Number Journeys

Year Level

Year 3 (Ages approx. 7-8)

Duration

60 minutes

Class Size

25 students

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Curriculum Links (New Zealand Curriculum Refresh)

Strand: Number and Algebra

• Develop number knowledge and strategies related to addition and subtraction of numbers up to at least 100.
• Use place value understanding to support efficient addition and subtraction.
• Represent mental and written strategies, including using empty number lines (Figures NZC Phase 1, Year 3 expectations) , .

Achievement Aim:
By the end of Year 3, students should:

• Add and subtract whole numbers up to at least 100, using efficient mental strategies and written methods including the vertical-column method.
• Use materials and diagrams such as number lines and place-value materials to explain their thinking, and represent addition and subtraction problems.
• Develop problem-solving skills through practical contexts and word problems involving addition and subtraction (including change, result, and start unknown types) , .

Key Competencies Developed:

• Thinking: Applying addition and subtraction strategies in various contexts.
• Using language, symbols, and texts: Explaining and representing thinking with number lines and place value materials.
• Managing self: Working independently or collaboratively on problem-solving tasks.
• Relating to others: Discussing strategies and reasoning with peers and teacher.

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Learning Objective

By the end of this lesson, students will be able to:

• Add and subtract numbers up to 100 using mental strategies and the vertical-column method.
• Represent addition and subtraction problems and their thinking on an empty number line.
• Use place value materials to support understanding of regrouping and partitioning in addition and subtraction.
• Solve practical word problems involving addition and subtraction and explain their strategies verbally.

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Resources Needed

• Empty number line templates (on hand or whiteboard version)
• Place value materials: PV blocks, discs, and PV money sets
• Counters or multilink cubes
• 10s frames
• Word problem cards with addition and subtraction scenarios up to 100
• Whiteboards and markers for students
• Assessment task sheets (simple practical addition/subtraction tasks)
• Visual aids/posters on addition and subtraction vocabulary and number line examples

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Lesson Outline

1. Introduction (10 minutes)

• Begin with an interactive discussion: Pose simple addition and subtraction sentences up to 100 (e.g., 37 + 18, 65 – 23). Ask students how they would solve these mentally or with materials.
• Introduce the empty number line as a tool for representing their thinking visually. Show an example on the board: e.g., 37 + 18 starting at 37 on the number line, making jumps to reach the answer.
• Briefly demonstrate linking place value thinking with the number line jumps (e.g., adding 10 then adding 8).

2. Activity 1 – Guided Practice with Number Lines and PV Materials (15 minutes)

• Distribute empty number line sheets and place value materials.
• Present an addition problem (e.g., 54 + 26). Model physically partitioning 26 into 20 and 6 using PV blocks then show these jumps on the empty number line.
• Have students replicate this with their materials and number lines for two given addition and two subtraction problems.
• Circulate, encourage verbal explanations: "Why did you jump 20 first? How did the blocks help you understand the problem?"

3. Activity 2 – Problem Solving with Word Problems (20 minutes)

• Group students in pairs or small groups. Provide word problem cards (e.g., "There are 48 people at a party. 27 more arrive. How many people are there now?" or "There were 73 candies, and 25 were eaten. How many are left?").
• Students use place value materials and number lines to solve problems.
• Ask each group to present one problem and explain their use of the empty number line and materials.
• Support diverse thinking about addition and subtraction with “start unknown”, “change unknown”, and “result unknown” types.

4. Independent Practice and Assessment (10 minutes)

• Give students a short practical task sheet (or use small whiteboards) to solve addition and subtraction problems up to 100, requiring them to:
  • Show their working on an empty number line.
  • Use drawings or symbols representing place value materials if they wish.
  • Provide a verbal explanation to the teacher or a peer summarising their method and reasoning.

5. Wrap-Up and Reflection (5 minutes)

• Recap the usefulness of the empty number line and PV materials in understanding addition and subtraction.
• Ask students to share one thing they learned or found helpful.
• Highlight correct vocabulary use (add, subtract, jumps, partition, regroup).

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Assessment Methods

• Formative: Observe and listen during activities for correct use of number lines and place value materials. Check students’ verbal explanations for understanding.
• Written/Practical: Review the independent practice work for accurate calculation and use of empty number line representation.
• Verbal: Confer individually or in small groups on problem-solving reasoning and use of resources. Ask guiding questions about their strategies.

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Differentiation / Teaching Considerations

• For students needing extra support: Use physical number lines taped on desks and concrete PV blocks before moving to drawing on paper.
• For students needing extension: Introduce problems involving numbers just over 100 or combining multiple steps with addition and subtraction.
• Provide a mixture of “start unknown”, “change unknown” and “result unknown” problem types to foster flexible thinking.
• Encourage the use of mathematical language and symbols to explain thinking, reinforcing the connection between concrete materials and abstract notation.

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This lesson plan strongly aligns with key achievement aims and teaching sequences in the New Zealand Curriculum Refresh, Phase 1 Year 3 Mathematics, particularly numerical operations and using appropriate representations to model thinking 【4:18†Te Mataiaho Maths 0-tical materials, number lines, verbal reasoning, and written work offers varied entry points for all learners in this age group, implementing best practices indicated in the curriculum documentation.