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• 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

• VC2MFST01

  collect, sort and compare data represented by objects and images in response to given investigative questions that have only 2 outcomes and relate to familiar situations

  Elaborations

  • using data displays to answer simple questions such as ‘How many students answered “yes” to having pets?’
  • collecting and deciding how to organise data to answer yes/no questions; for example, in relation to the question ‘Do more people in our class today have shoes with laces than without?’, explaining that lining up and matching shoes with and without laces one-to-one will answer the question
  • collecting data through everyday activities or events and sorting the collected data; for example, sorting toys into categories such as ‘toys that move’ and ‘toys that don’t move’
  • creating classroom charts and rosters using stickers to represent data; and comparing and interpreting the representations
  • investigating statistical contexts after reading a story; for example, after reading The Waterhole by Graeme Base, asking and responding to questions like ‘What different animals did you see?’, ‘How many different types of animals were there?’ or ‘Were there more tigers or kangaroos?’
  • exploring what and how information from the environment is collected and used by Aboriginal and/or Torres Strait Islander Peoples to predict weather events

  VC2MFST01 | Mathematics | Mathematics Version 2.0 | Foundation Level | Statistics

• VC2M7M03

  describe the relationship between π 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 2π
  • 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 π 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

• 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

• VC2M4N10

  follow and create algorithms involving a sequence of steps and decisions that use addition or multiplication to generate sets of numbers; identify and describe any emerging patterns

  Elaborations

  • creating an algorithm that will generate number sequences involving multiples of one to 10 using digital tools to assist, identifying and explaining emerging patterns, and recognising that number sequences can be extended indefinitely
  • creating a basic flow chart that represents an algorithm that will generate a sequence of numbers using multiplication by a constant term; using a calculator to model and follow the algorithm, and recording the sequence of numbers generated; and checking results and describing any emerging patterns
  • using a multiplication formula in a spreadsheet and the ‘fill down’ function to generate a sequence of numbers (for example, entering the number ‘1’ in the cell A1, using ‘fill down’ to cell A100, entering the formula ‘=A1*4’ in the cell B1 and using the ‘fill down’ function to generate a sequence of 100 numbers) and describing emerging patterns
  • creating an algorithm that will generate number sequences involving multiples of one to 10, using digital tools to assist, identifying and explaining emerging patterns, and recognising that number sequences can be extended indefinitely

  VC2M4N10 | Mathematics | Mathematics Version 2.0 | Level 4 | Number

• VC2M3ST03

  conduct guided statistical investigations involving the collection, representation and interpretation of data for categorical and discrete numerical variables with respect to questions of interest

  Elaborations

  • creating a poster, flow chart or infographic that describes the process of statistical investigation, and the components, tools and types of data that can be collected, represented and interpreted for a purpose
  • collaboratively working through a whole-class investigation by choosing a question of interest, using an efficient collection method and recording collected data, and then interpreting the data in terms of the question
  • planning and carrying out investigations that involve collecting data; for example, narrowing the focus of a question such as ‘Which is the most popular breakfast cereal?’ to ‘Which is the most popular breakfast cereal among Year 3 students in our class?’
  • conducting a whole-class statistical investigation into the best day to hold an open day for parents by creating a simple survey, collecting the data by asking the parents, representing and interpreting the results, and deciding as a class which day would be best
  • investigating seasonal calendars of Aboriginal and/or Torres Strait Islander Peoples by collecting data and creating frequency tables and spreadsheets based on environmental indicators, and creating one-to-one data displays about frequency of environmental indicators for the current season

  VC2M3ST03 | Mathematics | Mathematics Version 2.0 | Level 3 | Statistics

• VC2M1M03

  describe the duration and sequence of events using years, months, weeks, days and hours

  Elaborations

  • naming, listing and using familiar units of time, such as hours, days, weeks and years
  • comparing the number of days in the months of the year and explaining how the months cycle from one year to the next
  • sequencing familiar events, including representing time, on pictorial timelines
  • discussing events and activities and deciding whether they would take closer to an hour, a day, a week, a month or a year; for example, it takes a day for the sun to rise and fall and rise again, but it takes less than an hour for me to walk to school
  • investigating durations of time represented in Aboriginal and/or Torres Strait Islander seasonal calendars

