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• VC2M9P03

  design and conduct repeated chance experiments and simulations using digital tools to estimate probabilities that cannot be determined exactly

  Elaborations

  • using digital tools to conduct probability simulations that demonstrate the relationship between the probability of compound events and the individual probabilities
  • comparing experiments that differ only by being undertaken with replacement or without replacement
  • conducting two-step chance experiments using systematic methods to list outcomes of experiments and to list outcomes favourable to an event
  • using repeated trials of Aboriginal and/or Torres Strait Islander children’s instructive games, for example, Gorri from all parts of Australia, to calculate the probabilities of winning and not winning 

  VC2M9P03 | Mathematics | Mathematics Version 2.0 | Level 9 | Probability

• VC2M8ST02

  analyse and report on the distribution of data from primary and secondary sources using random and non-random sampling techniques

  Elaborations

  • investigating different methods of sampling used to collect data, considering the source and size of samples
  • comparing the sampling methods of simple random, systematic, stratified, quota, clustered or convenience, or judgement, and discussing the reliability of conclusions about the context that could be drawn
  • defining and distinguishing between probabilistic terms such as ‘random’, ‘sample space’, ‘sample’ and ‘sample distribution’
  • investigating primary and secondary data sources relating to reconciliation between Aboriginal and Torres Strait Islander Peoples and non-Indigenous Australians, analysing and reporting on findings

  VC2M8ST02 | Mathematics | Mathematics Version 2.0 | Level 8 | Statistics

• VC2M9ST02

  analyse how different sampling methods, and different samples using the same method, can affect the results of surveys and how choice of representation can be used to support a particular point of view

  Elaborations

  • investigating and analysing different visualisations of data such as infographics found in the media and commenting on the strengths, weaknesses and possible biases of particular examples
  • discussing the impact of decreased landline usage or an increased aversion to answering calls from unknown numbers on survey data 
  • exploring potential cultural bias relating to Aboriginal and Torres Strait Islander Peoples by critically analysing sampling techniques in statistical reports 

  VC2M9ST02 | Mathematics | Mathematics Version 2.0 | Level 9 | Statistics

• VC2M8ST04

  plan and conduct statistical investigations involving samples of a population; use ethical and fair methods to make inferences about the population and report findings, acknowledging uncertainty

  Elaborations

  • using data such as electricity consumption to draw conclusions about the impacts of events, such as pandemics, on households or business
  • identifying situations where the collection of data from a sample is necessary due to efficiency, cost or restricted time for collection of data, and is sufficiently reliable for making inferences about a population
  • exploring progress in reconciliation between Aboriginal and Torres Strait Islander Peoples and non-Indigenous Australians, investigating and evaluating sampling techniques and methods to gather relevant data to measure progress

  VC2M8ST04 | Mathematics | Mathematics Version 2.0 | Level 8 | Statistics

• VC2M1A02

  recognise, continue and create repeating patterns with numbers, symbols, shapes and objects, identifying the repeating unit and recognising the importance of repetition in solving problems

  Elaborations

  • interpreting a repeating pattern sequence created by someone else, noticing and describing the repeating part of the pattern and explaining how they know what comes next in the sequence
  • generalising a repeating pattern by identifying the unit of repeat and representing the elements using numbers, letters or symbols; for example, representing the repeating pattern of stamp, stamp, clap, stamp, clap, pause, stamp, stamp, clap, stamp, clap as SSCSC SSCSC …, recognising the elements that are repeating, describing the unit of repeat as SSCSC and continuing the pattern
  • recognising within the sequencing of natural numbers that 0–9 digits are repeated both in and between the decades and using this pattern to continue the sequence and name two-digit numbers beyond 20
  • identifying the repeating patterns in Aboriginal and/or Torres Strait Islander systems of counting, exploring different ways of representing numbers including oral and gestural language
  • considering how the making of shell or seed necklaces by Aboriginal and/or Torres Strait Islander Peoples includes practices such as sorting shells and beads based on colour, size and shape, and creating a repeating pattern sequence

  VC2M1A02 | Mathematics | Mathematics Version 2.0 | Level 1 | Algebra

• VC2M8M07

  use mathematical modelling to solve practical problems involving ratios and rates, including distance-time problems for travel at a constant speed and financial contexts; formulate problems; interpret and communicate solutions in terms of the situation, reviewing the appropriateness of the model

