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Math Live – Tessellations: Assessment Task

Grade: 6 Strand: Shape and Space (Transformations) Outcome: 6

SPECIFIC LEARNER OUTCOMES – Space and Shape (Transformations)

SS 6 Perform a combination of translations, rotations and/or reflections on a single 2-D shape, with and without technology, and draw and describe the image.

PROCESSES

Communication (C), Connections (CN), Mental Mathematics and Estimation (ME), Problem Solving (PS),

Reasoning (R), Technology (T), Visualization (V)

C, CN, V, PS, T

EVIDENCE the student has achieved the outcomes Each student will:

• identify regular polygons that tessellate and those that do not.

• explain in words and pictures how to recognize a tessellation.

• create a tessellating shape by combining at least two regular polygons.

• cover a given area by tessellating a shape across its surface.

TEACHER NOTE

• In this assessment task, students will be asked to demonstrate their understanding of

transformational geometry by testing out whether regular polygons will tessellate across a surface. Students will first show that equilateral triangles and regular hexagons will tessellate whereas a regular pentagon will not. Then students will create new tessellating shapes by combining regular polygons and cover a given area with their shape.

• Materials required: Cut-out shapes of regular polygons (blackline master provided), isometric grid paper, (coloured pencils – optional).


• Tessellations are arrangements of shapes (plane figures), which completely cover a

surface without gaps or overlapping. They are repeating patterns created by a series of flips, slides, or turns. Some shapes are easier to tessellate than other because they involve less transformations.

Slides only Slides and flips

Although not part of the elementary curriculum, some students may discover that polygons will only tessellate if the angles of its vertices are a multiple of 360º. Triangles tessellate because any triangle and its image can be combined to form one shape with angles adding up to 360º.

All quadrilaterals will, therefore, tessellate because their interior angles always add up to 360º. However, regular pentagons (5 angles of 108º or 540º) will not tessellate. Regular hexagons will tessellate as the sum of their angles is 720º.

• Early finishers can colour their tessellation patterns.


TANTALIZING TESSELLATIONS- Student Assessment Task

Your class is creating jigsaw puzzles by tessellating shapes across a surface. Your teacher has given you regular polygon shapes to make your puzzle.

(Draw, cut out, or trace the shapes on the sheet provided).

1. Which of the following regular polygons will tessellate across a surface? Trace your work on the grids below and then complete the table.

Regular Polygon Tessellates Does not tessellate

Equilateral triangle

Regular pentagon

Regular hexagon

Equilateral Triangle

Regular Pentagon


Regular Hexagon

2. Your friend still does not understand what exactly a tessellation is. Explain how you would define a tessellation using words and drawings.


3. Make a tessellating shape by combining two or more polygons. Colour each type of polygon the same colour. Trace your tessellating shape below.

4. Create your jigsaw puzzle by tessellating the shape you created across the grid below. Use the same colours for your tessellating shape as you did above.


Regular Polygons

Ideas for Polygon Shapes


Math Live – Tessellations: Scoring Guide

Level

Criteria

Identifies shapes which tessellate

Question #1

Explains how to recognize a tessellation

Question #2

Creates a tessellating shape to cover a surface

Questions #3 and #4

Wow!

Provides a detailed explanation by using specific mathematical

criteria supported by an accurate

pictorial representation

Creates a unique shape from at least two different polygons and repeats this shape across the grid to

illustrate how it tessellates

Yes

Correctly identifies which shapes will

tessellate and supports this with accurate pictorial representations

Provides a general explanation

supported by an accurate pictorial

representation

Creates a shape from at least two polygons and

repeats this shape across the grid to illustrate how it

tessellates

Yes, but…

Correctly identifies which shapes will

tessellate but fails to support this with accurate pictorial representations

Provides an explanation that

may be misleading or vague; it also

may not be supported by a

pictorial representation

Creates a shape from polygons but fails to

clearly illustrate how this shape will tessellate

across the grid

No, but…

Incorrectly identifies which shapes will

tessellate and/or fails to draw accurate

pictorial representations

Provides an incorrect or incomplete

explanation which is not supported by

a pictorial representation

Creates a shape which will not tessellate and/or

fails to illustrate a repeating pattern across

the grid

Insufficient / Blank

No score awarded due to insufficient

evidence of student learning based on the requirements of the

assessment task

No score awarded due to insufficient

evidence of student learning based on

the requirements of the assessment

task

No score awarded due to insufficient evidence of

student learning based on the requirements of the

assessment task


Wow!



(Draw, cut-out or trace the shapes on the sheet provided).



Regular Pentagon

Wow!

Regular hexagon


Math Live © 2009 Alberta Education (www.learnalberta.ca)

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Wow!




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Yes






Regular Pentagon


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Regular hexagon



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Yes




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Yes, but






Regular Pentagon


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Regular hexagon (n/a)



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Yes, but




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No, but




1. Which of the following regular polygns will tessellate across a surface? Trace your work on the grids below and then complete the table.


Regular Pentagon


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Regular hexagon (n/a)



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No, but


n/a



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math live – tessellations: assessment task · math live – tessellations: assessment task grade:...

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