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• VC2M6N09

  use mathematical modelling to solve practical problems involving rational numbers and percentages, including in financial contexts; formulate the problems, choosing operations and using efficient mental and written calculation strategies, and using digital tools where appropriate; interpret and...

  Elaborations

  • modelling practical situations involving percentages using efficient calculation strategies to find solutions, such as mental calculations, spreadsheets, calculators or a variety of informal jottings, and interpreting the results in terms of the situation, for example, purchasing items during a sale
  • modelling situations involving earning money and budgeting, asking questions such as ‘Can I afford it?’, ‘Do I need it?’ and ‘How much do I need to save for it?’ and developing a savings plan or budget for an upcoming event or personal purchase
  • modelling and solving the problem of creating a budget for a class excursion or family holiday, using the internet to research costs and expenses, and representing the budget in a spreadsheet, creating and using formulas to calculate totals

  VC2M6N09 | Mathematics | Mathematics Version 2.0 | Level 6 | Number

• 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

• VC2M4SP02

  represent and approximate composite shapes and objects in the environment, using combinations of familiar shapes and objects

  Elaborations

  • identifying common shapes that form part of a composite shape by re-creating these shapes using physical or virtual materials
  • physically or virtually using cubes to make three-dimensional models that approximate real objects; for example, building a virtual environment by using a computer software program to construct objects out of cubes
  • approximating complex shapes and objects in the environment with familiar shapes and objects; for example, drawing cartoon animals by combining familiar shapes
  • recognising how familiar shapes and objects are used in logos and other graphics to represent more complex shapes, and creating logos using graphic design software

  VC2M4SP02 | Mathematics | Mathematics Version 2.0 | Level 4 | Space

• VC2M8P02

  determine all possible outcome combinations for 2 events, using two-way tables, tree diagrams and Venn diagrams, and use these to determine probabilities of specific events in practical situations

  Elaborations

  • describing events using language of ‘at least’, exclusive ‘or’ (A or B but not both), inclusive ‘or’ (A or B or both) and ‘and’
  • using the relation Pr(A and B) + Pr(A and not B) + Pr(not A and B) + Pr(not A and not B) = 1 to calculate probabilities, including the special case of mutually exclusive events where Pr(A and B) = 0
  • using Venn diagrams or two-way tables to demonstrate the difference between events that are mutually exclusive, such as whether a coin toss will land on a head or a tail, and those that are not mutually exclusive, such as people who have blonde hair and people who have blue eyes
  • exploring Aboriginal and/or Torres Strait Islander children’s instructive games, for example, Battendi from the Ngarrindjeri Peoples of Lake Murray and Lake Albert in southern Australia, applying possible combinations and relationships and calculating probabilities using two-way tables and Venn diagrams

  VC2M8P02 | Mathematics | Mathematics Version 2.0 | Level 8 | Probability

• VC2M3N05

  multiply and divide one- and two-digit numbers, representing problems using number sentences, diagrams and arrays, and using a variety of calculation strategies

  Elaborations

  • applying knowledge of numbers and the properties of operations using a variety of ways to represent multiplication or division number sentences; for example, using a Think Board to show different ways of visualising 8 × 4, such as an array, a diagram and a worded problem
  • using part-part-whole and comparative models to visually represent multiplicative relationships and choosing whether to use multiplication or division to solve problems
  • matching or creating a problem scenario or story that can be represented by a given number sentence involving multiplication and division; for example, using given number sentences to create worded problems for others to solve
  • formulating connected multiplication and division expressions by representing situations from Aboriginal and/or Torres Strait Islander Peoples’ cultural stories and dances about how they care for Country/Place, such as turtle egg gathering, using number sentences

  VC2M3N05 | Mathematics | Mathematics Version 2.0 | Level 3 | Number

• VC2M4M04

  estimate and compare angles using angle names including acute, obtuse, straight angle, reflex and revolution, and recognise their relationship to a right angle

  Elaborations

  • classifying the interior angles of a range of shapes, using examples of angles to identify acute, obtuse, right and reflex angles
  • identifying angles within the environment and estimating whether they are acute, obtuse, right or reflex
  • creating a right-angle template using cardboard or a double-folded piece of paper and using it to compare angles in the environment, commenting on whether they are smaller than or greater than a right angle
  • using different measuring tools such as a spirit level or set squares to determine whether lines or objects are straight, square or perpendicular (at right angles)

  VC2M4M04 | Mathematics | Mathematics Version 2.0 | Level 4 | Measurement

• VC2M3P02

  conduct repeated chance experiments; identify and describe possible outcomes, record the results, and recognise and discuss the variation

  Elaborations

  • identifying the possible outcomes of a chance experiment, creating a tally chart to record results, carrying out a few trials and tallying the results for each trial, and then responding to the questions ‘How did your results vary for each trial?’ and ‘How do the results vary across the class?’
  • conducting repeated trials of chance experiments such as tossing a coin, throwing a dice, drawing a coloured or numbered ball from a bag, or using a coloured spinner with equal partitions, and identifying the variation in the number of heads/fives/reds between trials

