šŸ“‹ Teaching Resources ā†’ šŸ“„ Whakapapa & Mathematical Thinking
Pāngarau / Mathematics

Identity-safe maths inquiry ā€¢ Patterns, branching, and networks ā€¢ Years 8-11 ā€¢ Ready to use tomorrow

Whakapapa & Mathematical Thinking

Use this handout to make pattern, branching, and network thinking visible without forcing personal disclosure. It helps ākonga work with mathematical models while staying clear that whakapapa is more than a tree or formula.

Ingoa / Name
Akomanga / Class

Best for

Growing patterns, powers of two, table building, network mapping, and culturally grounded maths conversations where teacher care and identity safety matter.

Kaiako use

Use fictional or non-personal models first. Keep the focus on mathematical structure and on the limits of the model, not on requiring students to reveal personal whakapapa or whānau details.

Ākonga use

Students can identify a branching pattern, extend a rule, map relationships, and explain one thing the model shows well and one thing it hides.

Free maths scaffold, premium adaptation path

This version is ready to teach with non-personal examples. Te Wānanga can adapt it into a junior branching-pattern lesson, a senior exponent inquiry, or a local ecological-network version while keeping the identity-safe framing explicit.

  • Swap in fictional whānau, species, or awa-to-moana relationship models.
  • Create support, core, and extension versions for mixed-readiness groups.
  • Save the adapted version and continue later in My Kete or Creation Studio.
Adapt this in Te Wānanga Open Creation Studio Compare paid workflow options

Kaiako planning snapshot

  • Use length: 35-55 minutes depending on whether students complete the full network map and reflection.
  • Grouping: Whole-class modelling first, then pairs or independent work for the pattern table and map.
  • Prep: Decide which non-personal example you will use first: fictional whānau, species relationships, or another branching system.
  • Teaching move: Say clearly that this is a mathematical model, not a full definition of whakapapa.
Pāngarau Pattern and rule

Resources already provided

  • Identity-safe entry options
  • Branching pattern table
  • Relationship map drawing space
  • Model-limit reflection prompts
  • Curriculum companion for teacher planning clarity

If you want a culturally grounded branching-pattern task without unsafe personal disclosure, the supports are already here.

Ngā Whāinga Akoranga / Learning Intentions

  • We are learning to identify and extend a branching mathematical pattern.
  • We are learning to use a table, rule, or diagram to represent relationships.
  • We are learning to explain what a mathematical model can and cannot show.

Paearu Angitu / Success Criteria

  • I can extend the pattern and describe the rule.
  • I can represent relationships in a diagram or table.
  • I can explain one important limit of the model.

Curriculum integration / Te Marautanga alignment

Use the linked curriculum companion to make growing patterns, repeated multiplication, and mathematically respectful cultural framing explicit in your planning.

Mathematics Patterns Modelling limits

Identity-safe starting point

You do not need to map your own whānau. Choose a fictional example, a species relationship model, or another branching system if that feels safer. The mathematics still works, and the reflection on model limits remains important.

What each lens can show

Whakapapa helps us notice

  • Relationship, connection, and belonging
  • How people, places, and species are not isolated
  • That meaning is more than a count or diagram

Mathematics helps us notice

  • Repeating structure and growth patterns
  • Tables, rules, and branching diagrams
  • What can be represented clearly and compared

Choose a safe model

Option 1

Use a fictional whānau example with made-up names.

Option 2

Use an ecological relationship map, such as awa to moana or seed to forest.

Option 3

Use another branching pattern your kaiako approves.

Branching pattern table

Generation back Repeated multiplication Number in the model What do you notice?
0 1 1
1 1 x 2 2
2 2 x 2 4
3
4

Relationship map

Sketch a branching or network diagram for your chosen model. Label at least three kinds of relationship, influence, or connection.

What does the model hide?

Reflection prompt

Name one thing the mathematical model shows clearly and one thing it cannot show well enough on its own.

Support, core, and stretch pathway

Support

Finish the table with a partner and use the fictional example only.

Core

Complete the table, draw the map, and explain one model limit.

Stretch

Compare a branching tree model with a more complex network and explain which is more accurate.

Hononga Marautanga Ā· 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.

Aronga Mātauranga Māori

Mathematics has always been part of mātauranga Māori ā€” in the navigation of Te Moana-nui-a-Kiwa, in the architectural precision of wharenui, in the sophisticated storage and accounting systems of rua kÅ«mara, and in the patterns of kōwhaiwhai and tukutuku that encode mathematical relationships in visual form. When Māori students engage with mathematics, they are not encountering something foreign: they are meeting a domain of knowledge that their tÄ«puna practised with extraordinary sophistication. Framing mathematical learning through whakapapa ā€” connecting concepts to real Māori contexts ā€” is not "cultural add-on" but recognition of where much mathematical knowledge lives in this land.

Ngā Rauemi Tautoko Ā· Resources already provided