Pāngarau • Whakapapa • Years 7-10 • Patterns and reasoning

Whakapapa Mathematics Connections

Use this handout to explore how whakapapa can open up mathematical thinking about growing patterns, exponents, and representation. The maths model is useful, but it is only a model: whakapapa is a living relationship system, not just a diagram of numbers.

Ingoa / Name
Akomanga / Class

Best for

Years 7-10 pāngarau lessons on exponents, growing patterns, tables, and reasoning where teachers want a culturally grounded entry point.

Kaiako use

Use it as a bridge between pattern spotting and abstract notation. It works best when the class already understands that whakapapa carries people, place, and story, not only mathematical rules.

Ākonga use

Students can complete a pattern table, explain exponent notation, and test where the model breaks down in real whakapapa because of overlap and shared ancestry.

Free classroom starter, premium localisation path

This version is ready to print as-is. If you want a junior scaffold, graphing extension, bilingual maths vocabulary, or a localised whakapapa/context brief, Te Wānanga can adapt it for your class without reducing mātauranga Māori to decorative context.

  • Swap in a simpler pattern table or a richer algebra extension.
  • Create support, core, and stretch versions for mixed readiness.
  • Save your adapted sequence into My Kete or Creation Studio.
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Kaiako planning snapshot

  • Use length: 35-50 minutes for one lesson, or longer if you graph the patterns and compare models.
  • Grouping: Teacher modelling first, then pairs for table completion and reasoning.
  • Prep: Clarify that mathematical doubling is a simplified model and that real whakapapa includes overlap, relationships, and lived complexity.
  • Teaching move: Ask students to notice both where the pattern helps and where the cultural reality is richer than the rule.
Exponents Growing patterns

Resources already provided

  • Pattern table and write-on reasoning prompts
  • Exponent and table-to-rule scaffold
  • Model-limit discussion prompt about real whakapapa
  • Draw space for graphs or pattern models
  • Curriculum companion for teacher-only planning clarity

If the lesson mentions exponent practice, pattern explanation, or response space, those supports already exist on this page.

Ngā Whāinga Akoranga / Learning Intentions

  • We are learning how growing patterns can be represented in tables, words, and exponent notation.
  • We are learning how whakapapa structures can provide a meaningful context for mathematical reasoning.
  • We are learning how to explain the limits of a mathematical model.

Paearu Angitu / Success Criteria

  • I can complete a growing pattern table and identify the rule.
  • I can explain how exponent notation represents repeated multiplication.
  • I can describe one reason real whakapapa does not behave exactly like the simple model.

Curriculum integration / Te Marautanga alignment

Use the companion page to make the curriculum link explicit around exponent notation, growing patterns, and the careful use of culturally grounded mathematical contexts.

Mathematics Exponents Growing patterns
Open curriculum companion

Why this matters in Aotearoa

In Aotearoa, strong maths teaching does not need to sit apart from culture. This handout uses whakapapa as a doorway into pattern, rule, and explanation while keeping the mātauranga Māori lens visible and honest.

The key teaching safeguard is this: whakapapa is not “just maths”. The model helps us think, but it does not replace the lived reality of whānau, relationship, and shared ancestry.

Part 1: Spot the pattern

Generation back Ancestors in the simple model As a power of 2
0 1 2⁰
1 2 2¹
2 4 2²
3 8 2³
4 ________________ ________________
5 ________________ ________________

Part 2: Explain the rule

The pattern changes by: ______________________________________________

The rule in words is: ________________________________________________

The rule using exponent notation is: _________________________________

Part 3: Test the model

If you keep doubling forever, the numbers become huge very quickly. Use this space to reason about what that tells you.

What happens by generation 10? _______________________________________

Why does the simple doubling model stop matching real life exactly?

Part 4: Represent the pattern another way

Choose one: draw a graph, make a branching diagram, or create a table that extends the pattern.

Alternative response mode: explain the pattern orally to a partner while they sketch the graph, or use a calculator and labelled sticky notes before writing the final rule.

Support, core, and stretch pathways

Support

Complete only the first part of the table, use multiplication facts, and talk through the rule before writing so the task stays chunked and manageable.

Core

Complete the table, explain the rule, and write one sentence about why the model has limits.

Stretch

Extend the pattern, compare exponent notation with graphing, or explain pedigree collapse in your own words using examples.

Neurodiversity and inclusion note: offer calculator support, oral rehearsal, colour coding, and partner reasoning before expecting a polished written explanation.

Teach this tomorrow

Print or share

  • One copy per learner
  • Optional calculators and graph paper

Decide before class

  • Whether students already need a quick recap on exponents or powers
  • How you will explain the model limits respectfully

Good progress looks like

  • Students identify the rule and can explain it in words and symbols
  • Students recognise that the context is meaningful but not simplistic

Natural continuation

  • Move into graphing, geometric patterns, or ratio and growth tasks
  • Adapt it in Te Wānanga for a stronger algebra or extension pathway

Hononga Marautanga · Curriculum Alignment

Social Sciences — Tikanga ā-Iwi

Level 3–4: Understand how cultural identity, whakapapa, and tikanga shape people's place in their community and the world; recognise and respect the significance of te Tiriti o Waitangi and the contribution of Māori culture to Aotearoa New Zealand's national identity.

Te Reo Māori — Language and Culture

Level 3–4: Use te reo Māori to express identity, whakapapa, and cultural concepts with accuracy and respect; understand the significance of place names, personal names, and whakapapa as cultural knowledge systems.

Aronga Mātauranga Māori

Whakapapa is not only a genealogical record — it is a mathematical and philosophical system for understanding relationships and patterns across time. Traditional Māori scholars could trace whakapapa across many generations with extraordinary accuracy, understanding that each connection carried implications for rights, obligations, and identity. When students apply mathematical thinking to whakapapa — counting generations, calculating relationships, mapping branching patterns — they are engaging with a knowledge system that has always been both relational and structured. Mathematics and mātauranga Māori are not in opposition: they are two different languages for describing the same reality of pattern and connection.

Ngā Rauemi Tautoko · Support Materials

📋 Teacher Planning Snapshot

Ngā Whāinga Ako — Learning Intentions

Students will engage with this resource to deepen understanding of Te Ao Māori — exploring whakapapa, tikanga, and cultural identity as living systems that shape who we are in Aotearoa New Zealand.

Ngā Paearu Angitū — Success Criteria

  • ✅ Students can explain key concepts from this resource using their own words.
  • ✅ Students can connect tikanga Māori and whakapapa to real-world examples in Aotearoa.

Differentiation & Inclusion

Scaffold support: Provide sentence starters, visual glossaries, or graphic organisers to give entry-level access for students who need additional support. Offer extension tasks that deepen cultural inquiry — for example, exploring local hapū histories or interviewing a kaumātua.

ELL / ESOL: Pre-teach key kupu Māori (whakapapa, tikanga, mana, mauri) with bilingual glossaries where available. Allow students to respond in their home language as a bridge to English expression.

Inclusion: Use accessible formats — clear headings, adequate whitespace, chunked tasks. Neurodiverse learners benefit from structured choice in how they demonstrate understanding (oral, visual, written). Acknowledge that students may hold personal connections to the cultural content.

Mātauranga Māori lens: This unit centres Te Ao Māori as a living knowledge system. Whakapapa is not merely genealogy but a relational framework linking people, place, and time. Tikanga grounds behaviour in kaupapa Māori principles. Approach content with aroha and manaakitanga.

Prior knowledge: No specialist prior knowledge required for entry-level engagement. Best used after relevant lesson sequences, or as a standalone introduction to cultural identity.

Curriculum alignment