Lesson 3: Translation Rules

Year 9 60 mins Geometry

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

📋 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