Elimination Strategy

Lesson 6 of 16: Mastering 3x3 Systems

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WALT (We Are Learning To)

Solve systems of three simultaneous equations using the elimination method.

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Success Criteria

• Students can apply elimination steps systematically to simplify and solve 3x3 systems.
• Students gain confidence in interpreting and verifying solutions both algebraically and graphically.
• Students can create their own 3x3 elimination problems to deepen understanding.

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Curriculum Alignment

This lesson aligns with the New Zealand Curriculum Refresh (Te Mātaiaho Mathematics and Statistics, Phase 5 and 6), specifically:

• Algebra and Equations: Form and solve systems of linear equations with three variables using elimination and substitution methods.
• Mathematical Processes: Apply systematic approaches, logical reasoning, and persistence when solving multi-step problems.
• Achievement Standards Context: Supports preparation for NCEA Level 1 and Level 2 standards relating to simultaneous linear equations and algebraic methods .

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Learner Group

• Year 13 mathematics students
• Class size: 30 students

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Lesson Duration

• 60 minutes

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Resources Needed

• Whiteboard and markers
• Student notebooks
• Calculators
• Pre-prepared 3x3 simultaneous equations handouts
• Graphing software or graphing calculators (optional)
• Dyslexia-friendly printed worksheets (use clear font such as Comic Sans or Arial, spaced text, bullet points)

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Lesson Plan Breakdown

1. Introduction & Activation (10 minutes)

• Welcome class, recap previous lesson on solving 2x2 systems by elimination.
• Use a quick quiz question: Solve a simple 2x2 system by elimination on the board to refresh procedural memory.
• Discuss why solving 3x3 systems is important: Applications in engineering, economics, and natural sciences.
• WALT and Success Criteria displayed clearly for student reference.
• Briefly discuss the steps of elimination extended to three variables.

Differentiation: Use verbal explanation with real-world contexts; provide an outline sheet with steps and terminology to support diverse learners, including those with dyslexia (clear layout, key terms in bold).

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2. Guided Demonstration (15 minutes)

• Teacher-led worked example: Solve the 3x3 system by elimination step-by-step:

  [ \begin{cases} 2x + y - z = 8 \ -3x - y + 2z = -11 \ -2x + y + 2z = -3 \end{cases} ]

• Explicitly model:

  • Choosing equations to eliminate one variable.
  • Forming new 2x2 systems.
  • Solving reduced systems.
  • Back-substitution to find all variables.

• Emphasize notation clarity and careful calculation.

• Use mathematical vocabulary: coefficients, variables, substitution, elimination, solution set.

Differentiation: Students can ask for slow walkthroughs or visual aids; teacher provides printed notes with annotated steps.

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3. Collaborative Practice (20 minutes)

• Students work in pairs to solve 2 different 3x3 systems of simultaneous equations.
• Provide problems differentiated by difficulty:
  • Standard: Clear integer coefficients.
  • Challenge: Include fractions or decimals for advanced learners.
• Encourage verbalising their thinking process to partner.
• Teacher circulates, offering scaffolding, hints, or extensions to individuals or pairs.

Extension Activity: Advanced learners begin creating their own 3x3 elimination problems for peers to solve.

Dyslexia-Friendly Support: Allow students to use coloured overlays or dyslexia-friendly fonts on worksheets; offer formula sheets and step reminders.

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4. Whole-Class Reflection & Discussion (10 minutes)

• Selected pairs present their solutions and method insights.
• Discuss common difficulties and strategies to overcome them.
• Highlight the importance of checking solutions by substituting back into original equations.
• Connect with graphical interpretations (optional digital demo).

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5. Independent Application and Challenge (5 minutes)

• Assign an open-ended task: Create your own simultaneous 3x3 equations that can be solved using elimination and solve them.
• Encourage creativity and ownership of learning.

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6. Plenary and Next Steps (5 minutes)

• Recap WALT and success criteria—invite students to self-assess confidence.
• Discuss the next lesson’s focus: substituting methods and real-world applications.
• Provide homework: solve one 3x3 system by elimination and verify by substitution.

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Differentiation Strategies

• Use a mix of verbal, visual, and kinesthetic instructions.
• Provide structured step-by-step notes and highlighted key vocabulary.
• Scaffold learning with worked examples before independent practice.
• Circulate to give targeted support or challenge tasks.
• Dyslexia-friendly materials: use coloured paper, font choices, and spacing.

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Extension Ideas for Advanced Learners

• Challenge to solve 3x3 systems with fractional coefficients or parameters.
• Create real-world modelling problems requiring 3x3 elimination.
• Explore solving 3x3 systems using matrix elimination methods or technology.
• Investigate graphical interpretation of 3D systems.

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Assessment

• Formative via observation during pair work and class discussions.
• Evaluate student-created problems for conceptual understanding.
• Check accurate solution and justification in homework.

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Key Competencies Addressed

• Thinking: Logical reasoning and problem-solving.
• Using language, symbols, and texts: Mathematical vocabulary and notation.
• Managing self: Perseverance through multi-step problems.
• Relating to others: Collaborative work and communication.
• Participating and contributing: Sharing and defending mathematical thinking with peers.

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This lesson plan integrates the New Zealand Curriculum Refresh focus on conceptual understanding, procedural fluency, and multiple access points for diverse learners, promoting agency and resilience in mathematics learning .