- explaining the properties of shapes that make tessellating possible
- creating tessellations
- identifying tessellations in the environment.
[C, CN, PS, T, V]
(a) |
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). |
(b) |
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°). |
(c) |
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). |
(d) |
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). |
(e) |
Identify different transformations (translations, reflections, rotations, and combinations of any of the three) present within a tessellation. |
(f) |
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. |
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