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• VC2MFA01

  follow a short sequence of instructions; recognise, copy, continue and create repeating patterns represented in different ways

  Elaborations

  • carrying out a specified sequence of actions to move an object from one location to another
  • playing a simple rule-based game, moving a specified number of places according to the result on a dice in a chance-based game
  • recognising, copying and describing different repeating patterns using materials, shapes, sounds and movements during activities and play; for example, making a bead necklace and describing the pattern they have created, such as ‘red, blue, green, red, blue, green, red, blue, green’, or copying repeating patterns of drumbeats or dance moves during music activities
  • recognising repeating patterns used at home and in daily activities to help make tasks easier or to solve problems; for example, setting the table to eat
  • recognising and describing repeating patterns that can be observed on Country/Place and in Aboriginal and Torres Strait Islander artwork, cultural performances and material cultures, for example, shell and seed necklaces, dances and songs

  VC2MFA01 | Mathematics | Mathematics Version 2.0 | Foundation Level | Algebra

• VC2M9M05

  use mathematical modelling to solve practical problems involving direct proportion, rates, ratio and scale, including financial contexts; formulate the problems and interpret solutions in terms of the situation; evaluate the model and report methods and findings

  Elaborations

  • modelling situations that involve direct proportion (such as pro rata pay rates, exchange rates, multiple quotes for a job, conversion between scales or other appropriate science contexts); for example, situations that involve Hooke’s law and other science contexts involving wavelengths and frequencies
  • modelling situations that impact on image editing used in social media and how proportion may not be maintained and can result in distorted images
  • modelling situations involving compliance with building and construction standards in design and construction, such as the rise and tread of staircases, and vertical and horizontal components of escalators
  • modelling situations involving the application of rates in practical contexts, for example, density, birth, flow or heartbeats
  • exploring fire techniques in land management practices used by Aboriginal and Torres Strait Islander Peoples that use proportion relationships, including the rate of fire spread in different fuel types to wind speed, temperature and relative humidity

  VC2M9M05 | Mathematics | Mathematics Version 2.0 | Level 9 | Measurement

• VC2M8M02

  solve problems involving the volume and capacity of right prisms using appropriate units

  Elaborations

  • using models to demonstrate the number of cubic centimetres in a cubic metre and relating this to capacities of millilitres and litres, recognising that one millilitre is equivalent to one cm³
  • solving practical problems involving volume and capacity, for example, optimal packaging and production
  • choosing which measurements are useful to consider when solving practical problems in context; for example, when purchasing a new washing machine, the dimensions are useful when determining whether it will fit in the available space in the laundry and its capacity is useful when considering the maximum washing load it can carry
  • investigating, reasoning and finding solutions to measurement problems involving dimensions, rates, volume and capacity of objects; for example, given the dimensions of a pool and the rate of flow from a tap, determining how long it will take to fill the pool to its normal capacity

  VC2M8M02 | Mathematics | Mathematics Version 2.0 | Level 8 | Measurement

• VC2M3N01

  identify, explain and use the properties of odd and even numbers

  Elaborations

  • identifying even numbers using skip counting by twos or by grouping even collections of objects in twos
  • explaining why all numbers that end in the digits 0, 2, 4, 6 and 8 are even and that numbers ending in 1, 3, 5, 7 and 9 are odd
  • explaining why some materials can be shared evenly between 2 people without leaving a remainder and some cannot
  • explaining the patterns involved in adding, subtracting and multiplying odd and even numbers (for example, even + even = even, odd + even = odd, odd + odd = even) and using this to decide whether answers to addition, subtraction and multiplication calculations are correct or not
  • following an algorithm consisting of a flow chart with a series of instructions and decisions to determine whether a number is even or odd; and using the algorithm to identify which elements of a set of numbers are divisible by 2

  VC2M3N01 | Mathematics | Mathematics Version 2.0 | Level 3 | Number

• 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

• VC2M6N02

  identify and describe the properties of prime, composite, square and triangular numbers and use these properties to solve problems and simplify calculations

