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Australian Curriculum Year 5 ACMMG114 Describe transla-ons, reﬂec-ons and rota-ons of two-‐dimensional shapes. Iden-fy line and rota-onal symmetries Introductory Ac9vity Process Key Idea Tessella-ons are created by transforming two -‐ dimensional shapes to make a pa>ern with no gap or overlay. Resources internet templates of 2D shapes to cut out grid paper, dot paper, triangle-‐grid paper tracing paper cardboard scissors pictures of tessella-ons in real-‐life -‐ eg. brick wall, -led ﬂoor, scales on a ﬁsh, mosaics, honeycomb etc. Vocabulary transforma-ons, pa>erns, shapes, rota-on, reﬂec-on, transla-on, gaps, overlaps, repeat, direc-on, regular, semi-‐regular, vertex, polygon, regular, tessella-on, Equivalent, equiangular, equilateral Show students a piece of artwork that illustrates tessella-ons eg. Escher h>p://www.bing.com/images/search?q=Escher +Tessella-ons&FORM=RESTAB#a Discuss how the pa>erns were made -‐ draw out the mathema-cal language needed – rota-on, ﬂip, transform, etc. Write onto word wall. Review work done in MAG 5.17 Transforma-ons on rota-ons, reﬂec-ons and transla-ons. Write the word tessellate on the board and explain that this word refers to a special kind of pa>erning where cover a surface is covered by repeated use of a single shape, without gaps or overlapping. This is oZen referred to as -ling or mosaics. Discuss the tessella-ons that students have no-ced in everyday life -‐ such as concrete retaining walls, paving, brick walls, -led ﬂoors, etc. Record examples on a poster for future reference. If possible, ﬁnd some pictures to add. Ask students to observant and look around the school for tessella-ng pa>erns. Record them with photos for an image gallery. Discover the 2D plane shapes that are used in these tessella-ons and record also. The word "tessellate" is derived from the Greek word "tesseres," which in English means "four." The ﬁrst -lings were made from square -les. A regular polygon has 3 or 4 or 5 or more sides and angles, all equal. A regular tessella0on means a tessella-on made up of congruent regular polygons. Regular means that the sides and angles of the polygon are all equivalent i.e., the polygon is both equiangular and equilateral. Congruent means that the polygons that you put together are all the same size and shape. Ac9vity Process-‐Inves-gate Ask students to explore the rules for tessella-ng shapes and the diﬀerence between regular and semi-‐ regular tessella-ons using the websites: h>p://www.coolmath4kids.com/tesspag1.html OR h>p://www.mathsisfun.com/geometry/ tessella-on.html Teacher scaﬀolds the ac-vity with the FISH strategy Give students in pairs templates of a variety of 2D shapes. Ask them to trace and cut at least 16 of each shape and then see if they can tessellate the shapes. Glue each onto paper and describe how the tessella-ons were created using language from the word wall-‐ eg. rotate, vertex, ﬂip, slide etc. Students then ‘Think, Pair, Share’ what they have created. Con-nue with a variety of shapes. At the end of the ac-vity, discuss as a class the shapes that tessellated easily, which ones did not, why, what did you have to do to some of the shapes to make them tessellate. Diﬀeren-ate by Using a class set of pa>ern blocks to draw a tessella-ng pa>ern that ﬁlls a 10cm x 10cm space and uses: a) only triangles b) only hexagons c) only trapezia d) hexagons and triangles Sourced from ICE-‐EM Mathema7cs Australian Curriculum Edi7on Year 5 Book 2, Cambridge University Press Digital Learning Rota-onal Symmetry h>p://www.spraoischool.com/ Use the iPad app Symmetry School Learning Geometry. Op-onally If you register you will be able to gain access to Symmetry School Online and can use the site with an IWB for display either as a class focus or group ac-vi-es. The easy level has a show me func-on The hard level provides for a challenge level Inves9ga9on-‐Ac-vity adapted from: h>p://www.nzmaths.co.nz/resource/tessella-ng-‐art Start by reminding students that: rota-ng lengths, areas, angles do not change but orienta-on does. reﬂec-on lengths, areas and angles do not change but orienta-on does transla-on lengths, areas, angles and orienta-on do not change. enlargement angles and orienta-on do not change but lengths and areas do Become a tessella-on ar-st using h>p://www.mathsisfun.com/geometry/tessella-on-‐ ar-st.html Use microsoZ word to insert shape -‐ copy -‐ paste to create a tessella-ng pa>ern Variety of webquests, ac-vi-es and worksheets available at: h>p://ethemes.missouri.edu/themes/1791 h>p://mathsyear7.wikispaces.com/Tessella-ons h>p://www.math-‐salamanders.com/tessella-ons-‐in-‐ geometry-‐2.html h>p://www.superteacherworksheets.com/tessella-ons/ tessellate-‐1_YESNO.pdf Give each student a square cardboard -le. Ask them to cut a piece out of one side of the square. A>ach the cut out piece to the opposite side of the square with cellotape. Will your new shape tessellate? Try it and see. Have the students trace their new shapes several -mes onto blank sheets of paper to see if the altered shape tessellates. Discuss. • Is your altered shape symmetric? • What type of symmetry does it have? • Does the new shape have to be symmetric to tessellate? When altering a square by transla-ng opposite sides to form a new tessella-ng ﬁgure, the altera-on does not have to be symmetrical. Have the students repeat the altering process with other quadrilaterals that tessellate, for example, parallelograms and rectangles. Also include "wonky" quadrilaterals. Not all altera-ons will create tessella-ng shapes and this a useful discovery. The key to crea-ng tessella-ng shapes is altering opposite sides in exactly the same way. Remind students of their Notan designs created in MAG 5.1.17 Allow -me to share and discuss at the end of the ac-vity. • What did you discover about altering shapes to create new shapes that also tessellate? • Why do you think it is possible to alter shapes in this way and s7ll end up with a shape that tessellates? • Did you create any shapes that do not tessellate? Why do you think that they won’t tessellate? Context for Learning -‐ Real life experiences: We see pa>erns all around. Tessella-ons occur oZen in nature, art and architecture. Ancient Greeks and Romans used tessella-ons made of mosaic -les, granite and stone to cover walls and ﬂoors. Islamic art and architecture contains many examples of very elaborate tessella-ons decora-ng the ﬂoors, walls and ceilings of mosques and palaces. Ar-st M.C. Escher uses varia-ons on tessella-ons in his artwork. He started by crea-ng simple tessella-ons and then distor-ng and altering them to create the art for which he is famous. Assessment Standard In Year 5 students describe transforma-ons of two-‐dimensional shapes and iden-fy line and rota-onal symmetry Each student needs to complete a whole and independent op-on for assessment to meet the standard. Whole class Assessment -‐ Give students an example of a tessella-ng pa>ern. Ask them to describe how the pa>ern was made using the terminology learnt. Independent Assessment Task-‐Student chooses Choose an op-on that suits the level of individual students or students choose their own op-on: Op0on 1 -‐ Use one pa>ern block repeatedly to tesselate. Take a photo and describe the pa>ern using the terminology learnt. Op0on 2 -‐ Create an irregular shape and demonstrate how it can be tessellated without leaving gaps. Describe the pa>ern using the terminology learnt. Op0on 3 -‐ Draw a tessella-on pa>ern that uses ﬁve plane shapes and four colours. Describe the pa>ern using the terminology learnt