K–10Mathematics K–10 Syllabus
The new Mathematics K–10 Syllabus (2022) is to be implemented from 2024 and replaces the Mathematics K–10 Syllabus (2012).
School sectors are responsible for implementing syllabuses and are best placed to provide schools with specific guidance and information on implementation given their understanding of their individual contexts.
Content
Stage 1
- 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
- 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
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
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
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
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
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
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 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.
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.