System of Equations

Lesson Overview

• Lesson Number: 6 of 16
• Unit: Mastering Simultaneous Equations
• Lesson Title: Solving 3x3 Systems by Elimination
• Duration: 60 minutes
• Class Size: 30 Year 13 students
• Location: Waiheke Island Secondary High School, New Zealand

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Curriculum Alignment

• Learning Area: Mathematics and Statistics
• Level: Phase 5 (Years 11–13) according to New Zealand Curriculum Refresh (Te Mātaiaho)
• Achievement Objective:
  • Number & Algebra: Solve increasingly complex systems of linear equations involving 3 variables using algebraic techniques, including elimination.
  • Mathematical Processes: Develop procedural fluency, critical reasoning, represent problems algebraically, and communicate mathematical thinking clearly.
• Key Competencies: Thinking; Using Language, Symbols, and Text; Managing Self; Relating to Others

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Learning Intentions

• WALT (We Are Learning To):
  Solve 3x3 systems of simultaneous equations using the elimination method.

• Success Criteria:

  • Students can apply systematic elimination strategies to reduce and solve 3x3 linear systems.
  • Students can explain each elimination step with clear mathematical notation and reasoning.
  • Students can check the reasonableness of their solutions and interpret the results.

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Resources

• Whiteboard and markers
• Projector for worked examples
• Student handouts containing examples and exercises
• Graphing calculators or algebra software (e.g., GeoGebra)
• Visual aids with key vocabulary and dyslexia-friendly fonts (e.g., OpenDyslexic)

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Lesson Plan Breakdown

Time	Activity	Description	Differentiation/Extension
0–10min	Introduction & Recap	- Recap solving 2x2 simultaneous equations by elimination (using worked examples).

• Activate prior knowledge with a quick group warm-up on elimination basics and setting up equations. | - Provide clear dyslexic-friendly printed notes summarising key steps.
• Use colour-coded steps for visual clarity. | | 10–25min | Guided Practice: Solving 3x3 Systems | - Teacher-led step-by-step worked examples of 3x3 systems using elimination (breaking down each operation clearly).
• Include identification of variable elimination pairs and careful manipulation of equations.
• Use clear notation, highlight common errors and misconceptions. | - Scaffolded support: small groups work with teacher for additional guidance.
• Visual flowcharts showing elimination steps for students needing structure. | | 25–40min | Collaborative Practice | - Students work in pairs on scaffolded worksheet problems of increasing difficulty.
• Encourage verbalising steps to develop communication skills.
• Teacher circulates to provide targeted formative feedback, address misconceptions. | - For diverse learners: pair stronger students with those needing support for peer scaffolding.
• Provide manipulatives or algebra tiles as needed. | | 40–50min | Independent Problem Solving | - Challenge students to solve a 3x3 system independently, including word problem context to link to real-life applications (e.g., budgeting or resource allocation). | - Extension for advanced learners: Create their own 3x3 elimination system problems and solve.
• Use technology (graphing calculators/software) to verify solutions. | | 50–60min | Reflection & Assessment | - Review solutions together, discuss different approaches.
• Students self-assess their understanding against success criteria.
• Exit ticket: Solve a short elimination problem and check solution reasonableness. | - Provide sentence starters and vocabulary support for explanations.
• Encourage students to reflect using both written and oral formats. |

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Differentiation Strategies

• Explicit step-by-step teaching with worked examples and error analysis to reduce cognitive overload.
• Use of visuals and flowcharts for process support.
• Flexible grouping for peer learning and targeted support.
• Dyslexia-friendly materials and fonts, colour coding key steps and vocabulary.
• Opportunity for hands-on manipulatives and algebra tiles for tactile learners.
• Use of digital tools for verification and conceptual reinforcement for tech-savvy students.

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Assessment Strategies

• Ongoing formative assessment through questioning and monitoring student work during activities.
• Use of exit ticket to assess individual understanding of elimination method.
• Peer and self-assessment to develop metacognition and identify areas of difficulty.
• Teacher observation of student discussion and problem-solving strategies during pair work to inform next steps.

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Links to Broader Curriculum and Competencies

• Encourages critical thinking by identifying elimination pairs and logical error correction.
• Builds mathematical communication skills through paired discussion and reflection.
• Develops agency and perseverance as students tackle challenging multi-step problems.
• Connects mathematical content to real-world contexts to increase relevance and student engagement.

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Teacher Notes

• Monitor student anxiety and cognitive load; provide breaks for clarification when needed.
• Emphasise the process’s generalisability — mastering 3x3 elimination lays groundwork for higher mathematics.
• Highlight the connection between algebraic manipulation and geometric interpretations where possible.

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This lesson plan directly integrates advice from the New Zealand Curriculum Refresh documents: it emphasises clear, explicit teaching of new concepts broken into manageable steps, provides rich and authentic tasks with multiple entry points, supports diverse learners with scaffolds and targeted feedback, and encourages collaborative and reflective mathematical communication and reasoning.