Te Reo Māori · Pāngarau / Mathematics · Years 3–8

Traditional Counting Systems

Ngā Tau Māori · Numbers and Counting in Te Reo — learning to count in te reo Māori and exploring traditional mathematical systems of Aotearoa.

Ingoa / Name
Akomanga / Class
Rā / Date

Subject

Mathematics (Pāngarau) and Te Reo Māori — integrated activity

Year Level

Years 3–8 (NZC Levels 2–4)

Duration

45–60 minutes; pronunciation warm-up 10 minutes

Curriculum

Number knowledge; Te Reo Māori vocabulary; measurement — traditional and modern systems

Free class-ready resource, premium progression path

This handout is ready to print. For extended te reo vocabulary sequences, pronunciation audio links, or cross-curricular maths-language units, Te Wānanga can build a full sequence.

  • Generate tau extension activities (ngā tau 20–1000).
  • Add whakatauki that use numbers and patterns.
  • Save a te reo maths sequence in My Kete.
Adapt this in Te Wānanga Open Creation Studio Compare paid workflow options

Ngā Whāinga Akoranga · Learning Intentions

  • We are learning to say and write the numbers 1–20 in te reo Māori.
  • We are learning to use the pattern of te reo number words to build larger numbers.
  • We are learning to describe traditional Māori measurement systems.
  • We are learning to translate number sentences between English and te reo Māori.

Paearu Angitu · Success Criteria

  • I can say numbers 1–10 in te reo Māori with correct pronunciation.
  • I can write numbers 11–20 using the tekau mā pattern.
  • I can complete a counting sequence with missing te reo numbers.
  • I can translate five number sentences from English into te reo Māori.

Hononga Marautanga · Curriculum Alignment

NZC Mathematics — Number
  • Number knowledge: counting sequences
  • Number identification: reading and writing numbers
  • Place value: understanding tens and ones
  • Measurement: non-standard and traditional units
Te Reo Māori integration
  • Tau — number vocabulary
  • Pronunciation patterns: vowels and digraphs
  • Te kore — zero in Māori cosmology
  • Base-10 logic in te reo number structure

Horopaki · Context — Pāngarau Māori

Long before European arrival, Māori had sophisticated systems for counting, measuring, navigation, and construction. The number system in te reo Māori is logical, consistent, and entirely base-10 — making it an elegant companion to modern mathematics. Ngā tau (the numbers) are part of everyday kōrero and carry the mana of centuries of use.

The concept of te kore (zero, the void) is ancient in Māori cosmology — it describes the state before creation: nothingness from which all things emerge. This deep philosophical idea parallels the mathematical concept of zero as a placeholder and a number in its own right.

Ngā Tau 1–20 · Numbers 1–20

Pronunciation guide: all vowels are pronounced clearly — a (ah), e (eh), i (ee), o (oh), u (oo). The letters wh are pronounced as an f sound in most dialects.

Tau / Numeral Te Reo Māori Pronunciation guide Tau / Numeral Te Reo Māori Pronunciation guide
1 Tahi tah-hee 11 Tekau mā tahi teh-kow mah tah-hee
2 Rua roo-ah 12 Tekau mā rua teh-kow mah roo-ah
3 Toru toh-roo 13 Tekau mā toru teh-kow mah toh-roo
4 Whā fah 14 Tekau mā whā teh-kow mah fah
5 Rima ree-mah 15 Tekau mā rima teh-kow mah ree-mah
6 Ono oh-noh 16 Tekau mā ono teh-kow mah oh-noh
7 Whitu fee-too 17 Tekau mā whitu teh-kow mah fee-too
8 Waru wah-roo 18 Tekau mā waru teh-kow mah wah-roo
9 Iwa ee-wah 19 Tekau mā iwa teh-kow mah ee-wah
10 Tekau teh-kow 20 Rua tekau roo-ah teh-kow

Notice the pattern: Numbers 11–19 are all built as Tekau mā [digit] — literally "ten and [number]". Twenty is Rua tekau — "two tens". This is exactly how the base-10 system works!

Mahi 1 · Activity 1: Counting Patterns — Fill in the Sequence

Complete each sequence by writing the missing te reo Māori number words.

Sequence A — Count by ones

Tahi, rua, , whā, , , whitu, , , tekau.

Sequence B — Count by twos

Rua, , ono, , tekau, , , tekau mā ono, , rua tekau.

Sequence C — Count backwards

Rua tekau, , tekau mā waru, , tekau mā ono, , , tekau mā toru.

Ngā Tau Nui · Building Bigger Numbers

The pattern continues:

  • 30 = Toru tekau
  • 25 = Rua tekau mā rima
  • 47 = Whā tekau mā whitu
  • 100 = Kotahi rau
  • 1,000 = Kotahi mano

Try these:

33 in te reo =  

56 in te reo =  

Iwa tekau mā rua =  

Whā tekau =  

Ine Māori · Traditional Measurement Systems

Before standardised measurement, Māori used body measurements and natural references. These were practical, portable, and community-calibrated — everyone in a hapū could use the same system without tools.