  Elaborations

  • modelling simple motion problems, finding one of distance travelled, time taken or average speed, given the other 2 quantities
  • modelling and solving problems related to situations such as scales on maps and plans, the mixing of chemicals or ingredients, or calculating magnification factors applying relevant ratios and proportions
  • modelling problems involving converting money amounts using different exchange rates and applying them when planning and budgeting for overseas travel
  • modelling situations involving financial contexts (for example, income tax, using taxation rates on annual income, comparing different taxation brackets and rates of pay) or comparing the benefits of different phone plans using different call rates and associated fees to determine the best plan
  • modelling situations involving the use of ratios in radiocarbon dating methods, including the ratio of carbon-14 to carbon-12 isotopes in organisms, to measure dates of Aboriginal and Torres Strait Islander Peoples’ habitation on the Australian continent
  • modelling situations involving ratio and its application in the making of string and cordage by Aboriginal and/or Torres Strait Islander Peoples, including the ratio of length to the mass of a rope, the strength of the ply in proportion to a rope’s pulling force, and the proportion of fibre for the length of string required

  VC2M8M07 | Mathematics | Mathematics Version 2.0 | Level 8 | Measurement

• VC2M1M01

  compare directly and indirectly and order objects and events using attributes of length, mass, capacity and duration, communicating reasoning

  Elaborations

  • using a piece of string to indirectly compare the length of several objects, deciding which will fit within a space, and using comparative language to describe the order (shortest, short, longer, longest)
  • ordering the mass of 3 or more objects, such as rocks, using hefting and balance scales, and using comparative language to explain the order (lightest, light, heavier, heaviest) and how they decided on the order
  • pouring sand, rice or water from one container to another to compare and order the capacity of 3 or more containers, and describing the order of the results in terms of which holds the most/least and those in between
  • creating sand timers from everyday items or recycled materials and comparing them to order the duration of time required for the sand to run through
  • investigating situations where Aboriginal and/or Torres Strait Islander Peoples estimate, compare and communicate measurements, for example, situations involving the duration of seasons, understanding animal behaviour using the length of animal tracks, or investigating capacity through Aboriginal and/or Torres Strait Islander water management techniques, such as traditional water-carrying vessels and rock holes

  VC2M1M01 | Mathematics | Mathematics Version 2.0 | Level 1 | Measurement

• VC2M8M05

  recognise and use rates to solve problems involving the comparison of 2 related quantities of different units of measure

  Elaborations

  • identifying examples of rates in the real world, including constant rates, rate of pay, cost per kilogram, recipes, simple interest and average rates
  • applying rates to solve problems involving the conversion between different units of measure; for example, using a conversion rate to convert distances from miles to kilometres, or using currency exchange rates to determine the price of items
  • applying rates to calculate solutions to problems in different contexts, for example, required run rates in cricket, dilution of concentrated chemicals and comparing the petrol consumption rates of different vehicles
  • using taxation tables to calculate an individual's annual income tax
  • investigating the application of rates in Aboriginal and Torres Strait Islander Peoples’ land management practices, including the rate of fire spread under different environmental conditions such as fuel types, wind speed, temperature and relative humidity; the conservation of water by Aboriginal and Torres Strait Islander Peoples by estimating rates of water evaporation based on surface area and climatic conditions

  VC2M8M05 | Mathematics | Mathematics Version 2.0 | Level 8 | Measurement

• VC2M10A14

  solve simple exponential equations

  Elaborations

  • investigating exponential equations derived from authentic mathematical models based on population growth
  • recognising that in a table of values, if the ratio between consecutive values of the dependent variable is constant, then it is an exponential relation
  • investigating the links between algebraic and graphical representations of exponential functions using graphing software
  • using digital tools with symbolic manipulation functionality to systematically explore exponential relations
  • investigating Aboriginal and/or Torres Strait Islander ranger groups’ and other groups’ programs that attempt to eradicate feral animals for survival of native animals on Country/Place, exploring the competition between feral and native animals and their impact on natural resources by formulating exponential equations for population growth for each animal species 

  VC2M10A14 | Mathematics | Mathematics Version 2.0 | Level 10 | Algebra

• VC2M7A04

  investigate, interpret and describe relationships between variables represented in graphs of functions developed from authentic data

