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• VCMMG292

  Develop the conditions for congruence of triangles

  Elaborations

  • investigating the minimal conditions needed for the unique construction of triangles, leading to the establishment of the conditions for congruence (SSS, SAS, ASA and RHS)
  • solving problems using the properties of congruent figures
  • constructing triangles using the conditions for congruence

  VCMMG292 | Mathematics | Level 8 | Measurement and Geometry | Geometric reasoning

• 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

• VCMMG316

  Use the enlargement transformation to explain similarity and develop the conditions for triangles to be similar

  Elaborations

  • establishing the conditions for similarity of two triangles and comparing this to the conditions for congruence
  • using the properties of similarity and ratio, and correct mathematical notation and language, to solve problems involving enlargement. For example, scale diagrams
  • using the enlargement transformation to establish similarityunderstanding that similarity and congruence help describe relationships between geometrical shapes and are important elements of reasoning and proof

  VCMMG316 | Mathematics | Level 9 | Measurement and Geometry | Geometric reasoning

• VCMNA129

  Investigate the conditions required for a number to be odd or even and identify 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

  VCMNA129 | Mathematics | Level 3 | Number and Algebra | Number and place value

• VC2M8SP01

  identify the conditions for congruence and similarity of triangles and explain the conditions for other sets of common shapes to be congruent or similar, including those formed by transformations

  Elaborations

  • developing an understanding of what it means for shapes to be congruent or similar
  • using the enlargement transformation and digital tools to develop sets of similar shapes
  • investigating sufficient conditions to establish that 2 triangles are congruent
  • applying logical reasoning and tests for congruence and similarity, to problems and proofs involving plane shapes
  • comparing angle and side measurements of shapes under transformation to answer questions such as ‘What changes?’ and ‘What stays the same?’
  • establishing that 2 shapes are congruent if one lies exactly on top of the other after one or more transformations, including translations, reflections and rotations, and recognising that the matching sides and the matching angles are equal

  VC2M8SP01 | Mathematics | Mathematics Version 2.0 | Level 8 | Space

• VCMSP177

  Identify events where the chance of one will not be affected by the occurrence of the other

  Elaborations

  • explaining that the probability of a new baby being either a boy or a girl does not depend on the sex of the previous baby

  VCMSP177 | Mathematics | Level 4 | Statistics and Probability | Chance

• VC2M10P01

  use the language of ‘if … then …’, ‘given’, ‘of’ and ‘knowing that’ to investigate conditional statements and identify common mistakes in interpreting such language, and describe and interpret situations involving conditional probability; design and conduct simulations using digital tools to model...

  Elaborations

  • using two-way tables and Venn diagrams to understand conditional statements using the language of ‘if … then …’, ‘given’, ‘of’ and ‘knowing that’ and identifying common mistakes in interpreting such language
  • using arrays and tree diagrams to represent, interpret and compare probabilities of dependent and independent events 
  • using samples of different sizes with and without replacement from a population to identify when the difference in methods becomes negligible
  • using simulations to gather data on frequencies for situations involving chance that appear to be counterintuitive, such as the three-door problem or the birthday problem
  • identifying situations in real life where probability simulations are used for decision-making, such as supply and demand of product, insurance risk and queueing 
  • using simulation to predict the number of people likely to be infected with a strain of flu or virus

  VC2M10P01 | Mathematics | Mathematics Version 2.0 | Level 10 | Probability

• VCMMG265

  Investigate conditions for two lines to be parallel and solve simple numerical problems using reasoning

  Elaborations

  • constructing parallel and perpendicular lines using their properties, a pair of compasses and a ruler, and dynamic geometry software
  • defining and identifying the relationships between alternate, corresponding and co-interior angles for a pair of parallel lines cut by a transversal

  VCMMG265 | Mathematics | Level 7 | Measurement and Geometry | Geometric reasoning

• VCMSP348

  Use the language of ‘if ....then, ‘given’, ‘of’, ‘knowing that’ to investigate conditional statements and identify common mistakes in interpreting such language

  Elaborations

  • using two-way tables and Venn diagrams to understand conditional statements
  • using arrays and tree diagrams to determine probabilities

  VCMSP348 | Mathematics | Level 10 | Statistics and Probability | Chance

• VC2M10P02

  describe the results of two- and three-step chance experiments, both with and without replacements, assign probabilities to outcomes and determine probabilities of events; investigate the concept of independence

  Elaborations

  • recognising that a subsequent event can be dependent, and that this will affect the way its probability is calculated, for example, cards chosen from a standard deck without replacement, conditional selection problems from a fixed sample size, or the Bertrand’s box paradox

  VC2M10P02 | Mathematics | Mathematics Version 2.0 | Level 10 | Probability

• VC2M10A15

  use mathematical modelling to solve applied problems involving inverse proportion, growth and decay, including in financial contexts to establish the compound interest formula as repeated applications of simple interest; formulate problems, choosing to apply linear, quadratic or exponential models...

