Exploring 2D Shapes

Curriculum Reference

This lesson aligns with the New Zealand Curriculum Refresh for Mathematics and Statistics Phase 3 (Years 7-8) focusing on Geometry:

• Classify and name shapes based on their attributes, including regular and irregular polygons such as triangles and quadrilaterals.
• Describe properties of shapes including edges, vertices, lines of symmetry, and rotational symmetry.
• Use mathematical language accurately to describe geometric concepts.
• Develop spatial reasoning and visualisation skills.
• Support communication of mathematical thinking through diagrams, verbal explanations, and use of symbols .

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WALT (We Are Learning To)

• Identify and classify 2D regular and irregular polygons, focusing on triangles and quadrilaterals.
• Describe shape attributes clearly, including sides, edges, vertices, and lines of symmetry.
• Understand and demonstrate line and rotational symmetry in polygons.
• Develop reasoning and vocabulary for explaining geometric properties.

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Success Criteria

• I can correctly name and classify polygons including different types of triangles and quadrilaterals.
• I can identify and count the number of edges and vertices on shapes.
• I can recognise and explain lines of symmetry and rotational symmetry in 2D shapes.
• I can use appropriate geometric vocabulary to describe shapes and their properties.
• I can create shapes with specific attributes using given materials.

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Lesson Duration

60 minutes
Class size: 25 students

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Resources Needed

• Sets of 2D shapes including regular and irregular polygons (triangles, quadrilaterals, pentagons, hexagons)
• Mirrors for symmetry exploration
• Tracing paper
• Pattern blocks, attribute blocks, and tangrams
• Whiteboards and markers or digital tablets for sketching
• Word wall or vocabulary cards with terms like vertex, edge, regular, irregular, symmetry, rotation
• Dyslexia-friendly double-spaced handouts with clear fonts and diagrams

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Lesson Outline

1. Introduction and Engagement (10 minutes)

• Begin with a brief interactive warm-up: Show a set of mixed polygons (regular and irregular) and ask students to sort by different attributes (number of sides, regularity). Use think-pair-share to discuss observations.
• Introduce WALT and connect to prior knowledge of basic polygons from earlier years. Use clear language and visuals.
• Display key vocabulary with definitions on the whiteboard and introduce in both English and some te reo Māori equivalents if appropriate (e.g., tapatoru for triangle).

2. Explicit Teaching (15 minutes)

• Teacher demonstration:
  • Identify regular vs irregular polygons focusing on triangles and quadrilaterals (equilateral, isosceles, scalene triangles; squares, rectangles, rhombuses, trapeziums).
  • Describe properties: number of sides, vertices, edges, angles.
  • Show how to find lines of symmetry using mirrors and tracing paper; introduce the concept of rotational symmetry with examples.
• Use think-aloud strategy to model reasoning, e.g., “This square has four equal sides and four right angles, so it’s regular.”
• Pose questions to encourage student predictions about symmetry and properties.

3. Guided Practice (15 minutes)

• Provide sets of physical shapes and ask students to:
  • Identify and classify shapes using a checklist of properties.
  • Use mirrors to find lines of symmetry and draw them on tracing paper.
  • Identify if shapes have rotational symmetry and demonstrate the rotation (90°, 180°).
• Circulate to support diverse learners by breaking tasks into manageable steps.
• Use vocabulary cards and sentence starters for students needing language support.
• Dyslexia-friendly reading: Make sure handouts are read together, with paired peer reading for decoding support.

4. Independent Activity (15 minutes)

• Challenge students to create their own polygons (triangles or quadrilaterals) using pattern blocks or drawing, ensuring they specify attributes (e.g., number of sides, symmetry).
• Ask students to write or verbally describe the attributes of their shape using correct vocabulary.
• Extension for advanced learners: Design an irregular polygon and explain why it is irregular, including less obvious attributes (e.g., unequal sides but equal angles). Introduce simple classification with Venn diagrams or tables.

5. Plenary and Reflection (5 minutes)

• Class discussion reflecting on what makes polygons regular or irregular, and why symmetry matters.
• Students share their created shapes and descriptions.
• Review WALT and success criteria.
• Highlight students’ use of mathematical vocabulary and reasoning.
• Encourage perseverance by recognising effort and strategies used.

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Differentiation Strategies

• Visual aids: Use diagrams, physical shapes, and step-by-step instructions.
• Pair work for peer support, especially for language learners.
• Vocabulary cards with pictures and definitions.
• Dyslexia-friendly strategies: clear font, -chunking information, oral instructions, and peer reading support.
• Scaffold tasks by chunking: first identify attributes, then classify, then describe symmetry.
• Provide sentence starters for written or oral explanation (e.g., “My shape has ___ edges and ___ lines of symmetry because ___.”)

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Extension Activities for Advanced Learners

• Explore classification of polygons beyond triangles and quadrilaterals (pentagons, hexagons).
• Use algorithmic thinking to create classification flowcharts or Venn diagrams for polygons based on attributes.
• Investigate examples of symmetry and transformation in Māori kōwhaiwhai patterns as a cultural connection.
• Use digital tools or geometry software to explore transformation properties of polygons (rotation, reflection, translation).

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Assessment for Learning

• Observe student participation during guided practice and discussions.
• Review students’ shape creations and their verbal/written descriptions for accuracy and use of vocabulary.
• Use questioning throughout the lesson to check conceptual understanding of attributes and symmetry.
• Use exit card activity: One thing I learned about polygons is..., One question I still have is...

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Notes on Teaching Style and Cultural Responsiveness

• Incorporate te reo Māori terms for shapes to connect learning culturally.
• Encourage students to find polygons and symmetry in their environment and in artworks or cultural designs around them.
• Use positive language to foster curiosity and mathematical risk-taking.

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This lesson plan is designed to meet the New Zealand Curriculum Refresh requirements precisely for Years 7-8 geometry learning outcomes with a focus on student engagement, inclusivity, and vocabulary development. It balances explicit teaching with hands-on experiential learning to cater to diverse learners and advanced students .