Lesson 6: Design Project (Summative)
The Challenge: Pattern Architect
Brief: Design an original geometric pattern for a specific purpose (e.g., a school entryway, a book cover, a sports uniform).
Your design must demonstrate your understanding of transformations and symmetry.
Project Constraints
- Use at least FOUR repetitions of a base motif.
- Include at least two types of transformation (e.g. Rotation + Reflection).
- Have at least one line of symmetry in the final design.
- Be presented on A3 paper or digital equivalent.
🎥 Media Anchor (8 mins)
Video: Designing with Geometric Transformations
- Which two transformations will strengthen the mathematical quality of your design?
- What evidence in your final draft proves those rules were applied accurately?
Submission Requirements
1. The Design (Visual)
High quality, accurate drawing. Ruler used for straight lines. Consistent colouring or shading.
2. The Justification (Written)
Write a paragraph explaining your math:
- "My base motif is..."
- "I transformed it by..." (Give specific rules like 90° clockwise).
- "This created a pattern with..." (Describe the symmetry).
3. Cultural Statement (Ethical)
If you used Māori-inspired designs:
- Acknowledge where the inspiration came from.
- Explain how you have been respectful (not copying sacred stories, finding your own meaning).
Assessment Rubric
| Criteria | Developing | Proficient | Advanced |
|---|---|---|---|
| Transformations | Uses 1 transformation correctly. | Uses 2+ transformations correctly and accurately. | Combines complex transformations (e.g. glide reflection). |
| Communication | Uses some math keywords. | Clear description of rules (centre points, mirror lines). | Detailed justification linking rules to visual outcome. |
| Precision | Some gaps or inaccurate lines. | Neat and mostly accurate grid work. | Precision drawing, perfect tessellation/alignment. |
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.
- Algebra — Knowledge: - Interpreting rules of the form y = mx + c and using a combination of substitution and tables to plot points from the linear graph, connecting the points to form a line - Ide…
- Statistics — Knowledge: - irrational number - like roots - original amount - precision.
- 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…
- Number — Knowledge: - Recording, comparing, and ordering whole and decimal numbers using scientific notation (e.g. 3.14 × 103) - Finding equivalent fractions, simplifying fractions, and convertin…
📋 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).