NSW Syllabuses

# Mathematics K–10 - Stage 1 - Measurement and Geometry Three-Dimensional Space

## Three-Dimensional Space 1

### Outcomes

#### A student:

• MA1-1WM

describes mathematical situations and methods using everyday and some mathematical language, actions, materials, diagrams and symbols

• MA1-14MG

sorts, describes, represents and recognises familiar three-dimensional objects, including cones, cubes, cylinders, spheres and prisms

### Content

• Students:
• Recognise and classify familiar three-dimensional objects using obvious features (ACMMG022)
• manipulate and describe familiar three-dimensional objects, including cones, cubes, cylinders, spheres and prisms
• identify and name familiar three-dimensional objects, including cones, cubes, cylinders, spheres and prisms, from a collection of everyday objects
• select an object from a description of its features, eg find an object with six square faces (Reasoning)
• use the terms 'surface', 'flat surface' and 'curved surface' in describing familiar three-dimensional objects
• identify the type and number of flat and curved surfaces of three-dimensional objects, eg 'This prism has eight flat surfaces', 'A cone has two surfaces: one is a flat surface and the other is a curved surface' (Reasoning)
• use the term 'face' to describe the flat surfaces of three-dimensional objects with straight edges, including squares, rectangles and triangles
• distinguish between 'flat surfaces' and 'curved surfaces' and between 'flat surfaces' and 'faces' when describing three-dimensional objects (Communicating)
• sort familiar three-dimensional objects according to obvious features, eg 'All these objects have curved surfaces'
• select and name a familiar three-dimensional object from a description of its features, eg find an object with six square faces
• recognise that three-dimensional objects look different from different vantage points
• identify cones, cubes, cylinders and prisms when drawn in different orientations, eg
• recognise familiar three-dimensional objects from pictures and photographs, and in the environment

### Background Information

In Stage 1, students begin to explore three-dimensional objects in greater detail. They continue to describe the objects using their own language and are introduced to some formal language. Developing and retaining mental images of objects is an important skill for these students. Manipulation of a variety of real three-dimensional objects and two-dimensional shapes in the classroom, the playground and outside the school is crucial to the development of appropriate levels of language and representation.

A cube is a special prism in which all faces are squares. In Stage 1, students do not need to be made aware of this classification.

### Language

Students should be able to communicate using the following language: object, cone, cube, cylinder, sphere, prism, surface, flat surface, curved surface, face.

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 cones, cylinders and spheres, are not classified as faces. Similarly, flat surfaces with curved boundaries, such as the circular surfaces of cones and cylinders, are not faces.

## Three-Dimensional Space 2

### Outcomes

#### A student:

• MA1-1WM

describes mathematical situations and methods using everyday and some mathematical language, actions, materials, diagrams and symbols

• MA1-14MG

sorts, describes, represents and recognises familiar three-dimensional objects, including cones, cubes, cylinders, spheres and prisms

### Content

• Students:
• Describe the features of three-dimensional objects (ACMMG043)
• use the terms 'flat surface', 'curved surface', 'face', 'edge' and 'vertex' appropriately when describing three-dimensional objects
• describe the number of flat surfaces, curved surfaces, faces, edges and vertices of three-dimensional objects using materials, pictures and actions, eg 'A cylinder has two flat surfaces, one curved surface, no faces, no edges and no vertices', 'This prism has 5 faces, 9 edges and 6 vertices' (Communicating)
• distinguish between objects, which are 'three-dimensional' (3D), and shapes, which are 'two-dimensional' (2D), and describe the differences informally, eg 'This is a two-dimensional shape because it is flat'
• relate the terms 'two-dimensional' and 'three-dimensional' to their use in everyday situations, eg a photograph is two-dimensional and a sculpture is three-dimensional (Communicating, Reasoning)
• recognise that flat surfaces of three-dimensional objects are two-dimensional shapes and name the shapes of these surfaces
• sort three-dimensional objects according to particular attributes, eg the shape of the surfaces
• explain the attribute or multiple attributes used when sorting three-dimensional objects (Communicating, Reasoning)
• represent three-dimensional objects, including landmarks, by making simple models or by drawing or painting
• choose a variety of materials to represent three-dimensional objects, including digital technologies (Communicating)
• explain or demonstrate how a simple model was made (Communicating, Reasoning)

### Background Information

Refer to background information in Three-Dimensional Space 1.

### Language

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

The term 'vertex' (plural: vertices) refers to the point where three or more faces of a three-dimensional object meet (or where two straight sides of a two-dimensional shape meet).

In geometry, the term 'edge' refers to the interval (straight line) formed where two faces of a three-dimensional object meet.

Refer also to language in Three-Dimensional Space 1.