![]() Investigate the use of tessellation in cultural designs such as the mosaic art and architecture of the Moors, Greeks, and Persians in Europe and China and Japan in Asia. The contexts for this unit can be adapted to suit the interests and cultural backgrounds of your students. Motivate students to add a new, undiscovered tessellation to the class display. displaying the work of students as models for others, especially students who provide explanations about why particular tessellations work.Then open the investigation to more complex regular polygons triangles, squares, pentagons and hexagons, until generalisations about angles around a vertex emerge. restricting the set of shapes at first, e.g.allowing access to calculators and digital tools, so the investigations are more about spatial reasoning than calculation.The difficulty of tasks can be varied in many ways including: Share ideas with the whole class regularly. encouraging students to work collaboratively in partnerships, and to share and justify their ideas.Make the table accessible to students so they can make predictions about sets of shapes that will and will not tessellate organising the data about regular polygons in a table, especially the measures of internal angles.directly modelling examples of tessellations, and explaining your reasoning about why the combinations of shapes around each vertex will work.Will regular hexagons tessellate? How do you know?, and ask students to justify why they believe patterns occur encourage anticipation of results when manipulating polygons, e.g.providing physical manipulatives, regular polygons, or virtual equivalents, so that students can experiment with shapes.Here are some approaches to enabling participation. The geometric focus opens up opportunities for visual reasoning that might prove engaging for students who find numeric reasoning challenging. This unit is designed for students to learn and practise outcomes at Level 4 of mathematics in the New Zealand Curriculum. All that they need to know here is how to sum the interior angles of various regular polygons to 360°. Moving on from here, the children can consider semi-regular tilings. This unit follows on from Keeping in Shape from Level 3, where regular tessellations are first discussed. In this unit, students are led through the steps needed to establish that there are only three regular polygons that tile the plane. This information is accessible to Level 4 students. To be able to fully understand the concept of tessellations using regular polygons, you need to recognise their symmetry, and be able to calculate the size of their interior angles. They also provide a nice application of some of the basic properties of polygons. Tessellations are a neat and symmetric form of decoration. They play a significant role in tapa cloth design and creation, and in Islamic art that features designs commonly built around star polygons. You can see them in the pattern on carpets and decorative patterns on containers and packaging. Tessellations are frequently found in kitchen and bathroom tiles and lino.
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