Week Nine: Geometry

Week Nine Space (Geometry)
Big Ideas	Geometry: •          An organized, logical and coherent system for the study of shape, space and measurement. It is as old as civilization itself! It is one of the earliest forms of mathematics (e.g., navigation by the stars, Egyptian & Aztec pyramids, Roman aqueducts) •          Geometry involves the study of 1D (lines), 2D (planes) & 3D (solid) shapes. Bloom’s taxonomy : 1        Knowledge: rote reproduction of the correct response (know formulae / rules); 2        Comprehension: explaining the response in the student’s words (understand formulae); 3        Application: applying the knowledge to a practical situation (area of classroom); 4        Analysis: to be able to isolate the crucial components of the knowledge (a square has…); 5        Synthesis: recombining elements to yield new knowledge (use area of a rectangle knowledge to create formulae for area of a circle); 6        Evaluation: applying higher order principles to test the worth of the new knowledge (Am I right? How do I know? Where’s my proof?).
Demonstrate concept skills and strategies	Concept: geometry is seeing different shapes that are 1D, 2D, 3D and knowing their mathematical shape. The measurement of shape, space and measurement Skills: there are skills to each different dimension of shapes as well as to each individual shape. Working out their area, perimeter, volume Strategies: using formulas to work out the dimensions of the different shapes by looking at the shapes and being able to offhand work out these dimensions.
Demonstrate Language model
Demonstrate/ describe teaching strategies	http://nrich.maths.org/content/id/4832/polygons.swf Starting with tessellation makes learning about the shapes art as they are making a pattern through the shapes while starting with easy and small shapes. This can then me moved onto a real world situation that can be done in the classroom as well as having students looking at shapes at home and how they could make a pattern out of shapes from home (2016).
Describe misconception	Prisms and pyramids. These two different types of shapes usually get mixed together and course a misconception as they are alike in name and share some same attributes. This extends onto educators spending time with students on these shapes and this can be done with making shapes out of paper and learning their nets as students are able to get physical experiences of the shapes with sensory motor gaining a deeper understanding. This is through students exploring what the shapes looks like in different forms as well as are able to play with the shape and find out what it can do.
ACARA	Mathematics / Foundation Year / Measurement and Geometry / Shape / ACMMG009 Sort, describe and name familiar two-dimensional shapes and three-dimensional objects in the environment Elaborations sorting and describing squares, circles, triangles, rectangles, spheres and cubes  (Australian Curriculum and Assessment Reporting Authority [ACARA], 2014)
Resources and ideas	Below is an online game for students to play and work with while further extending their knowledge and having a deeper understanding about the shapes using this game. This is because students are able to play with the shapes learning about rotation and exploring the net of each shape such as the cube. If not able to print the net it could be made by the students. ("3-D Shapes", 2016) Paper folding is an exploring activity with students learning how to make each shape with a deep understanding and then are able to make art and explore what they can create with their shapes, such as the link below has links to 2d and 3d shapes outlines for printing. ("Geometric Shapes To Print, Cut, Color and Fold", 2016).
Concise synthesis textbook	Primary mathematics has a primary element of students having a understanding of the properties or attributes of objects and the relationship among the geometric shape. Students learning about shapes involves them learning about symmetry, length of sides, size of angles, parallel and perpendicular sides, convex and concave shapes, altitude, classification schemes, number of sides and vertices. Geometry also deals with location, movement, maps, and plans which further describe direction, distance and position. Having students examining location and movement gives meaning to their world by them describing these elements and give order to their surroundings.
References	3-D Shapes. (2016). Bgfl.org. Retrieved 29 May 2016, from http://www.bgfl.org/bgfl/custom/resources_ftp/client_ftp/ks2/maths/3d/index.htm         (2016). Nrich.maths.org. Retrieved 29 May 2016, from http://nrich.maths.org/content/id/4832/polygons.swf          Australian Curriculum and Assessment Reporting Authority. (2014). Foundation to Year 10 Curriculum: Language, Language for Interaction (ACELA1428). Retrieved from http://www.australiancurriculum.edu.au/english/Curriculum/F10?y=F&y=7&y=8&y=9&y=10&s=LA&s=LT&s=LY&layout=1          Reys, R. (2012). Helping students learn mathematics (pp. 139-163). Milton, QLD: WILEY. Geometric Shapes To Print, Cut, Color and Fold. (2016). Fun-stuff-to-do.com. Retrieved 29 May 2016, from http://www.fun-stuff-to-do.com/geometric-shapes-to-print.html

Week Eight: Measurement concept and skills: focusing on perimeter

Week Eight 1.      Measurement concepts and skills; 2.      Teaching sequence for measurement; and  3. Common physical and geometric measures.
Big Ideas	Through measurement being included in the classroom is giving students a hands on approach to learning how mathematics is practical, further developing other mathematical ideas. Because of this measurement in the classroom can be a fun experience that’s educational and can be extended off and linked into the real world. importance of measurement concepts and skills 1        Essential in everyday life e.g., money, time 2        Links number knowledge to spatial situations e.g., measuring volumes, areas, lengths and angles 3        Provides interesting, life-like problem-solving opportunities e.g., which chocolate is the best value? How many meters of tiles will cover my kitchen floor? Connects mathematics with other curriculum areas
Demonstrate concept skills and strategies	Concept: calculating perimeter of the outside of shape Skills: being first able to use an item near the student and using that item to measure, further extending onto calculating a perimeter of whole elements. Strategies: by first learning how to measure with using everyday items gives students a foreground to build their knowledge upon.
Demonstrate Language model
Demonstrate/ describe teaching strategies	The below activity gives students a hands on approach to learning perimeter that can be measured with items that are only on their desk, opening their minds up to how items can be measured and with what measurement tool (Reys, 2012).
Describe misconception	Some students are able to measure 8cm although are not able to draw 8cms. Doing activities as below asking students on grid paper to make a shape of 8 squares and then counting the outside of the shape. This further develops their knowledge of perimeter while becoming confident in their measuring skills (Reys,2012).
ACARA	Mathematics / Foundation Year / Measurement and Geometry / Using units of measurement / ACMMG006  (Australian Curriculum and Assessment Reporting Authority [ACARA], 2014)
Resources and ideas	http://www.connectionslearning.com/_public/flash/geoboard/geoboard.swf The above link contains virtual Geoboards, this boards can also be a hard copy resource in the classroom. The Geoboards allows students to make basic shapes and then further extending on to creative shapes and working out their perimeter.
Concise synthesis textbook	Measurement together with geometry is one of the three strands from the Australian Curriculum (ACARA, 2014). Measuring process consists of identifying the events and attribute, measuring with informal and then standard units and then extending onto applying measurement to real world situations.
References	Australian Curriculum and Assessment Reporting Authority. (2014). Foundation to Year 10 Curriculum: Language, Language for Interaction (ACELA1428). Retrieved from http://www.australiancurriculum.edu.au/english/Curriculum/F10?y=F&y=7&y=8&y=9&y=10&s=LA&s=LT&s=LY&layout=1          Reys, R. (2012). Helping students learn mathematics (pp. 139-163). Milton, QLD: WILEY.          Virtural Geoboards. (2016). Connectionslearning.com. Retrieved 29 May 2016, from http://www.connectionslearning.com/_public/flash/geoboard/geoboard.swf