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• VCMNA132

  Recognise and explain the connection between addition and subtraction

  Elaborations

  • demonstrating the connection between addition and subtraction using partitioning or by writing equivalent number sentences
  • solving simple word problems involving addition or subtraction

  VCMNA132 | Mathematics | Level 3 | Number and Algebra | Number and place value

• VC2M5N05

  solve problems involving addition and subtraction of fractions with the same or related denominators, using different strategies

  Elaborations

  • using different ways to add and subtract fractional amounts by subdividing different models of measurement attributes; for example, adding half an hour and three-quarters of an hour using a clock face, adding a $\frac{3}{4}$ cup of flour and a $\frac{1}{4}$ cup of flour, subtracting $\frac{3}{4}$ of a metre from 2 $\frac{1}{4}$ metres
  • representing and solving addition and subtraction problems involving fractions by using jumps on a number line, or bar models, or making diagrams of fractions as parts of shapes
  • using materials, diagrams, number lines or arrays to show and explain that fraction number sentences can be rewritten in equivalent forms without changing the quantity, for example, $\frac{1}{2}+\frac{1}{4}$ is the same as $\frac{2}{4}+\frac{1}{4}\mathrm{ }$

  VC2M5N05 | Mathematics | Mathematics Version 2.0 | Level 5 | Number

• 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

• VC2M10A12

  solve linear equations involving simple algebraic fractions

  Elaborations

  • solving a wide range of linear equations, including those involving one or 2 simple algebraic fractions, and checking solutions by substitution
  • representing word problems, including those involving fractions, as equations and solving them to answer the question

  VC2M10A12 | Mathematics | Mathematics Version 2.0 | Level 10 | Algebra

• VCMMG095

  Measure and compare the lengths, masses and capacities of pairs of objects using uniform informal units

  Elaborations

  • understanding that in order to compare objects, the unit of measurement must be the same size
  • lifting to compare the mass of objects using words, for example, heavier, lighter, same
  • measuring the capacity of containers using uniform material, for example cups or buckets

  VCMMG095 | Mathematics | Level 1 | Measurement and Geometry | Using units of measurement

• VCMNA340

  Solve linear equations involving simple algebraic fractions

  Elaborations

  • solving a wide range of linear equations, including those involving one or two simple algebraic fractions, and checking solutions by substitution
  • representing word problems, including those involving fractions, as equations and solving them to answer the question

  VCMNA340 | Mathematics | Level 10 | Number and Algebra | Linear and non-linear relationships

• VCMNA253

  Extend and apply the laws and properties of arithmetic to algebraic terms and expressions

  Elaborations

  • identifying order of operations in contextualised problems, preserving the order by inserting brackets in numerical expressions, then recognising how order is preserved by convention
  • moving fluently between algebraic and word representations as descriptions of the same situation

  VCMNA253 | Mathematics | Level 7 | Number and Algebra | Patterns and algebra

• VCMNA139

  Use a function machine and the inverse machine as a model to apply mathematical rules to numbers or shapes

  Elaborations

  • finding and describing simple rules in words to solve problems
  • using simple function machines to represent and apply a process or the inverse process, such as increase or decrease the value of a number by a specified amount

  VCMNA139 | Mathematics | Level 3 | Number and Algebra | Patterns and algebra

• VCMNA035

  Use number names in sequence to count in everyday situations, initially from one to five

  Elaborations

  • developing fluency in forward counting to five using words, sign or augmentative and alternative communication (AAC) in meaningful contexts, including everyday experiences and stories
  • knowing that the forward sequence of counting words occurs in the same order, for example always communicating numbers in the same sequence, indicating when another person uses number names in the wrong sequence
  • developing one-to-one correspondence by recognising that each object is counted, by indicating an object during counting situations, for example, indicating by pointing, activating a switch or eye gaze

  VCMNA035 | Mathematics | Level C | Number and Algebra | Number and place value

• VCMMG099

  Give and follow directions to familiar locations

  Elaborations

  • understanding that people need to give and follow directions to and from a place, and that this involves turns, direction and distance
  • understanding the meaning and importance of words such as ‘clockwise’, ‘anticlockwise’, ‘forward’ and ‘under’ when giving and following directions
  • interpreting and following directions around familiar locations

  VCMMG099 | Mathematics | Level 1 | Measurement and Geometry | Location and transformation

• VCMNA072

  Compare, order and make correspondences between collections, initially to 20, and explain reasoning

  Elaborations

  • comparing and ordering items of like and unlike characteristics using the words ‘more’, ‘less’, ‘same as’ and ‘not the same as’ and giving reasons for these answers
  • understanding and using terms such as ‘first’ and ‘second’ to indicate ordinal position in a sequence.
  • using objects which are personally and culturally relevant to students

