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• 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

• 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

• VC2M5SP02

  construct a grid coordinate system that uses coordinates to locate positions within a space; use coordinates and directional language to describe position and movement

  Elaborations

  • understanding how the numbers on the axes on a grid coordinate system are numbers on a number line and are used to pinpoint locations
  • discussing the conventions of indicating a point in a grid coordinate system; for example, writing the horizontal axis number first and the vertical axis number second, and using brackets and commas
  • comparing a grid reference system to a grid coordinate system (first quadrant only) by using both to play strategy games involving location; for example, in playing the game Quadrant Commander, deducing that in a grid coordinate system the lines are numbered (starting from zero), not the spaces
  • placing a coordinate grid over a contour line, drawing and listing the coordinates of each point in the picture, asking a peer to re-create the drawing using only the list of coordinates, and discussing the reasons for the potential similarities and differences between the 2 drawings

  VC2M5SP02 | Mathematics | Mathematics Version 2.0 | Level 5 | 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

• VC2M8A03

  use mathematical modelling to solve applied problems involving linear relations, including financial contexts involving profit and loss; formulate problems with linear functions, and choose a representation; interpret and communicate solutions in terms of the context, and review the appropriateness...

  Elaborations

  • modelling situations involving linear functions, including practical contexts such as taxi fares involving flag fall fees, motion in a straight line at a constant speed, trade quotes involving call-out fees, cooking that includes resting or cooling times, or water leakage from water tanks, interpreting the constant rate of change and initial value in context, and identifying when values of a model lie within a given range
  • modelling problems in practical situations and interpreting solutions within the context of the problem, including giving attention to all units of measure and whether results are suitable; for example, once a water tank is empty no more water can flow from it
  • modelling financial problems involving pay rates, using a table of values to represent the pay amounts and hours worked using an hourly rate of pay, and graphing the relationship to make inferences
  • modelling patterns on Country/Place and exploring their connections and meaning to linear equations, using the model as a predictive tool and critiquing results by connecting back to Country/Place

  VC2M8A03 | Mathematics | Mathematics Version 2.0 | Level 8 | Algebra

• VC2M9A02

  simplify algebraic expressions, apply the distributive law to expand algebraic expressions including binomial products, and factorise monic quadratic expressions

  Elaborations

  • expanding combinations of binomials such as x+7x+8, x+7x-8,  x-7x+8,  (x-7)(x-8) to identify expansion and factorisation patterns related to x+ax+b=x2+a+bx+ab, where a and b are integers
  • using manipulatives such as algebra tiles or area models to expand or factorise algebraic expressions with readily identifiable binomial factors; for example, x+1x+3=x2+4x+3, (x-5)2=x2-10x+25 or (x-3)2+4=x2-6x+9+4=x2-6x+13
  • recognising the relationship between expansion and factorisation, and using digital tools to systematically explore the factorisation of x2+mx+n where m and n are integers

  VC2M9A02 | Mathematics | Mathematics Version 2.0 | Level 9 | Algebra

• VC2M4N06

  develop efficient mental and written strategies and use appropriate digital tools for solving problems involving addition and subtraction, and multiplication and division where there is no remainder

  Elaborations

  • using and choosing efficient calculation strategies for addition and subtraction problems involving larger numbers, for example, place value partitioning, inverse relationship, compatible numbers, jump strategies, bridging tens, splitting one or more numbers, extensions to basic facts, algorithms and digital tools where appropriate
  • using physical or virtual materials to demonstrate doubling and halving strategies for solving multiplication problems; for example, for 5 × 18, using the fact that double 5 is 10 and half of 18 is 9; or using 10 × 18 = 180, then halving 180 to get 90; or applying the associative property of multiplication, where 5 × 18 becomes 5 × 2 × 9, then 5 × 2 × 9 = 10 × 9 = 90 so that 5 × 18 = 90
  • using an array to represent a multiplication problem, connecting the idea of how many groups and how many in each group with the rows and columns of the array, and writing an associated number sentence
  • using materials or a diagram to solve a multiplication or division problem, by writing a number sentence and explaining what each of the numbers within the number sentence refers to
  • representing a multiplicative situation using materials, array diagrams and/or a bar model, and writing multiplication and/or division number sentences, based on whether the number of groups, the number per group or the total is missing, and explaining how each number in their number sentence is connected to the situation
  • using place value partitioning, basic facts and an area or region model to represent and solve multiplication problems; for example, for 16 × 4, thinking 10 × 4 and 6 × 4, then 40 + 24 = 64, or a double double strategy where double 16 is 32, double this is 64, so 16 × 4 is 64

  VC2M4N06 | Mathematics | Mathematics Version 2.0 | Level 4 | Number

• VC2M6N08

  approximate numerical solutions to problems involving rational numbers and percentages, using appropriate estimation strategies