  VC2M3P02 | Mathematics | Mathematics Version 2.0 | Level 3 | Probability

• VC2M8P01

  recognise that complementary events have a combined probability of one; use this relationship to calculate probabilities in applied contexts

  Elaborations

  • understanding that knowing the probability of an event allows the probability of its complement to be found, including for those events that are not equally likely, such as getting a specific novelty toy in a supermarket promotion
  • using the relationship that for a single event A, Pr(A) + Pr(not A) = 1; for example, if the probability that it rains on a particular day is 80%, the probability that it does not rain on that day is 20%, or the probability of not getting a 6 on a single roll of a fair dice is $1-\frac{1}{6}=\frac{5}{6}$
  • using the sum of probabilities to solve problems, such as the probability of starting a game by throwing a 5 or 6 on a dice is $\frac{1}{3}$ and probability of not throwing a 5 or 6 is $\frac{2}{3}$

  VC2M8P01 | Mathematics | Mathematics Version 2.0 | Level 8 | Probability

• VC2M10ASP06

  design, test and refine solutions to spatial problems using algorithms and digital tools; communicate and justify solutions 

  Elaborations

  • designing and making scale models of three-dimensional objects using digital tools; for example, making components of a puzzle using a three-dimensional printer, and planning and designing the puzzle using principles of tessellations
  • applying a computational thinking approach to solving problems involving networks, for example, connectedness, coverage and weighted measures, such as taking different routes and choosing the most efficient route to take when travelling by car using virtual map software 
  • defining and decomposing spatial problems, creating and applying algorithms to generate solutions, and evaluating and communicating solutions in terms of the problem; for example, designing a floor plan for a department store that limits congestion at key areas such as check-outs, changing rooms and near popular sale items
  • designing, creating and testing algorithms using pseudocode or flow charts for producing self-similar patterns; and validating algorithms using a range of test cases to compare their output
  • exploring geospatial technologies used by Aboriginal and/or Torres Strait Islander communities, to consider spatial problems including position and transformation

  VC2M10ASP06 | Mathematics | Mathematics Version 2.0 | Level 10A | Space

• VC2M2N03

  recognise and describe one-half as one of 2 equal parts of a whole and connect halves, quarters and eighths through repeated halving

  Elaborations

  • creating halves of a range of collections sets by sharing collections into 2 equal groups; for example, comparing half of a set of 12 washers with half of a set of 8 bolts to identify how they both represent one-half of their respective set
  • creating halves using measurement attributes – for example, explaining that ‘a half is one part out of 2 equal parts of a whole’; equally folding a strip of paper, dividing a lump of playdough or separating a cup of water into 2 equal parts, and then selecting one of the parts and naming it ‘one-half’; or comparing half of a collection of 10 counters with half of a shape or object and explaining how each shows one-half of the respective whole
  • using repeated halving to subdivide shapes and objects in different ways to make corresponding halves, quarters and eighths; naming the parts and comparing the size of them to notice that they are all the same size; and demonstrating that a quarter is a half of a half and that an eighth is a half of a quarter
  • dividing a shape into equal parts and relating the number of parts to the unit fraction; for example, if there are 4 equal parts then each part is one-quarter and if there are 8 equal parts then each is one-eighth

  VC2M2N03 | Mathematics | Mathematics Version 2.0 | Level 2 | Number

• VC2M7A05

  generate tables of values from visually changing patterns or the rule of a function; describe and plot these relationships on the Cartesian plane

  Elaborations

  • plotting points from a table of values generated using simple linear functions and recognising patterns, such as the points lie on a straight line
  • discussing and using variables to create a general rule and using the rule to determine the value of the dependent variable for any given value of the independent variable; for example, plotting the value of the circumference of a circle for varying values of radius
  • using function machines to generate a table of ordered pairs using input and output values, plotting the relationships on a Cartesian plane and describing the graph in terms of shape
  • using diagrams and manipulatives to form linear growth patterns, representing these patterns in tables and describing the relationship in terms of the way the pattern is growing and in the context of the situation

  VC2M7A05 | Mathematics | Mathematics Version 2.0 | Level 7 | Algebra

• VC2M6A03

  design and use algorithms involving a sequence of steps and decisions that use rules to generate sets of numbers; identify, interpret and explain emerging patterns

  Elaborations

  • using an algorithm to create extended number sequences involving rational numbers, using a rule and digital tools, and explaining any emerging patterns
  • designing an algorithm to model operations, using the concept of input and output, describing and explaining relationships and any emerging patterns; for example, using function machines to model operations and recognising and comparing additive and multiplicative relationships
  • designing an algorithm or writing a simple program to generate a sequence of numbers based on the user’s input and a chosen operation, discussing any emerging patterns; for example, generating a sequence of numbers and comparing how quickly the sequences are growing in comparison to each other using the rule ‘add 2 to the input number’ compared to multiplying the input number by 2

  VC2M6A03 | Mathematics | Mathematics Version 2.0 | Level 6 | 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

