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Tessellation Design Studio

Students explore the mathematical art of tessellations by creating repeating patterns that completely cover a plane without gaps or overlaps, combining geometry with creativity.

Duration

90 minutes

Group Size

Individual/Pairs

Grade Level

Grade 6

Subject

Mathematics/Art

Learning Outcomes

Students will be able to:

  • Understand the mathematical principles of tessellations
  • Create regular and semi-regular tessellations
  • Apply transformations (rotation, reflection, translation)
  • Analyze angle relationships in tessellating patterns

Curriculum Standards:

G3.3 - Creating Tessellations
G3.2 - Geometric Transformations
G2.1 - Angle Relationships

Materials Needed

Physical Materials:

  • • Pattern blocks (triangles, squares, hexagons)
  • • Cardboard or foam sheets
  • • Scissors and craft knives
  • • Colored paper and markers
  • • Rulers and protractors
  • • Tracing paper
  • • Glue sticks and tape

Digital Tools:

  • • Tessellation software (TesselManiac)
  • • GeoGebra tessellation activities
  • • Digital art programs
  • • Online pattern generators
  • • Tablets for digital design

Activity Instructions

Phase 1: Tessellation Exploration (20 minutes)

  1. 1. Examine tessellations in nature and art (honeycomb, M.C. Escher)
  2. 2. Explore Caribbean cultural patterns in textiles and architecture
  3. 3. Use pattern blocks to create simple tessellations
  4. 4. Identify which regular polygons tessellate and why

Phase 2: Regular Tessellation Creation (25 minutes)

  1. 1. Create tessellations using equilateral triangles
  2. 2. Design square-based tessellations
  3. 3. Explore hexagonal tessellations
  4. 4. Calculate angle measures to verify tessellation properties
  5. 5. Document findings about angle sums at vertices

Phase 3: Semi-Regular Tessellations (25 minutes)

  1. 1. Combine different regular polygons
  2. 2. Create patterns using triangles and hexagons
  3. 3. Design squares and octagon combinations
  4. 4. Verify that angles sum to 360° at each vertex

Phase 4: Creative Design Studio (20 minutes)

  1. 1. Design original tessellation patterns
  2. 2. Create modified shapes that still tessellate
  3. 3. Add artistic elements while maintaining mathematical properties
  4. 4. Present designs explaining mathematical principles

Assessment Strategies

Formative Assessment:

  • • Understanding of tessellation principles
  • • Accuracy of angle calculations
  • • Creative problem-solving approaches
  • • Mathematical vocabulary usage
  • • Pattern recognition skills

Summative Assessment:

  • • Completed tessellation portfolio
  • • Mathematical explanations quality
  • • Design creativity and accuracy
  • • Understanding of transformation concepts
  • • Presentation of final designs

Differentiation & Extensions

Support Strategies:

  • • Pre-cut tessellation pieces
  • • Guided angle measurement sheets
  • • Visual pattern templates
  • • Step-by-step instruction cards
  • • Digital tessellation tools

Challenge Extensions:

  • • 3D tessellation exploration
  • • Hyperbolic tessellations
  • • Computer programming patterns
  • • Historical tessellation research
  • • Large-scale collaborative murals

Real-World Connections:

  • • Caribbean architectural patterns
  • • Traditional craft designs
  • • Islamic geometric art
  • • Modern graphic design
  • • Nature pattern analysis