Space

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.

• Recognising, comparing, sorting and matching shapes
  
  
• Developing the everyday language of location

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.

• Folding and Symmetry
  
  
• Identifying shapes
  
  
• Simple transformations

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.

• Fitting shapes together: Part 1 and Part 2
  
  
• From Appearance to Properties
  
  
• Grid reference and compass points

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.

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

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.

• Changing conceptions of shapes
  
  
• Congruence from rotations and reflections
  
  
• Scales on maps
  
  
• Understanding contour lines

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).

• Latitude and longitude
  
  
• Angles in circles