# Tessellation Worksheet

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K-12: Materials at high school level.

Objective:

• Introduction to some basic ideas about tessellations.
• Manipulatives are used to help develop our intuition.
• Explore how many tessellations we can make using just one type of geometric shape.

## Materials

• Pattern blocks
 Printed version of the Tessellations, a first look Exploration, dimmed: File:Tessellations-PatternBlocks.pdf
• Printed copy of the Tessellations, a first look Exploration.

## Tessellations

When polygons are fitted together to fill a plane with no gaps or overlaps, the pattern is called a tessellation. You have seen them in floor tilings, quilts, art designs, etc. Tessellation patterns can be made from one shape or from more than one shape; here our investigation will use one shape at a time.

We will start with a hands-on approach, and use pattern blocks to explore tessellations.

1. Use the green tiles to create a tessellation by equilateral triangles. Sketch one tessellation.
1. Use the blue tiles to create a tessellation by rhombuses. Sketch one tessellation. Can you make another one that looks different? Sketch that one too.
1. Use the red tiles to create a tessellation by isosceles trapezoids. Sketch one tessellation. Can you make another one that looks different? Sketch that one too.
1. Use the yellow tiles to create a tessellation by hexagons. Sketch one tessellation.
1. Look at Escher's Regular Division of the Plane Drawings numbers 1-21 (Visions of Symmetry pg 116-132). Make a list of the geometric shapes that are used to tessellate the plane.

Handin: A sheet with answers to all questions.