ThreeDimensional Space 1
Outcomes
A student:

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

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

 MA314MG
identifies threedimensional objects, including prisms and pyramids, on the basis of their properties, and visualises, sketches and constructs them given drawings of different views
 identify and determine the number of pairs of parallel faces of threedimensional objects, eg 'A rectangular prism has three pairs of parallel faces'
 identify the 'base' of prisms and pyramids
 recognise that the base of a prism is not always the face where the prism touches the ground (Reasoning)
 name prisms and pyramids according to the shape of their base, eg rectangular prism, square pyramid
 visualise and draw the resulting cut face (plane section) when a threedimensional object receives a straight cut
 recognise that prisms have a 'uniform crosssection' when the section is parallel to the base
 recognise that the base of a prism is identical to the uniform crosssection of the prism (Reasoning)
 recognise a cube as a special type of prism (Communicating)
 recognise that pyramids do not have a uniform crosssection when the section is parallel to the base
 identify, describe and compare the properties of prisms and pyramids, including:
 number of faces
 shape of faces
 number and type of identical faces
 number of vertices
 number of edges
 describe similarities and differences between prisms and pyramids, eg between a triangular prism and a hexagonal prism, between a rectangular prism and a rectangular(based) pyramid (Communicating, Reasoning)
 determine that the faces of prisms are always rectangles except the base faces, which may not be rectangles (Reasoning)
 determine that the faces of pyramids are always triangles except the base face, which may not be a triangle (Reasoning)
 Connect threedimensional objects with their nets and other twodimensional representations (ACMMG111)
 visualise and sketch threedimensional objects from different views, including top, front and side views
 reflect on their own drawing of a threedimensional object and consider how it can be improved (Reasoning)
 examine a diagram to determine whether it is or is not the net of a closed threedimensional object
 explain why a given net will not form a closed threedimensional object (Communicating, Reasoning)
 visualise and sketch nets for given threedimensional objects
 recognise whether a diagram is a net of a particular threedimensional object (Reasoning)
 visualise and name prisms and pyramids, given diagrams of their nets
 select the correct diagram of a net for a given prism or pyramid from a group of similar diagrams where the others are not valid nets of the object (Reasoning)
 show simple perspective in drawings by showing depth
Background Information
In Stage 3, the formal names for particular prisms and pyramids are introduced while students are engaged in their construction and representation. (Only 'family' names, such as prism, were introduced in Stage 2.) This syllabus names pyramids in the following format: square pyramid, pentagonal pyramid, etc. However, it is also acceptable to name pyramids using the word 'based', eg squarebased pyramid, pentagonalbased pyramid.
Prisms have two bases that are the same shape and size. The bases of a prism may be squares, rectangles, triangles or other polygons. The other faces are rectangular if the faces are perpendicular to the bases. The base of a prism is the shape of the uniform crosssection, not necessarily the face on which it is resting.
Pyramids differ from prisms as they have only one base and all the other faces are triangular. The triangular faces meet at a common vertex (the apex). Pyramids do not have a uniform crosssection.
Spheres, cones and cylinders do not fit into the classification of prisms or pyramids as they have curved surfaces, not faces, eg a cylinder has two flat surfaces and one curved surface.
A section is a representation of an object as it would appear if cut by a plane, eg if the corner were cut off a cube, the resulting cut face would be a triangle. An important understanding in Stage 3 is that the crosssections parallel to the base of a prism are uniform and the crosssections parallel to the base of a pyramid are not.
Students could explore these ideas by stacking uniform objects to model prisms, and by stacking sets of seriated shapes to model pyramids, eg
Note: such stacks are not strictly pyramids, but they do assist understanding.
In geometry, a threedimensional object is called a solid. The threedimensional object may in fact be hollow, but it is still defined as a geometrical solid.
Language
Students should be able to communicate using the following language: object, shape, threedimensional object (3D object), prism, cube, pyramid, base, uniform crosssection, face, edge, vertex (vertices), apex, top view, front view, side view, depth, net.
In Stage 1, students were introduced to the terms 'flat surface' and 'curved surface' for use in describing cones, cylinders and spheres, and the terms 'faces', 'edges' and 'vertices' for use in describing prisms and pyramids.
National Numeracy Learning Progression links to this Mathematics outcome
When working towards the outcome MA3‑14MG the subelements (and levels) of Understanding geometric properties (UGP2UGP3) 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.
ThreeDimensional Space 2
Outcomes
A student:

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

 MA314MG
identifies threedimensional objects, including prisms and pyramids, on the basis of their properties, and visualises, sketches and constructs them given drawings of different views
 create prisms and pyramids using a variety of materials, eg plasticine, paper or cardboard nets, connecting cubes
 construct as many rectangular prisms as possible using a given number of connecting cubes (Problem Solving)
 create skeletal models of prisms and pyramids, eg using toothpicks and modelling clay or straws and tape
 connect the edges of prisms and pyramids with the construction of their skeletal models (Problem Solving)
 construct threedimensional models of prisms and pyramids and sketch the front, side and top views
 describe to another student how to construct or draw a threedimensional object (Communicating)
 construct threedimensional models of prisms and pyramids, given drawings of different views
Background Information
In Stage 3, students are continuing to develop their skills of visual imagery, including the ability to perceive and hold an appropriate mental image of an object or arrangement, and to predict the orientation or shape of an object that has been moved or altered.
Refer also to background information in ThreeDimensional Space 1.
Language
Students should be able to communicate using the following language: object, shape, threedimensional object (3D object), prism, cube, pyramid, base, uniform crosssection, face, edge, vertex (vertices), top view, front view, side view, net.
National Numeracy Learning Progression links to this Mathematics outcome
When working towards the outcome MA3‑14MG the subelements (and levels) of Understanding geometric properties (UGP2UGP3) 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.