  Elaborations

  • using the definition of a prime number to explain why one is not a prime number
  • testing numbers by using division to distinguish between prime and composite numbers, recording the results on a number chart to identify any patterns
  • representing composite numbers as a product of their factors, including prime factors when necessary and using this form to simplify calculations involving multiplication, such as 15 × 16 as 5 × 3 × 4 × 4, which can be rearranged to simplify calculation to 5 × 4 × 3 × 4 = 20 × 12
  • identifying and describing the product of a number with itself as square; for example, 3 × 3 is the same as 3²
  • using spreadsheets to list all the numbers that have up to 3 factors, using combinations of only the first 3 prime numbers, recognising any emerging patterns, making conjectures and experimenting with other combinations

  VC2M6N02 | Mathematics | Mathematics Version 2.0 | Level 6 | Number

• VC2M6P01

  describe probabilities using fractions, decimals and percentages; recognise that probabilities lie on numerical scales of 0–‍1 or 0%–100%; use estimation to assign probabilities that events occur in a given context, using common fractions, percentages and decimals

  Elaborations

  • recognising that the probability of an event occurring can be represented numerically as either a number ranging from zero to one or a percentage from 0% to 100% where zero or 0% means it will not happen and one or 100% means it is certain to happen
  • using a scale of zero to one or 0% to 100% to estimate chances of events
  • listing the different possible outcomes for rolling a dice and using a scale to locate the relative probability by considering the chance of more than or less than for each possible event, for example, the probability of getting a number greater than 4
  • recognising the language used to describe situations involving uncertainty, such as what it means to be ‘lucky’, a ‘75% chance’ of rain or a ‘1-in-100 years’ flood
  • exploring Aboriginal and/or Torres Strait Islander children’s instructive games, such as Weme from the Warlpiri Peoples of Central Australia, to investigate and assign probabilities that events will occur, indicating their estimated likelihood

  VC2M6P01 | Mathematics | Mathematics Version 2.0 | Level 6 | Probability

• VC2M9SP01

  recognise the constancy of the sine, cosine and tangent ratios for a given angle in right-angled triangles using properties of similarity

  Elaborations

  • understanding the terms ‘base’, ‘altitude’, ‘hypotenuse’, and ‘adjacent’ and ‘opposite’ sides to an angle, in a right-angled triangle, and identifying these for a given right-angled triangle
  • investigating patterns to reason about nested similar triangles that are aligned on a coordinate plane, connecting ideas of parallel sides and identifying the constancy of ratios of corresponding sides for a given angle
  • establishing an understanding that the sine of an angle can be considered as the length of the altitude of a right-angled triangle with a hypotenuse of length one unit and similarly the cosine as the length of the base of the same triangle, and relating this to enlargement and similar triangles
  • relating the tangent of an angle to the altitude and base of nested similar right-angled triangles, and connecting the tangent of the angle at which the graph of a straight line meets the positive direction of the horizontal coordinate axis to the gradient of the straight line

  VC2M9SP01 | Mathematics | Mathematics Version 2.0 | Level 9 | Space

• VC2M3SP02

  interpret and create two-dimensional representations of familiar environments, locating key landmarks and objects relative to each other

  Elaborations

  • designing the layout of a space; for example, designing a proposed games room or a classroom using a blank sheet of paper as the boundary and cut-outs of shapes to represent furniture from a top-view perspective
  • locating themselves within a space, such as a basketball court, oval, stage or assembly hall, guided by a simple hand-held plan indicating the different positions of the participants in the activity
  • sketching a map indicating where they have hidden an object within the classroom, swapping maps with partners and then providing feedback about what was helpful and what was confusing on the map
  • identifying differences in the representation of a place on a map, in an aerial photograph, in a street view and in a satellite image, and discussing the different information the representations can give
  • exploring land maps or cultural maps used by Aboriginal and Torres Strait Islander Peoples to locate, identify and position important landmarks such as waterholes

  VC2M3SP02 | Mathematics | Mathematics Version 2.0 | Level 3 | Space

• VC2M5ST01

  acquire, validate and represent data for nominal and ordinal categorical and discrete numerical variables to address a question of interest or purpose using software including spreadsheets; discuss and report on data distributions in terms of highest frequency (mode) and shape, in the context of the data

