Symmetry and Patterns

Overview

In this third lesson of the Shape, Space and Measure unit, students explore symmetry as a property of familiar two-dimensional shapes and patterns. They use folding, mirrors and pattern blocks to predict, test and explain lines of symmetry before applying their understanding to complete half-drawn designs.

Learning intentions

• WALT identify and describe lines of symmetry in familiar 2D shapes.
• WALT predict and test whether a shape or design is symmetrical.
• WALT use reflection to complete a symmetrical pattern.
• WALT explain how folding and mirrors provide evidence of symmetry.

Success criteria

• I can draw a line of symmetry on a 2D shape.
• I can predict where a mirror line might be before testing it.
• I can use folding, a mirror or matching blocks to check my thinking.
• I can create or complete a design so both sides match by reflection.

Curriculum links

• Mathematics and Statistics — Geometry: exploring and describing properties of shapes, including symmetry and reflection.
• Mathematics and Statistics — Spatial reasoning: using visual models, folding and mirrors to investigate relationships between shapes.
• Mathematics and Statistics — Mathematical practices: predicting, testing, explaining and communicating mathematical thinking.
• Mathsteasers: using higher-order thinking questions to challenge learners and deepen understanding through relevant mathematical problem solving.

Lesson structure (45 minutes)

1. 0–5 min · Hook and notice. Teacher opens with the hook and symmetry examples and shows a butterfly, a leaf, a koru-inspired pattern and a deliberately non-symmetrical design; students silently decide which images could be split into matching halves, then share what they notice with a partner.

2. 5–12 min · Teach the idea. Teacher introduces the term line of symmetry as a line that divides a shape or design into two matching reflected parts, modelling a paper fold and a transparent mirror; students predict, test and help draw lines of symmetry on the examples in the symmetry teaching slides. Emphasise that a line may be vertical, horizontal or diagonal, and that a shape can have more than one line of symmetry.

3. 12–22 min · Hands-on investigation. Teacher places students in pairs and provides pattern blocks, paper shapes and mirrors, explaining that students must predict first, then test by folding or placing the mirror along a possible line; students record the number and position of lines of symmetry they find and discuss whether each shape has none, one or more than one. Provide the symmetry mirror templates to students who need a structured starting point, using the dotted mirror line to practise completing reflected halves.

4. 22–35 min · Guided application. Teacher demonstrates how to complete one half-drawn design from the symmetry and patterns worksheet, checking equal distance from the mirror line and matching position, colour and shape; students complete the remaining designs independently or with a partner. Circulate and ask, “How did you predict this point would move?” and “What evidence shows that your design is symmetrical?”

5. 35–41 min · Create and explain. Teacher challenges students to use pattern blocks or squared paper to create a symmetrical design with at least one line of symmetry, then displays the design challenge and discussion prompts; students swap designs with a partner, identify the line or lines of symmetry and explain how they checked them.

6. 41–45 min · Plenary and exit check. Teacher displays three quick examples, including one non-example, and asks students to show thumbs up, sideways or down before explaining their reasoning; students complete the final reflection on the symmetry reflection section by drawing a line of symmetry on one shape and writing one way they tested it.

Resources

• the symmetry and patterns slide deck
• the symmetry and patterns worksheet
• the symmetry mirror templates
• Transparent symmetry mirrors
• Pattern blocks
• Paper 2D shapes for folding
• Plain paper or squared paper
• Pencils, coloured pencils and rulers
• Board or display screen

Assessment

• Listen for students using line of symmetry, matching halves, reflection and mirror line accurately during partner investigations.
• Observe whether students predict before testing and whether their completed designs match in position, shape and colour on both sides.
• Review the exit reflection for an accurately drawn line and a valid explanation of how symmetry was checked.

Differentiation

• Support students with dyslexia or working-memory barriers by giving one instruction at a time, using clear visual examples, allowing verbal explanations and providing uncluttered worksheet sections with large spaces.
• For autistic students, preview the lesson sequence, use consistent pair roles such as predictor and tester, and provide a quiet workspace or reduced-choice set of shapes if needed.
• Use transparent mirrors, folding and partially completed designs as concrete scaffolds. Trace or lightly mark the possible mirror line before students draw.
• Extend confident students by asking them to investigate which familiar shapes have more than one line of symmetry, create a design with two or more lines, and justify how they know they have found all possible lines.