  VCMNA072 | Mathematics | Foundation Level | Number and Algebra | Number and place value

• VCMNA053

  Recognise number name, numerals and quantities, initially up to five and beyond

  Elaborations

  • responding to key vocabulary and questions about ‘how many’
  • using one-to-one matching of number words, sign or augmentative and alternative communication (AAC) representation for objects to five
  • matching numerals to the correct number of items initially to five using number games, software, cards and everyday situations

  VCMNA053 | Mathematics | Level D | Number and Algebra | Number and place value

• 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

• VC2M1SP02

  give and follow directions to move people and objects to different locations within a space

  Elaborations

  • interpreting and following directions around familiar locations, and understanding the meaning and importance of the words when giving directions; for example, using words like ‘forwards’ and ‘backwards’, ‘straight ahead’, ‘left’ or ‘right’ to describe movement and giving instructions like ‘Keep going straight until you reach the end of this passage and then turn to your right’
  • creating and following an algorithm consisting of a set of instructions to move an object to a different location; for example, role-playing being a robot and following step-by-step instructions given by another classmate to move from one place to another, only moving as instructed
  • following directions to move people into different positions within a line using both ordinal and positional language to describe their position; for example, directly comparing heights and following directions using ordinal and positional language to line up in height order
  • describing a familiar journey across Country/Place using directional language

  VC2M1SP02 | Mathematics | Mathematics Version 2.0 | Level 1 | Space

• VCMNA069

  Establish understanding of the language and processes of counting by naming numbers in sequences, initially to and from 20, moving from  any starting point

  Elaborations

  • reading stories from other cultures featuring counting in sequence to assist students to recognise ways of counting in local languages and across cultures
  • identifying the number words in sequence, backwards and forwards, and reasoning with the number sequences, establishing the language on which subsequent counting experiences can be built
  • developing fluency with forwards and backwards counting in meaningful contexts, including stories and rhymes
  • understanding that numbers are said in a particular order and there are patterns in the way we say them

  VCMNA069 | Mathematics | Foundation Level | Number and Algebra | Number and place value

• VC2MFM01

  identify and compare attributes of objects and events, including length, capacity, mass and duration, use direct comparisons and communicate reasoning

  Elaborations

  • using language to describe the measurement attributes of length, mass, capacity and duration, and connecting the words with the appropriate attribute; for example, using words like ‘tall’, ‘short’, ‘wide’, ‘long’ and ‘high’ to describe the attribute of length
  • directly comparing pairs of objects to say which is longer/shorter, and explaining or demonstrating how they know; for example, standing back-to-back to determine who is taller or choosing to line up the bases of a spoon and fork to decide which is longer and explaining why
  • starting 2 events at the same time to decide which takes longer; for example, putting on a pair of sandals with buckles or Velcro, describing the duration using familiar terms and reasoning, ‘I took a longer time because I’m still learning to do up my buckles’
  • directly comparing pairs of everyday objects from the kitchen pantry to say which is heavier/lighter; for example, hefting a tin of baked beans and a packet of marshmallows or comparing the same pair of objects to say which is longer/shorter and discussing comparisons

  VC2MFM01 | Mathematics | Mathematics Version 2.0 | Foundation Level | Measurement

• VC2M10A08

  solve linear inequalities and graph their solutions on a number line

  Elaborations

  • representing word problems with simple linear inequalities and solving them to answer questions
  • graphing regions corresponding to inequalities in the Cartesian plane (for example, graphing $2x+3y<24)\mathrm{ }$and verifying using a test point such as (0, 0)

  VC2M10A08 | Mathematics | Mathematics Version 2.0 | Level 10 | Algebra

• 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

• 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

• VC2M7A02

  apply the associative, commutative and distributive laws to aid mental and written computation, and formulate algebraic expressions using constants, variables, operations and brackets

  Elaborations

  • simplifying calculations
  • forming simple estimates for calculations involving multiple and/or combined operations
  • generalising arithmetic expressions to algebraic expressions involving constants, variables, operations and brackets; for example,$7+7+7=3\times 7$, $x+x+x=3\times x$ noting that $3x$ includes implied multiplication and recognising the difference between $3x+4$ and $3\left(x+4\right)$
  • formulating algebraic expressions that represent mathematical relationships; for example, translating from words to symbols in ‘think of a number’ type activities
  • recognising and applying the concept of variable as something that can change in value, investigating the relationships between variables, and the application to processes on Country/Place, including how cultural expressions of Aboriginal and Torres Strait Islander Peoples, such as storytelling, communicate mathematical relationships that can be represented as mathematical expressions

  VC2M7A02 | Mathematics | Mathematics Version 2.0 | Level 7 | Algebra