TwoDimensional Space 1
Outcomes
A student:

 MA21WM
uses appropriate terminology to describe, and symbols to represent, mathematical ideas

 MA23WM
checks the accuracy of a statement and explains the reasoning used

 MA215MG
manipulates, identifies and sketches twodimensional shapes, including special quadrilaterals, and describes their features
Content
 Students:
 Compare and describe features of twodimensional shapes, including the special quadrilaterals
 manipulate, compare and describe features of twodimensional shapes, including the special quadrilaterals: parallelograms, rectangles, rhombuses, squares, trapeziums and kites
 determine the number of pairs of parallel sides, if any, of each of the special quadrilaterals (Reasoning)
 use measurement to establish and describe side properties of the special quadrilaterals, eg the opposite sides of a parallelogram are the same length

identify and name the special quadrilaterals presented in different orientations, eg
 explain why a particular quadrilateral has a given name, eg 'It is a parallelogram because it has four sides and the opposite sides are parallel' (Communicating, Reasoning)
 name a shape, given a written or verbal description of its features (Reasoning)
 recognise the vertices of twodimensional shapes as the vertices of angles that have the sides of the shape as their arms
 identify right angles in squares and rectangles
 group parallelograms, rectangles, rhombuses, squares, trapeziums and kites using one or more attributes, eg quadrilaterals with parallel sides and right angles
 identify and describe twodimensional shapes as either 'regular' or 'irregular', eg 'This shape is a regular pentagon because it has five equal sides and five equal angles'

identify regular shapes in a group that includes irregular shapes, such as a regular pentagon in a group of pentagons, eg
(Reasoning)  explain the difference between regular and irregular twodimensional shapes (Communicating, Reasoning)
 recognise that the name of a shape does not change if its size or orientation in space is changed (Reasoning)
 draw representations of regular and irregular twodimensional shapes in different orientations
 construct regular and irregular twodimensional shapes from a variety of materials, eg cardboard, straws, pattern blocks
 determine that a triangle cannot be constructed from three straws if the sum of the lengths of the two shorter straws is less than the length of the longest straw (Reasoning)
 compare the rigidity of twodimensional frames of three sides with the rigidity of those of four or more sides
 construct and manipulate a foursided frame and explain how adding a brace can make a foursided frame rigid (Communicating, Reasoning)
 Identify symmetry in the environment (ACMMG066)
 identify lines of symmetry in pictures, artefacts, designs and the environment, eg Aboriginal rock carvings or Asian lotus designs
 identify and draw lines of symmetry on given shapes, including the special quadrilaterals and other regular and irregular shapes
 determine and explain whether a given line through a shape is a line of symmetry (Communicating, Reasoning)
 recognise and explain why any line through the centre of (and across) a circle is a line of symmetry (Communicating, Reasoning)
Background Information
The special quadrilaterals are the parallelogram, rectangle, rhombus, square, trapezium and kite.
Regular shapes have all sides equal and all angles equal. In Stage 2, students are expected to be able to distinguish between regular and irregular shapes and to describe a polygon as either regular or irregular, eg a regular pentagon has five equal sides and five equal angles.
It is important for students to have experiences with a variety of shapes in order to develop flexible mental images. Students need to be able to recognise shapes presented in different orientations.
When constructing polygons using materials such as straws of different lengths for sides, students should be guided to an understanding that: sometimes a triangle cannot be made from 3 straws; a figure made from 3 lengths, ie a triangle, is always flat; a figure made from 4 or more lengths need not be flat; a unique triangle is formed, if a triangle can be formed, from 3 given lengths; more than one twodimensional shape can result if more than 3 lengths are used.
When using examples of Aboriginal rock carvings and other Aboriginal art, it is recommended that local examples be used wherever possible. Consult with local Aboriginal communities and education consultants for such examples.
Language
Students should be able to communicate using the following language: shape, twodimensional shape (2D shape), circle, triangle, quadrilateral, parallelogram, rectangle, rhombus, square, trapezium, kite, pentagon, hexagon, octagon, regular shape, irregular shape, orientation, features, properties, side, parallel, pair of parallel sides, opposite, length, vertex (vertices), angle, right angle, symmetry, line (axis) of symmetry, rigid.
The term 'polygon' (derived from the Greek words meaning 'many angles') refers to closed shapes with three or more angles and sides. While the angles are the focus for the general naming system used for shapes, polygons are more usually understood in terms of their sides. Students are not expected to use the term 'polygon'. However, some students may explore other polygons and so benefit from being introduced to the collective term.
Students could explore the language origins of the names of polygons.
The term 'diamond' is often used in everyday contexts when describing quadrilaterals with four equal sides. However, 'diamond' is not the correct geometrical term to name such quadrilaterals; the correct term is 'rhombus'.
National Numeracy Learning Progression links to this Mathematics outcome
When working towards the outcome MA2‑15MG the subelements (and levels) of Understanding geometric properties (UGP2UGP4) 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:

