Tessellations
A tessellation is a pattern of shapes that fit perfectly together without any gaps or overlaps. These shapes can be simple, such as triangles or squares, or more complex, such as hexagons or irregular polygons. Tessellations are a form of mathematical art and can be found in nature, architecture, and art throughout history.
Types of Tessellations
There are three main types of tessellations:
- Regular Tessellations: These are made up of one regular polygon, such as equilateral triangles, squares, or hexagons, that fit together to cover a plane without any gaps or overlaps.
- Semiregular Tessellations: These are made up of two or more regular polygons, with the same arrangement of shapes meeting at each vertex.
- Irregular Tessellations: These are made up of irregular polygons that fit together to cover a plane without any gaps or overlaps.
Study Guide
Here are some key concepts to understand when studying tessellations:
- Types of Tessellations: Understand the differences between regular, semiregular, and irregular tessellations and be able to identify examples of each type.
- Transformations: Learn about the transformations, such as translation, rotation, and reflection, that can be used to create tessellations.
- Tessellation Artists: Explore the work of artists who have used tessellations in their art, such as M.C. Escher.
- Mathematical Properties: Understand the mathematical principles behind tessellations, such as the angles and shapes that fit together to create a tessellating pattern.
By understanding these concepts, you will be able to recognize and create tessellating patterns and appreciate the mathematical and artistic beauty of tessellations.
.◂Math Worksheets and Study Guides Sixth Grade. Area of Coordinate Polygons
Study Guide
Area of Coordinate Polygons 
Activity Lesson
Area of Coordinate Polygons Worksheet/Answer key
Area of Coordinate Polygons Worksheet/Answer key
Area of Coordinate Polygons Worksheet/Answer key
Area of Coordinate Polygons
Activity LessonWorksheet/Answer keyWorksheet/Answer keyWorksheet/Answer keyThe resources above cover the following skills:
Geometry (NCTM)
Specify locations and describe spatial relationships using coordinate geometry and other representational systems.
Use coordinate geometry to represent and examine the properties of geometric shapes.
Use coordinate geometry to examine special geometric shapes, such as regular polygons or those with pairs of parallel or perpendicular sides.
Use visualization, spatial reasoning, and geometric modeling to solve problems.
Use geometric models to represent and explain numerical and algebraic relationships.
Measurement (NCTM)
Apply appropriate techniques, tools, and formulas to determine measurements.
Select and apply techniques and tools to accurately find length, area, volume, and angle measures to appropriate levels of precision.
Connections to the Grade 6 Focal Points (NCTM)
Measurement and Geometry: Problems that involve areas and volumes, calling on students to find areas or volumes from lengths or to find lengths from volumes or areas and lengths, are especially appropriate. These problems extend the students' work in grade 5 on area and volume and provide a context for applying new work with equations.