  VC2M1M03 | Mathematics | Mathematics Version 2.0 | Level 1 | Measurement

• VC2M6M02

  establish the formula for the area of a rectangle and use it to solve practical problems

  Elaborations

  • using the relationship between the length and area of square units and the array structure to derive a formula for calculating the area of a rectangle from the lengths of its sides
  • using one-centimetre grid paper to construct a variety of rectangles, recording the side lengths and the related areas of the rectangles in a table to establish the formula for the area of a rectangle by recognising the relationship between the length of the sides and its calculated area
  • solving problems involving the comparison of lengths and areas using appropriate units
  • investigating the connection between the perimeters of different rectangles with the same area and between the areas of rectangles with the same perimeter

  VC2M6M02 | Mathematics | Mathematics Version 2.0 | Level 6 | Measurement

• VC2M8M03

  solve problems involving the circumference and area of a circle using formulas and appropriate units

  Elaborations

  • deducing that the area of a circle is between 2 radius squares and 4 radius squares, and using 3 × radius² as a rough estimate for the area of a circle
  • investigating the area of circles using a square grid or by rearranging a circle divided into smaller and smaller sectors or slices to resemble a close approximation of a rectangle
  • applying the formulas for the area and circumference of a circle to solve practical problems, and using one of the measures of radius, diameter, circumference or area to deduce the value of the other measures; for example, determining the length of material needed to edge a round table, given its dimensions as the area of the tabletop
  • exploring traditional weaving designs by Aboriginal and Torres Strait Islander Peoples and investigating the significance and use of circles

  VC2M8M03 | Mathematics | Mathematics Version 2.0 | Level 8 | Measurement

• VC2M5ST03

  plan and conduct statistical investigations by posing questions or identifying a problem and collecting relevant data; choose appropriate displays and interpret the data; communicate findings within the context of the investigation

  Elaborations

  • posing questions about insect diversity in the playground, and collecting data by taping a one-metre-square piece of paper to the playground and observing the type and number of insects on it over time
  • posing a question or identifying a problem of interest; collecting, interpreting and analysing the data; and discussing if the data generated provides the information necessary to answer the question
  • developing survey questions that are objective, without opinion, and have a balanced set of answer choices without bias
  • exploring Aboriginal and/or Torres Strait Islander ranger groups’ and other groups’ biodiversity detection techniques to care for Country/Place, posing investigative questions, and collecting and interpreting related data to represent and communicate findings

  VC2M5ST03 | Mathematics | Mathematics Version 2.0 | Level 5 | Statistics

• VC2M5N03

  compare and order common unit fractions with the same and related denominators, including mixed numerals, applying knowledge of factors and multiples; represent these fractions on a number line

  Elaborations

  • using pattern blocks to represent equivalent fractions; selecting one block or a combination of blocks to represent one whole, and making a design with shapes; and recording the fractions to justify the total
  • creating a fraction wall from paper tape to model and compare a range of different fractions with related denominators, and using the model to play fraction wall games
  • connecting a fraction wall model and a number line model of fractions to say how they are the same and how they are different; for example, explaining 14 on a fraction wall represents the area of one-quarter of the whole, while on the number line 14 is identified as a point that is one-quarter of the distance between zero and one
  • using an understanding of factors and multiples as well as equivalence to recognise efficient methods for the location of fractions with related denominators on parallel number lines; for example, explaining on parallel number lines that 210 is located at the same position on a parallel number line as 15 because 15 is equivalent to 210
  • converting between mixed numerals and improper fractions to assist with locating them on a number line

  VC2M5N03 | Mathematics | Mathematics Version 2.0 | Level 5 | Number

• VC2M6A02

  find unknown values in numerical equations involving brackets and combinations of arithmetic operations, using the properties of numbers and operations

  Elaborations

  • using brackets and the order of operations to write number sentences and appreciating the need for an agreed set of rules to complete multiple operations within the same number sentence; for example, for 40 ÷ 2 × (4 + 6) = □, you solve what is in the brackets first then complete the number sentence from left to right as there is no hierarchy between division and multiplication
  • constructing equivalent number sentences involving brackets and combinations of the 4 operations, and explaining the need to have shared agreement on the order of operations when solving problems involving more than one operation to have unique solutions
  • finding pairs of unknown values in numerical equations that make the equation hold true; for example, listing possible combinations of natural numbers that make this statement true: 6 + 4 × 8 = 6 × Δ + □

