What direction are they now facing?
- One full turn is 360°.
- One quarter-turn is 360° ÷ 4 = 90°.
- 90° clockwise from north points east.
So the direction is: east, or bearing 090°.
Practice 1 — Quick turns
- What direction is a half-turn clockwise from north? __________________________
- What direction is a quarter-turn anticlockwise from east? ____________________
- What bearing is a three-quarter-turn clockwise from north? ___________________
- Why is a bearing more precise than saying “go that way”? ____________________
Practice 2 — Route reasoning
Scenario: You travel east from a starting point, then turn a quarter-turn clockwise, then travel again.
- What direction is the second part of the route? ______________________________
- What bearing is that direction close to? ____________________________________
- What landmark or cue might help you check you stayed on course? ______________
Show your thinking
Explain one answer in words as well as numbers.
Design a simple route
Sketch a short route using at least two direction changes. Label the turns or bearings clearly.
Support, core, and stretch
Support
Work with quarter-turn language only and use the direction bank to keep the task chunked and manageable.
Core
Complete both practice tasks and explain one answer using words and numbers.
Stretch
Convert route changes into bearings and justify which cue or landmark would be most useful in checking the route.
Neurodiversity and inclusion note: offer oral rehearsal, a worked example kept visible, and alternative response modes before expecting independent written explanation.
Teach this tomorrow
Print or share
- One copy per learner
- Optional local map or camp route image
Decide before class
- Whether your class is ready for formal bearings or still needs turn language first
- What local route example will make the mathematics feel real
Good progress looks like
- Students can justify the direction change, not just state it
- The number work remains connected to place and purpose
Natural continuation
- Move into the broader navigation handout or local map work
- Adapt the route problems in Te Wānanga
Hononga Marautanga · Curriculum Alignment
Social Sciences — Tikanga ā-Iwi
Level 3–4: Investigate social, cultural, environmental, and economic questions; gather and evaluate evidence from diverse sources; communicate findings and reasoning clearly for different audiences and purposes.
English — Communication
Level 3–4: Read, interpret, and evaluate information texts; write clearly and purposefully for specific audiences; apply critical thinking skills to evaluate sources and construct well-reasoned responses.
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.
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.