Modelling Cultural Futures

Overview

In this ninth lesson of “Algebra for Kapa Haka”, students apply algebraic modelling to a fictional kapa haka preservation and revitalisation proposal. They build on earlier work with expressions, equations, formulae, sequences, tables and graphs, while recognising that cultural knowledge, permissions and decisions belong with appropriate knowledge holders.

Learning intentions

• WALT identify assumptions, variables, known facts and estimates in a project brief.
• WALT select and use an appropriate algebraic model to represent fictional data.
• WALT explain how consultation, permission and consent shape a proposal.
• WALT communicate mathematical reasoning clearly and respectfully.

Success criteria

• I can identify the variables and assumptions in my group’s proposal.
• I can use an expression, equation, formula, sequence, table or graph appropriately.
• I can distinguish supplied facts from estimates and explain uncertainty.
• I can explain why kaumātua, whānau, kaiako and other knowledge holders must guide cultural decisions.

Curriculum links

• Pāngarau: Tau me te Taurangi — using algebraic relationships, patterns, formulae, tables and graphs to model situations and justify decisions.
• Te Ao Māori: recognising Mātauranga Māori, tikanga, whakapapa and connections to iwi, hapū and whenua as knowledge requiring appropriate care and authority.
• Marau ā-Kura: adapting the fictional context to local aspirations and te reo ā-iwi only where the kura has approved knowledge and guidance.
• Mathematical and collaborative competencies: reasoning, communicating, evaluating evidence and making responsible decisions.

Lesson structure (60 minutes)

1. 0–10 min · Revisit tikanga and project brief. Teacher welcomes students, revisits the unit’s agreed boundaries and displays the learning intentions using the opening and tikanga slides; clarify that today’s project is fictional and students must not copy waiata, actions, pūrākau, whakapapa, local tikanga or recordings. Students sort examples into “mathematical decision”, “estimate” and “cultural decision”, then explain why cultural decisions require consultation and consent.

2. 10–20 min · Examine a fictional case. Teacher reads aloud and plays the audio-supported case brief from the fictional project case slides: a kura is considering a programme to support intergenerational learning, provide rehearsal access and store approved recordings, but no local cultural content is supplied. Students annotate the modelling and ethical process planner to identify the proposal’s purpose, known facts, estimates, variables and questions for knowledge holders.

3. 20–35 min · Choose and analyse a model. Teacher forms groups of four and distributes a fictional dataset and role cards: facilitator, mathematics checker, cultural-care checker and recorder/presenter. Groups use the modelling and ethical process planner to choose an expression, equation, formula, sequence, table or graph. They calculate or represent the supplied data, label units, state assumptions and mark which claims require consultation. Confer with groups using: “What does each variable mean?”, “Which values are known?”, “How could this model mislead?” Students may use a spreadsheet, graph paper or calculators.

4. 35–48 min · Prepare a proposal model. Teacher directs groups to create a model poster or one-slide proposal using the modelling instructions and checklist slides. Each proposal must include the initiative’s purpose, variables, model, worked example or graph, facts versus estimates, one limitation and two consultation or consent steps. Students prepare a clear explanation without presenting themselves as experts in mātauranga Māori.

5. 48–56 min · Peer critique. Teacher pairs groups and displays the three criteria on the peer-critique slides: mathematical accuracy, usefulness and cultural care. Students give one strength and one specific improvement, using respectful language. Groups check calculations, question unsupported assumptions and identify whether the proposal leaves authority with kaumātua, whānau, kaiako or other appropriate knowledge holders.

6. 56–60 min · Individual reflection and checkpoint. Teacher asks students to complete the final boxes on the individual reflection section and collects it as the formative checkpoint. Students answer: “What is my model showing?”, “Which part is an estimate?”, and “What must be consulted or consented to before this proposal could proceed?”

Resources

• the complete modelling and critique slide deck
• the modelling and ethical process planner
• Fictional project case and datasets
• Calculators and devices with spreadsheet access
• Graph paper, large paper and coloured pens
• Consent and tikanga prompt cards
• Accessible exemplars and modelling rubric
• Timer or visible countdown

Assessment

• During the proposal conference, check that students can define variables, explain assumptions and distinguish facts from estimates.
• Use model-checking questions to assess algebraic reasoning, appropriate representation, calculation accuracy and interpretation.
• Review peer critique and individual reflection for evidence that students understand consultation, permission and consent. Assess mathematical reasoning and ethical process, not cultural authenticity.

Differentiation

• Provide dyslexic learners with the teacher-read brief, audio version, short headings, high-contrast accessible font, glossary, visual project template, chunked data, speech-to-text and oral conferencing. Accept spoken explanations alongside written work.
• Support ADHD learners with milestone cards, role choice, a visible timer, movement-friendly collaboration, brief teacher check-ins and a defined group product.
• Provide sentence starters: “The variable ___ represents…”, “We estimate ___ because…”, and “Before this could proceed, we would consult…”.
• Offer an accessible worked exemplar and partially completed table or graph for students needing additional scaffolding. Encourage confident students to explain their model to another group rather than completing all calculations for peers.

Extension

• Compare two different models for the same dataset and justify which is more useful.
• Test sensitivity by changing one variable and describing how the proposal changes.
• Discuss uncertainty, limitations and which additional evidence would be needed before decision-making.