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• 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

• VC2M2SP02

  locate positions in two-dimensional representations of a familiar space; move positions by following directions and pathways

  Elaborations

  • interpreting maps of familiar places and identifying the position of key features
  • understanding that we use maps to receive and give directions and to describe place and spatial relationships between places
  • using a classroom seating plan to locate a new seating position and giving directions to other classmates to find their seats
  • following and creating movement instructions that need to be carried out to move through a 4 × 4 grid mat on the classroom floor or on a computer screen, for example, one forward, 2 to the right and one backwards and so on to reach a target square; or using a robotic toy to follow a path on a street scene on a floor mat, adjusting their instructions to the robot toy as they consider the order of their instructions, the direction and how far they want the toy to travel
  • moving around a two-dimensional maze using directional language to describe turns and changes in direction, including saying, for example, ‘clockwise’, ‘anticlockwise’, ‘quarter turn to the left’ and ‘take the path to the right’

  VC2M2SP02 | Mathematics | Mathematics Version 2.0 | Level 2 | Space

• VC2M4ST03

  conduct statistical investigations, collecting data through survey responses and other methods; record and display data using digital tools; interpret the data and communicate the results

  Elaborations

  • creating a survey to collect class responses to a preferred movie choice, and recording data responses using spreadsheets; graphing data using a column graph or other appropriate representations; and interpreting the results of the survey and reporting findings back to the class
  • conducting a statistical investigation and acquiring data from different online sources; 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
  • investigating different contexts in which statistical investigations can take place and the types of questions to ask to collect data relevant to the context; for example, investigating supermarket customer complaints that breakfast cereals with the most sugar are positioned at children’s eye level, discussing what questions they would need to ask and answer

  VC2M4ST03 | Mathematics | Mathematics Version 2.0 | Level 4 | Statistics

• VC2M4A02

  recall and demonstrate proficiency with multiplication facts up to 10 × 10 and related division facts, and explain the patterns in these; extend and apply facts to develop efficient mental and written strategies for computation with larger numbers without a calculator

  Elaborations

  • using arrays on grid paper or created with blocks or counters to develop, represent and explain patterns in multiplication facts up to 10 × 10; and using the arrays to explain the related division facts
  • using materials or diagrams to develop and record multiplication strategies such as doubling, halving, commutativity and adding one more or subtracting from a group to reach a known fact; for example, creating multiples of 3 on grid paper and doubling to find multiples of 6, and recording and explaining the connections to the × 3 and × 6 multiplication facts: 3, 6, 9, … doubled is 6, 12, 18, …
  • using known multiplication facts for 2, 3, 5 and 10 to establish multiplication facts for 4, 6, 7, 8 and 9 in different ways; for example, using multiples of 10 to establish the multiples of 9 as ‘to multiply a number by 9 you multiply by 10 then take the number away’: 9 × 4 = 10 × 4 − 4, so 9 × 4 is 40 − 4 = 36; or using multiples of 3 as ‘to multiply a number by 9 you multiply by 3, and then multiply the result by 3 again’
  • using arrays and known multiplication facts for twos and fives to develop the multiplication facts for sevens, applying the distributive property of multiplication; for example, when finding 6 × 7, knowing that 7 is made up of 2 and 5, and using an array to show that 6 × 7 is the same as 6 × 2 + 6 × 5 = 12 + 30, which is 42

  VC2M4A02 | Mathematics | Mathematics Version 2.0 | Level 4 | Algebra

• VC2M5N04

  recognise that 100% represents the complete whole and use percentages to describe, represent and compare relative size; connect familiar percentages to their decimal and fraction equivalents

  Elaborations

  • recognising applications of percentages used in everyday contexts, for example, the bar model used for charging devices indicating the percentage of power remaining, and advertising in retail contexts relating to discounts or sales
  • creating a model by subdividing a whole (for example, using 10 × 10 grids to represent various percentage amounts) and recognising complementary percentages (such as 30% and 70%) combine to make 100%
  • creating a model by subdividing a collection of materials, such as blocks or money, to connect decimals and percentage equivalents of tenths and the commonly used fractions $\frac{1}{2}$, $\frac{1}{4}$ and$\mathrm{ }\frac{3}{4}$; for example, connecting that one-tenth or 0.1 represents 10% and one-half or 0.5 represents 50%, and recognising that 60% of a whole is 10% more of the whole than 50%
  • using physical and virtual materials to represent the relationship between decimal notation and percentages, for example, 0.3 is 3 out of every 10, which is 30 out of every 100, which is 30%

