TwoDimensional Space 1
Outcomes
A student:

 MA11WM
describes mathematical situations and methods using everyday and some mathematical language, actions, materials, diagrams and symbols

 MA13WM
supports conclusions by explaining or demonstrating how answers were obtained

 MA115MG
manipulates, sorts, represents, describes and explores twodimensional shapes, including quadrilaterals, pentagons, hexagons and octagons
Content
 Students:
 Recognise and classify familiar twodimensional shapes using obvious features (ACMMG022)
 identify vertical and horizontal lines in pictures and the environment and use the terms 'vertical' and 'horizontal' to describe such lines
 relate the terms 'vertical' and 'horizontal' to 'portrait' and 'landscape' page orientation, respectively, when using digital technologies (Communicating)
 identify parallel lines in pictures and the environment and use the term 'parallel' to describe such lines
 recognise that parallel lines can occur in orientations other than vertical and horizontal (Reasoning)
 give everyday examples of parallel lines, eg railway tracks (Reasoning)
 manipulate, compare and describe features of twodimensional shapes, including triangles, quadrilaterals, pentagons, hexagons and octagons
 describe features of twodimensional shapes using the terms 'side' and 'vertex' (Communicating)
 sort twodimensional shapes by a given attribute, eg by the number of sides or vertices
 explain the attribute used when sorting twodimensional shapes (Communicating, Reasoning)

identify and name twodimensional shapes presented in different orientations according to their number of sides, including using the terms 'triangle', 'quadrilateral', 'pentagon', 'hexagon' and 'octagon', eg

recognise that the name of a shape does not change when the shape changes its orientation in space, eg a square turned on its vertex is still a square
(Communicating, Reasoning)  select a shape from a description of its features (Reasoning)
 recognise that shapes with the same name may have sides of equal or different lengths (Reasoning)
 recognise that rectangles and squares are quadrilaterals
 identify and name shapes embedded in pictures, designs and the environment, eg in Aboriginal art
 use computer drawing tools to outline shapes embedded in a digital picture or design (Communicating)
Background Information
Manipulation of a variety of real objects and shapes is crucial to the development of appropriate levels of visualisation, language and representation.
The skills of discussing, representing and visualising threedimensional objects and twodimensional shapes are developing in Stage 1 and must be fostered through practical activities and communication. It is important that students have experience involving a broad range and variety of objects and shapes in order to develop flexible mental images and language.
Students need to be able to recognise shapes presented in different orientations. They need to develop an understanding that changing the orientation of a shape does not change its features or its name. In addition, students should have experiences identifying both regular and irregular shapes, although it is not expected that students understand or distinguish between regular and irregular shapes in Stage 1. Regular shapes have all sides and all angles equal.
Many shapes used in Aboriginal art are used with specific meanings. Local Aboriginal communities and many education consultants can provide examples. Further exploration of such meanings could be incorporated in students' studies within the Creative Arts Key Learning Area.
Language
Students should be able to communicate using the following language: shape, circle, triangle, quadrilateral, square, rectangle, pentagon, hexagon, octagon, orientation, features, side, vertex (vertices), vertical, horizontal, portrait (orientation), landscape (orientation), parallel.
The term 'vertex' (plural: vertices) refers to the point where two straight sides of a twodimensional shape meet (or where three or more faces of a threedimensional object meet).
The term 'shape' refers to a twodimensional figure. The term 'object' refers to a threedimensional figure.
National Numeracy Learning Progression links to this Mathematics outcome
When working towards the outcome MA1‑15MG the subelements (and levels) of Understanding geometric properties (UGP2) describe observable behaviours that can aid teachers in making evidencebased decisions about student development and future learning.
The progression subelements and indicators can be viewed by accessing the National Numeracy Learning Progression.
TwoDimensional Space 2
Outcomes
A student:

 MA11WM
describes mathematical situations and methods using everyday and some mathematical language, actions, materials, diagrams and symbols