  Elaborations

  • using familiar fractions, decimals and percentages to approximate calculations, such as 0.3 of 180 is about 13 of 180, or 52% is about 12
  • choosing appropriate estimation strategies including rounding to the nearest whole number, knowledge of multiples of 2, 5 or 10 and partitioning numbers, in contexts such as measuring or cost per unit
  • recognising the effect of rounding on calculations involving fractions or decimals and saying what numbers the answer will be between
  • recognising the usefulness of estimation to check calculations for contexts such as dividing wood into a number of lengths, calculating cost per unit, reducing a recipe or dividing the cost of dinner for a group into individual amounts
  • verifying solutions by estimating percentages in suitable contexts, such as discounts, using common percentages of 10%, 25%, 30%, 50% and 1%
  • investigating estimation strategies to make decisions about steam cooking in ground ovens by Aboriginal and/or Torres Strait Islander Peoples, including catering for different numbers of people and resources needed for cooking

  VC2M6N08 | Mathematics | Mathematics Version 2.0 | Level 6 | Number

• 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 34 cup of flour and a 14 cup of flour, subtracting 34 of a metre from 2 14 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, 12+14 is the same as 24+14 

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

• VC2M9A01

  apply the exponent laws to numerical expressions with integer exponents and the zero exponent, and extend to variables

  Elaborations

  • representing decimals in exponential form; for example, 0.475 can be represented as 0.475=410+7100+51000=4×10-1+7×10-2+5×10-3 and 0.00023 as 23 × 10^-5
  • simplifying and evaluating numerical expressions, involving both positive and negative integer exponents, explaining why; for example, 5-3=153=(15)3=1125 and connecting terms of the sequence 125, 25, 5, 1, 15, 125, 1125… to terms of the sequence 53, 52,51, 50, 5-1, 5-2, 5-3...
  • relating the computation of numerical expressions involving exponents to the exponent laws and the definition of an exponent; for example, 23÷25=2-2=122=14 and (3×5)2=32×52=9×25=225
  • recognising exponents in algebraic expressions and applying the relevant exponent laws and conventions; for example, for any non-zero natural number a, a0=1, x1=x,  r2=r×r,  h3=h×h×h,  y4=y×y×y×y, and 1w×1w=1w2=w-2
  • relating simplification of expressions from first principles and counting to the use of exponent laws; for example,
    (a2)3=a×a×a×a×a×a=a×a×a×a×a×a=a6;
    b2×b3=b×b×b×b×b=b×b×b×b×b=b5; y4y2=y×y×y×yy×y=y21=y2 and (5a)2=5×a×5×a=5 ×5×a×a=25×a2=25a2 
  • applying the exponent laws to simplifying expressions involving products, quotients, and powers of constants and variables; for example, (2xy)3xy4=8x3y3xy4=8x2y-1
  • relating the prefixes for SI units from pico- (trillionth) to tera- (trillion) to the corresponding powers of 10; for example, one pico-gram = 10^-12 grams and one terabyte = 10¹² bytes

  VC2M9A01 | Mathematics | Mathematics Version 2.0 | Level 9 | Algebra

• 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

• VC2MFN03

  quantify and compare collections to at least 20 using counting and explain or demonstrate reasoning

  Elaborations

  • establishing the language and process of counting, and understanding that each object must be counted only once, that the arrangement of objects does not affect how many there are and that the last number counted answers the question of ‘How many?’; for example, saying numbers in sequence while playing and performing actions
  • using counting to compare the size of 2 or more collections of like items to justify which collection contains more or fewer items
  • using counting and one-to-one correspondence to quantify the number of items required for a purpose; for example, when asked to collect enough scissors for each member of their group to have a pair, counting each member and using the total count to know how many to collect
  • discussing how different cultures may have alternative ways of representing the count; for example, discussing how some people of the Asia region use an abacus or Chinese hand gestures
  • using body-tallying that involves body parts and one-to-one correspondence from counting systems of Aboriginal and/or Torres Strait Islander Peoples to count to 20

  VC2MFN03 | Mathematics | Mathematics Version 2.0 | Foundation Level | Number

• VC2M8M07

  use mathematical modelling to solve practical problems involving ratios and rates, including distance-time problems for travel at a constant speed and financial contexts; formulate problems; interpret and communicate solutions in terms of the situation, reviewing the appropriateness of the model

  Elaborations

  • modelling simple motion problems, finding one of distance travelled, time taken or average speed, given the other 2 quantities
  • modelling and solving problems related to situations such as scales on maps and plans, the mixing of chemicals or ingredients, or calculating magnification factors applying relevant ratios and proportions
  • modelling problems involving converting money amounts using different exchange rates and applying them when planning and budgeting for overseas travel
  • modelling situations involving financial contexts (for example, income tax, using taxation rates on annual income, comparing different taxation brackets and rates of pay) or comparing the benefits of different phone plans using different call rates and associated fees to determine the best plan
  • modelling situations involving the use of ratios in radiocarbon dating methods, including the ratio of carbon-14 to carbon-12 isotopes in organisms, to measure dates of Aboriginal and Torres Strait Islander Peoples’ habitation on the Australian continent
  • modelling situations involving ratio and its application in the making of string and cordage by Aboriginal and/or Torres Strait Islander Peoples, including the ratio of length to the mass of a rope, the strength of the ply in proportion to a rope’s pulling force, and the proportion of fibre for the length of string required