• VC2M2M03

  identify the date and determine the number of days between events using calendars

  Elaborations

  • using calendars to locate specific dates and identify what day it is, to determine the date 2 weeks prior to or after a given date
  • creating a class calendar to enter specific dates relevant to the class, for example, students’ birthdays, school assemblies, sports carnivals or class excursions
  • using addition and a calendar to model and solve the problem ‘How many days are left in this year?’ by identifying the number of days left in this month and in each of the remaining months, and using addition to model and solve the problem
  • identifying and locating specific days or dates on a calendar, for example, school holidays, sports days, Anzac Day, Easter, Diwali or Ramadan

  VC2M2M03 | Mathematics | Mathematics Version 2.0 | Level 2 | 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

• VC2M2M04

  recognise and read the time represented on an analog clock to the hour, half-hour and quarter hour

  Elaborations

  • creating an analog clock from a paper plate, showing the placement of the numbers and the 2 hands, and explaining how long it takes for the 2 hands to move around the clock face and what time unit each is showing
  • recognising and describing the relationship between the movement of the hands on an analog clock and the duration of time it represents; for example, connecting the language of ‘half past’ to mean when the ‘big hand’ will be at half past the hour and recognising this position as being halfway around its full cycle
  • dividing a clock face into halves and quarters, and connecting the subdivisions with telling the time to the half-hour and quarter hour; and explaining the meaning of ‘quarter past’ and ‘quarter to’ referring to the hour

  VC2M2M04 | Mathematics | Mathematics Version 2.0 | Level 2 | Measurement

• VC2M6ST02

  identify statistically informed arguments presented in traditional and digital media; discuss and critique methods, data representations and conclusions

  Elaborations

  • investigating data representations in the media and discussing what they illustrate and the messages the people who created them might want to convey
  • evaluating reports and secondary data relating to the distribution and use of non-renewable resources around the world
  • identifying potentially misleading data representations in the media; for example, graphs with broken axes or non-linear scales, graphics not drawn to scale, data not related to the population about which the claims are made and pie charts in which the whole pie does not represent the entire population about which the claims are made
  • investigating both traditional and digital media relating to Aboriginal and Torres Strait Islander Peoples, identifying and critiquing statistically informed arguments

  VC2M6ST02 | Mathematics | Mathematics Version 2.0 | Level 6 | Statistics

• VC2M4A01

  find unknown values in numerical equations involving addition and subtraction, using the properties of numbers and operations

  Elaborations

  • demonstrating the commutative properties of addition using materials, diagrams and number lines; for example, using number lines to demonstrate that 5 + 2 = 2 + 5, and demonstrating that 2 + 2 + 3 = 7 and 2 + 3 + 2 = 7 and 3 + 2 + 2 = 7
  • using balance scales and informal uniform units to create addition or subtraction number sentences showing equivalence, such as 7 + 8 = 6 + 9, and to find unknowns in equivalent number sentences, such as 6 + 8 = □ + 10
  • using relational thinking and knowledge of equivalent number sentences to explain whether equations involving addition or subtraction are true; for example, explaining that 27 − 14 = 17 − 4 is true and using a number line to show the common difference is 13

  VC2M4A01 | Mathematics | Mathematics Version 2.0 | Level 4 | Algebra

• VC2M5M04

  estimate, construct and measure angles in degrees, using appropriate tools, including a protractor, and relate these measures to angle names

  Elaborations

  • using a protractor to measure angles in degrees and classifying these angles using angle names; for example, an acute angle is less than 90°, an obtuse angle is more than 90° and less than 180°, a right angle is equal to 90° and a reflex angle is more than 180° and less than 360°
  • estimating the size of angles in the environment using a clinometer and describing the angles using angle names
  • using a ruler and protractor to construct triangles, given the angle measures and side lengths
  • using a protractor to measure angles when creating a pattern or string design within a circle
  • recognising the size of angles within shapes that do and do not tessellate, measuring the angles and using the sum of angles to explain why some shapes will tessellate and other shapes do not

  VC2M5M04 | Mathematics | Mathematics Version 2.0 | Level 5 | Measurement

• VC2M2SP01

  recognise, compare and classify shapes, referencing the number of sides and using spatial terms such as ‘opposite’, ‘parallel’, ‘curved’ and ‘straight’

  Elaborations

  • sorting a collection of shapes in different ways based on their features, such as number of sides, whether all sides are equal and whether pairs of opposite sides are parallel; for example, sorting collections of triangles and other polygons
  • manipulating shapes and recognising that different orientations do not change the shape; for example, cutting out pictures of various shapes and recognising that they are still classified as the same shape even if they are upside down or on their side
  • investigating the shapes of different sporting fields, describing and labelling their features, including sidelines, centre circles and goal squares; for example, labelling the lines on a basketball court and using spatial terms to describe them
  • creating regular shapes using digital tools, describing and observing what happens when you manipulate them; for example, dragging or pushing vertices to produce irregular shapes, or moving or rotating a shape

  VC2M2SP01 | Mathematics | Mathematics Version 2.0 | Level 2 | Space