 MA115MG
manipulates, sorts, represents, describes and explores twodimensional shapes, including quadrilaterals, pentagons, hexagons and octagons
Content
 Students:
 Describe and draw twodimensional shapes, with and without the use of digital technologies (ACMMG042)
 use the term 'twodimensional' to describe plane (flat) shapes
 make representations of twodimensional shapes in different orientations using concrete materials
 combine and split single shapes and arrangements of shapes to form new shapes, eg create a hexagon from six triangles (Communicating)
 draw and name twodimensional shapes in different orientations, with and without the use of digital technologies
 recognise that the name of a shape does not change if its size or orientation in space is changed (Reasoning)
 Investigate the effect of onestep slides and flips, with and without the use of digital technologies (ACMMG045)
 identify a onestep slide or flip of a single shape and use the terms 'slide' and 'flip' to describe the movement of the shape
 perform a onestep slide or flip with a single shape
 recognise that sliding or flipping a shape does not change its size or features (Reasoning)
 describe the result of a onestep slide or flip of a shape, eg 'When I flip the shape, it is the same but backwards' (Communicating)
 record the result of performing onestep slides and flips, with and without the use of digital technologies
 copy and manipulate a shape using the computer functions for slide and flip (Communicating)
 make designs with line symmetry using paperfolding, pattern blocks, drawings and paintings
 recognise the connection between line symmetry and performing a flip (Reasoning)
 Identify and describe halfturns and quarterturns (ACMMG046)
 identify full, half and quarterturns of a single shape and use the terms 'turn', 'fullturn', 'halfturn' and 'quarterturn' to describe the movement of the shape
 identify and describe amounts of turn using the terms 'clockwise' and 'anticlockwise'
 perform full, half and quarterturns with a single shape
 recognise that turning a shape does not change its size or features (Reasoning)
 describe the result of a turn of a shape, eg 'When the shape does a halfturn, it is the same but upsidedown' (Communicating)
 record the result of performing full, half and quarterturns of a shape, with and without the use of digital technologies
 copy and manipulate a shape using the computer function for turn (Communicating)
 determine the number of halfturns required for a fullturn and the number of quarterturns required for a fullturn
 connect the use of quarter and halfturns to the turn of the minute hand on a clock for the passing of quarter and halfhours (Communicating, Reasoning)
Background Information
In Stage 1, students need to have experiences involving directions and turning. Discussions about what represents a 'fullturn', a 'halfturn' and a 'quarterturn' will be necessary. Relating this information to students physically may be helpful, eg by playing games such as 'Simon Says' with Simon saying to make turns.
Digital technologies such as computer drawing tools may use the terms 'move', 'rotate' and 'flip horizontal', or various other terms, to describe transformations. The icons for these functions may assist students in locating the required transformations.
Language
Students should be able to communicate using the following language: shape, twodimensional shape (2D shape), circle, triangle, quadrilateral, square, rectangle, pentagon, hexagon, octagon, orientation, features, symmetry, slide, flip, turn, fullturn, halfturn, quarterturn, clockwise, anticlockwise.
In Stage 1, students refer to the transformations of shapes using the terms 'slide', 'flip' and 'turn'. While in Stage 2, students are expected to use the terms 'translate', 'reflect' and 'rotate', respectively.
Linking the vocabulary of halfturns and quarterturns to students' experiences with clocks may be of benefit.
A shape is said to have line symmetry if matching parts are produced when it is folded along a line of symmetry. Each part represents the 'mirror image' of the other.
National Numeracy Learning Progression links to this Mathematics outcome
When working towards the outcome MA1‑15MG the subelements (and levels) of Interpreting fractions (InF1) and Understanding geometric properties (UGP2UPG4) describe observable behaviours that can aid teachers in making evidencebased decisions about student development and future learning.
The progression subelements and indicators can be viewed by accessing the National Numeracy Learning Progression.