  Elaborations

  • modelling problems involving inverse proportion in real-life contexts such as travel time decreasing with increased travel speed, the brightness of luminous objects decreasing with distance, or household expenditure and savings, and solving related equations
  • modelling situations and choosing between linear, quadratic and exponential models by representing relationships in a table of values and recognising that linear functions have constant first differences, quadratic functions have constant second differences and exponential functions have a constant ratio between consecutive values of the dependent variable
  • modelling situations involving exponential growth and decay, and contrasting this with linear growth or decay, for example, situations involving constant percentage change and constant ratio, and determining doubling time and half-life and approximate intervals for which the values of the model lie within a given range
  • modelling situations that involve working with authentic information, data and interest rates to calculate compound interest and solve related problems
  • modelling and investigating how exponential equations are used in carbon dating to estimate the age of Aboriginal and Torres Strait Islander artefacts or material culture
  • modelling situations involving the growth of native animal populations on Country/Place with varying reproductive behaviour, using exponential functions and critiquing their applicability to real-world situations

  VC2M10A15 | Mathematics | Mathematics Version 2.0 | Level 10 | Algebra

• VC2MFN06

  represent practical situations that involve equal sharing and grouping with physical and virtual materials and use counting or subitising strategies

  Elaborations

  • using materials to role-play equal sharing; for example, sharing pieces of fruit or a bunch of grapes between 4 people and discussing how you would know they have been shared equally; or, when playing card games where each player is dealt the same number of cards, counting the number of cards after the deal to ensure they have the same amount
  • representing situations that involve counting several items; for example, starting with 9 beads or 6 $1 coins and then sharing them equally between 3 people by subitising or counting each group by ones to decide how many beads or coins each person will receive
  • exploring instructive games of Aboriginal and/or Torres Strait Islander Peoples that involve sharing; for example, playing Yangamini of the Tiwi Peoples of Bathurst Island to investigate and discuss equal sharing

  VC2MFN06 | Mathematics | Mathematics Version 2.0 | Foundation Level | Number

• VC2MFN01

  name, represent and order numbers, including zero to at least 20, using physical and virtual materials and numerals

  Elaborations

  • responding to a request to collect a quantity of objects or reading a numeral and selecting the associated quantity of items from a collection to match the number required; for example, collecting 9 paintbrushes after hearing the word ‘nine’
  • recognising the order in the sequence of numbers to 20 and identifying the number that is ‘one less’ than a given number and the number that is ‘one more’; for example, playing instructive card games that involve reading and ordering number cards, or using counting songs, storybooks and rhymes to establish the forwards and backwards counting sequence of numbers in the context of active counting activities
  • understanding and using terms to indicate ordinal position in a sequence; for example, filling in the missing term in ‘first’, ‘second’, ‘third’, … ‘fifth’ …, or creating a number track using cards with the numerals zero to 20 and describing positions using terms such as ‘first’, ‘last’, ‘before’, ‘after’ and ‘between’
  • recognising, writing and reading numerals written on familiar objects; for example, recognising and reading numerals in images, text or illustrations in storybooks, or writing a numeral on a container as a label to show how many objects it contains
  • connecting quantities to number names and numerals when reading and reciting stories and playing counting games or determining and reasoning about the size of sets of objects within Aboriginal and/or Torres Strait Islander Peoples’ instructive games, for example, Segur etug from Mer Island in the Torres Strait region

  VC2MFN01 | Mathematics | Mathematics Version 2.0 | Foundation Level | Number

• VC2M2N01

  recognise, represent and order numbers to at least 1000 using physical and virtual materials, numerals and number lines

  Elaborations

  • recognising missing numbers on different number lines, for example, a number line with 1800 on one end and 2200 on the other, with every decade numbered
  • recognising and locating the position of pieces within hundreds chart puzzles using knowledge of the order of natural numbers
  • reading and writing numerals, and saying and ordering two-, three- and four-digit numbers using patterns in the number system, including numbers with zeros in different places and numbers that look and sound similar (such as 808, 880, 818 and 881)
  • collecting large quantities of materials for recycling (for example, ring pulls, bottle tops and bread tags) and grouping them into ones, tens and hundreds, and using the materials to show different representations of two- and three-digit numbers

  VC2M2N01 | Mathematics | Mathematics Version 2.0 | Level 2 | Number

• VC2M1N01

  recognise, represent and order numbers to at least 120 using physical and virtual materials, numerals, number lines and charts

