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NSW Syllabuses

Mathematics K–10 - Stage 2 - Measurement and Geometry Three-Dimensional Space

Three-Dimensional Space 1

Outcomes

A student:

  • MA2-1WM

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

  • MA2-3WM

    checks the accuracy of a statement and explains the reasoning used

  • MA2-14MG

    makes, compares, sketches and names three-dimensional objects, including prisms, pyramids, cylinders, cones and spheres, and describes their features

Content

  • Students:
  • Make models of three-dimensional objects and describe key features (ACMMG063)
  • recognise and describe the use of three-dimensional objects in a variety of contexts, eg buildings, packaging (Communicating) LCCT
  • describe and compare curved surfaces and flat surfaces of cylinders, cones and spheres, and faces, edges and vertices of prisms (including cubes) and pyramids L
  • describe similarities and differences between prisms (including cubes), pyramids, cylinders, cones and spheres (Communicating) LCCT
  • use a variety of materials to make models of prisms (including cubes), pyramids, cylinders, cones and spheres, given a three-dimensional object, picture or photograph to view
  • deconstruct everyday packages that are prisms (including cubes) to create nets, eg cut up tissue boxes
  • recognise that a net requires each face to be connected to at least one other face (Reasoning) CCT
  • investigate, make and identify the variety of nets that can be used to create a particular prism, such as the variety of nets that can be used to make a cube, eg 
    The image shows 3 different nets of a cube.
    (Communicating, Problem Solving, Reasoning) L
  • distinguish between (flat) nets, which are 'two-dimensional', and objects created from nets, which are 'three-dimensional' (Communicating, Reasoning) L

Background Information

The formal names for particular prisms and pyramids are not introduced in Stage 2. Prisms and pyramids are to be treated as classes for the grouping of all prisms and all pyramids. Names for particular prisms and pyramids are introduced in Stage 3.

Language

Students should be able to communicate using the following language: object, two-dimensional shape (2D shape), three-dimensional object (3D object), cone, cube, cylinder, prism, pyramid, sphere, surface, flat surface, curved surface, face, edge, vertex (vertices), net.

In geometry, the term 'face' refers to a flat surface with only straight edges, as in prisms and pyramids, eg a cube has six faces. Curved surfaces, such as those found in cylinders, cones and spheres, are not classified as 'faces'. Similarly, flat surfaces with curved boundaries, such as the circular surfaces of cylinders and cones, are not 'faces'.

The term 'shape' refers to a two-dimensional figure. The term 'object' refers to a three-dimensional figure.

Three-Dimensional Space 2

Outcomes

A student:

  • MA2-1WM

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

  • MA2-3WM

    checks the accuracy of a statement and explains the reasoning used

  • MA2-14MG

    makes, compares, sketches and names three-dimensional objects, including prisms, pyramids, cylinders, cones and spheres, and describes their features

Content

  • Students:
  • Investigate and represent three-dimensional objects using drawings
  • identify prisms (including cubes), pyramids, cylinderscones and spheres in the environment and from drawings, photographs and descriptions L
  • investigate types of three-dimensional objects used in commercial packaging and give reasons for some being more commonly used (Communicating, Reasoning) CCTPSC
  • sketch prisms (including cubes), pyramids, cylinders and cones, attempting to show depth
  • compare their own drawings of three-dimensional objects with other drawings and photographs of three-dimensional objects (Reasoning)
  • draw three-dimensional objects using a computer drawing tool, attempting to show depth (Communicating) ICT
  • sketch three-dimensional objects from different views, including top, front and side views
  • investigate different two-dimensional representations of three-dimensional objects in the environment, eg in Aboriginal art (Communicating) ICTAHC
  • draw different views of an object constructed from connecting cubes on isometric grid paper
  • interpret given isometric drawings to make models of three-dimensional objects using connecting cubes

Background Information

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.

Refer also to background information in Three-Dimensional Space 1.

Language

Students should be able to communicate using the following language: object, two-dimensional shape (2D shape), three-dimensional object (3D object), cone, cube, cylinder, prism, pyramid, sphere, top view, front view, side view, isometric grid paper, isometric drawing, depth.

Refer also to language in Three-Dimensional Space 1.