Algebra for Preservation

Overview

In this final lesson, ākonga synthesise the algebraic skills developed across the unit to create and present a feasible, culturally safe proposal for a kapa haka preservation or revitalisation initiative. They work with a fictional or locally approved context without speaking for, naming, or representing a community without permission.

Learning intentions

• WALT use algebra to model costs, participation, growth or access within a meaningful context.
• WALT communicate mathematical reasoning using expressions, equations, formulae, sequences, tables and/or graphs.
• WALT develop a respectful proposal that considers consultation, consent, kaitiakitanga, mana, access and intergenerational transmission.
• WALT collaborate effectively, explain assumptions and limitations, and respond to questions.

Success criteria

• I can collaboratively define a need without speaking for a community.
• I can construct and solve relevant algebraic models using at least three algebraic tools.
• I can show calculations, tables and/or graphs and explain my assumptions and limitations.
• I can describe consultation and consent, explain how the initiative supports mana and intergenerational transmission, and present clearly.
• I can respond thoughtfully to questions and reflect on my individual algebra contribution.

Curriculum links

• Pāngarau — Tau me te Taurangi: patterns and relationships, algebraic thinking, expressions, equations, formulae and sequences.
• Pāngarau — mathematical communication and problem solving: represent, solve, interpret and justify mathematical ideas in a meaningful context.
• Marau ā-Kura: connect learning with local aspirations, tikanga, pūrākau or community priorities only where guidance and permission have been provided.
• Te Reo Rangatira: use whakarongo, kōrero, tuhituhi and whakaatu to communicate mathematical and cultural reasoning clearly.

Lesson structure (60 minutes)

1. 0–8 min · Brief and roles. Open the opening challenge and project brief slides and read the accessible project brief aloud, supported by audio if available. Remind students that no one must disclose identity or perform kapa haka, and that local names, waiata, actions, recordings and tikanga require appropriate guidance and permission. In groups of five, students assign facilitator, algebra lead, cultural-safety lead, evidence designer and presenter; roles may rotate.

2. 8–15 min · Confirm the scenario. Display the scenario and cultural-safety prompts and distribute the Algebra for Preservation project canvas. Teams choose a fictional or locally approved scenario, define a need in neutral language, and write two or three measurable success indicators, such as participation, access, cost or continuity. Each team identifies what would require consultation or consent rather than assuming community views.

3. 15–38 min · Build and test the proposal. Keep the algebra toolkit and milestone checklist visible. Teams develop a proposal using at least three tools, choosing from expressions and evaluation, equations, formulae, sequences, tables, graphs, expansion or factorisation. Their canvas must show a defined variable, calculations, a solved model, assumptions, limitations and an explanation of feasibility. Pause at 23 and 32 minutes for milestone checks: the teacher conferences with groups, checks calculations and asks, “What does this value mean in the context?” Students use calculators or spreadsheet/graphing tools to test their model and revise errors.

4. 38–48 min · Prepare the presentation. Show the two-minute presentation structure and rubric. Groups create one visual model and rehearse a two-minute explanation covering the need, algebra, recommendation, assumptions, limitations, consultation and consent plan, and links to mana, access, kaitiakitanga and intergenerational transmission. Students may present orally, visually or by video, using speech-to-text and rehearsed speaking notes where helpful.

5. 48–56 min · Present and question. Use presentation prompts and peer-feedback routine to keep each presentation to two minutes, followed by one minute for questions. Listening groups record “two stars and a whakaaro”: two specific strengths and one constructive idea or question. The teacher notes mathematical accuracy, interpretation, collaboration and cultural safety against the four-point rubric.

6. 56–60 min · Individual reflection. Distribute the final section of the project canvas and individual reflection. Students self-assess against the success criteria and explain one algebraic representation they contributed, what it means, one assumption or limitation, and one change they would make after feedback. Collect the reflection separately from the group proposal to support the individual 40% assessment component.

Resources

• the Algebra for Preservation presentation deck
• the Algebra for Preservation project canvas
• Calculators
• Spreadsheet or graphing tools
• Presentation materials or a shared digital workspace
• Accessible-font rubric and reflection sheet
• Audio version or teacher read-aloud of the brief
• Speech-to-text tools, headphones and quiet planning space

Assessment

• Use group conferences, milestone checkpoints and calculation checks as formative evidence of algebraic modelling and interpretation.
• Assess the group proposal (60%) for accurate use of three or more representations, interpretation and limitations, collaboration, feasibility, and a culturally safe, co-designed approach.
• Assess the individual explanation and reflection (40%) for mathematical understanding, contribution, response to feedback and explanation of assumptions. Use peer “two stars and a whakaaro” feedback to inform the final judgement.

Differentiation

• Provide the dyslexia-friendly brief as audio or teacher read-aloud, use plain-language instructions, an accessible font, visual checklists, reduced copying and sentence starters such as “Our variable represents…” and “This model assumes…”.
• Allow dyslexic learners to present orally, visually or by video; provide speech-to-text, rehearsed speaking notes and a partially completed canvas where needed.
• Support ākonga with ADHD through role rotation, visible 8–10 minute milestones, movement breaks, a quiet planning space and choice of presentation format.
• Confer privately with groups that need help selecting an appropriate variable or algebraic tool. Advanced learners can include sensitivity analysis, compare funding scenarios or revise their model after peer feedback.

Extension

• Complete a sensitivity analysis by changing one assumption and explaining how the recommendation changes.
• Compare two funding or participation scenarios using the same algebraic model.
• Revise the proposal after feedback and justify which mathematical and consultation changes were made.