Mathematics (including pre-numeracy)

Definition and rationale

Mathematics is a way of making sense of the world. The mathematics key learning area helps students to know about mathematics, know how to do mathematics and know when and where to use it now and in the future. All people need the capacity to make sense of and to be critical about numerical information. To achieve this they need a disposition to think and act mathematically and the confidence and intuition to apply mathematical concepts to explore and solve everyday problems that confront them.

Skills needed for mathematics include mental computation and deep understandings of how numbers work. They also require meta-cognitive/higher-order skills such as reflection, analysis, estimation, justification, synthesis and communication skills needed to describe each of these in appropriate language and format. These skills are learned through Working Mathematically.

Major outcomes

By engaging in relevant and purposeful mathematical learning experiences, students will:

Ä    develop the knowledge, skills and positive dispositions required to operate confidently and competently in the areas of number, algebra, measurement, space, and chance and data

Ä    think, reason and work mathematically when applying mathematical knowledge and skills in a variety of contexts.

In Number, students read, write and understand the meaning, order and relative magnitudes of whole, decimal and fractional numbers. They understand the meaning, use and connection between the four operations that are used to solve problems. They use mental, pen and paper and technology computation strategies meeting needed degrees of accuracy and checking for reasonableness of answers.

Summary of outcomes at different junctures

Number – Students read, write and understand the meaning, order and relative magnitudes of whole, decimal and fractional numbers. They understand the meaning, use and connection between the four operations that are used to solve problems. They use mental, pen and paper and technology computation strategies meeting needed degrees of accuracy and checking for reasonableness of answers.

Ä    At Year 3, students will work with whole numbers to 999, money representations and simple fractions. Application in problem situations will use the four operations and involve whole numbers only.

Ä    At Year 5, students will work with whole numbers to 9 999, common and decimal fractions, cash transactions and methods of payment. Application will involve using the four operations (including multi-step problems) and whole numbers and decimal fractions in context.

Ä    At Year 7, students will work with whole numbers and common and decimal fractions of any size, key percentages, and factors influencing financial decisions. Application will involve using the four operations (involving multi-step problems), whole numbers and common and decimal fractions.

Ä    At Year 9, students will work with rational numbers (whole numbers, common and decimal fractions and integers), index notation, rates, ratios and options to make informed financial decisions. Application will involve using the four operations with rational numbers, rates, ratios, direct proportion and money.

Algebra – Students understand that relationships between objects or numbers can be described using patterns and simple rules. They develop understandings of methods, symbol systems for expressing generalisation, and language associated with balancing and solving equations.

Ä    At Year 3, students create and explain patterns, identify and describe relationships using rules and use backtracking to reverse the effects of rules involving operations. They represent and describe equivalence in equations that involve addition and subtraction.

Ä    At Year 5, students create and continue number patterns, identify, describe and represent relationships between two quantities and use backtracking to reverse any one of the four operations. They represent and describe equivalence in equations that involve combinations of multiplication and division or addition and subtraction.

Ä    At Year 7, students identify and create representations of patterns and functions and apply backtracking to solve simple equations that involve combinations of the four operations. They create and interpret equations, explain the effect of order of operations, and justify solutions to equations.

Ä    At Year 9, students interpret and compare different representations of linear and simple non-linear functions and solve the related problems. They interpret and solve linear equations related to realistic problems using algebraic and graphical methods.

Measurement – Students estimate and measure length, mass, area, volume and time and describe these using standard and non-standard units; they know which tool to use and can measure accurately.

Ä    At Year 3, students use non-standard and standard units to estimate, measure and order the size of objects. They use a calendar to locate and sequence events, read and interpret key times on 12-hour displays, and measure and compare durations of time.

Ä    At Year 5, students use forms of standard units when measuring, comparing and ordering, and estimate using a range of personal referents. They read, record and calculate with 12-hour time, and interpret calendars and simple timetables related to daily activities.

Ä    At Year 7, students choose appropriate units when estimating and measuring and explain relationships between dimensions when investigating areas, volumes of prisms and lengths of boundaries. They read record and calculate with 24-hour time and develop timetables and calendars to plan and organise events or activities.

Ä    At Year 9, students develop formulae to calculate areas, volumes and lengths of boundaries where the relationships between dimensions are known, and investigate a range of other shapes to explain the relationships between dimensions. They interpret and solve realistic problems related to time management and time zones within Australia.

Students collect, organise, summarise, display and interpret data and can measure and describe uncertainty and make predictions.

Ä    At Year 3, students collect and organise data and create and interpret displays to investigate their own and others’ questions. They identify and classify familiar events according to the likelihood of occurrence.

Ä    At Year 5, students design and trial a variety of data collection methods; use sources of data to investigate questions; organise data and create suitable displays and identify and interpret elements of the displays. They identify all possible outcomes of familiar situations or actions and, for these sample spaces, order the likelihood of occurrence of the identified outcomes using experimental data.

Ä    At Year 7, students plan and carry out data collections using their own data record templates, choose and construct appropriate displays and make comparisons about the data based on the displays. They analyse experimental data and compare numerical results with predicted results to inform judgments about the likelihood of particular outcomes.

Ä    At Year 9, students plan investigations involving discrete and continuous data, produce and compare data displays involving grouping, and compare measures of location. They model and determine probabilities for single events to justify statements and decisions.

Space – Students understand that geometric properties can be used to identify, describe, sort, visualise and create 2D shapes and 3D objects. They can construct and interpret maps identifying location, direction and movement through familiar and unfamiliar environments.

Ä    At Year 3, students describe and sort 2D shapes and 3D objects according to geometric properties and can identify them from different orientations. They can create simple personal maps, plans and grids and give directions to locate places or objects.

Ä    At Year 5, students describe the defining geometric properties of groups of 3D and 2D shapes and make models using nets. They read and create maps and plans using a range of conventions; and describe locations and give directions using compass points, angles and grids.

Ä    At Year 7, students analyse the geometric properties of a range of 3D and 2D shapes to classify shapes into families and their subgroups and can justify their reasoning. They interpret maps and plans with reference to conventions including latitude and longitude and movements using compass points and distance.

Ä    At Year 9, students analyse the relationships between the properties of shapes, lines and angles to explain similarity and congruence and to create representations of geometric objects that satisfy design specifications. They interpret maps and globes referring to latitude and longitude, interpret and describe plans that use scale, and describe movements using compass bearings and distance.

For more information contact your Head of Campus.