 MA21WM
uses appropriate terminology to describe, and symbols to represent, mathematical ideas

 MA22WM
selects and uses appropriate mental or written strategies, or technology, to solve problems

 MA23WM
checks the accuracy of a statement and explains the reasoning used

 MA215MG
manipulates, identifies and sketches twodimensional shapes, including special quadrilaterals, and describes their features
Content
 Students:
 Compare and describe twodimensional shapes that result from combining and splitting common shapes, with and without the use of digital technologies (ACMMG088)

combine common twodimensional shapes, including special quadrilaterals, to form other common shapes or designs, eg combine a rhombus and a triangle to form a trapezium
 describe and/or name the shape formed from a combination of common shapes (Communicating)
 follow written or verbal instructions to create a common shape using a specified set of two or more common shapes, eg create an octagon from five squares and four triangles (Communicating, Problem Solving)
 use digital technologies to construct a design or logo by combining common shapes (Communicating)

split a given shape into two or more common shapes and describe the result, eg 'I split the parallelogram into a rectangle and two equalsized triangles'
 compare the area of the given shape with the area of each of the shapes it is split into, eg if a pentagon is split into five equal triangles, describe the area of the pentagon as five times the area of one triangle, or the area of one triangle as \(\frac{1}{5}\) of the area of the pentagon (Communicating, Reasoning)
 record the arrangements of common shapes used to create other shapes, and the arrangement of shapes formed after splitting a shape, in diagrammatic form, with and without the use of digital technologies

record different combinations of common shapes that can be used to form a particular regular polygon, eg a hexagon can be created from, or split into, many different arrangements, such as
(Communicating, Problem Solving)
 Create symmetrical patterns, pictures and shapes, with and without the use of digital technologies (ACMMG091)
 create symmetrical patterns, designs, pictures and shapes by translating (sliding), reflecting (flipping) and rotating (turning) one or more common shapes
 use different types of graph paper to assist in creating symmetrical designs (Communicating)
 use digital technologies to create designs by copying, pasting, reflecting, translating and rotating common shapes (Communicating, Problem Solving)
 apply and describe amounts of rotation, in both 'clockwise' and 'anticlockwise' directions, including halfturns, quarterturns and threequarterturns, when creating designs (Communicating, Problem Solving)
 describe the creation of symmetrical designs using the terms 'reflect', 'translate' and 'rotate' (Communicating, Reasoning)
 create and record tessellating designs by reflecting, translating and rotating common shapes
 use digital technologies to create tessellating designs (Communicating)
 determine which of the special quadrilaterals can be used to create tessellating designs (Reasoning)
 explain why tessellating shapes are best for measuring area (Communicating, Reasoning)
 identify shapes that do and do not tessellate
 explain why a shape does or does not tessellate (Communicating, Reasoning)
 draw the reflection (mirror image) to complete symmetrical pictures and shapes, given a line of symmetry, with and without the use of digital technologies
Background Information
Students should be given the opportunity to attempt to create tessellating designs with a selection of different shapes, including shapes that do not tessellate.
Language
Students should be able to communicate using the following language: shape, twodimensional shape (2D shape), triangle, quadrilateral, parallelogram, rectangle, rhombus, square, trapezium, kite, pentagon, hexagon, octagon, line (axis) of symmetry, reflect (flip), translate (slide), rotate (turn), tessellate, clockwise, anticlockwise, halfturn, quarterturn, threequarterturn.
In Stage 1, students referred to the transformations of shapes using the terms 'slide', 'flip' and 'turn'. In Stage 2, they are expected to progress to the use of the terms 'translate', 'reflect' and 'rotate', respectively.
National Numeracy Learning Progression links to this Mathematics outcome
When working towards the outcome MA2‑15MG the subelements (and levels) of Number patterns and algebraic thinking (NPA3), Interpreting fractions (InF3InF4) and Understanding geometric properties (UGP2UGP4) 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.