  VC2M8M07 | Mathematics | Mathematics Version 2.0 | Level 8 | Measurement

• VC2M2M02

  identify common uses and represent halves, quarters and eighths in relation to shapes, objects and events

  Elaborations

  • demonstrating how food items can be cut in halves, quarters or eighths; for example, cutting pizzas, slices, cakes or sandwiches into equal parts by halving, then halving again to form quarters and eighths, ensuring that the parts are equal
  • investigating cup and spoon measures used in cooking and discussing what half or quarter of a cup or tablespoon measure means, and using sand or water to compare these to the full cup and tablespoon measures
  • demonstrating and using halves and quarters in folding activities; for example, folding paper in half and quarters and ensuring that the pieces are the same size
  • recognising that halves and quarters can be used to describe lengths, positions and distances; for example, describing the halfway point in a race or instructing someone to stand halfway between 2 chairs
  • discussing that halves and quarters are used to describe durations of time, including durations of time in sporting events, and what this means; for example, discussing how the sirens used during an Australian Rules football game represent quarter time, half-time and three-quarter time during the game, or recognising and using half an hour or quarter of an hour to describe a duration of time

  VC2M2M02 | Mathematics | Mathematics Version 2.0 | Level 2 | Measurement

• VC2M7M05

  demonstrate that the interior angle sum of a triangle in the plane is 180° and apply this to determine the interior angle sum of other shapes and the size of unknown angles

  Elaborations

  • using concrete materials to demonstrate that the sum of the interior angles of a triangle is 180°; for example, using paper triangles and tearing to demonstrate that the interior angles when combined form 180°
  • using decomposition and the angle sum of a triangle to generalise the interior angle sum of an n-sided polygon, as 180n-2=180n-360

  VC2M7M05 | 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

• VC2M4M01

  use scaled and digital instruments to interpret unmarked and partial units to measure and compare lengths, masses, capacities, durations and temperatures, using appropriate units

  Elaborations

  • reading the mass of objects measured with digital and analog kitchen scales and explaining what unit of mass the lines on the analog scales refer to
  • deciding on which attribute, unit and measuring instrument to use to compare the length and mass of various things, such as the distance travelled by an object in a science investigation; and explaining the use of units such as grams or millimetres to give accurate measures when needed
  • using scaled instruments such as tape measures, measuring jugs, kitchen scales and thermometers to record measures using whole units (for example, 560 millimetres) or whole and part units (for example, 5.25 metres, 1.75 litres, 2.5 kilograms, 28.5° Celsius)
  • reading and interpreting the scale of an analog clock without marked minutes to estimate the time to the nearest minute and to determine the duration of time between events
  • using the timer or alarm function of a clock to alert when a specified duration has elapsed from a given starting time, for example, for the different activities of an exercise routine
  • making a scaled measuring instrument such as a tape measure, ruler, sand timer, sundial or measuring cup using scaled instruments and direct comparisons
  • exploring the different types of scaled instruments used by Aboriginal and/or Torres Strait Islander ranger groups and other groups to make decisions about caring for Country/Place, and modelling these in local contexts

  VC2M4M01 | Mathematics | Mathematics Version 2.0 | Level 4 | Measurement

• 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 34 as 3 in each 4, showing this within related fractions like 68 or seeing that 25 means 2 in each 5 so it can be shown within 410
  • 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 48=24=12 ; 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 14 of a metre and connecting this to 0.25 metres or 25 centimetres, or finding 110 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, 14 of 12 is 3, 13 of 12 is 4

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

• VC2M7N03

  find equivalent representations of rational numbers and represent positive and negative rational numbers and mixed numbers on a number line

  Elaborations

  • investigating equivalence of fractions using common multiples and a fraction wall, diagrams or a number line to show that a fraction such as 23 is equivalent to 46 and 69 and therefore 23 < 56
  • expressing a fraction in simplest form using common divisors
  • applying and explaining the equivalence between fraction, decimal and percentage representations of rational numbers, for example, 16%, 0.16, 16100 and 425, using manipulatives, number lines or diagrams
  • representing positive and negative fractions and mixed numerals on various intervals of the real number line, including intervals that are not symmetrical about zero

  VC2M7N03 | Mathematics | Mathematics Version 2.0 | Level 7 | Number

• 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 13 of a quantity can be achieved by dividing by 3, and how knowledge of 13 of a quantity can be used to find 23 or 43 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, 3313 % and 13 , keeping to percentages that are equivalent to fractions with small denominators such as 6623 % and 12.5%
  • representing a situation with a mathematical expression, for example, numbers and symbols such as 14 × 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