Problem Solving

Overview

Unit: Mastering Addition and Subtraction
Lesson: 6 of 6
Duration: 60 minutes
Class size: 25 Year 3 students
Curriculum: New Zealand Curriculum Refresh (Te Mātaiaho Maths, Years 0–8, Phase 1)
Focus: Apply addition and subtraction in mixed-operation problem-solving contexts.

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Learning Intentions (WALT)

• We Are Learning To apply addition and subtraction strategies to solve word problems involving mixed operations.

Success Criteria

Students will:

• Identify whether to add or subtract when faced with a word problem.
• Use mathematical language to explain their reasoning.
• Solve word problems accurately and justify their answers clearly.

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Curriculum Links

From New Zealand Curriculum Refresh - Mathematics and Statistics:

• Number and Algebra (Year 3):

  • Use place value understanding to add and subtract numbers up to 1,000.
  • Solve word problems involving addition and subtraction using various strategies (including splitting, jumping on number lines, and known facts).
  • Explain and connect horizontal and vertical-column addition and subtraction methods.
  • Work with a variety of problem types (result unknown, change unknown, start unknown).
  • Use mathematical language including 'add', 'subtract', 'equals', and 'difference' to express operations and reasoning.
  • Decode and solve word problems, representing them as equations.
  • Support solution approaches with representations such as number lines, ten frames, and manipulatives.

• Key Competencies:

  • Thinking: Strategising and problem-solving with addition and subtraction.
  • Using Language, Symbols, and Text: Expressing mathematical ideas verbally and in writing, including justifications.
  • Managing Self: Working independently or collaboratively to solve problems.

• Teaching and Learning Principles:

  • Support active exploration, use of concrete materials and visual models (bar models, materials, diagrams).
  • Scaffold independent reasoning through worked examples and verbalising thinking (think-alouds).
  • Develop fluency through varied contexts and repeated exposure to families of facts.

Reference: Te Mātaiaho Maths 0–8 documents (Phase 1, Year 3 sections)

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Resources

• Whiteboard and markers
• Individual whiteboards and markers for students
• Ten frames and counters
• Number lines (classroom and printed individual copies)
• Word problem cards featuring mixed operation contexts
• Problem-solving recording sheets for students
• Digital tool (if available) for interactive problem solving
• Concrete materials (e.g., counters, blocks)

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Lesson Breakdown

Time	Activity	Description	Notes
0-10 minutes	Introduction & Recap	- Recap addition and subtraction facts and strategies with a quick oral quiz using ten frames and number lines.

• Introduce today's WALT and success criteria clearly on the board.
• Use a worked example problem on the board demonstrating a mixed operation word problem (e.g., "Lina has 25 stickers. She gave 7 to her friend, then got 10 more. How many does she have now?") with think-aloud strategy modelling. | Highlight operation identification strategy (look for keywords: gave → subtract, got more → add). | | 10-20 minutes | Guided Practice with Word Problems | - Present 3 carefully chosen word problems on the board involving addition and subtraction steps.
• Use bar models/number lines for visualising each problem.
• Guide students in pairs to decide: Which operation first? Then solve.
• Circulate and support students.
• Share solutions with class; discuss reasoning and confirm correct operation choices. | Use sentence starters: "I know I need to ___ first because ___." | | 20-40 minutes | Independent Practice | - Distribute mixed-operation word problems cards to pairs or small groups.
• Students record their solving process on sheets: identify operation, solve, explain their reasoning in words or drawing.
• Encourage use of number lines, counters, or drawings.
• Teacher circulates to facilitate, prompt understanding, and challenge thinking with questions. | Differentiate by varying problem complexity. Include some adding more than one step. | | 40-50 minutes | Math Talk & Reflection | - Group sharing: select pairs to present their problem and solution method.
• Focus on explaining "why I added/subtracted here" and how they know their answer is correct.
• Use this time as formative assessment to gauge understanding. | Emphasise correct mathematical vocabulary. | | 50-60 minutes | Plenary: Success Criteria Check & Exit Slip | - Recap WALT and success criteria.
• Quick exit slip: one word problem to solve independently on mini whiteboards for teacher to quickly check.
• Provide verbal praise and targeted feedback for next steps. | Collect exit slips for assessment. |

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Assessment and Feedback

• Formative Assessment: Teacher observation during paired and independent work, focusing on operation identification, use of representations, and justifications.
• Exit Slip: A single mixed operation word problem to check individual understanding and accuracy.
• Use student explanations and drawings to assess reasoning and understanding of the operations applied.
• Give verbal feedback emphasizing the language of operations and correct mathematical strategies.

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Differentiation

• Provide visual aids and extra concrete materials for learners needing support.
• Challenge advanced learners by including multi-step problems that link to multiplication facts or larger numbers (up to 1000).
• Scaffold writing explanations with sentence frames or prompts.

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Reflection for Next Lesson

• Review common areas of confusion with operation choice.
• Plan mini-lessons or interventions on key vocabulary or strategies as needed.
• Integrate cross-curriculum problems involving real-life contexts to sustain engagement.

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This lesson plan embodies the spirit and requirements of the New Zealand Curriculum Refresh for Year 3 mathematics, specifically targeting Year 3 learning objectives for addition and subtraction operations, problem-solving practices, and communication competencies . The use of think-alouds, concrete materials, and bar models aligns with research-backed teaching strategies promoted in the refreshed curriculum to deepen conceptual understanding and support diverse learners.