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Gold Seal Lesson:
Making A
Tessellation
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Copernicus
Education Gateway
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Subject:
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Mathematics
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Grade:
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5-8
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ICLE Standards:
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Geometry: Explore transformations of geometric
figures.
Mathematical Connections: Apply mathematical
modeling and thinking to other disciplines.
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Performance Task:
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The Dutch artist M.C. Escher (1898-1972) used the idea of translations to create some unusual works of art.
These art works are tessellations produced by translations. A tessellation is a tiling of the plane using one
or more shapes in a repeated pattern with no holes or gaps. Although irregular shapes can be tessellated,
regular polygons are the easiest to work with for the beginner. Counter tops and floors are often tessellated
with square pieces. Your task is to create two tessellation, one using a square and the other using an
equilateral triangle as your basic shape to tessellate. To make your tessellation, use the following procedure.
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Using a piece of tag board or heavy cardboard, carefully construct and cut out a square.
Many size squares can be used, but a 5-by-5 inch is probably the most convenient for this
task. The square will be used as a template or tile to create your tessellation.
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Create a geometric design on your square. Make it interesting but not too complex. Your
design should contain elements of congruence, similarity and some type of
transformation. Cut out the design with scissors or an art knife.
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On a large piece of construction paper or poster board, place your square in the upper
left hand corner. Trace the outline of your square and your cut out design inside the
square.
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Now translate your square to the right and down, tracing the square and design after
each translation. You may rotate your square as well as translating it. If you do, just be
sure that you follow a pattern so that your final design is consistent. Continue this process
until your whole sheet of paper or board is filled.
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Now color or paint your design to make it an attractive “work of art.”
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Repeat steps 1-5 using an equilateral triangle. When using the equilateral triangle as
your basic shape, you must rotate as well as translate to completely fill in your plane.
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Knowledge / Skills:
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Understand the properties and classification triangles by sides (i.e., scalene, isosceles, and equilateral). (m16)
Understand the properties and classification of quadrilaterals by orientation (e.g., parallelogram, rectangle, rhombus, square, and trapezoid). (m27)
Apply transformation concepts to understand and create congruent and similar figures. (m49)
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Rubric:
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3 Points = The student is able to work independently on all aspects of the task. He/she creates two tiles, both including the concepts outlined in the procedure. The student demonstrates a high level of
understanding of transformations and makes an attractive and neat tessellation.
2 Points = The student needs some assistance in performing the task. Not all concepts outlined in the procedure are included in the tile design. But, the student does makes corrections/adjustments when advised and demonstrates limited understanding of transformations. The tessellation is fairly attractive, but not particularly neat.
1 Point = The student does not complete the task. He/she needs constant assistance in creating the
tiles. Most concepts outlined in the procedure are not included in the tile design. The student has difficulty responding to suggestions and demonstrates little understanding of transformations. The tessellation is sloppy and unattractive.
0 Points = The student does not attempt the task.
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Keywords:
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GEOMETRY
CONGRUENCE
QUADRILATERALS
SYMMETRY
TESSELLATIONS
TRIANGLES
MODELS & CONSTRUCTIONS
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Grades:
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Kg [] - 1 [] - 2 [] - 3 [] - 4 [] - 5 [x] - 6 [x] - 7 [x] - 8 [x] - 9 [] - 10 [] - 11 [] - 12 []
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ICLE Application:
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D
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© 2000 International
Center for Leadership in Education
1587 Route 146 - Rexford - NY - 12148
518.399.2776 Fax: 518.399.7607
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