  Elaborations

  • reading, writing and naming numerals and ordering two-digit numbers from zero to at least 120, using patterns within the natural number system, including numbers that look and sound similar, for example, 16, 60, 61 and 66
  • using number tracks or positioning a set of numbered cards in the correct order and relative location by pegging them on an empty number line
  • using hundreds charts to build understanding and fluency with numbers; for example, collaboratively building a hundreds chart using cards numbered from zero to 99, or colour-coding the count of tens in a hundreds chart using one colour to represent the number of tens and another to represent the number of ones
  • recognising that numbers are used in all languages and cultures but may be represented differently in words and symbols (for example, through kanji numbers in Japanese and characters in Chinese) and that there are alternative numeration systems (for example, using special characters for 10 and 100 and other multiples of 10 in Japanese and Chinese numeration)

  VC2M1N01 | Mathematics | Mathematics Version 2.0 | Level 1 | Number

• VC2MFN05

  represent practical situations, including simple financial situations, involving addition, subtraction and quantification with physical and virtual materials and use counting or subitising strategies

  Elaborations

  • using role-play and materials to represent mathematical relationships in stories; for example, role-playing ‘Eight kangaroos were drinking at the river and 3 hopped away’, drawing a picture and using materials to represent the situation, discussing, and recording the result of the action with a numeral
  • role-playing or actively engaging in situations that involve quantifying or comparing collections of items or simple money transactions; for example, engaging with the question ‘Do we have enough scissors for our group so that each person has their own pair?’, or role-playing using $1 coins to pay for items in a shop where items are priced in whole dollars
  • representing situations expressed in Aboriginal and/or Torres Strait Islander stories, such as ‘Tiddalick, the greedy frog’, that describe additive situations and their connections to Country/Place
  • representing addition and subtraction situations found in leaf games involving sets of objects used to tell stories, such as games from the Warlpiri Peoples of Yuendumu in the Northern Territory

  VC2MFN05 | Mathematics | Mathematics Version 2.0 | Foundation Level | Number

• VC2M1N02

  partition one- and two-digit numbers in different ways using physical and virtual materials, including partitioning two-digit numbers into tens and ones

  Elaborations

  • building knowledge and understanding of the part-part-whole facts to 10, using physical and virtual materials; for example, using virtual ten-frames through a digital app or website to identify pairs of numbers that combine to make 10
  • using physical and virtual materials to partition numbers into counts of tens and ones; for example, recognising 35 as 3 tens and 5 ones or as 2 tens and 15 ones
  • using part-part-whole reasoning and physical or virtual materials to represent 24, then partitioning 24 in different ways and recording the partitions using numbers; for example, 10, 10 and 4 combine to make 24 or 10 and 14 combine to make 24

  VC2M1N02 | Mathematics | Mathematics Version 2.0 | Level 1 | Number

• VC2M1N04

  add and subtract numbers within 20, using physical and virtual materials, part-part-whole knowledge to 10 and a variety of calculation strategies

  Elaborations

  • using drawings, physical and virtual materials, and number combinations within 10 to add and subtract collections to 20
  • adding and subtracting numbers within 20, using a variety of representations and strategies, such as counting on, counting back, partitioning and part-part-whole knowledge of numbers to 10; for example, using partitioning and combining 7+5=7+3+2=10+2=12
  • developing and using strategies for one-digit addition and subtraction based on part-part-whole relationships for each of the numbers to 10 and subitising with physical and virtual materials; for example, 8 and 6 is the same as 8 and 2 and 4
  • representing story problems involving addition and subtraction of numbers within 20 using a Think Board; recognising and using + and − symbols and the equal sign (=) to represent the operations of addition and subtraction; and showing and explaining the connections between any materials used using the language of plus and minus, and the numbers within the story problem
  • creating and performing addition and subtraction stories told through Aboriginal and/or Torres Strait Islander dances

  VC2M1N04 | Mathematics | Mathematics Version 2.0 | Level 1 | Number

• 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

• VC2M1N05

  use mathematical modelling to solve practical problems involving additive situations, including simple money transactions; represent the situations with diagrams, physical and virtual materials; use calculation strategies to solve the problem

  Elaborations

  • modelling problems involving addition and subtraction presented in stories, using a Think Board to represent the problem, solving the problem using physical materials and explaining the connections between any materials used, the Think Board diagram and the numbers within the story
  • modelling simple money problems involving addition and subtraction using whole dollar amounts; for example, setting up a shop and role-playing practical problems of buying and selling goods, using addition and subtraction with play money and prices in whole dollar amounts; or solving the problem ‘I had $14 and was given $15 for my birthday’ using addition to answer the problem
  • modelling a variety of different additive situations to solve practical problems; for example, keeping track of the number of people on a bus as it stops to pick up and drop off passengers or the number of people entering a lift

  VC2M1N05 | Mathematics | Mathematics Version 2.0 | Level 1 | Number