Year+7+-+HWEO+-+Week+1

TESSELLATIONS

Investigate which regular polygons tessellate.

Demonstrate your results for equilateral triangles, squares, pentagons, hexagons and octagons (as a minimum). Diagrams should be drawn accurately by hand where possible.

Do you think that a regular heptagon would tessellate?

Are there properties of these shapes which determine whether they tessellate or not?

Research some of the following and present examples:

Daisy Designs  Tumbling Block Designs  Tessellations with other non regular geometric shapes, for example a triangle  Tessellations using translations  Tessellations using rotations  Tessellations using reflections  Tessellations using capital letters  Semi regular tessellations  Mauritis Cornelis Escher  Tessellations in 3-d (in nature) <span style="font-family: 'Comic Sans MS',cursive; font-size: 140%;"> Tangrams <span style="font-family: 'Comic Sans MS',cursive; font-size: 140%;"> Wall Paper patterns <span style="font-family: 'Comic Sans MS',cursive; font-size: 140%;"> Maori symbols that tessellate <span style="font-family: 'Comic Sans MS',cursive; font-size: 140%;"> Kow haiw hai <span style="font-family: 'Comic Sans MS',cursive; font-size: 140%;"> Tukutuku patterns <span style="font-family: 'Comic Sans MS',cursive; font-size: 140%;"> Taniko

<span style="font-family: 'Comic Sans MS',cursive; font-size: 140%;">Ensure your work includes some Maori patterns.

<span style="font-family: 'Comic Sans MS',cursive; font-size: 150%;">WALLPAPER DESIGN

<span style="font-family: 'Comic Sans MS',cursive; font-size: 140%;"> Create your own wallpaper design using your research which you would like to hang on your bedroom wall.

<span style="font-family: 'Comic Sans MS',cursive; font-size: 140%;"> Your submitted piece of work needs to include original brainstorming ideas regarding theme and colour, any designs which you considered before selecting the final design and most importantly two full colour examples of your wallpaper. The examples should demonstrate how the wallpaper lines up between sections when hung. The minimum size for each example is an A4 piece of paper. If necessary the detail of parts of the pattern may be drawn on a computer, but the translation and pattern repeat interval must be constructed by hand.

<span style="font-family: 'Comic Sans MS',cursive; font-size: 140%;"> If you have additional time you may research other types of wall covering and/or attempt the Paving Paths problem below.

<span style="font-family: 'Comic Sans MS',cursive; font-size: 140%;"> Please ensure all work is named on the back.

<span style="font-family: 'Comic Sans MS',cursive; font-size: 150%;">EXTENSION

<span style="font-family: 'Comic Sans MS',cursive; font-size: 140%;"> Paving Paths problem:

<span style="font-family: 'Comic Sans MS',cursive; font-size: 140%;"> How many different ways can I lay 10 paving slabs each 50 cm by 1 metre, to make a path 1 metre wide from my back door into my garden, without cutting any of the paving slabs?

<span style="font-family: 'Comic Sans MS',cursive; font-size: 140%;"> Answers should be presented with a detailed method.

<span style="font-family: 'Comic Sans MS',cursive; font-size: 140%;">All students are expected to conference with Mrs Attard every morning their classroom is doing classroom maths during this assignment.

<span style="color: #ff0000; font-family: 'Comic Sans MS',cursive; font-size: 140%;">Work is due Wednesday 12th November, all students are expected to submit some work on tessellations including considering multiple regular polygons and why they may or may not tessellate along with research on a minimum of three patterns plus two pieces of wallpaper.