  Elaborations

  • using graphs to analyse a building’s electricity or gas usage over a period of time, the value of shares on a stock market, or the temperature during a day, interpreting and discussing the relationships they represent
  • using travel graphs to compare the distance travelled to and from school, interpreting and discussing features of travel graphs such as the slope of lines and the meaning of horizontal line segments
  • telling the story behind what is being represented in graphs of functions, for example, graphs representing pouring rates or distance versus time
  • using graphs of evaporation rates to explore and discuss Aboriginal and Torres Strait Islander Peoples’ methods of water resource management

  VC2M7A04 | Mathematics | Mathematics Version 2.0 | Level 7 | Algebra

• VC2M4M03

  solve problems involving the duration of time including situations involving ‘am’ and ‘pm’ and conversions between units of time

  Elaborations

  • calculating the amount of time between 2 events, such as the start and finish of a movie, a bus journey or a flight, including cases where the starting and finishing times are written using ‘am’ and ‘pm’ notation
  • converting units of time using relationships between units, such as 60 minutes in an hour and 60 seconds in a minute, to solve problems; for example, creating a daily timetable for an activity such as an athletics carnival or planning an exercise routine with activities and rests
  • exploring Aboriginal and/or Torres Strait Islander Peoples’ explanations of the passing of time through cultural accounts about cyclic phenomena involving the sun, moon and stars

  VC2M4M03 | Mathematics | Mathematics Version 2.0 | Level 4 | Measurement

• VC2M1M03

  describe the duration and sequence of events using years, months, weeks, days and hours

  Elaborations

  • naming, listing and using familiar units of time, such as hours, days, weeks and years
  • comparing the number of days in the months of the year and explaining how the months cycle from one year to the next
  • sequencing familiar events, including representing time, on pictorial timelines
  • discussing events and activities and deciding whether they would take closer to an hour, a day, a week, a month or a year; for example, it takes a day for the sun to rise and fall and rise again, but it takes less than an hour for me to walk to school
  • investigating durations of time represented in Aboriginal and/or Torres Strait Islander seasonal calendars

  VC2M1M03 | Mathematics | Mathematics Version 2.0 | Level 1 | Measurement

• VC2M9M01

  solve problems involving the volume and surface area of right prisms, cylinders and composite objects using appropriate units

  Elaborations

  • analysing nets of objects to generate short cuts and establish formulas for surface area 
  • determining the amount of material needed to make can-coolers for a class fundraising project and working out the most cost-efficient way to cut out the pieces
  • finding different prisms that have the same volume but different surface areas, making conjectures as to what type of prism would have the smallest or largest surface area
  • investigating objects and technologies of Aboriginal and Torres Strait Islander Peoples, analysing and connecting surface area and volume, and exploring their relationship to their capacity

  VC2M9M01 | Mathematics | Mathematics Version 2.0 | Level 9 | Measurement

• VC2M7M06

  use mathematical modelling to solve practical problems involving ratios of lengths, areas and volumes; formulate problems, interpret and communicate solutions in terms of the situation, justifying choices made about the representation

  Elaborations

  • using fractions to model and solve ratio problems involving comparison of quantities, and considering part-part and part-whole relations
  • modelling and solving practical problems involving ratios of length, capacity or mass, such as in construction, design, or food or textile production; for example, mixing concrete, the golden ratio in design, mixing a salad dressing
  • modelling the situation using manipulatives, diagrams and/or mathematical discussion; for example, mixing primary colours in a variety of ratios to investigate how new colours are created and the strength of those colours
  • investigating commercialised substances founded on Aboriginal and/or Torres Strait Islander Peoples’ knowledges of substances, including pharmaceuticals and toxins, understanding how ratios are used in their development

  VC2M7M06 | Mathematics | Mathematics Version 2.0 | Level 7 | Measurement

• VC2M8M03

  solve problems involving the circumference and area of a circle using formulas and appropriate units

  Elaborations

  • deducing that the area of a circle is between 2 radius squares and 4 radius squares, and using 3 × radius² as a rough estimate for the area of a circle
  • investigating the area of circles using a square grid or by rearranging a circle divided into smaller and smaller sectors or slices to resemble a close approximation of a rectangle
  • applying the formulas for the area and circumference of a circle to solve practical problems, and using one of the measures of radius, diameter, circumference or area to deduce the value of the other measures; for example, determining the length of material needed to edge a round table, given its dimensions as the area of the tabletop
  • exploring traditional weaving designs by Aboriginal and Torres Strait Islander Peoples and investigating the significance and use of circles

  VC2M8M03 | Mathematics | Mathematics Version 2.0 | Level 8 | Measurement

• VC2M5N09

  use mathematical modelling to solve practical problems involving additive and multiplicative situations, including simple financial planning contexts; formulate the problems, choosing operations and efficient mental and written calculation strategies, and using digital tools where appropriate;...

