Stage 2 – STEM Activity 8

Now you see it

A rectangle filled with broad arrows that fit together forming a tessellating (tiling) pattern. Half of the rectangle has arrows placed together in outline and the other half of the rectangle continues the pattern made by the arrows but those arrows pointing downwards (diagonally) are coloured red and those pointing upwards (diagonally) are coloured blue.

Description of activity

Students are challenged to create a tessellating pattern and use it purposefully in a product, eg a cover for their mathematics book.

This activity could take approximately 90 minutes to:

research patterns in nature
devise the tessellating pattern and
make the product.

Context

Students learn about patterns, symmetry and asymmetry, rotation and reflection. They can recognise repeating patterns.

Outcomes

Skills

ST2‑4WS investigates their questions and predictions by analysing collected data, suggesting explanations for their findings, and communicating and reflecting on the processes undertaken
ST2‑5WT applies a design process and uses a range of tools, equipment, materials and techniques to produce solutions that address specific design criteria
MA2-1WM uses appropriate terminology to describe, and symbols to represent, mathematical ideas
MA2-2WM selects and uses appropriate mental or written strategies, or technology, to solve problems

Knowledge and understanding

MA2‑15MG manipulates, identifies and sketches two-dimensional shapes, including special quadrilaterals, and describes their features
MA2-16MG identifies, describes, compares and classifies angles
ST2‑10LW describes that living things have life cycles, can be distinguished from non-living things and grouped, based on their observable features
ST2‑16P describes how products are designed and produced, and the ways people use them
VAS2.1 represents the qualities of experiences and things that are interesting or beautiful by choosing among aspects of subject matter
VAS2.2 uses forms to suggest the qualities of subject matter

Resources

Thin cardboard in squares to use as a stencil, blank A4 paper, pencils, ruler and erasers
Sticky tape, scissors
Extra supplies as determined by the product to be made

Work, health and safety

Check relevant Work, health and safety guidelines.
Provide warnings on the use of scissors and cutting tools.

Evidence of work for assessment purposes

Notes describing the methods used in the tests that were carried out
A record of results of all tests comprising tables and pictures
A statement summarising the results of the investigation.

STEM teaching and learning activities

Discuss images of patterns in nature in terms of symmetry, eg nautilus shell, zebra markings.
Show the YouTube video Fractals in nature and discuss if any of the patterns are symmetric and/or repeating.
Students draw a repeating pattern using images of patterns in nature as stimulus.
Show how repeating patterns are used in the built environment, as shown in Tessellations: Real life examples.
Students observe the patterns present around the playground. Students record these patterns as a sketch or photo and identify them as symmetrical or asymmetrical.
Students discuss the criteria used to define their choices.
Students find several examples of symmetry present in both living and non-living things. Sort images of these examples in a table, as shown below.
Discuss the types of products that can be decorated or made up of individual pieces and decide as a class what products will be made, eg a gift card, or tessellations arranged in a border and glued onto a picture frame.
Challenge students to design and produce a solution that they could decorate using their own tessellating design.
Demonstrate how to create a simple tessellation stencil.
Students create their own tessellation stencil.
Demonstrate how to use the stencil to create the tessellated pattern.
Students create their own coloured tessellated pattern.
Students apply their decoration to their product.
Students give feedback on their peers’ work.

Vocabulary list

Dimension – properties in space, line, plane or volume
Fractal – a repeating pattern that may change in size
Illusion – a misleading image
Optical – having to do with sight or light
Pattern – a repeated design or sequence
Rotate – move in a circle round a fixed point or axis
Symmetry – exactly similar parts facing each other or around an axis
Tessellation – an arrangement of shapes closely fitted together, especially of polygons, in a repeated pattern without gaps or overlapping
Translate – moving a shape without rotating or flipping it. The shape still looks exactly the same, just in a different place

Key inquiry questions

Do all living things show some form of symmetry?
Most living things do show some form of symmetry, but it is generally not exact. Refer students to the tables they generated to see the overlap between them.

What products would be suited to be decorated with their tessellations?
Determine the characteristics of a product that would enable the clear display of a tessellation, eg flat surfaces, an area larger than the tessellating pattern. Examples could include, wrapping paper, gift cards, floor tiles, textiles or wall posters.

Discuss and decide upon the attributes of the product, eg if the product is a greeting card:

how big should it be?
what is the occasion?
how would that affect the colours used?

How can symmetry and patterning be used in art?
Discuss how decorations are used in many cultures and how patterns and tessellations are an important part of cultural expression, eg Sumerian temples, the Alhambra in Spain.

In what ways can tessellation be considered as a form of art?
Find examples of optical illusions: both two dimensional (2D) and three dimensional (3D). They have been used in paintings, buildings and even clothing throughout history to decorate and inspire.
M.C. Escher is probably the most famous optical illusion artist and his work is easily accessible on the internet. Encourage students to look at images of his work and the products that use them as illustrations and describe the types of patterns in evidence.

Support materials

Teacher resources

M.C. Escher: examples of tessellations
Tessellations.org: provides a method for creating a stencil and describes how to create the tessellation
YouTube video: Simple Tessellation
YouTube video: How to Make Tessellations

Diversity of learners

For additional support

Tessellation shapes, templates or nets can be provided to students.

For extension

Tessellations can be drawn using a simple paint program and the ‘cut’ and ‘paste’ functions to create the original shape and the tessellation and the ‘fill’ function to add colour.
Discuss and identify patterns in nature, eg Fractals, Fibonacci series, snowflakes.
Research tromp l’oeil illusions (sometimes called a tromploy) and their use in street art and building decoration.

Review

This STEM activity allows students to investigate their natural and built environments and provide a way for them to appreciate mathematics in nature. It allows research that extends students’ knowledge of patterns as a key concept in art and architecture. It is designed to extend students’ graphical skills and as a simple introduction to making a product for an identified purpose.