0.5

At 0.5, the work of a student progressing towards the standard at Level 1 demonstrates, for example:

• sorting of objects according to shape
• matching of shapes to solve puzzles; for example, jigsaw puzzles
• naming of common two-dimensional objects according to geometrical shape
• use of the terms next to, beside or in front of to describe their own location relative to other students
• sequences of movements following simple directions

• Recognising, comparing, sorting and matching shapes

1.0 Standard

At Level 1, students recognise, copy and draw points, lines and simple free-hand curves. They identify basic two-dimensional shapes such as triangles, circles and squares and three-dimensional solids and objects such as boxes and balls. They recognise the interior and exterior of shapes and objects. They sort geometric objects according to simple descriptions. They place and orientate shapes according to simple descriptions such as next to , beside, in front of, behind, over and under.

They develop and follow simple instructions to move and place shapes and objects in familiar situations in relation to what they can see, and to move themselves from one place to another.

• Developing the everyday language of location

1.25

At 1.25, the work of a student progressing towards the standard at Level 2 demonstrates, for example:

• recognition of lines, corners and boundaries in two-dimensional shapes
• classification of shapes according to number of sides
• representation of squares, rectangles, circles and triangles using freehand drawing, templates and technology
• recognition and naming of spheres and cubes
• identification of main features on local maps

1.5

At 1.5, the work of a student progressing towards the standard at Level 2 demonstrates, for example:

• recognition of congruence of two shapes
• identification of shapes with symmetry
• labelling and use of points on diagrams to specify lines, corners and boundaries
• sorting of objects onto a venn diagram labelled with shape information
• production of similar figures by enlargement

• Folding and Symmetry

1.75

At 1.75, the work of a student progressing towards the standard at Level 2 demonstrates, for example:

• recognition of whether a single transformation produces a congruent or similar shape
• identification of the important features of two-dimensional shapes and use of these distinguishing features to compare and contrast various shapes
• production of simple patterns with transformations (flips, slides, turns)
• specification of instructions for movement, including relative position and quarter turns left and right
• decomposition of three-dimensional shapes into their respective nets; for example, by cutting up boxes
• construction of informal local maps

• Identifying shapes

2.0 Standard

At Level 2, students recognise lines, surfaces and planes, corners and boundaries; familiar two-dimensional shapes including rectangles, rhombuses and hexagons, and three-dimensional shapes and objects including pyramids, cones, and cylinders. They arrange a collection of geometric shapes, such as a set of attribute blocks, into subsets according to simple criteria, and recognise when one set of shapes is a subset of another set of shapes. They recognise and describe symmetry, asymmetry, and congruence in these shapes and objects. They accurately draw simple two-dimensional shapes by hand and construct, copy and combine these shapes using drawing tools and geometry software. They apply simple transformations to shapes (flips, turns, slides and enlargements) and depict both the original and transformed shape together. They specify location as a relative position, including left and right, and interpret simple networks, diagrams and maps involving a small number of points, objects or locations.

• Simple transformations

2.25

At 2.25, the work of a student progressing towards the standard at Level 3 demonstrates, for example:

• use of instructions to create tessellations such as in paving and brickwork patterns
• recognition and naming of familiar three-dimensional shapes
• use of ‘vertical’ and ‘horizontal’ to describe orientation
• determination of approximate north by considering the position of the sun
• use of a grid to refer to objects on a map

• Fitting shapes together

2.5

At 2.5, the work of a student progressing towards the standard at Level 3 demonstrates, for example:

• identification of shapes in terms of faces, edges and vertices
• representation of angles formed dynamically; for example, between the hands of a clock or between their own limbs, and explanations of these angles in terms of simple fractions of a complete revolution
• construction of prisms and pyramids from their two-dimensional nets
• orientation of north, south, east and west from their own current position

• From Appearance to Properties

2.75

At 2.75, the work of a student progressing towards the standard at Level 3 demonstrates, for example:

• knowledge of the names of polygons using Greek prefixes; for example, hex agon
• construction of balls (for example, tennis balls, footballs, soccer balls and beach balls) from flexible, two-dimensional pieces of material, and a template
• representation of an object by drawing its plan
• construction of a model for an angle using rotation of lines

3.0 Standard

At Level 3, students recognise and describe the directions of lines as vertical, horizontal or diagonal. They recognise angles are the result of rotation of lines with a common end-point. They recognise and describe polygons. They recognise and name common three-dimensional shapes such as spheres, prisms and pyramids. They identify edges, vertices and faces. They use two-dimensional nets, cross-sections and simple projections to represent simple three-dimensional shapes. They follow instructions to produce simple tessellations (for example, with triangles, rectangles, hexagons) and puzzles such as tangrams. They locate and identify places on maps and diagrams. They give travel directions and describe positions using simple compass directions (for example, N for North) and grid references on a street directory.

• Grid reference and compass points

3.25

At 3.25, the work of a student progressing towards the standard at Level 4 demonstrates, for example:

• recognition of angles between lines, particularly when lines are parallel or perpendicular
• use of scaled grids to draw similar figures (enlarged or reduced)
• use of a graphical scale to determine actual size and distance from a map
• interpretation of maps of their own immediate environment using various scales; for example, school ground, suburb, state, country
• description of a path by a set of coordinates

• Angles

3.5

At 3.5, the work of a student progressing towards the standard at Level 4 demonstrates, for example:

• classification and sorting of two-dimensional shapes using the properties of lines (curvature, orientation and length) and angles (less than, equal to, or greater than 90°)
• construction or selection of possible objects given a plan (bird’s eye view) or an elevation (side view)
• construction of transformed shapes and patterns by stamping, folding and rotating
• representation of relationships within a family (people or animals) through use of a tree diagram (network)