  Elaborations

  • recognising that ordinal data is a form of categorical data even though the data being collected might be numbers, for example, a rating scale using numbers 1–5 to represent the categories people can choose from when asked, ‘What rating would you give this film out of 5?’
  • determining the mode for a set of data and discussing that there may be more than one mode
  • identifying the best methods of presenting data to illustrate the results of investigations and justifying the choice of representations
  • acquiring data through chance experiments, discussing and reporting on the distribution of outcomes and how this relates to equal and unequal outcomes
  • using digital systems to validate data; for example, recognising the difference between numerical, text and date formats in spreadsheets, and setting data types in a spreadsheet to make sure a date is input correctly
  • investigating data relating to the reconciliation process between Aboriginal and Torres Strait Islander Peoples and non-Indigenous Australians, posing questions, discussing and reporting on findings

  VC2M5ST01 | Mathematics | Mathematics Version 2.0 | Level 5 | Statistics

• VC2M8A02

  graph linear relations on the Cartesian plane using digital tools where appropriate; solve linear equations and one-variable inequalities using graphical and algebraic techniques; verify solutions by substitution

  Elaborations

  • recognising that in a table of values, if the first difference between consecutive values of the dependent variable is constant, then it is a linear relation
  • graphing linear functions and relations of the form x=a , y=a , x ≤a , x>a , y ≤a , y>a on the Cartesian plane for known values of a
  • completing a table of values, plotting the resulting points on the Cartesian plane and determining whether the relationship is linear
  • graphing the linear relationship ax+b=c for given values of a, b and c and identifying from the graph where ax+b <c or where ax+b >c
  • solving linear equations of the form ax+b=c and one-variable inequalities of the form ax+b <c or ax+b >c where a > 0 using inverse operations and digital tools, and checking solutions by substitution
  • solving linear equations such as 3x+7=6x-9 , representing these graphically, and verifying solutions by substitution

  VC2M8A02 | Mathematics | Mathematics Version 2.0 | Level 8 | Algebra

• VC2M5P01

  list the possible outcomes of chance experiments involving equally likely outcomes and compare to those that are not equally likely

  Elaborations

  • discussing what it means for outcomes to be equally likely and comparing the number of possible and equally likely outcomes of chance events; for example, when drawing a card from a standard deck of cards there are 4 possible outcomes if you are interested in the suit, 2 possible outcomes if you are interested in the colour or 52 outcomes if you are interested in the exact card
  • discussing how chance experiments that have equally likely outcomes can be referred to as random chance events; for example, if all the names of students in a class are placed in a hat and one is drawn at random, each person has an equally likely chance of being drawn
  • commenting on the chance of winning games by considering the number of possible outcomes and the consequent chance of winning
  • investigating why some games are fair and others are not; for example, drawing a track game to resemble a running race and taking it in turns to roll 2 dice, where the first runner moves a square if the difference between the 2 dice is zero, one or 2 and the second runner moves a square if the difference is 3, 4 or 5, and responding to the questions ‘Is this game fair?’, ‘Are some differences more likely to come up than others?’ and ‘How can you work that out?’
  • comparing the chance of a head or a tail when a coin is tossed, whether some numbers on a dice are more likely to be facing up when the dice is rolled, or the chance of getting a 1, 2 or 3 on a spinner with uneven regions for the numbers
  • discussing supermarket promotions such as collecting stickers or objects and whether there is an equal chance of getting each of them

  VC2M5P01 | Mathematics | Mathematics Version 2.0 | Level 5 | Probability

• VC2M6A01

  recognise and use rules that generate visually growing patterns and number patterns involving rational numbers

