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• VC2M1A01

  recognise, continue and create pattern sequences, with numbers, symbols, shapes and objects including Australian coins, formed by skip counting, initially by twos, fives and tens

  Elaborations

  • using number charts, songs, rhymes and stories to establish skip counting sequences of twos, fives and tens
  • using shapes and objects to represent a growing pattern formed by skip counting; for example, using blocks or beads to represent the growing patterns 2, 4, 6, 8, 10 … and 5, 10, 15, 20 …
  • recognising the patterns in sequences formed by skip counting; for example, recognising that skip counting in fives starting from zero always results in either a 5 or zero as the final digit
  • counting by twos, fives or tens to determine how much money is in a collection of coins or notes of the same denomination, for example, 5-cent, 10-cent and $2 coins or $5 and $10 notes
  • using different variations of the popular Korean counting game Sam-yuk-gu for generating skip counting pattern sequences

  VC2M1A01 | Mathematics | Mathematics Version 2.0 | Level 1 | Algebra

• 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

• VC2M1ST01

  acquire and record data for categorical variables in various ways including using digital tools, objects, images, drawings, lists, tally marks and symbols

  Elaborations

  • discussing methods of collecting data to answer a question such as ‘What types of rubbish are found in the playground?’, sharing ideas and trying out some of the suggested methods, reviewing the data collected and explaining how they might change the way they collect data next time
  • collecting and recording information on a topic of interest using lists (for example, ‘How many people follow a particular football team’ or ‘What colour eyes each person has’), examining the data to generate some questions that it could answer, and then rearranging the data or collecting different data to answer the question
  • creating a tally to record data while observing events such as the year level of students using the bike shed, deciding on the possible categories before the observations are taken, and then reviewing the data afterwards to notice whether the tally was effective
  • using star charts with stickers or emojis to represent class data; for example, using emojis on a personal feeling chart to represent how they are feeling each day or using emojis to represent activities on the class calendar
  • exploring ways of representing, sharing and communicating data through stories and symbols used by Aboriginal and Torres Strait Islander Peoples

  VC2M1ST01 | Mathematics | Mathematics Version 2.0 | Level 1 | Statistics

• Mathematics Version 2.0: Level 1 achievement standards

  By the end of Level 1, students connect number names, numerals and quantities, and order numbers to at least 120. They demonstrate how one- and two-digit numbers can be partitioned in different ways and that two-digit numbers can be partitioned into tens and ones. Students partition collections...

  Level description | Mathematics | Mathematics Version 2.0 | Level 1

• Mathematics Version 2.0: Level 7 description

  In Level 7, learning in Mathematics builds on each student’s prior learning and experiences. Students engage in a range of approaches to the learning and doing of mathematics that develop their understanding of and fluency with concepts, procedures and processes by making connections...

  Level description | Mathematics | Mathematics Version 2.0

• Mathematics | Mathematics Version 2.0: Structure

  Mathematics is presented in 11 levels, from Foundation to Level 10.

  Level 10 also includes Level 10A, which provides opportunities for students to extend their exploration of mathematical notions and further their mathematical studies.

  Strands

  The curriculum is organised into 6 interrelated...

  Overview material | Mathematics Version 2.0

• Mathematics | Mathematics Version 2.0: Learning in Mathematics Version 2.0

  Learning in Mathematics emphasises the importance of providing opportunities for students to develop proficiency in mathematics. This development of proficiency is achieved in how content is explored or developed, that is, how students experience the thinking and doing of mathematics.

  Proficiency...

