Week+8+-+Transformations+and+symmetry

__**Learning Activity 8.1: Exploring tessellations**__

//Mathematics challenge: Achor 15/07/2011//

Rhombus and triangles Rhombus and hexagons Rhombus and rhombus Trapezium and rhombus Trapezium and triangles Trapezium and hexagons
 * Which of the pattern block pieces tessellate? Hexagons, squares, triangles, rhombus, trapezium
 * Find at least three distinct patterns for the way a rhombus can tessellate (the blue pattern block piece).
 * How many distinct ways are there to form a tessellation with the trapezium (the red pattern block piece)?

__**Learning Activity 8.2: Learning and teaching symmetry and transformations**__

//Learning Activity 8.2 Record Chart: Learning and teaching symmetry and transformations//
 * **Ideas and examples that are //familiar// to me from my own experiences with mathematics learning and teaching** || **Ideas and examples related to mathematics learning and teaching that are //new// to me** ||
 * - Can test for symmetry by folding paper in half or using mirror. || - Transformations process by which shape is transformed, rather than new shape.- Shapes can be transformed by sliding, flipping (reflection), or turning (rotating).- Children can make transformation patterns using pattern block pieces.- Tessellations are exciting & motivating for children p.455.- Children should understand tessellations uses pattern rather than random placing of shapes.- Can make Escher like tessellations using square paper, cutting out section and replacing section on opposite side.- Children may have difficulties with lines of symmetry at angles, rather than verticle. ||
 * **Questions I have and related things I do not understand from my reading**(See if any of your //Maths Mates Group// have any ideas for you in answering one of these questions.) ||

//Achor 15/07/2011//


 * **Ideas and examples that are //familiar// to me from my own experiences with mathematics learning and teaching** || **Ideas and examples related to mathematics learning and teaching that are //new// to me** ||
 * * One form a transformation is translation.
 * Tessellations are a great way to study the properties of shapes and learn about patterns.
 * Symmetrical shapes are used to create architecture
 * The easiest method to test if a shape is symmetrical is to draw or fold a line right down the middle. || * Enlargement is also a form of transformation. As well as dilation.
 * Patterns are mostly generated through turns according to different angles. ||
 * **Questions I have and related things I do not understand from my reading**(See if any of your //Maths Mates Group// have any ideas for you in answering one of these questions.) ||

__**Learning Activity 8.3:** //**Tessellation Treasure Chest**//__

**Part A** - Cronulla honeycomb - Paving in mall - Lattice in garden

**Part B** Outline a mathematics learning activity for children that would use tessellation examples from their //Tessellation Treasure Chest// to develop an aspect of //symmetry//. - Find symmetry of shapes using mirror & explain why they placed line where they did. - Find symmetry of shapes by folding paper & explain why they placed line where they did. - Classify the shapes according to symmetry - Recreate another paving option using rangoli patterns - Give students pieces of cards using shapes in treasure chest, and have them recreate symmetrical shapes. Outline a mathematics learning activity for children that would use tessellation examples from their //Tessellation Treasure Chest// to develop an aspect of //transformations.// use block pieces to create patterns using forms of transformation. Create an artwork by using rotation / translation / reflection

Vicki 15/7/11

Achor 15/07/11 Part A • Tiling in the bathroom • Brick wall • Patchwork quilt Part B

Students are to create a mosaic using shapes that tessellate. This can be a cross curriculum activity of maths and visual arts. Students are asked to investigate a large group of cut out shapes and come up with at least one transformation possibility for each shape.
 * 1) Outline a mathematics learning activity for children that would use tessellation examples from their //Tessellation Treasure Chest// to develop an aspect of //symmetry//.
 * 1) Outline a mathematics learning activity for children that would use tessellation examples from their //Tessellation Treasure Chest// to develop an aspect of //transformations.//

__**Learning Activity 8.4: Further developing your teaching ideas**__

Achor 15/07/11 Tessellations by transforming shapes Can sliding the same shape or mirroring the same shape create tessellations? Remember tessellations have no gaps and do not overlap eachother.

**__Learning Activity 8.5 Assessment 1__**

Achor 15/07/11 Using ICT (Information communication technology) in mathematical lessons not all puts the students in control for creating their own learning it also allows the teacher to become the facilitator instead of the demonstrator or instructor. Tessellations are a great opportunity for teacher to do cross curriculum activities especially with visual art. The ancient Greeks knew the mathematical and artistic properties of shapes (Booker, et al, 2010) and often used it to create architecture and art pieces. Students can have a fun time learning about shapes using the computer due to the fact it allows them to experiment and learn valuable technical skills in IT.

As a group try to identify 6 essential things for your Treasure Chest. What would they be? Lia has mentioned on the DB that she won't be able to do this week's submission. Any takers???