  Elaborations

  • investigating patterns such as the number of tiles in a geometric pattern, or the number of dots or other shapes in successive repeats of a strip or border pattern, looking for patterns in the way the numbers increase or decrease
  • using a calculator or spreadsheet to experiment with number patterns that result from multiplying or dividing; for example, 1 ÷ 9, 2 ÷ 9, 3 ÷ 9 …, 210 × 11, 211 × 11, 212 × 11 …, 111 × 11, 222 × 11, 333 × 11 …, or 100 ÷ 99, 101 ÷ 99, 102 ÷ 99 …
  • creating an extended number sequence that represents an additive pattern using decimals; for example, representing the additive pattern formed as students pay their $2.50 for an incursion as 2.50, 5.00, 7.50, 10.00, 12.50, 15.00, 17.50 …
  • investigating the number of regions created by successive folds of a sheet of paper (one fold, 2 regions; 2 folds, 4 regions; 3 folds, 8 regions) and describing the pattern using everyday language
  • creating a pattern sequence with materials, writing the associated number sequence and then describing the sequence with a rule so someone else can replicate it with different materials; for example, using matchsticks or toothpicks to create a growing pattern of triangles using 3 for one triangle, 5 for 2 triangles and 7 for 3 triangles and describing the pattern as ‘Multiply the number of triangles by 2 and then add one for the extra toothpick in the first triangle’

  VC2M6A01 | Mathematics | Mathematics Version 2.0 | Level 6 | Algebra

• VC2M9M03

  solve spatial problems, applying angle properties, scale, similarity, ratio, Pythagoras’ theorem and trigonometry in right-angled triangles

  Elaborations

  • investigating the applications of Pythagoras’ theorem in authentic problems, including applying Pythagoras’ theorem and trigonometry to problems in surveying and design
  • applying the formula for calculation of distances between points on the Cartesian plane from their coordinates, emphasising the connection to vertical and horizontal displacements between the points 
  • understanding the relationship between the corresponding sides of similar right-angled triangles and establishing the relationship between areas of similar figures and the ratio of corresponding sides, the scale factor
  • using images of proportional relationships to estimate actual measurements (for example, taking a photograph of a person standing in front of a tree and using the image and scale to estimate the height of the tree), discussing the findings and ways to improve the estimates
  • investigating theorems and conjectures involving triangles, for example, the triangle inequality and generalising links between the Pythagorean rule for right-angled triangles, and related inequalities for acute and obtuse triangles, determining the minimal sets of information for a triangle from which other measures can all be determined
  • using knowledge of similar triangles, Pythagoras’ theorem, rates and algebra to design and construct a Biltmore stick, used to measure the diameter and height of a tree, and calculating the density and dry mass to predict how much paper could be manufactured from the tree

  VC2M9M03 | Mathematics | Mathematics Version 2.0 | Level 9 | Measurement

• VC2M3M02

  measure and compare objects using familiar metric units of length, mass and capacity, and instruments with labelled markings

  Elaborations

  • making a measuring tape using metric units of length and using it to measure and compare things, for example, the girth of a tree; and explaining that the lines on a ruler show the beginning and end of each unit
  • using a strip of one-centimetre grid paper to measure and compare the length of objects, connecting this with centimetre units on a ruler and using fractions of a graduation to give a more accurate measure
  • discussing how the capacity of a container or object usually refers to the amount of liquid it can hold, measured in millilitres and litres, and comparing the capacity of different sizes of familiar drinks (for example, 600-millilitre, one-litre, 2-litre and 3-litre milk containers)
  • measuring and comparing the mass of objects and capacity of containers, using measuring jugs and kitchen or other scales and standard metric units of millilitres, litres, grams and kilograms; and interpreting and explaining what the lines on the measuring jug or scales mean
  • comparing the capacity of different beakers used in science lessons and using the numbered graduations to measure out different capacities of liquid

  VC2M3M02 | Mathematics | Mathematics Version 2.0 | Level 3 | Measurement

• VC2M2N05

  multiply and divide by one-digit numbers using repeated addition, equal grouping, arrays and partitioning to support a variety of calculation strategies

  Elaborations

  • making and naming arrays and using bar models to solve simple multiplication or sharing problems; for example, making different arrays to represent 12 and naming them as ‘3 fours’, ‘2 sixes’, ‘4 threes’ and ‘6 twos’, using physical or virtual materials to make arrays or using bar models to demonstrate that ‘3 fours’ is equal to ‘4 threes’
  • finding the total number represented in an array by partitioning the array using subitising and number facts; for example, describing how they determined the total number of dots arranged in a ‘3 fives’ array by saying, ‘I saw 2 fives, which is 10, and then 5 more, which makes 15’
  • recognising problems that can be solved using division and identifying the difference between dividing a set of objects into 3 equal groups and dividing the same set of objects into groups of 3
  • using a Think Board to solve partition and quotition division problems; for example, sharing a prize of $36 between 4 people, using materials, a diagram and skip counting to find the answer, and explaining whether the answer ‘9’ refers to people or dollars
  • using materials or diagrams, and skip counting, to solve repeated equal-quantity multiplication problems; for example, writing a repeated addition number sentence and using skip counting to solve the problem ‘Four trays of biscuits with 6 on each tray – how many biscuits are there?’

