# Mathematics Version 2.0

## Structure

Mathematics is presented in 11 levels, from Foundation to Level 10.

Level 10 also includes Level 10A, which provides opportunities for students to extend their exploration of mathematical notions and further their mathematical studies.

#### Strands

The curriculum is organised into 6 interrelated strands. The strands group the content descriptions, to provide both a focus and a clear sequence for the development of related concepts and skills across levels.

The 6 strands are:

• Number
• Algebra
• Measurement
• Space
• Statistics
• Probability (commencing at Level 3).

An expectation of mathematical proficiency has been embedded into curriculum content across all strands to ensure that students develop mastery in mathematics through the development and application of increasingly sophisticated and refined mathematical understanding and fluency, reasoning and problem-solving skills. The concepts, skills, procedures and processes essential to the learning of mathematics are organised under the 6 interrelated strands, in a sequence of development that increases in depth and breadth across the years of schooling.

Natural connections exist between the content of these strands; for example, Number and Algebra build on an understanding of number systems and the properties of operations to describe relationships and formulate generalisations. Statistics and Probability have strong connections that rely on and build on the important links between them. Measurement relates not only to Space but is also foundational to all strands, enhancing their practical relevance. Combined with Number, it provides a means to quantify, compare, communicate and make sense of situations where metrics may provide insight. It is important that students develop the capability to identify and use the many connections that exist within and across the strands of Mathematics.

The 6 strands also specify content aimed at progressively developing students’ knowledge and use of mathematical, statistical and computational thinking through the processes of mathematical modelling, computational thinking, statistical investigation, probability experiments and simulations. When students are actively engaged in learning experiences involving the mathematical processes, they draw on and further develop their mathematical understanding, fluency, reasoning and problem-solving skills in an integrated way.

##### Number

The Number strand develops ways of working with mental constructs that deal with correspondence, magnitude and order, for which operations and their properties can be defined. Numbers have wide-ranging application and specific uses in counting, measuring and other means of quantifying situations and objects. Number systems are constructed to deal with different contexts and problems involving finite and infinite, and discrete and continuous sets. Students apply number sense and strategies for counting and representing numbers as they explore the magnitude and properties of numbers, apply a range of strategies for computation and understand the connections between operations. Developing number sense and the ability to work effectively with numbers is critical to being an active and productive citizen who is successful at work and in future learning, who is financially literate, and who engages with the world and other individuals.

##### Algebra

The Algebra strand develops ways of using symbols and symbolic representations to think and reason about relationships in both mathematical and real-world contexts. It provides a means for manipulating mathematical objects, recognising patterns and structures, making connections, understanding properties of operations and the concept of equivalence, abstracting information, working with variables, solving equations and generalising number and operation facts and relationships. Algebra connects symbolic, graphic and numeric representations. Students recognise patterns and understand the concepts of variable and function as they build on their understanding of the number system to describe relationships, formulate generalisations, recognise equivalence, and solve equations and inequalities. Algebra deals with situations of generality, communicating abstract ideas applied in areas such as science, health, finance, sport, engineering, and building and construction.

##### Measurement

The Measurement strand develops ways of quantifying aspects of the human and physical world. Measures and units are defined and selected to be relevant and appropriate to the context. Measurement is used to answer questions, show results, demonstrate value, justify allocation of resources, evaluate performance, identify opportunities for improvement and manage results. Students develop an increasingly sophisticated understanding of size, shape, relative position and movement of two-dimensional figures in the plane and three-dimensional objects in space. They make meaningful measurements of quantities, choosing appropriate metric units of measurement. They build an understanding of the connections between units and calculate derived measures such as area, speed and density. Measurement underpins understanding, comparison and decision-making in many personal, societal, environmental, agricultural, industrial, spatial, health and economic contexts.

##### Space

The Space strand develops ways of visualising, representing and working with the location, direction, shape, placement, proximity and transformation of objects at macro, local and micro scales in natural and constructed worlds. It underpins students’ capacity to make pictures, diagrams, maps, projections, networks, models and graphics that enable the manipulation and analysis of shapes and objects through actions and the senses. This includes notions such as surface, region, boundary, curve, object, dimension, connectedness, symmetry, direction, congruence and similarity. Students investigate properties and apply their understanding of them to define, compare and construct figures and objects as they learn to develop geometric arguments. These notions apply to art, design, architecture, planning, transportation, construction and manufacturing, physics, engineering, chemistry, biology and medicine.

##### Statistics

The Statistics strand develops ways of collecting, understanding and describing data and its distribution. Statistics provides a story, or a means to support or question an argument, and enables exploratory data analysis that underpins decision-making and informed judgement. Statistical literacy requires an understanding of statistical information and processes, including an awareness of data and the ability to estimate, interpret, evaluate and communicate with respect to variation in the real world. Statistical literacy provides a basis for critical scrutiny of an argument, the accuracy of representations, and the validity and reliability of inferences and claims. The effective use of data requires acknowledging and expecting variation in the collection, analysis and interpretation of data arising for categorical and numerical variables. Students recognise and analyse data and draw inferences. They represent, summarise and interpret data and undertake purposeful investigations involving the collection and interpretation of data, as well as building skills to critically evaluate statistical information and develop intuitions about data. Statistics is used in business, government, research, sport, health care and media for critical and informed evaluation of issues, arguments and decision-making.

##### Probability

The Probability strand develops ways of dealing with uncertainty and expectation, making predictions, and characterising the chance of events, or how likely events are to occur from both empirical and theoretical bases. It provides a means of considering, analysing and utilising the chance of events, and recognising random phenomena for which it is impossible to exactly determine the next observed outcome before it occurs. In contexts where chance plays a role, probability provides experimental and theoretical ways to quantify how likely it is that a particular event will occur, or how likely it is that a proposition is the case. This enables students to understand contexts involving chance and to build mathematical models surrounding risk and decision-making in a range of areas of human endeavour. These include finance, science, business management, epidemiology, games of chance, computer science and artificial intelligence. Students recognise variation, assess likelihood and assign probabilities using experimental and theoretical approaches.

#### Achievement standards

Achievement standards describe what students are typically able to understand and do, and they are the basis for reporting student achievement.

Students’ mastery of concepts under the 6 strands is indicated by their ability to demonstrate proficiency against the achievement standards. Each achievement standard in Mathematics has been organised into paragraphs that reflect each of the strands.

In Mathematics, students progress along a curriculum continuum that provides the first achievement standard at Foundation and then at Levels 1, 2, 3, 4, 5, 6, 7, 8, 9 and 10.

#### Content descriptions

In Mathematics, content descriptions sequence and describe the mathematical knowledge and skills that teachers need to teach and students are expected to learn.

#### Elaborations

Elaborations are examples that provide guidance on how the curriculum may be transformed into a classroom activity or learning opportunity. They are provided as advisory material only and are not mandated.

Note: The Mathematics elaborations will be subject to further refinement in late 2023, once the Victorian Curriculum F–10 Version 2.0 cross-curriculum priorities and capabilities are finalised.