**Here is what I have so far! Hopefully we can all get something together for this week. **

** As a group try to identify 6 essential things for your treasure chest. What would they be? ** ** A wide variety of mediums that provide both hands on activity as well as engagement of deeper learning is a necessity when learning about tessellation. Research has shown that the use of physic materials, including paper models, plastic or wooden geometric shapes, geo boards and solids can be helpful in developing geometric representations (Clements, 2004 as cited in Reys, et. al, 2009, p. 351). Having these various mediums available in the treasure chest will allow for the teacher to cover a diverse range of understandings. Using the paint and paper is suited to younger students; this typically would involve placing various blobs of paint in the middle of a piece of paper, folding it in half to create a symmetrical picture or butterfly. Dot paper, sheet cut outs of the alphabet and plastic shapes provide opportunity to create tessellations and explore the effects of various skills associated with geometry such as rotation, translation and reflection as well as requiring students to find symmetry. Also the use of ICT programs allows students to work interactively with numerous programs and websites and make their own tessellations and patterns in a fun and relatable way. For example the computer program ‘Tesselmania’ could be used to allow students to explore and make their own discoveries. **
 * 1) ** Paint and paper **
 * 2) ** Dot paper **
 * 3) ** Sheet cut outs with letters of the alphabet **
 * 4) ** Plastic shapes **
 * 5) ** Geo Boards **
 * 6) ** Tessellation programs on the computer **

** Reys, R., Lindquist, M., Lambdin, D., & Smith, N. (2009). //Helping children learn mathematics// (9th ed.). Hoboken, New Jersey: John Wiley & Sons **

** Sarah Wright 19.7.11 **

**As a group try to identify 6 essential things for your treasure chest. What would they be?**
 * 1) **Photo of honeycomb from a beehive**
 * 2) **Tesselated tiles used for paving**
 * 3) **Images of animal tesselations from artists namely Escher**
 * 4) **Tangram puzzles**
 * 5) **Wallpaper patterns**
 * 6) **Tessellation activities to see what fits and doesn't fit**

Using physical and pictorial materials is an effective way for students to develop visualization and spatial reasoning. Using tangible objects especially from nature helps children to visualise tesselation patterns in a everyday life. This encourages them to look for meanings in patterns in their daily lives without having to look far. Manipulating shapes and rearranging them helps students to visualize geometric shapes and properties (Reys, Lindquist, Lambdin, & Smith, 2009). Adam T 20/07

1. 3D representations such as tins, cereal boxes, toblerone packets, matchstick and popstick models that students can see through. 2. 2D template shapes. 3. Geoboard (and string!) 4. Illuminations website 5. Graph paper 6. Examples of prior work

The first three suggestions are included as "geometry is very visual" (Booker, Bond, Sparrow & Swan, 2010, p. 400). Using visual aids that are also manipulatives allows children a more hands on experience towards mathematics. The fourth, the illuminations website, is included for its diversity in activites offered. Using the website also encourages the use of ICT in mathematics, which is supported by the Australian Curriculum. Graph paper is included as this may be a medium the children use in drawing their own representations of whatever concept they are studying at the time, whether it be shape, space, measurement etc The sixth, and final suggestion, is included so that children can see the improvement they have made in their learning. This may be particularly useful for children who begin to doubt their own knowledge at times. If a student reverts towards learned helplessness on a concept that they have prior shown understanding in, looking back at prior work where they have shown understanding may be of use to bolster their confidence (Reys, Lindquist, Lambdin & Smith, 2009).

Reference:

Booker, G., Bond, D., Sparrow, L. & Swan, P. (2010). //Teaching Primary Mathematics,// (4th Ed.). Frenchs Forest, New South Wales : Pearson Australia

Reys, R. Lindquist, M., Lambdin. D, & Smith. N, (2009). //Helping Children Learn Mathematics,// (9th Ed.). Hoboken, New Jersey : John Wiley and Sons

Suzanne 21/07/2011

**As a group try and identify six essential things for your treasure chest? What would they be?**

1. Cookie cutters that tesselate so children can draw around them to create a tessellation.

2. Pictures of tessellations in text books.

3. View tessellations by Escher.

4. Digital cameras so children can take their own photos of tessellations.

5. Interactive tessellation activities on the computer. For example, Illuinations or The Learning Federation sites.

6. Cuisenaire rods to challenge children to design their own paving patterns.

Kerrie Wyer 22/7/11.

As no-one has put their hand up to do this week's collation, I've put something together based on the four submissions. Can anyone who looks at the page please have a look through, check spelling, grammar, sentence structure, referencing etc. If I have stepped on anyone's toes by doing this, sorry - but I really didn't want to get to tomorrow night and not have a submission ready for the week. Cheers, Suzanne 23/07/2011

A wide variety of mediums that provide both hands on activity as well as engagement of deeper learning is a necessity when learning about tessellation. Research has shown that the use of physic materials, including paper models, plastic or wooden geometric shapes, geo boards and solids can be helpful in developing geometric representations (Clements, 2004 as cited in Reys, et. al, 2009, p. 351). With this in mind, these are the six items from a student's treasure chest that we have come up with:

1. 3D representations such as tins, cereal boxes, toblerone packets, matchstick and popstick models that students can see through. 2. 2D template shapes. 3. Geoboard 4. Tangram puzzles 5. Websites, such as Illuminations and The Leaning Federation 6. Images of tessellations, including those of Escher

The first four suggestions are included as "geometry is very visual" (Booker, Bond, Sparrow & Swan, 2010, p. 400). Using visual aids that are also manipulatives allows children a more hands on experience towards mathematics. To manipulate shapes and rearrange them helps students to visualise geometric shapes and their properties (Reys, Lindquist, Lambdin, & Smith, 2009). Also by having these various mediums available in the treasure chest allows for the teacher to demonstate and cover a diverse range of concepts and understandings.

The fifth, websites that promote mathematical learning, are included for the diversity in activites that the websites offered. Use of ICT in mathematics, (among other subject areas) is also supported by the Australian Curriculum.

Tessellation images have been included as using pictorial materials is an effective way for students to develop visualisation and spatial reasoning. Using images, particularly from nature can help children to see tessellation in their daily lives. This in turn encourages students to look for meanings in patterns without having to look far.