  VC2M2N05 | Mathematics | Mathematics Version 2.0 | Level 2 | Number

• VC2M7N08

  compare, order and solve problems involving addition and subtraction of integers

  Elaborations

  • using less-than and greater-than notation in expressions when comparing and ordering integers; for example, negative 5 is less than positive 2 and can be represented as -5<+2; -3>-6
  • discussing language such as ‘addition’, ‘subtraction’, ‘magnitude’, ‘difference’ and ‘sign’ and synonyms of these terms
  • ordering, adding and subtracting integers using a number line

  VC2M7N08 | Mathematics | Mathematics Version 2.0 | Level 7 | Number

• VC2M3ST01

  acquire data for categorical and discrete numerical variables to address a question of interest or purpose by observing, collecting and accessing data sets; record the data using appropriate methods, including frequency tables and spreadsheets

  Elaborations

  • using efficient ways to collect and record data (for example, written surveys, online surveys, polling the class using interactive digital mediums) and representing and reporting the results of investigations
  • developing questions of interest and using surveys, observations or experiments to collect categorical, discrete numerical or qualitative data sets and discussing what kind of data can be used to help inform or answer the question in a statistical investigation
  • using lists, tallies, symbols and digital data tables to record and display data collected during a chance experiment, for interpretation
  • using different online sources to access data; for example, using online query interfaces to select and retrieve data from an online database such as weather records, data frequency mapping software such as Google Trends, or the World Health Organization
  • using software to sort and calculate data when solving problems; for example, sorting discrete numerical and categorical data in ascending or descending order and automating simple arithmetic calculations using nearby cells and the summation (‘sum’) function in spreadsheets to calculate total frequencies of collected data

  VC2M3ST01 | Mathematics | Mathematics Version 2.0 | Level 3 | Statistics

• VC2M10AA04

  explore the inverse relationship between exponential functions and logarithmic functions and the solution of related equations

  Elaborations

  • using the definition of a logarithm and the exponent laws to establish the logarithm laws
  • evaluating 10x for decimal values of x and relating this to a logarithm base 10 scale; solving exponential equations algebraically using logarithms with base 10, for example, 5000×1.01x=10 000⇒x= log10(2)log10(1.01)≈69.66 ; and connecting to the graph of the corresponding function

  VC2M10AA04 | Mathematics | Mathematics Version 2.0 | Level 10A | Algebra

• VC2M10AP01

  explore counting principles, and factorial notation as a representation that provides efficient counting in multiplicative contexts, including calculations of probabilities

  Elaborations

  • applying the multiplication principle to problems involving combinations including probabilities relating to sampling with and without replacement, and representing these using tree diagrams
  • understanding that a set with n elements has 2ⁿ different subsets formed by considering each element for inclusion or not in combination, and that these can be systematically listed using a tree diagram or a table; for example, the set {a, b, c} has 2³ = 8 subsets which are { ∅, {a}, {b}, {c}, {a, b}, {a, c}, {b, c}, {a, b, c}}
  • using the definition of n! to represent and calculate in contexts that involve choices from a set; for example, how many different combinations of 3 playing cards from a pack? How many if the suits are ignored? How many with and without replacement?
  • performing calculations on numbers expressed in factorial form, such as n!r! to evaluate the number of possible arrangements of n objects in a row, r of which are identical; for example, 5 objects, 3 of which are identical, can be arranged in a row in
    5!3!=5×4×3×2×13×2×1= 20 different ways

  VC2M10AP01 | Mathematics | Mathematics Version 2.0 | Level 10A | Probability