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 | Tamatea-kai-ariki | 7 | ________________________ |
| Full moon | Rākaunui | 16 | ________________________ |
| Waning | Tangaroa-ā-roto | 24 | ________________________ |
These names and nights follow one published list, from Ngāti Kahungunu, as given by Te Ara (Maramataka: the lunar calendar). Other iwi name and count the nights differently, so use your own rohe's maramataka where you have it.
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
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.
Ngā Rauemi ā-Waho · External Resource Bank
NZ sources for deeper inquiry. Each card was checked against its live page on 5 October 2026 and has a kaiako usage note.
🔬 Science Learning Hub — Māori ways of knowing – weather and climate
sciencelearn.org.nz/resources/2961-maori-ways-of-knowing-weather-and-climate
Kaiako use: Read before the lesson. The article has a section headed "Maramataka" and one headed "Local maramataka", which states: "There are many maramataka and tohu, and they vary from iwi to iwi." Use that section to frame the "local variation" discussion after the maths tasks are complete.
🏛️ Te Papa Tongarewa — Maramataka Learning Resource
tepapa.govt.nz — Maramataka learning resource
Kaiako use: The page offers two PDF downloads: a one-page A3 Maramataka poster and a learning resource with suggested activities. The poster sets out the months of the year by season, with the activities traditionally done in each month. It shows months, not moon phases, so display it for the seasonal timing tasks (Tasks 3 and 4), not the lunar cycle table. Te Papa lists the resource as suitable for ages 5–10.
🌙 Living by the Stars — Ngā Mata o te Marama (Moon Phases)
livingbythestars.co.nz/pages/nga-mata-o-te-marama-poster
Kaiako use: This page describes the Ngā Mata o te Marama poster, which it says includes hand actions, moon images and names for each of the moon phases. It links to two videos: one explaining how to use the poster, and a waiata with hand actions for learning the sequence of the moon. A possible extension for students who finish the calculation tasks early. Note: no download link for the poster was found on this page, and the site has a separate shop.
📻 RNZ — Puanga Matariki audio collection
rnz.co.nz/collections/matariki
Kaiako use: A collection page of RNZ audio items about Matariki. The items listed are dated 2008 to 2015 and include discussions, waiata and whakataukī. The collection page does not show how long each item runs, so listen first and choose. One item that fits Tasks 3 and 4 is "Māori star lore" (Nine To Noon, 30 May 2013, about 11 minutes), in which Dr Pauline Harris discusses how Māori and other societies used the sun, stars and planets to track time. Play an excerpt as an opener before the seasonal planning reflection.
Accessibility: Audio only. No transcript was found on the "Māori star lore" page, so plan another way in for students who cannot hear the audio. Put key vocabulary on the board before playing.
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.