  VC2M5N04 | Mathematics | Mathematics Version 2.0 | Level 5 | 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

• VC2M1M01

  compare directly and indirectly and order objects and events using attributes of length, mass, capacity and duration, communicating reasoning

  Elaborations

  • using a piece of string to indirectly compare the length of several objects, deciding which will fit within a space, and using comparative language to describe the order (shortest, short, longer, longest)
  • ordering the mass of 3 or more objects, such as rocks, using hefting and balance scales, and using comparative language to explain the order (lightest, light, heavier, heaviest) and how they decided on the order
  • pouring sand, rice or water from one container to another to compare and order the capacity of 3 or more containers, and describing the order of the results in terms of which holds the most/least and those in between
  • creating sand timers from everyday items or recycled materials and comparing them to order the duration of time required for the sand to run through
  • investigating situations where Aboriginal and/or Torres Strait Islander Peoples estimate, compare and communicate measurements, for example, situations involving the duration of seasons, understanding animal behaviour using the length of animal tracks, or investigating capacity through Aboriginal and/or Torres Strait Islander water management techniques, such as traditional water-carrying vessels and rock holes

  VC2M1M01 | Mathematics | Mathematics Version 2.0 | Level 1 | Measurement

• VC2M5M02

  solve practical problems involving the perimeter and area of regular and irregular shapes using appropriate metric units

  Elaborations

  • investigating problem situations involving perimeter, for example, ‘How many metres of fencing are required around a paddock, or around a festival event?’
  • using efficient ways to calculate the perimeters of rectangles, such as adding the length and width together and doubling the result
  • solving measurement problems such as ‘How much carpet would be needed to cover the entire floor of the classroom?’, using square metre templates to directly measure the floor space
  • creating a model of a permaculture garden, dividing the area up to provide the most efficient use of space for gardens and walkways, labelling the measure of each area, and calculating the amount of resources needed, for example, compost to cover the vegetable garden
  • using a physical geoboard or a virtual geoboard app to recognise the relationship between area and perimeter and solve problems; for example, investigating what is the largest and what is the smallest area that has the same perimeter
  • exploring the designs of fishing nets and dwellings of Aboriginal and Torres Strait Islander Peoples, investigating the perimeter, area and purpose of the shapes within the designs

  VC2M5M02 | Mathematics | Mathematics Version 2.0 | Level 5 | Measurement

• VC2M3N04

  add and subtract two- and three-digit numbers using place value to partition, rearrange and regroup numbers to assist in calculations without a calculator

  Elaborations

  • using partitioning and part-part-whole models and the inverse relationship between addition and subtraction to solve addition or subtraction problems, making informal written ‘jottings’ to keep track of the numbers if necessary
  • using physical or virtual grouped materials or diagrams to make proportional models of numbers to assist in calculations, for example, to calculate 214 + 325, representing 214 as 2 groups of 100, one group of 10 and 4 ones and 325 as 3 groups of 100, 2 groups of 10 and 5 ones, resulting in 5 groups of 100, 3 groups of 10 and 9 ones, which is 539
  • choosing between standard and non-standard place value partitions to assist with calculations, for example, to solve 485 + 365, thinking of 365 as 350 + 15, then adding the parts, 485 + 15 = 500, 500 + 350 = 850
  • solving subtraction problems efficiently by adding or subtracting a constant amount to both numbers to create an easier calculation; for example, 534 − 395, adding 5 to both numbers to make 539 − 400 = 139
  • justifying choices about partitioning and regrouping numbers in terms of their usefulness for particular calculations when solving problems
  • applying knowledge of place value to assist in calculations when solving problems involving larger numbers; for example, calculating the total crowd numbers for an agricultural show that lasts a week

