Lesson 1: Patterns as Mathematics
Learning Intention
I can identify and describe geometric transformations (translation, rotation, reflection) in patterns.
Success Criteria
- I can look at a pattern and say "what repeats" and "what changes".
- I can use the words translation (slide), rotation (turn), and reflection (flip) correctly.
- I can label these transformations on a simple pattern.
🎥 Media Anchor (8 mins)
Video: Patterns and Sequences Introduction
- Which transformation is most visible in the starter pattern, and how can you justify it?
- What mathematical language will make your pattern description precise?
Lesson Sequence
1. Hook: Notice & Wonder (10 mins)
Display: Show a large image of a Tukutuku panel or a complex tiling pattern.
Think-Pair-Share:
- What shapes do you see?
- How do the shapes move across the board?
- Is it the same shape repeating, or does it change?
2. Explicit Teaching: The Language of Movement (15 mins)
Introduce the three key rigid transformations using physical movement:
- Translation (Slide): Move a book across a desk without turning it. "It just slides."
- Rotation (Turn): Pin a piece of paper in the middle and spin it. "It turns around a centre point."
- Reflection (Flip): Hold your hands up like a mirror. "It flips over a line."
Cultural Connection: Look at a Kōwhaiwhai rafter pattern. Is it sliding (translation) or flipping (reflection)?
3. Investigation: Pattern Detective (25 mins)
Task: Students are given a worksheet with 4 different patterns (2 Māori, 2 generic geometric).
- Circle the "base shape" (motif) that repeats.
- Draw arrows to show where it moves.
- Label the movement: Translation, Rotation, or Reflection.
Extension: Find a pattern in the room (e.g. carpet, exercises book grid) and describe it.
4. Wrap Up (10 mins)
Exit Ticket: Draw a shape (like a triangle). Draw it again after a Translation.
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 — Knowledge: - The area of a circle is given by A = πr2. - The surface area of a solid object is a measure of the total area that the surface of the object occupies. - The general formula …
- Statistics — Practices: - Critically considering data visualisations, including those from contemporary media, to see if they support or misrepresent the data
📋 Teacher Planning Snapshot
Unit-wide intent — Te Aronga o te Wāhanga
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).
Unit-wide outcomes — Ngā Putanga o te Wāhanga
These describe the whole unit. Assess this lesson against its own success criteria above, not against these.
- ✅ 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: Grid templates plus two patterns already annotated with their transformation named. Extension: describe a pattern's repeat unit formally.
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: Tukutuku panels sit on a precise grid, and reading that grid mathematically is a legitimate analysis. State the boundary plainly with ākonga: the geometry we describe is OUR analytical lens on a sourced example — it is not a claim about what the weavers intended the pattern to encode.
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
- Te Mātaiaho (2025) · Mathematics and Statistics · Phase 4 (Years 9–10) · Geometry (Knowledge): “- A set of points in a plane can be transformed by translation, reflection about a line, and rotation about a fixed point.”
- NZC (2007) · Mathematics and Statistics · Level 5: “Define and use transformations and describe the invariant properties of figures and objects under these transformations.”