  Overview material | Mathematics Version 2.0

• VC2M4ST02

  analyse the effectiveness of different displays or visualisations in illustrating and comparing data distributions, then discuss the shape of distributions and the variation in the data

  Elaborations

  • suggesting questions that can be answered by a given data display and using the display to answer these questions
  • interpreting data representations in the media and other forums where symbols represent one-to-many relationships and how this can be challenging when the representations use part-whole representations
  • comparing different student-generated diagrams, tables and graphs, describing their similarities and differences and commenting on the usefulness of each representation for interpreting the data

  VC2M4ST02 | Mathematics | Mathematics Version 2.0 | Level 4 | Statistics

• 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

• 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

• VC2M4ST01

  acquire data for categorical and discrete numerical variables to address a question of interest or purpose using digital tools; represent data using many-to-one pictographs, column graphs and other displays or visualisations; interpret and discuss the information that has been created

  Elaborations

  • investigating many-to-one data displays using digital tools and graphical software, interpreting and discussing key features
  • understanding that data can be represented with one symbol representing more than one piece of data, and that it is important to read all information about a representation before making judgements
  • constructing graphs of data collected through observation during science experiments, recording, interpreting and discussing the results in terms of the scientific study
  • acquiring samples of data using practical activities, observations or repeated chance experiments; recording data using tally charts, digital tables or spreadsheets; and graphing, discussing and comparing the results using a column graph
  • using secondary data of fire burns to construct data displays that assist Aboriginal and/or Torres Strait Islander ranger groups and other groups to care for Country/Place

  VC2M4ST01 | Mathematics | Mathematics Version 2.0 | Level 4 | Statistics

• VC2M7M03

  describe the relationship between $\pi$ and the circumference, radius and diameter of a circle

  Elaborations

  • recognising the features of circles and their relationships to one another; for example, labelling the parts of a circle including centre, radius, diameter and circumference and using one of radius, diameter or circumference to determine the measure of the other 2; and understanding that the diameter of a circle is twice the radius, or that the radius is the circumference divided by $2\pi$
  • comparing the circumference of circles in relation to their radius and diameter with materials and measuring, to establish measurement formulas; for example, using a compass to draw several circles, then using string to approximate the circumference, comparing the length of string to the diameter of the circle
  • investigating $\pi$ as the constant in the proportional relationship between the circumference of a circle and its diameter, and historical approximations from different civilisations, including Egypt, Babylon, Greece, India and China
  • investigating the applications and significance of circles in everyday life of Aboriginal and Torres Strait Islander Peoples, such as in basketry, symbols and architecture, recognising the relationships between the centre, radius, diameter and circumference

  VC2M7M03 | Mathematics | Mathematics Version 2.0 | Level 7 | Measurement

• 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

• 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

• 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

• VC2M6N07

  solve problems that require finding a familiar fraction, decimal or percentage of a quantity, including percentage discounts, choosing efficient calculation strategies with and without digital tools

  Elaborations

  • explaining how $\frac{1}{3}$ of a quantity can be achieved by dividing by 3, and how knowledge of $\frac{1}{3}$ of a quantity can be used to find $\frac{2}{3}\mathrm{ }$or $\frac{4}{3}\mathrm{ }$of the same quantity, using situations involving money, length, duration, mass or capacity
  • investigating percentage discounts of 10%, 25% and 50% in an online toy sale, using their equivalent decimal representations of 0.10, 0.25 and 0.50 to calculate the amount of discount on sale items, with and without digital tools
  • linking percentages to their decimal equivalent of tenths and hundredths and using these to determine percentage discounts; for example, finding a 30% discount by using its equivalence to 0.3, dividing by 10 and multiplying the result by 3 to give 30%
  • explaining the equivalence between percentages and fractions, for example, 33$\frac{1}{3}\mathrm{ }$% and $\frac{1}{3}\mathrm{ }$, keeping to percentages that are equivalent to fractions with small denominators such as 66$\frac{2}{3}\mathrm{ }$% and 12.5%
  • representing a situation with a mathematical expression, for example, numbers and symbols such as $\frac{1}{4}$ × 24, that involves finding a familiar fraction or percentage of a quantity; and using mental strategies or a calculator and explaining the result in terms of the situation in question

  VC2M6N07 | Mathematics | Mathematics Version 2.0 | Level 6 | Number