  VC2M3N04 | Mathematics | Mathematics Version 2.0 | Level 3 | Number

• 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

• VC2M4M02

  recognise ways of measuring and approximating the perimeter and area of shapes and enclosed spaces, using appropriate formal and informal units

  Elaborations

  • recognising that perimeter is the sum of the lengths that form the boundary of a shape or enclosed space; choosing suitable units from a range of objects to measure around the boundary of a shape such as a garden bed; comparing the results to say which unit was an appropriate choice for the context; and using a piece of string or rope to measure the perimeter of irregular shapes and enclosed spaces, including those that have curved sections
  • creating a range of rectangles representing ‘paddocks’ on grid paper and establishing different methods of working out the length of the boundary fences; and explaining that the more efficient methods involve adding the side lengths rather than counting squares
  • recognising that area is the space enclosed by the boundary of a shape or the surface of an object; measuring and comparing the area of shapes using an array of paper tiles or mosaic squares, including part units to fill gaps at the edge of the shapes; and comparing the total areas by combining the fractional parts to make whole units
  • demonstrating how to use one unit repeatedly to measure the area of a shape (for example, using one paper square to measure and compare the area of a rectangle and a triangle) and recording and explaining how they used part units to give a more accurate measure, and why they needed to ensure there were no gaps or overlaps
  • investigating the ways Aboriginal and/or Torres Strait Islander ranger groups and other groups measure areas of land to make decisions about fire burns to care for Country/Place

  VC2M4M02 | Mathematics | Mathematics Version 2.0 | Level 4 | Measurement

• 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

• VC2M7N02

  represent natural numbers in expanded notation using powers of 10, and as products of powers of prime numbers using exponent notation

  Elaborations

  • relating the sequences 10, 100, 1000, 10 000 … and 10¹, 10², 10³, 10⁴ …
  • applying and explaining the connections between place value and expanded notations, for example, $7000=7\times {10}^3$ and $3750=3\times {10}^3+7\times {10}^2+5\times {10}^1$
  • applying knowledge of factors to strategies for expressing natural numbers as products of powers of prime factors, such as repeated division by prime factors or creating factor trees, for example, $48=6\times 8=2\times 3\times 2\times 2\times 2=3^1\times 2^4=3\times 2^4$
  • developing familiarity with the sequence 1, 2, 4, 8, 16, 32, 64, 128, 256, 512 and powers of 2; the sequence 1, 3, 9, 27, 81, 243, 729 and powers of 3; and the sequence 1, 5, 25, 125, 625 and powers of 5
  • solving problems involving lowest common multiples and greatest common divisors (highest common factors) for pairs of natural numbers by comparing their prime factorisation

  VC2M7N02 | Mathematics | Mathematics Version 2.0 | Level 7 | Number

• VC2M4N03

  find equivalent representations of fractions using related denominators and make connections between fractions and decimal notation

  Elaborations

  • extending fraction families within collections of materials, for example, by seeing $\frac{3}{4}$ as 3 in each 4, showing this within related fractions like $\frac{6}{8}$ or seeing that $\frac{2}{5}$ means 2 in each 5 so it can be shown within $\frac{4}{10}$
  • creating models of equivalent fractions by subdividing capacity measures into smaller fractions; for example, half a cup of flour could be shown as two-quarters or four-eighths of a cup of flour
  • folding paper to show equivalence between different fractions; for example, folding A4 paper in half and half again, repeating to form eighths and demonstrating that $\frac{4}{8}=\frac{2}{4}=\frac{1}{2}$ ; or folding paper strips into fifths and tenths, and recording as both fractions and decimals
  • identifying and using the connection between fractions of metres and decimals; for example, finding $\frac{1}{4}$ of a metre and connecting this to 0.25 metres or 25 centimetres, or finding $\frac{1}{10}$ of a metre and connecting this with 0.10 metres or 10 centimetres
  • using array diagrams to show the relationship between fractions and division and multiplication of natural numbers, for example, 3 × 4 = 12, 12 ÷ 4 = 3, $\frac{1}{4}$ of 12 is 3, $\frac{1}{3}$ of 12 is 4

  VC2M4N03 | Mathematics | Mathematics Version 2.0 | Level 4 | Number