  Elaborations

  • modelling an everyday situation and determining which operations can be used to solve it using materials, diagrams, arrays and/or bar models to represent the problem; formulating the situation as a number sentence; and justifying their choice of operations in relation to the situation
  • modelling a series of contextual problems, deciding whether an exact answer or an approximate calculation is appropriate, and explaining their reasoning in relation to the context and the numbers involved
  • modelling financial situations such as creating financial plans; for example, creating a budget for a class fundraising event, using a spreadsheet to tabulate data and perform calculations
  • investigating how mathematical models involving combinations of operations can be used to represent songs, stories and/or dances of Aboriginal and Torres Strait Islander Peoples

  VC2M5N09 | Mathematics | Mathematics Version 2.0 | Level 5 | Number

• VC2M7P02

  conduct repeated chance experiments and run simulations with a large number of trials using digital tools; compare predicted with observed results, explaining the differences and the effect of sample size on the outcomes 

  Elaborations

  • developing an understanding of the law of large numbers through using experiments and simulations to conduct large numbers of trials for seemingly random events and discussing findings
  • conducting simulations using online simulation tools and comparing the combined results of a large number of trials to predicted results
  • exploring and observing Aboriginal and/or Torres Strait Islander children’s instructive games – for example, Koara from the Jawi and Bardi Peoples of Sunday Island in Western Australia – to investigate probability, predicting outcomes for an event and comparing with increasingly larger numbers of trials, and comparing observed and expected results

  VC2M7P02 | Mathematics | Mathematics Version 2.0 | Level 7 | Probability

• VC2M7SP01

  represent three-dimensional objects in 2 dimensions; discuss and reason about the advantages and disadvantages of different representations

  Elaborations

  • deconstructing packaging to identify shapes and nets
  • using different nets to construct prisms and determining which nets will make a cube, rectangular prism, triangular prism or pyramid
  • using aerial views of buildings and other three-dimensional structures to visualise the footprint made by the building or structure, identifying prisms that could approximate the structure
  • building objects by interpreting isometric and perspective drawings
  • using isometric and square grid paper to draw views of front, back, side, top and bottom of objects
  • exploring different two-dimensional representations of objects in Aboriginal and/or Torres Strait Islander artworks or cultural maps of Country/Place

  VC2M7SP01 | Mathematics | Mathematics Version 2.0 | Level 7 | Space

• VC2M5SP01

  connect objects to their nets and build objects from their nets using spatial and geometric reasoning

  Elaborations

  • designing and constructing exact nets for packaging particular-shaped items or collections of interest, taking into consideration how the faces will be joined and how the package will be opened
  • visualising folding some possible nets for a range of prisms and pyramids, predicting which will work and which cannot work, and justifying their choices, based on the number, size and position of particular shapes in each diagram
  • sketching nets for a range of prisms and pyramids considering the number, shape and placement of the faces, and testing by cutting and folding
  • investigating objects designed and developed by Aboriginal and/or Torres Strait Islander Peoples, such as those used in fish traps and instructive toys, identifying the shape and relative position of each face to determine the net of the object

  VC2M5SP01 | Mathematics | Mathematics Version 2.0 | Level 5 | Space

• VC2M6SP02

  locate points in the 4 quadrants of the Cartesian plane; describe changes to the coordinates when a point is moved to a different position in the plane

  Elaborations

  • understanding that the Cartesian plane provides a graphical or visual way of describing location with respect to a fixed origin
  • understanding that the axes are number lines that can have different scales, including fractions and decimals, depending on purpose
  • understanding that the horizontal coordinate is written first and is changed if there is a move to the left or right, whereas a move up or down will change the vertical coordinate
  • using the Cartesian plane to draw lines and polygons, listing coordinates in the correct order to complete a polygon
  • investigating and connecting land or star maps used by Aboriginal and Torres Strait Islander Peoples with the Cartesian plane through a graphical or visual way of describing location

  VC2M6SP02 | Mathematics | Mathematics Version 2.0 | Level 6 | Space