# 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. Show at least 12 triangles.
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. Show at least 12 shapes.
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. Show at least 12 shapes.
1. Use the yellow tiles to create a tessellation by hexagons. Sketch one tessellation. Show at least 12 shapes.
1. Look at Escher's Regular Division of the Plane Drawings given below. Note that Escher made these patterns by starting with something simple! Underneath the drawing write the polygon you see in the picture.
 Polygon: Polygon: Polygon: Polygon: Polygon: Polygon:

Handin: A sheet with answers to all questions.