Best for
Use when you want time measurement to connect to pattern, season, and practical decision-making rather than clock-only exercises.
Mathematics + mātauranga Māori • Years 7-10 • Time and pattern
Maramataka — Time and Mathematics
The maramataka is not “just a calendar”. It is a system of observation, timing, and decision-making. This handout helps ākonga work with time, pattern, and seasonal cycles while recognising the depth of knowledge held in maramataka practice.
Free pattern-and-time task, premium local maramataka variant
This version already works. Te Wānanga becomes useful when you want local iwi maramataka notes, alternate star prompts, or differentiated calculations added.
- Swap in local maramataka or Matariki references where appropriate.
- Add easier calculation support or stretch questions.
- Save a time-and-pattern inquiry sequence in My Kete.
Kaiako planning snapshot
- Use length: 30-40 minutes.
- Grouping: Individual calculation with paired discussion.
- Prep: Decide whether students need a visible lunar-cycle diagram.
- Teaching move: Ask students what the numbers help people decide.
Resources already provided
- Lunar-cycle table
- Calendar comparison prompt
- Matariki star-domain reminder
- Seasonal planning reflection
- Teacher-only curriculum companion
The mathematics becomes stronger when students explain the implication of the pattern, not only the answer.
Ngā Whāinga Akoranga / Learning Intentions
- We are learning how lunar cycles create repeating patterns in time.
- We are learning to compare different systems for marking time.
- We are learning how observation helps people plan activities and seasons.
Paearu Angitu / Success Criteria
- I can explain the approximate length of a lunar month.
- I can compare lunar and solar timing clearly.
- I can describe how maramataka supports practical decision-making.
1. Understand the lunar cycle
| Phase | Example Māori name | Approximate day | What might this help people decide? |
|---|---|---|---|
| New moon | Whiro | 1 | ________________________ |
| Crescent | Hoata | 3 | ________________________ |
| Half moon | Ōtāne | 7 | ________________________ |
| Full moon | Rākaunui | 15 | ________________________ |
| Waning | Tangaroa-ā-roto | 20 | ________________________ |
2. Compare lunar and solar time
Calculation
A lunar month is about 29.5 days. A solar year is about 365.25 days. How many lunar months fit into one solar year?
Interpretation
Why does this mean a lunar calendar and a solar calendar do not line up perfectly?
3. Matariki and seasonal timing
Tupuānuku
Food from the earth
Waitī / Waitā
Freshwater and saltwater food systems
Hiwa-i-te-rangi
Hopes and planning for the future
Prompt
How might a star cluster or seasonal marker help communities decide when to plant, harvest, travel, or gather?
4. Seasonal planning reflection
Write about one way observation and timing help reduce risk or improve decision-making.
Hononga Marautanga · Curriculum Alignment
Confidence labels: Verified = checked against published NZC/Te Mātaiaho text. Defensible = consistent with curriculum intent but not a verbatim quote.
Mathematics and Statistics — Pāngarau Verified
Number and Algebra, Level 3–4: Use additive and multiplicative strategies to solve problems involving fractions, decimals, and proportions in meaningful contexts.
How this handout aligns: The 29.5-day lunar month ÷ 365.25-day solar year calculation is a direct proportional reasoning task. Students move from arithmetic to interpretation — "what does this remainder mean for a calendar system?"
Mathematics and Statistics — Pāngarau Verified
Measurement, Level 3–4: Use appropriate scales, devices, and metric units for length, area, volume and capacity, weight (mass), temperature, angle, and time.
How this handout aligns: Students compare two measurement systems for time (lunar vs solar) and investigate why they produce different counts. This makes "unit of measurement" tangible rather than abstract.
Statistics, Level 4 Defensible
Investigate summary and comparison questions by using the statistical enquiry cycle.
How this handout aligns: The seasonal planning reflection asks students to reason from observational data (tohu/environmental signs) to decision-making — the core statistical thinking move of "what does this data help us decide?"
Nature of Science — Understanding About Science Verified
Appreciate that science is a way of explaining the world and that science knowledge changes over time. Identify ways in which scientists work together and provide evidence to support their ideas.
How this handout aligns: Maramataka is a system built from centuries of systematic observation. Positioning it alongside Western astronomy lets ākonga see that evidence-based knowledge systems exist in multiple traditions.
Ngā Rauemi ā-Waho · External Resource Bank
High-quality NZ sources for deeper inquiry. Each resource has a kaiako usage note.
🔬 Science Learning Hub — Maramataka: The Māori Calendar
sciencelearn.org.nz/resources/2545-maramataka-the-maori-calendar
Kaiako use: Read before the lesson to build your own understanding. The article explains how maramataka varies by iwi and region — use this to frame the "local variation" discussion after the maths tasks are complete. Student-accessible language.
🏛️ Te Papa Tongarewa — Maramataka Learning Resource
tepapa.govt.nz — Maramataka learning resource
Kaiako use: Downloadable classroom poster showing lunar months and seasonal tasks. Print the A3 poster for display during the lesson so students can reference moon phases while completing the table task. Good for visual learners and ESOL support.
🌙 Living by the Stars — Ngā Mata o te Marama (Moon Phases)
Kaiako use: Professor Rangi Matamua's resource includes a moon phase poster with hand actions and QR codes linking to waiata. Excellent extension for students who finish the calculation tasks early — they can explore how each moon phase name encodes observational knowledge. Note: some resources available for purchase only.
📻 RNZ — Matariki: The Science Behind the Stars
Kaiako use: Short audio segments (3–8 min) suitable for classroom listening. Use the Matariki episode as a 5-minute opener before the seasonal planning reflection (Task 3–4). Students hear how star observation connects to timing decisions — then they do the maths that underpins the same idea.
Accessibility: Audio only — no captions. Provide key vocabulary on the board before playing. Transcripts available on the RNZ website for hearing-impaired students.
Aronga Mātauranga Māori
Maramataka is not "just a calendar" and it is not a single national system. It is a living framework of observation, timing, and decision-making that varies by iwi, hapū, and place. Different communities read different tohu (signs) — the flowering of kōwhai, the arrival of specific bird species, the behaviour of marine life — alongside the lunar phases.
This handout uses the mathematics of lunar and solar cycles as an entry point, but the real depth of maramataka knowledge sits in the centuries of observation that produced it. Kaiako should frame the maths as a way into understanding the system, not as the system itself. Where possible, connect to local iwi maramataka practice — and name openly when you are teaching the general pattern rather than a specific tradition.