Exploring Tessellation

What are the key properties that define a tessellation?

• A tessellation is defined by shapes that fit together without gaps or overlaps, covering a surface completely and repeating infinitely.

• Tessellations are defined by random placement of shapes.

• Shapes that can overlap to create patterns.

• A tessellation must consist of only circular shapes.

How can tessellation be effectively used in artistic designs?

• Tessellation is only used in architecture.

• Tessellation can only be applied to 3D models.

• Tessellation is primarily a mathematical concept with no artistic value.

• Tessellation can create visually appealing patterns in murals, textiles, and digital art.

Identify an example of tessellation found in nature and explain its significance.

• Leaf patterns on trees

• Honeycomb structure in beehives.

• Fish scales on a fish's body

• Cracked earth in deserts

What role does symmetry play in creating tessellations?

• Symmetry allows shapes to fit together perfectly, creating a seamless pattern in tessellations.

• Symmetry only applies to three-dimensional shapes, not tessellations.

• Symmetry is irrelevant to the formation of tessellations.

• Symmetry disrupts the arrangement of shapes in tessellations.

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CCSS.4.G.A.3

Describe how tessellation can influence architectural design.

• Tessellation is primarily used for landscaping designs.

• Tessellation has no impact on the cost of construction materials.

• Tessellation influences architectural design by enhancing aesthetics, optimizing material use, and enabling innovative structural forms.

• Tessellation is only relevant in graphic design, not architecture.

What types of shapes can be used to create a tessellation?

• Only regular polygons can be used to create tessellations.

• Any shape that can fit together without gaps can be used, including irregular shapes.

• Only triangles and squares are suitable for tessellations.

• Shapes must be circular to form a tessellation.

How does the concept of translation apply to tessellations?

• Translation involves moving shapes without rotating or flipping them, which is essential in creating tessellations.

• Translation is not relevant to tessellations.

• Translation refers to the resizing of shapes in tessellations.

• Translation only applies to three-dimensional tessellations.

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CCSS.8.G.A.3

CCSS.HSG.CO.A.5

What mathematical principles are involved in the study of tessellations?

• Mathematical principles such as geometry, symmetry, and transformations are fundamental to understanding tessellations.

• Tessellations are based solely on artistic principles.

• Tessellations do not involve any mathematical principles.

• Only algebraic principles are relevant to tessellations.