Te Ingoa / Name Description Approximate modern equivalent
Mati Width of one finger (index finger) ~1.5–2 cm
Ringa Handspan — tip of thumb to tip of little finger, hand spread wide ~18–22 cm
Koiti Forearm length — elbow to tip of middle finger ~40–45 cm
Whanganga Armspan — fingertip to fingertip with arms outstretched ~160–190 cm
Aro / Aroaro The front of the body; used as a general body-length reference in some traditions ~height of a person

Practical activity: Measure your desk using ringa (handspans). Record your result:

My desk is   ringa long and   ringa wide.

Now measure in centimetres. How do the two measurements compare? Why might they differ between students?

Mahi 2 · Activity 2: Whakamārama — Translate into Te Reo

Write each number sentence below in te reo Māori. Use the numbers table on this page to help you.

Number sentences to translate

1. There are 15 students in our group.  
2. I have 8 pencils on my desk.  
3. The marae has 20 windows.  
4. We cooked 12 kūmara in the hāngī.  
5. There are 7 days in one week.  

Challenge: Write your own number sentence in te reo Māori about your classroom.

Aronga Mātauranga Māori

Numbers in te reo Māori are not simply translated labels placed over a European system — they are a window into a distinct way of knowing. Te kore (zero, the void) in Māori cosmology refers to the primordial nothingness before existence, a concept that carries philosophical depth far beyond arithmetic. The logical base-10 structure of ngā tau reflects the sophistication of Māori mathematical thinking. Learning to count in te reo is an act of cultural affirmation: it says that Indigenous languages hold rigorous mathematical knowledge and that mātauranga Māori belongs in every mathematics classroom.

Ngā Rauemi Tautoko · Support Materials

Resources already provided:

  • Numbers 1–20 table (numeral, te reo word, pronunciation guide)
  • Three counting pattern sequences with fill-in blanks
  • Building bigger numbers reference and practice
  • Traditional Māori measurement systems table (mati, ringa, koiti, whanganga, aro)
  • Five English-to-te-reo number sentence translation tasks

Aronga Rerekē · Differentiated Pathways

Entry-level support

Focus on numbers 1–10 only. Use the pronunciation guide to practise saying each number aloud before writing. Complete Sequence A only. For translation activity, provide a partially completed sentence frame: "Ko _____ ngā _____."

On-level

Complete all three counting sequences. Use the numbers table to write numbers 11–20 independently. Complete all five translation sentences and one original sentence. Measure desk with ringa and reflect on variability.

Extension / Whakaaro Hohonu

Research the base-20 counting system (ngahuru) used in some traditional Māori contexts and compare it with modern base-10. Write numbers 1–100 in te reo. Investigate: why might a culture use base-20 rather than base-10? Create a poster showing the logic of te reo number words for your class.

📋 Teacher Planning Snapshot

Ngā Whāinga Ako — Learning Intentions

Students will engage with this resource to build pāngarau (mathematical) understanding — developing number sense, pattern recognition, and mathematical reasoning through hands-on, culturally grounded activities that connect to tamariki's world.

Ngā Paearu Angitū — Success Criteria

  • ✅ Students can explain their mathematical thinking using words, objects, drawings, or symbols.
  • ✅ Students can apply the number or pattern concept in this resource to a real or everyday context.

Differentiation & Inclusion

Scaffold support: Use concrete materials (blocks, counters, fingers) for entry-level engagement before progressing to abstract representations. Offer extension challenges asking students to generalise a pattern, write their own word problem, or explain their strategy to a partner.

ELL / ESOL: Mathematical language is a discipline-specific barrier — pre-teach key terms (e.g., equals, more than, fewer, pattern, factor) using visual representations. Allow students to demonstrate mathematical understanding non-verbally or through drawing. Pair with a bilingual buddy where possible.

Inclusion: Embed choice in how students engage — oral, written, or diagrammatic responses are all valid. Neurodiverse learners benefit from short, chunked task sequences with immediate feedback loops. Avoid timed drills in favour of exploratory tasks that reward curiosity. Make the maths classroom a safe place to be wrong and try again.

Mātauranga Māori lens: Pāngarau is a living tradition in Te Ao Māori — from the geometric precision of tukutuku and kōwhaiwhai patterns to the navigational mathematics of waka hourua, and the seasonal calculations embedded in maramataka. Framing early number sense within these contexts shows tamariki that mathematics is a human, culturally rich endeavour — not a foreign import. Encourage students to see counting, measuring, and patterning as acts of knowing their world.

Prior knowledge: Designed for early learners. No prior formal mathematics knowledge required. Teachers should assess current number knowledge before selecting appropriate entry points.

Curriculum alignment