Lesson 4: Rotation & Reflection Rules
Learning Intention
I can perform reflections across a mirror line and rotations around a centre point.
Success Criteria
- I can reflect a shape across a vertical or horizontal line (equidistant).
- I can rotate a shape 90° or 180° around a specific point.
- I can describe the difference between a reflection and a rotation.
🎥 Media Anchor (8 mins)
Video: Rotation and Reflection Strategies
- What is the centre/line reference you need before applying a rotation or reflection?
- How does changing that reference alter the resulting pattern structure?
Lesson Sequence
1. Visual Hook (10 mins)
Show two images: One reflected in water (Reflection) and a pinwheel (Rotation).
Which one is which? How do you know?
2. Explicit Teaching: Reflection (15 mins)
Key Concept: Every point on the image is the same distance from the mirror line as the original.
Demo: Verify with a ruler. "A is 2 squares from the line, so A' must be 2 squares on the other side."
3. Explicit Teaching: Rotation (15 mins)
Key Concept: You need a Centre of Rotation. Use tracing paper.
1. Trace the Shape.
2. Put pencil on the Centre Point.
3. Turn the paper 90° (Quarter Turn). Trace the new position.
4. The Whāriki Block Challenge (20 mins)
Context: Whāriki (woven mats) often use rotational symmetry to create blocks.
Task: Start with one triangle motif in the top-left corner of a 2x2 grid.
- Level 1: Reflect it right, then reflect bottom.
- Level 2: Rotate it 90° clockwise three times to fill the grid.
- Level 3: Create a complex block using a mix of both.
Curriculum alignment
- Geometry — Knowledge: - A set of points in a plane can be transformed by translation, reflection about a line, and rotation about a fixed point.
- Geometry — Practices: - Representing and constructing 3D shapes, including rectangular and triangular prisms and pyramids, from nets and plan views drawings - Transforming 2D shapes in the coordina…
- Measurement — Practices: - Using Pythagoras’ theorem to:find the length of an unknown side in a right-angled trianglecheck if a triangle has a right anglecalculate the distance between two points in t…
- Algebra — Practices: - Multiplying or dividing by a negative number reverses an inequality. - The constant rate of change of a linear graph is the vertical change (how far it goes up or down) divi…
- Relationships — Practices: Recognising intense emotions in social situations and applying regulation strategies, such as reappraisal or self-talk with support and reflection to build confidence over tim…
📋 Teacher Planning Snapshot
Ngā Whāinga Ako — Learning Intentions
Students will engage with this resource to develop geometric thinking through the lens of Māori visual art — exploring symmetry, transformation, tessellation, and spatial reasoning through the mathematical structures embedded in tukutuku panels, kōwhaiwhai rafter patterns, tāniko weaving, and whakairo (carving).
Ngā Paearu Angitū — Success Criteria
- ✅ Students can identify and describe geometric properties (symmetry, rotation, reflection, translation) within Māori art forms.
- ✅ Students can design their own pattern using geometric transformations, connecting mathematical precision to cultural meaning.
Differentiation & Inclusion
Scaffold support: Provide grid templates and partially completed pattern examples for entry-level construction tasks. Allow students to trace and analyse existing patterns before creating their own. Extend capable students by asking them to calculate the mathematical properties of their design (angles, lines of symmetry, ratio of repeat unit to total pattern) and explain the transformation rules in formal mathematical language.
ELL / ESOL: Geometry is a highly visual domain — the spatial and pattern-based nature of this content naturally reduces language barriers. Key vocabulary (symmetry, reflection, rotation, translation, tessellation) should be taught using physical models and diagrams before text-based tasks. Students can demonstrate geometric understanding through drawing and construction without requiring English fluency.
Inclusion: Geometric pattern work is inherently accessible and engaging across learning styles — visual, kinaesthetic, and analytical learners all find entry points. Neurodiverse learners often excel at pattern recognition and spatial reasoning. Offer choice in medium: digital tools, grid paper, or physical construction with card. The cultural context provides motivating purpose for students who find abstract geometry disconnected from meaning.
Mātauranga Māori lens: Māori art is mathematics made visible. Tukutuku panels encode precise geometric grids requiring exact calculation of spacing, proportion, and symmetry. Kōwhaiwhai patterns use translational symmetry along the length of rafter beams — a sophisticated application of repeating geometric units. Tāniko weaving requires mental rotation and spatial reasoning to maintain pattern integrity across diagonal threads. Whakairo (carving) encodes symbolic meaning within geometric forms. Far from being decorative, these art forms represent generations of mathematical knowledge encoded in cultural practice. Teaching geometry through this lens shows ākonga that mathematics belongs to all cultures — and that Māori ancestors were sophisticated mathematicians.
Prior knowledge: Students should have foundational understanding of 2D shapes and basic transformation vocabulary. No prior knowledge of Māori art forms required — the unit introduces cultural context alongside mathematical content.
Curriculum alignment
- Geometry and Measurement — Shape: Apply the properties of symmetry, including line and rotational symmetry, to identify, describe, and create patterns and shapes.
- Geometry and Measurement — Transformation: Use the invariant properties of figures and objects under transformations (reflection, rotation, translation, or enlargement).