Tessellations & Transformations
Does It Tessellate?
Sort each shape into the correct column.
Match Transformation Types
Draw a line to match each transformation to its description.
Name the Transformation
Circle the correct transformation.
A shape slides 4 units right without turning
A shape flips over a horizontal line
A shape turns 180° around a point
A shape is a mirror image of the original
More Transformation Names
Circle the correct transformation.
A shape moves down 3 units
A shape turns 90° clockwise
A shape flips over a vertical line
A pattern uses slides and flips
Sort the Transformations
Sort each description into the correct transformation type.
Tessellation Basics
Answer each question about tessellations.
What does 'tessellate' mean? ___
Name 3 regular shapes that tessellate: ___
Why can't circles tessellate? ___
Describe the Tessellation
Describe what transformations create each tessellation.
A row of squares side by side: ___
Triangles alternating up and down: ___
A hexagonal tiling: ___
A brick wall pattern: ___
Rotation Angles
Circle the correct rotation angle.
A quarter turn is:
A half turn is:
A full turn is:
A three-quarter turn is:
Match Tessellation to Shapes
Draw a line to match each tessellation description to the shapes used.
Angles at a Vertex
For shapes to tessellate, angles at each meeting point must sum to 360°.
A square has angles of 90°. How many meet at each vertex? ___ (because ___ × 90° = 360°)
An equilateral triangle has angles of 60°. How many meet at each vertex? ___
A regular hexagon has angles of 120°. How many meet at each vertex? ___
A regular pentagon has angles of 108°. Can pentagons tessellate? ___
Transformation Coordinates
Describe each transformation using coordinates.
Translate the shape at (2, 3) by 4 units right. New position: ___
Reflect the point (3, 1) over the y-axis. New position: ___
Rotate a square 90° clockwise around the origin. What happens to its position? ___
Properties of Transformations
Circle the correct answer.
Which transformation changes orientation (left/right)?
Which transformation keeps the shape facing the same way?
Which transformations keep the shape the same size?
A glide reflection combines:
Tessellation in Real Life
Name real-life examples of each tessellation type.
Square tessellation example: ___
Triangular tessellation example: ___
Hexagonal tessellation example: ___
Semi-regular tessellation example: ___
Tessellation True or False
Circle TRUE or FALSE.
All quadrilaterals can tessellate
Only regular polygons can tessellate
Rectangles tessellate using only translations
A tessellation has no gaps or overlaps
Design a Tessellation
Create tessellating patterns.
Create a tessellation using only equilateral triangles.
Create a tessellation using squares and triangles combined.
Describe Your Design
Explain the transformations in your tessellations above.
What transformations did you use in your triangle tessellation? ___
What transformations did you use in your combined tessellation? ___
Could you create the same pattern using only translations? Explain: ___
Home Activity: Tessellation Art
Create beautiful tessellation art at home!
- 1Cut out identical shapes from cardboard and tile a piece of paper with no gaps.
- 2Look at floor tiles, brick walls or fabric patterns. Spot tessellations!
- 3Create a tessellation design using two different shapes.
- 4Use an online tessellation tool to experiment with shapes and transformations.
- 5Design wrapping paper using a tessellating pattern.
Translation Coordinates
Translate each point as directed and write the new coordinates.
(2, 3) translated 5 units right and 2 units down → ( ___ , ___ )
(-1, 4) translated 3 units left and 6 units up → ( ___ , ___ )
(0, -2) translated 4 units right and 4 units right → ( ___ , ___ )
(-3, -5) translated 3 units right and 5 units up → ( ___ , ___ )
Rotation Around a Centre Point
Describe what happens when each shape is rotated.
A square rotated 90° clockwise. New orientation: ___
The point (3, 0) rotated 90° clockwise around the origin → ( ___ , ___ )
The point (0, 4) rotated 180° around the origin → ( ___ , ___ )
Reflection Practice
Reflect each shape and identify the new position.
Triangle with vertices (1,1), (3,1), (2,4) reflected over x-axis: New vertices: ___, ___, ___
Rectangle (1,2), (4,2), (4,5), (1,5) reflected over y-axis: New vertices: ___, ___, ___, ___
Effect of Transformation on Coordinates
Circle the correct new coordinates.
(4, 2) reflected over x-axis:
(4, 2) reflected over y-axis:
(3, 1) rotated 90° clockwise around origin:
(2, 5) translated by (-3, +2):
Sort: Which Transformation Preserves Orientation?
Sort each transformation.
Combined Transformations
Apply the transformations in sequence.
Start at (2, 1). Translate (+3, -2), then reflect over x-axis. Final position: ( ___ , ___ )
Start at (-1, 3). Reflect over y-axis, then translate (-2, -1). Final position: ( ___ , ___ )
Match Transformation to Rule
Draw a line to match each transformation to its coordinate rule.
Symmetry in Tessellations
Investigate symmetry in tessellation patterns.
A square tessellation has ___ lines of symmetry per unit.
A triangular tessellation has rotational symmetry of order ___.
A hexagonal tessellation has ___ lines of symmetry per unit. Explain: ___
Semi-Regular Tessellations
Semi-regular tessellations use two or more regular polygons.
A tessellation uses squares and triangles. At each vertex: 2 squares and 2 triangles. Check angles: ___°×2 + ___°×2 = ___°
Name one other combination of regular polygons that could tessellate together: ___
Transformation Sequences in Art
M.C. Escher used transformations in art. Describe how.
Describe how a bird tessellation might use transformations: ___
Draw a simple Escher-style design using one shape and two transformations:
Transformation Survey
Students were asked which transformation they found easiest. Each icon = 1 student.
| Translation | |
| Reflection | |
| Rotation | |
| All equal |
What percentage found translation easiest?
How many more prefer translation over rotation?
What fraction found either reflection or translation easiest?
Tessellating Shapes in School
Find and tally how many of each shape tessellate in your classroom/school.
| Item | Tally | Total |
|---|---|---|
Square tiles | ||
Rectangular tiles | ||
Hexagonal patterns | ||
Triangular patterns |
Rotation Order of Symmetry
Find the order of rotational symmetry for each shape.
Square: order of rotational symmetry = ___
Equilateral triangle: order = ___
Regular hexagon: order = ___
Rectangle (not square): order = ___
Line Symmetry
Find the number of lines of symmetry for each shape.
Square: ___ lines of symmetry
Equilateral triangle: ___ lines of symmetry
Regular pentagon: ___ lines of symmetry
Regular hexagon: ___ lines of symmetry
What pattern do you notice? ___
Tessellation Rules
Investigate why shapes tessellate.
Why must angles at each vertex in a tessellation add up to exactly 360°? ___
A shape with one angle of 100°. Could it tessellate? How? ___
All triangles tessellate. Explain why: ___