Exploring Patterns and Equations

Lesson Overview

This 60-minute lesson is designed for Year 11 students in New Zealand to develop their understanding of algebraic patterns, linear and quadratic equations, and the connections between different mathematical representations. The lesson adheres strictly to the New Zealand Curriculum (NZC) and integrates cultural responsiveness in teaching, reflecting New Zealand’s bicultural foundation and multicultural society.

---

Curriculum Links

Achievement Objectives (Year 11, Te Mātaiaho – Mathematics and Statistics 2025)

• Algebra Strand:

  • Recognise relationships between elements of a linear or quadratic pattern, write an equation to represent the rule for the pattern, and use the equation to make conjectures.
  • Form and solve quadratic equations and interpret their graphs.
  • Represent exponential growth and decay using appropriate graphical forms.
  • Substitute into, rearrange, and simplify algebraic expressions or formulas.

• Number Strand:

  • Perform operations on positive and negative rational numbers, including integer powers and roots.
  • Apply rates and ratios with proportional reasoning.

• Key Competencies (NZC, pages 8-9):

  • Thinking: Critically and creatively solve problems.
  • Using language, symbols, and texts: Develop fluency in algebraic vocabulary and notation.
  • Managing self: Persevere through complex problems.
  • Relating to others: Collaborate and share reasoning.
  • Participating and contributing: Respect diverse perspectives and cultural contexts.

---

Learning Intentions

Students will:

• Analyse sequences and identify linear and quadratic patterns.
• Express patterns algebraically and explore their graphical representations.
• Solve quadratic equations and relate solutions to context and graphs.
• Develop procedural fluency with algebraic manipulation and solving techniques.
• Collaborate to justify mathematical reasoning through discussion and presentation.

---

Resources

• Whiteboard and markers
• Graph paper and rulers
• Calculators
• Digital projector for visualisations (optional)
• Pattern cards and algebra tiles (optional manipulatives)
• Worksheet with rich tasks (multiple pathways and difficulty levels)

---

Lesson Plan

Time	Activity	Description
0–5 mins	Introduction and Context Setting	Greet students with a Māori mihi. Set the context by linking algebraic patterns to real-world and cultural examples, e.g., traditional weaving patterns or architecture in Aotearoa. Share learning intentions and success criteria.
5–15 mins	Exploration of Patterns	Distribute pattern cards displaying linear and quadratic sequences. In pairs, students identify the rule verbally and in writing, discussing how the pattern might grow. Encourage use of first languages for explanation if helpful.
15–25 mins	Connecting Patterns to Equations	Teacher models translating patterns into algebraic expressions and equations using worked examples with think-alouds. Students attempt similar tasks on worksheets with multiple entry points. Introduce correct vocabulary and notation explicitly.
25–35 mins	Graphing and Visualisation	Using graph paper and rulers (or digital tools), students plot values from the algebraic patterns. Facilitated discussion on differences between linear and quadratic graphs and the significance of intercepts and curves.
35–45 mins	Solving Quadratic Equations	Teachers guide students through solving quadratic equations by factorising, linking to earlier pattern rules and graphs. Students practise on problems of increasing complexity with peer support.
45–55 mins	Rich Task—Problem Solving	Present a contextual problem (e.g., optimising the area of a rectangular Māori carving or weave with fixed perimeter) for students to solve using tables, graphs, and equations. Allow multiple solution methods.
55–60 mins	Reflection and Connecting Learning	Whole-class discussion to summarise insights. Students share different approaches and highlight perseverance strategies. Link learning back to success criteria and importance in real-world and cultural contexts.

---

Cultural Responsiveness

• Begin with a whakawhanaungatanga activity (brief greetings and sharing backgrounds) to build a positive learning environment.
• Use tukutuku (Māori lattice work) or kowhaiwhai patterns as rich contexts for exploring algebraic patterns, which honours Māori cultural heritage and encourages bicultural identity in mathematics.
• Invite students to share patterns or sequences from other cultures represented in the classroom to enrich learning and broaden perspectives.
• Use clear, respectful language and scaffold the use of mathematical terminology while validating students’ linguistic abilities, including te reo Māori and heritage languages, to foster engagement and inclusivity.
• Acknowledge the diverse strategies students bring to problem-solving, and support collaborative learning that values all voices and perspectives.

---

Assessment for Learning

• Monitor students’ ability to articulate pattern rules and their understanding of algebraic notation through ongoing questioning and paired discussions.
• Use exit ticket: A quick written reflection on one new thing learned, one question they still have, and one way they applied perseverance.
• Formative feedback during rich task activity focusing on reasoning and justification.

---

Extension Ideas

• Challenge interested students to explore exponential patterns and their real-life applications (e.g., population modelling).
• Investigate connections between algebraic patterns and traditional Māori storytelling or weaving mathematics.
• Introduce digital tools to simulate transformations and graph quadratic functions dynamically.

---

Teacher Reflection

• Reflect on the effectiveness of linking mathematics with cultural contexts for engagement.
• Evaluate the balance of explicit teaching and student-led inquiry.
• Assess strategies used to support diverse learners and plan adjustments accordingly.

---

This robust plan integrates the NZ Curriculum’s expectations around algebra, communication, problem-solving, and cultural responsiveness, to engage Year 11 learners meaningfully and skilfully within a 60-minute timeframe 【4:0†NZC Maths Phase 3.pdf】 .