TwoDimensional Space 1
Outcomes
A student:

 MA31WM
describes and represents mathematical situations in a variety of ways using mathematical terminology and some conventions

 MA32WM
selects and applies appropriate problemsolving strategies, including the use of digital technologies, in undertaking investigations

 MA33WM
gives a valid reason for supporting one possible solution over another

 MA315MG
manipulates, classifies and draws twodimensional shapes, including equilateral, isosceles and scalene triangles, and describes their properties
Content
 Students:
 Classify twodimensional shapes and describe their features
 manipulate, identify and name rightangled, equilateral, isosceles and scalene triangles
 recognise that a triangle can be both rightangled and isosceles or rightangled and scalene (Reasoning)
 compare and describe features of the sides of equilateral, isosceles and scalene triangles
 explore by measurement side and angle properties of equilateral, isosceles and scalene triangles
 explore by measurement angle properties of squares, rectangles, parallelograms and rhombuses
 select and classify a twodimensional shape from a description of its features
 recognise that twodimensional shapes can be classified in more than one way, eg a rhombus can be more simply classified as a parallelogram (Communicating, Reasoning)
 identify and draw regular and irregular twodimensional shapes from descriptions of their side and angle properties
 use tools such as templates, rulers, set squares and protractors to draw regular and irregular twodimensional shapes (Communicating, Problem Solving)
 explain the difference between regular and irregular shapes (Communicating)
 use computer drawing tools to construct a shape from a description of its side and angle properties (Communicating, Problem Solving)
 Describe translations, reflections and rotations of twodimensional shapes (ACMMG114)
 use the terms 'translate', 'reflect' and 'rotate' to describe the movement of twodimensional shapes
 rotate a graphic or object through a specified angle about a particular point, including by using the rotate function in a computer drawing program (Communicating)
 describe the effect when a twodimensional shape is translated, reflected or rotated, eg when a vertical arrow is rotated 90°, the resulting arrow is horizontal
 recognise that the properties of shapes do not change when shapes are translated, reflected or rotated (Reasoning)
 Identify line and rotational symmetries (ACMMG114)
 identify and quantify the total number of lines (axes) of symmetry (if any exist) of twodimensional shapes, including the special quadrilaterals and triangles
 identify shapes that have rotational symmetry and determine the 'order' of rotational symmetry
 construct designs with rotational symmetry, with and without the use of digital technologies (Communicating, Problem Solving)
 Apply the enlargement transformation to familiar twodimensional shapes and explore the properties of the resulting image compared with the original (ACMMG115)
 make enlargements of twodimensional shapes, pictures and maps, with and without the use of digital technologies
 overlay an image with a grid composed of small squares (eg 5 mm by 5 mm) and create an enlargement by drawing the contents of each square onto a grid composed of larger squares (eg 2 cm by 2 cm) (Communicating, Problem Solving)
 investigate and use functions of digital technologies that allow shapes and images to be enlarged without losing the relative proportions of the image (Problem Solving)
 compare representations of shapes, pictures and maps in different sizes, eg student drawings enlarged on a photocopier
 measure an interval on an original representation and its enlargement to determine how many times larger than the original the enlargement is (Problem Solving, Reasoning)
Background Information
A shape has rotational symmetry if a tracing of the shape, rotated part of a full turn around its centre, matches the original shape exactly.
The order of rotational symmetry refers to the number of times a figure coincides with its original position in turning through one full rotation, eg
'Scalene' is derived from the Greek word skalenos, meaning 'uneven'; our English word 'scale' is derived from the same word. 'Isosceles' is derived from the Greek words isos, meaning 'equals', and skelos, meaning 'leg'. 'Equilateral' is derived from the Latin words aequus, meaning 'equal', and latus, meaning 'side'. 'Equiangular' is derived from aequus and another Latin word, angulus, meaning 'corner'.
Language
Students should be able to communicate using the following language: shape, twodimensional shape (2D shape), triangle, equilateral triangle, isosceles triangle, scalene triangle, rightangled triangle, quadrilateral, parallelogram, rectangle, rhombus, square, trapezium, kite, pentagon, hexagon, octagon, regular shape, irregular shape, features, properties, side, parallel, pair of parallel sides, opposite, length, vertex (vertices), angle, right angle, line (axis) of symmetry, rotational symmetry, order of rotational symmetry, translate, reflect, rotate, enlarge.
A 'feature' of a shape or object is a generally observable attribute of a shape or object. A 'property' of a shape or object is an attribute that requires mathematical knowledge to be identified.
National Numeracy Learning Progression links to this Mathematics outcome
When working towards the outcome MA3‑15MG 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:

 MA31WM
describes and represents mathematical situations in a variety of ways using mathematical terminology and some conventions

 MA32WM
selects and applies appropriate problemsolving strategies, including the use of digital technologies, in undertaking investigations

 MA315MG
manipulates, classifies and draws twodimensional shapes, including equilateral, isosceles and scalene triangles, and describes their properties
Content
 Students:
 Investigate the diagonals of twodimensional shapes
 identify and name 'diagonals' of convex twodimensional shapes
 recognise the endpoints of the diagonals of a shape as the vertices of the shape (Communicating)
 determine and draw all the diagonals of convex twodimensional shapes
 compare and describe diagonals of different convex twodimensional shapes
 use measurement to determine which of the special quadrilaterals have diagonals that are equal in length (Problem Solving)
 determine whether any of the diagonals of a particular shape are also lines (axes) of symmetry of the shape (Problem Solving)
 Identify and name parts of circles
 create a circle by finding points that are all the same distance from a fixed point (the centre)
 identify and name parts of a circle, including the centre, radius, diameter, circumference, sector, semicircle and quadrant
 Investigate combinations of translations, reflections and rotations, with and without the use of digital technologies (ACMMG142)
 identify whether a twodimensional shape has been translated, reflected or rotated, or has undergone a number of transformations, eg 'The parallelogram has been rotated clockwise through 90° once and then reflected once'
 construct patterns of twodimensional shapes that involve translations, reflections and rotations using computer software
 predict the next translation, reflection or rotation in a pattern, eg 'The arrow is being rotated 90° anticlockwise each time'
 choose the correct pattern from a number of options when given information about a combination of transformations (Reasoning)
Background information
When drawing diagonals, students need to be careful that the endpoints of their diagonals pass through the vertices of the shape.
Language
Students should be able to communicate using the following language: shape, twodimensional shape (2D shape), circle, centre, radius, diameter, circumference, sector, semicircle, quadrant, triangle, equilateral triangle, isosceles triangle, scalene triangle, rightangled triangle, quadrilateral, parallelogram, rectangle, rhombus, square, trapezium, kite, pentagon, hexagon, octagon, regular shape, irregular shape, diagonal, vertex (vertices), line (axis) of symmetry, translate, reflect, rotate, clockwise, anticlockwise.
A diagonal of a twodimensional shape is an interval joining two nonadjacent vertices of the shape. The diagonals of a convex twodimensional shape lie inside the figure.
National Numeracy Learning Progression links to this Mathematics outcome
When working towards the outcome MA3‑15MG the subelements (and levels) of Number patterns and algebraic thinking (NPA3) and Understanding geometric properties (UGP4) 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.