Lesson 3: Translation Rules
Learning Intention
I can describe translations using specific rules and creating repeating border patterns.
Success Criteria
- I can write a rule for a translation like "3 units right, 2 units down".
- I can apply a translation rule to move a shape on a grid.
- I can create a frieze pattern (repeating strip) by translating a base tile.
🎥 Media Anchor (8 mins)
Video: Translation Rules in Patterns
- What translation vector best describes the repeated motif movement?
- How can you prove each repeated image is congruent to the original?
Lesson Sequence
1. Starter: GPS Directions (10 mins)
On a whiteboard grid, draw a dot at A and a dot at B. "How do I get from A to B?"
Encourage precise language: "Go right 4 squares, then go up 3 squares."
Math Notation (Extension): Introduce vector notation roughly: (4, 3) where first number is horizontal, second vertical.
2. Investigation: The Repeating Strip (25 mins)
Focus on Tukutuku panels often found in meeting houses.
Observation: Look at the Poutama (step) pattern. Is it just one shape sliding upwards?
Activity: Students investigate the "rules" of a border pattern.
- Take a base 2x2 grid shape.
- Translate it "2 right, 0 up". Repeat 5 times. What pattern do you get?
- Translate it "1 right, 1 up". What pattern is that? (Diagonal/Stairs).
3. Design Challenge: Code-a-Pattern (15 mins)
Goal: Write a translation code for a partner.
Student A: Draws a shape and a "destination" shape.
Student B: Writes the rule (e.g., "5 Left, 2 Down").
Student A: Checks if it works.
4. Plenary (10 mins)
Does a translation EVER turn the shape? (No). Does it EVER flip it? (No). The orientation stays exactly the same.
Curriculum alignment
- Statistics — Knowledge: - irrational number - like roots - original amount - precision.
- Algebra — Knowledge: - In the equation of a line y = mx + c, m and c represent constants (they are unchanging), y and x can vary, and all the values of x and y that satisfy the equation create an …
- Statistics — Knowledge: - accuracy - congruent - derived unit - hypotenuse.
- 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…
- Measurement — Knowledge: - A solution to a calculation cannot be more precise than the least precise number used in that calculation.
📋 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: Coordinate grids with the first translation vector supplied. Extension: express the repeat as a general rule rather than a single move.
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: Kōwhaiwhai run translational repeats along a rafter, so the maths of translation has a real referent here rather than an invented one. Ākonga describe the repeat; they do not infer purpose from it.
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 (Practices): “- Transforming 2D shapes in the coordinate plane by translation, reflection about a given line of symmetry, and rotation about a given point by a multiple of 90 degrees”
- NZC (2007) · Mathematics and Statistics · Level 5: “Define and use transformations and describe the invariant properties of figures and objects under these transformations.”