  VC2M6A02 | Mathematics | Mathematics Version 2.0 | Level 6 | Algebra

• 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

• VC2M1M02

  measure the length of shapes and objects using informal units, recognising that units need to be uniform and used end-to-end

  Elaborations

  • using 2 different units (for example, icy pole sticks and pencils) to measure the length of an object (for example, a desk), and explaining why the number of units used may be different
  • comparing the length of 2 objects, such as a desk and a bookshelf, by laying multiple copies of a unit and counting to say which is longer and how much longer; and explaining why they should not have gaps or overlaps between the units, as this will change the length of the unit
  • measuring the distance between 2 locations using footsteps, comparing the results and explaining why there may be different results, for example, referring to the different lengths of footsteps as using different units
  • measuring and comparing the length of objects using blocks; for example, comparing the height of 2 toys by stacking blocks one on top of the other and counting how many it takes to reach the height of each object to decide which is taller

  VC2M1M02 | Mathematics | Mathematics Version 2.0 | Level 1 | Measurement

• VC2M3M03

  recognise and use the relationship between formal units of time, including days, hours, minutes and seconds, to estimate and compare the duration of events

  Elaborations

  • estimating how long it would take to read a set passage of text, and sharing this information to demonstrate understanding of formal units of duration of time
  • planning a sequence of events based on estimates of the duration of each event; for example, planning a set of activities for a class party by estimating how long each game or activity will take
  • reading or setting the time on digital devices to the minute or second; for example, setting an online timing device to count down from a set time, or setting the time on a digital clock
  • using sand timers and digital timers to measure and check estimates of short durations of time, such as one minute, 3 minutes and 5 minutes
  • exploring how cultural accounts of Aboriginal and Torres Strait Islander Peoples explain cycles of time that involve the sun, moon and stars

  VC2M3M03 | Mathematics | Mathematics Version 2.0 | Level 3 | Measurement

• VC2M8M04

  solve problems involving time and duration, including using 12- and 24-hour time across multiple time zones

  Elaborations

  • using digital tools to investigate time zones around the world and convert from one zone to another, such as time in Perth, Western Australia, compared to Suva in Fiji or Toronto in Canada
  • recognising the challenges of planning regular virtual meeting times for a company that has both international staff and staff within different states and territories, and the impact daylight savings has due to multiple time zones, explaining the mathematical language used to communicate current time such as Coordinated Universal Time (UTC)+8, Australian Eastern Standard Time (AEST), Australian Central Standard Time (ACST) and Australian Western Standard Time (AWST)
  • planning an international travel itinerary that covers destinations in different time zones across Asia

  VC2M8M04 | Mathematics | Mathematics Version 2.0 | Level 8 | Measurement

• 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

• 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

• VC2M6SP03

  recognise and use combinations of transformations to create tessellations and other geometric patterns, using dynamic geometry software where appropriate

  Elaborations

  • using digital tools to create tessellations of shapes, including paver and tiling patterns, describing the transformations used and discussing why these shapes tessellate; and identifying shapes or combinations of shapes that will or will not tessellate, answering questions such as ‘Do all triangles tessellate?’
  • designing a school or brand logo using the transformation of one or more shapes and describing the transformations used
  • using dynamic geometry software and digital tools to experiment with transformations, for example, to demonstrate when the order of transformations produces different results; and experimenting with transformations and their application to fractals
  • designing an algorithm as a set of instructions to transform a shape, including getting back to where you started from; for example, programming a robot to move around the plane using instructions for movements, such as 2 down, 3 to the right, and combinations of these to transform shapes
  • investigating symmetry, transformation and tessellation in different shapes on Country/Place, including rock formations, insects, and land and sea animals, discussing the purpose or role symmetry plays in their physical structure

  VC2M6SP03 | Mathematics | Mathematics Version 2.0 | Level 6 | Space

• 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