Pattern and Function Inquiry

Overview

This 60-minute session engages 30 Year 11 students in New Zealand in exploring linear and quadratic patterns and their representations involving equations, tables, and graphs. Aligned with the New Zealand Curriculum (NZC) Te Mātaiaho Mathematics and Statistics strand for Year 11, the class will develop skills in forming and solving quadratic equations and interpreting their features. Activities foster critical thinking, connections across representations, and real-world applications, honouring the bicultural and multicultural context of Aotearoa New Zealand.

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Curriculum Alignment

Achievement Objectives (AO)

• Algebra:
  • Recognise relationships in linear and quadratic patterns, write rules as equations, and use these to make conjectures.
  • Form and solve quadratic equations; understand solution types and graph-parabola links.
  • For quadratic functions: create tables and graphs, interpret key features, and connect these to linear and exponential functions.
• Number:
  • Apply number properties and algebraic manipulation to investigate and solve problems.
• Key Competencies:
  • Thinking: Engage in patterns analysis and reasoning about representations.
  • Using language, symbols, and text: Correctly use algebraic notation and language.
  • Participating and contributing: Collaborate in group problem-solving.
  • Relating to others and Managing self: Respect multiple perspectives, persevere with challenging problems.

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Learning Outcomes

By the end of the lesson, students will:

1. Identify and describe linear and quadratic number patterns.
2. Formulate equations that represent these patterns.
3. Construct tables and graphs from these equations.
4. Interpret key features of graphs: intercepts, gradients, vertices.
5. Appreciate the cultural relevance of mathematical thinking in Aotearoa NZ.
6. Develop skills in collaboration, reasoning, and communication.

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Materials

• Whiteboard and markers
• Student workbooks/notebooks
• Graph paper
• Calculators
• Digital tools (if available): graphing software or apps such as GeoGebra
• Māori language number charts or greetings (to enhance bicultural connection)

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Lesson Plan

1. Introduction and Cultural Activation (~10 minutes)

• Mihi and Whanaungatanga: Begin with a brief mihi (greeting) in te reo Māori, acknowledging the whenua and tangata whenua, connecting mathematics to Māori perspectives of patterns in nature and whakapapa (genealogy).
• Hook Activity: Display a simple number pattern and invite students to detect the rule in pairs.
• Discuss how patterns and relationships are important in everyday life and in Māori culture (e.g., weaving patterns, maramataka lunar cycles).
• Clarify lesson goals and vocabulary: pattern, sequence, rule, function, equation.

2. Exploration of Linear Patterns (~10 minutes)

• Present a linear number pattern (e.g., 3, 7, 11, 15, ...) and challenge learners to:
  • Write the rule in an equation form (e.g., ( y = 4n - 1 ))
  • Make a table of values for n = 1 to 5
  • Plot the points on graph paper
• Discuss key graph features: straight lines, constant gradient.

3. Investigation of Quadratic Patterns (~15 minutes)

• Introduce a quadratic pattern (e.g., 1, 4, 9, 16, 25, ...) and guide students to:
  • Express the pattern algebraically (e.g., ( y = n^2 ))
  • Build a table for values of n = 1 to 5
  • Plot the parabolic shape of the graph
• Explain solution types of quadratic equations (briefly), linking to the graph's vertex and intercepts.
• Use visual tools and allow pairs to discuss the differences with linear graphs.

4. Group Activity – Connecting Representations (~15 minutes)

• Divide students into groups of 4-5; each group chooses or is given a pattern to analyse (linear or quadratic).
• Tasks: form a rule, create a table, plot a graph, describe the key features in context (e.g., growing populations, area of squares).
• Encourage use of te reo Māori numbers and terms when presenting.

5. Reflect and Consolidate (~5 minutes)

• Invite groups to share their findings with the class.
• Facilitate discussion on how the algebraic rules, tables, and graphs interconnect.
• Highlight the importance of mathematical communication and respecting diverse problem-solving approaches.

6. Closing and Extension (~5 minutes)

• Summarise main ideas and connect back to cultural contexts (e.g., patterns in harakeke flax weaving seen in Aotearoa).
• Set an extension challenge or reflection: Explore exponential patterns next lesson or investigate real-life scenarios involving quadratic equations.
• End with a karakia to foster a positive learning environment and gratitude for shared knowledge.

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Cultural Responsiveness

This lesson weaves Māori worldviews by:

• Starting with a mihi to affirm Māori as tangata whenua and establish cultural safety.
• Introducing mathematical patterns through indigenous lenses such as traditional weaving or natural cycles (maramataka).
• Incorporating te reo Māori for numbers and mathematical terms to normalise bilingual understanding.
• Encouraging respect for diverse approaches within group work, valuing multicultural contributions reflective of Aotearoa's society.
• Connecting mathematics to local contexts and knowledge systems, supporting identity and relevance.

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Assessment and Success Criteria

• Students demonstrate ability to articulate pattern rules algebraically.
• Tables and graphs reflect accurate calculations and plotting.
• Students explain graph features and compare linear vs quadratic shapes.
• Participation in group discussions evidences use of correct mathematical language and respect for peers.
• Reflective responses or exit ticket summarise learning and cultural connections.

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Teacher Reflection Suggestions

• Note how well students translate between representations and any misconceptions.
• Observe engagement with bicultural components and language use.
• Adjust the pacing or scaffolding as necessary for diverse learners.
• Reflect on group dynamics and cultural inclusion effects.

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This lesson harnesses the latest Te Mātaiaho draft 2025 NZC guidance for Year 11 Mathematics and Statistics, targeting algebraic understanding of linear and quadratic functions, enriched with culturally responsive pedagogy to engage all ākonga in the New Zealand context .