Identify, describe (in terms of translations, reflections, rotations, and combinations of any of the three), and reproduce (concretely or pictorially) a tessellation that is relevant to self, family, or community (e.g., a Star Blanket or wall paper).

Predict and verify which of a given set of 2-D shapes (regular and irregular) will tessellate and generalize strategies for determining whether a new 2-D shape will tessellate (i.e., an angle must be a factor of 360°).

Identify one or more 2-D shapes that will tessellate with a given 2-D shape and explain the choice (e.g., knowing that the sum of the measures of one angle from each of the 2-D shapes must be a factor of 360°, and if the given shape has an angle of 12°, then two shapes with angles of 13° and 5° can be used to tessellate with the original shape because $12 + 1 3 + 5 = 30$ which is a factor of 360 – these shapes would need to be repeated at least 12 times because $30 x 12$ is 360).

Design and create (concretely or pictorially) a tessellation involving one or more 2-D shapes, and document the mathematics involved within the tessellation (e.g., types of transformations, measures of angles, or types of shapes).

Identify different transformations (translations, reflections, rotations, and combinations of any of the three) present within a tessellation.

Make a new tessellating shape (polygonal or non-polygonal) by transforming a portion of a known tessellating shape and use the new shape to create an Escher-type design that can be used as a picture or wrapping paper.