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NSW Curriculum
NSW Education Standards Authority

K–10Mathematics K–10 Syllabus

Record of changes
Implementation for K–2 from 2023 and 3–10 from 2024
Expand for detailed implementation advice

Content

Stage 1

Three-dimensional spatial structure A
  • MAO-WM-01

    develops understanding and fluency in mathematics through exploring and connecting mathematical concepts, choosing and applying mathematical techniques to solve problems, and communicating their thinking and reasoning coherently and clearly

  • MA1-3DS-01

    recognises, describes and represents familiar three-dimensional objects

  • MA1-3DS-02

    measures, records, compares and estimates internal volumes (capacities) and volumes using uniform informal units

Three-dimensional spatial structure A
3D objects: Recognise familiar three-dimensional objects
  • Use the term ‘three-dimensional’ to describe a range of Loading 

  • Distinguish between objects, which are three-dimensional (3D) and Loading  which are Loading 

  • Identify and name familiar three-dimensional objects, including Loading , Loading , spheres and Loading  prisms

3D objects: Sort and describe three-dimensional objects
  • Manipulate and describe familiar three-dimensional objects

  • Use the term ‘Loading ' in describing familiar three-dimensional objects

  • Sort familiar three-dimensional objects according to obvious features

  • Use the term ‘Loading ’ to describe the flat surfaces of three-dimensional objects with straight Loading 

  • Select and name a familiar three-dimensional object from a description of its features

Volume: Measure and compare the internal volumes (capacities) of containers by filling
  • Use Loading  informal units to measure how much a Loading  will hold by counting the number of times a smaller container can be filled and emptied into the container being measured

  • Select appropriate informal units to measure the Loading  of containers

  • Recognise and explain the relationship between the size of a unit and the number of units needed (Reasons about relations)

  • Compare the Loading  of two or more containers using appropriate uniform informal units

  • Recognise and explain why containers of different shapes may have the same internal volume (Reasons about relations)

  • Estimate how much a container holds by referring to the number and type of uniform informal unit used and check by measuring

Volume: Measure the internal volume (capacity) of containers by packing
  • Pack Loading  units (eg blocks) into rectangular containers so that there are no gaps

  • Recognise that cubes pack better than other objects in rectangular containers (Reasons about spatial structure)

  • Estimate and measure the internal volume of a container by filling the container with Loading  informal units and counting the number of units used

  • Explain that if there are gaps when packing and stacking, this will affect the Loading  of measuring the internal volume

Volume: Construct volumes using cubes
  • Explore different rectangular prisms that can be made from a given number of cubes

  • Devise and explain strategies for stacking and counting units to form a rectangular prism (Reasons about spatial structure)

  • Record Loading , referring to the number and type of uniform informal unit used

Teaching advice for Three-dimensional spatial structure A

Why is it important?

Developing and retaining mental images of objects is an important skill for students. Manipulation of a variety of real three-dimensional geometric objects and two-dimensional shapes supports the development of relevant mathematical language and representation. Opportunities for these kinds of activities occur in the classroom, the playground and outside the school. Investigating the type of three-dimensional objects that are stackable makes use of the features of geometric objects in quantifying volume.

Teaching advice

Volume

The attribute of volume is the amount of space occupied by an object. Students in Stage 1 need experience in constructing volumes using informal units such as cubic blocks. Volume is formally measured in later stages using cubic units, such as:

  • cubic centimetres (cm3)
  • cubic metres (m3).

Internal volume (capacity)

Internal volume (capacity) refers to the amount a container can hold and is only used in relation to containers. It generally refers to liquid measurement, that is, the amount of liquid is equal to the internal volume of a container. Students in Stage 1 need experience in filling containers with: 

  • continuous materials such as water
  • discrete objects such as marbles.

Internal volume is formally measured in later stages using units, such as:

  • millilitres (mL)
  • litres (L).

Language

3D objects

The terms used to describe the dimensions of three-dimensional objects take different forms. Although ‘length’, ‘width’ and ‘height’ are commonly used for the three dimensions, the term ‘depth’ is sometimes used in place of height, particularly when referring to an internal dimension.

In everyday use, the context guides our choice of terms:

  • the ‘length’ of a piece of string
  • the ‘width’ of a doorway
  • the ‘height’ of a building
  • the ‘depth’ of a pool.

However, in describing an object that can readily change its orientation such as a wooden block, the choice of labels is not fixed. What would be described as the ‘height’ of the block will depend on how it is positioned.

The terms ‘length’, ‘width’ and ‘height can be introduced when students are engaged in using rectangular prisms.

In geometry, the term ‘face refers to a flat surface with only straight edges, as in prisms and pyramids. For example, a cube has six faces.

Curved surfaces, such as those found in conescylinders 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.

Internal volume (capacity)

When working with students in Stage 1 it is recommended that the terms ‘capacity and ‘internal volume’ be used interchangeably.

The internal volume of a closed container will be slightly less than its volume. Internal volume is based on the inside dimensions, while volume is determined by the outside dimensions of the container.

It is not necessary to refer to these definitions with students as capacity is not taught as a concept separate from volume until Stage 4.

Vocabulary

Students should be provided with opportunities to develop confidence in using some or all of the following terms to communicate:

  • object
  • cube
  • cylinder
  • sphere
  • flat/curved surface
  • face
  • edge
  • prism
  • internal volume/capacity
  • has more/has less
  • measure.