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
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).