Week+8+-+Transformations+and+symmetry

Cutting out pattern blocks and using them to form tessellations - patterns with no gaps.
 * Learning Activity 8.1 - Forming tessellation from pattern blocks**

Reading from Booker et al. p.455-465 ** Examples of tessellation in life:
 * Learning Activity 8.2 - Reading
 * **'Tessellation work can be a good vehicle for the application of spatial ideas and solving realistic problems .' i.e. the use of coloured rods to invent 'brick' patterns such as those found in walls, driveways, tiling. Students are to make a variety of patterns. **
 * ** cultural tessellations - Islamic patterns, spanish patterns, art (Escher tesselations, anmals/bird tiles) **
 * Symmetry - Analysis of symmetrical properties of polygons - tasks using a vertical line of symmetry to develop further aspects of bilateral symmetry in order make students aware of reflection lines (horizontal to the foot of the page, at an angle to it) and the fact that more than two lines of symmetry may exist in shapes. (p.461) - sorting alphabet letters by their line of symmetry (bilateral, rotational)
 * Location and arrangement - position, arrangement, direction - grids/maps.
 * 'Teaching geometry is not a matter of passing on information; it should assist children to develop processes of observation analysis, description, classification, visualization, representation, exploration and interference. (p. 469)'
 * Taken from Reys et al., 2009 -
 * Types of transformation : translation (slide), rotation (turn), reflection (flip).
 * Learning Activity 8.3 - Tessellation treasure chest
 * ** ** my rug in the lounge ** **
 * pineapples
 * ** ** butterflies ** **
 * turtle/tortoise shells
 * snail shells

A lesson to introduce //symmetry// might involve mirrors. Students could use mirrors to see if the symmetrical image in the mirror is the same as the one on the object. Could also use paint to make symmetrical butterflies (younger students).

A lesson to introduce //transformation// may involve students identifying the type of transformation shown in their 'treasure chest' patterns. They would need to sort them into reflection, rotation and translation, and justify their reasons why.

**Symmetry lesson:** Identify the symmetrical images in the photo. ** ** ** ** ** (The sink/taps are symmetrical, is the face?, the pattern of the mirror handle).** ** ** What type of symmetry is it? ** ** ** ** ** ** ** ** **** Where are the lines of symmetry? Are there more than one for some objects?
 * Learning Activity 8.4 -** **Further developing of lessons

Explore the 'shape tool' game from the illuminations website. Create combinations of shapes to form tessellations that have different characteristics (symmetrical, rotational transformation etc.). Similar to those provided with the activity: ** ** // 1. Unit learning outcome(s) for which this item provides evidence of learning // (type these out in words; do not identify by a number only) //**
 * Tessellation and patterns lesson:**
 * Can you use only orange squares and green triangles to create a regular pattern that tessellates?
 * What about yellow hexagons and orange squares?
 * …red trapezoids and blue parallelograms?
 * …blue parallelograms and pink rhombi?
 * //PLR 8
 * Identify, describe and apply effective teaching strategies for teaching mathematics.

2. **Description/outline of what you have learned and how this learning demonstrates the learning outcomes you have specified above**

At the conclusion of week's reading (Booker et al, 2009, p. 455-465), the multiple skills that learning geometry teaches students were summarized; '** ** ** processes of observation, analysis, description, classification, visualisation, representation, exploration and interference' (Booker et al, 209, p. 469). ** This allowed me the opportunity to once again realise the importance of teaching geometry in all areas of life, and the ability to articulate the reasons why geometry is taught. ** ** ** ** Learning activity 8.3 required the formulation of lesson plans regarding tessellation treasure chests. In order to help me, I resourced online lesson examples (www.etacuisenaire.com, [|illuminations.nctm.org]), then based my lessons on these examples. To do this, I had to revise how students best learn geometry, ways that help to facilitate this, and incorporate them into appealing lesson plans. They may use everyday items such as those found in the treasure chest (matchboxes, tiles) or more traditional manipulatives, such as blocks and cuisenaire rods.

A new idea was introduced in this weeks learning: types of transformation. This includes rotation, reflection and translation. These ideas were further consolidated by formulating lesson plans to teach these concepts.


 * 3.** **How this learning relates to your development as an effective primary mathematics teacher.

'Teaching geometry is not a matter of passing on information; it should assist children to develop processes of observation, analysis, description, classification, visualisation, representation, exploration and interference' (Booker et al, 2009, p. 469). This succinct explanation defines the reasons why geometry is taught in schools. Before studying the aspects of teaching geometry, I had thought the geometry was about angles, protractors and triangles. Now I have learned that there is much more to geometry: spatial concepts, the ability to describe, classify and represent information, as well as many other much-needed life skills.

Developing lesson plans, such as those in activity 8.3, allow me to use the theory that I learn to formulate lesson plans practical in their application. The skill to create lesson plan will be much needed and regularly utilized in my career as a teacher. To effectively teach my students, I will need to transfer the things I learn, into interactive lessons that are rich in content.

My own understand of transformational patterns was enhanced through the learning activities 8.3 and 8.4 this week. 'If students are asked to make conjunctures and justify their thinking, they develop a deeper understanding of the transformations' (Reys et al., 2009). This is what happened to me this week; to define each type of transformation, I had to compare the differences in examples of each pattern type. Using the activity on the illuminations website in conjunction with the learning activities, I was able to learn a new concept in much the same way students will. **