• Classifying shapes
• Line Symmetry - also called Mirror Symmetry
• Visualisation in 2 and 3 dimensions

3.75

At 3.75, the work of a student progressing towards the standard at Level 4 demonstrates, for example:

• construction of a copy of a shape, given details about side lengths and angles
• use of two-dimensional isometric drawings of three-dimensional objects, noting how shapes are not always preserved; for example, squares become parallelograms
• knowledge that the sum of angles at a point on a straight line is 180°
• use of a compass and compass directions to describe orientation in the school ground

4.0 Standard

At Level 4, students classify and sort shapes and solids (for example, prisms, pyramids, cylinders and cones) using the properties of lines (orientation and size), angles (less than, equal to, or greater than 90°), and surfaces. They create two-dimensional representations of three dimensional shapes and objects found in the surrounding environment. They develop and follow instructions to draw shapes and nets of solids using simple scale. They describe the features of shapes and solids that remain the same (for example, angles) or change (for example, surface area) when a shape is enlarged or reduced. They apply a range of transformations to shapes and create tessellations using tools (for example, computer software).

Students use the ideas of size, scale, and direction to describe relative location and objects in maps. They use compass directions, coordinates, scale and distance, and conventional symbols to describe routes between places shown on maps. Students use network diagrams to show relationships and connectedness such as a family tree and the shortest path between towns on a map.

• Networks

4.25

At 4.25, the work of a student progressing towards the standard at Level 5 demonstrates, for example:

• construction of a plan, elevations and cross-sections for a three-dimensional object
• knowledge of how features (for example, an angle) change, or not, when a shape undergoes a transformation (for example, a rotation)
• classification of polygons with reference to a definition or a key property
• construction of parallel and perpendicular lines
• use of a map reference to locate a point or region on a map
• use of networks to display relationships between people and pathways between objects

• Changing conceptions of shapes

4.5

At 4.5, the work of a student progressing towards the standard at Level 5 demonstrates, for example:

• identification of congruent shapes
• tessellation of suitable irregular shapes
• use of angle facts for a triangle
• use of conventional symbols and contours to describe a route marked on a map
• representation of pathways between objects as part of a network

• Congruence from rotations and reflections

4.75

At 4.75, the work of a student progressing towards the standard at Level 5 demonstrates, for example:

• knowledge of methods for creating the illusion of depth in a two-dimensional image, and description of the related process in geometrical terms
• production and analysis of images based on projection from a point (one point perspective) and a line
• calculation of size of objects using a numerical map scale
• use of bearings and distances to plot a route on a map
• equivalence of components of a three-dimensional object and its net; for example, vertices and nodes, arcs and edges, faces and regions

• Scales on maps

5.0 Standard

At Level 5, students construct two-dimensional and simple three-dimensional shapes according to specifications of length, angle and adjacency. They use the properties of parallel lines and transversals of these lines to calculate angles that are supplementary, corresponding, allied (co-interior) and alternate. They describe and apply the angle properties of regular and irregular polygons, in particular, triangles and quadrilaterals. They use two-dimensional nets to construct a simple three-dimensional object such as a prism or a platonic solid. They recognise congruence of shapes and solids. They relate similarity to enlargement from a common fixed point. They use single-point perspective to make a two-dimensional representation of a simple three-dimensional object. They make tessellations from simple shapes.

Students use coordinates to identify position in the plane. They use lines, grids, contours, isobars, scales and bearings to specify location and direction on plans and maps. They use network diagrams to specify relationships. They consider the connectedness of a network, such as the ability to travel through a set of roads between towns.

• Understanding contour lines

5.25

At 5.25, the work of a student progressing towards the standard at Level 6 demonstrates, for example:

• use of two-dimensional nets and line-segment models to investigate regular, semi-regular and irregular solids
• application of the angle properties of parallel lines and transversals to other geometrical problems
• knowledge of sets of conditions for pairs of triangles to be congruent
• use of Euler’s formula for polyhedra and their nets

5.5

At 5.5, the work of a student progressing towards the standard at Level 6 demonstrates, for example:

• recognition of the features of circles (centre, radius, diameter, chord, arc, semi-circle, circumference, segment, sector and tangent) and the associated angle relationships
• investigation of angle properties of circles and tangents
• representation of a point on the Earth’s surface in terms of its latitude and longitude
• identification of paths and circuits in network diagrams that illustrate connections between objects, locations and events

• Latitude and longitude

5.75

At 5.75, the work of a student progressing towards the standard at Level 6 demonstrates, for example:

• location of the great circle pathway between two points on a sphere
• application of geometrical transformations to graphs
• knowledge of latitude and longitude in geometrical terms

6.0 Standard

At Level 6, students represent two- and three-dimensional shapes using lines, curves, polygons and circles. They make representations using perspective, isometric drawings, nets and computer-generated images. They recognise and describe boundaries, surfaces and interiors of common plane and three-dimensional shapes, including cylinders, spheres, cones, prisms and polyhedra. They recognise the features of circles (centre, radius, diameter, chord, arc, semi-circle, circumference, segment, sector and tangent) and use associated angle properties.

Students explore the properties of spheres.

Students use the conditions for shapes to be congruent or similar. They apply isometric and similarity transformations of geometric shapes in the plane. They identify points that are invariant under a given transformation (for example, the point (2, 0) is invariant under reflection in the x-axis, so the x axis intercept of the graph of y = 2x - 4 is also invariant under this transformation). They determine the effect of changing the scale of one characteristic of two- and three-dimensional shapes (for example, side length, area, volume and angle measure) on related characteristics.

They use latitude and longitude to locate places on the Earth’s surface and measure distances between places using great circles.

Students describe and use the connections between objects/location/events according to defined relationships (networks).

• Angles in circles